NewWorldRecord 01 Feb 2006 - 00:37 CatherineJohnson

...set here at Kitchen Table math for most wrong answer:

#14, KUMON Math sheet F111b

If it's not a world record, it's definitely a personal best.

-- CatherineJohnson - 01 Feb 2006

SmartestTractorOnTeachingAlgebra 01 Feb 2006 - 02:49 CarolynJohnston

Catherine dared our contributor SmartestTractor to write up a brief description of her teaching methods -- which are inspired partly by the Carol Gambill method -- and she actually did! Like Matt Goff, she is very aggressively checking her kids' understanding of the previous night's homework every class period -- doing constant assessments of their understanding -- but there are some differences.

from Smartest Tractor:

I started using the Gambill Method this year. Unfortunately, the textbook I use does not have the answers in the back of the book. I have created solution pages and I put them on-line for the kids to look up.

I have attached the one of the files. I am looking for suggestions.

Is it clear? Easy to follow? Too cluttered? Should the solutions have a written explanation beside each line of the equation? As a parent, would this be useful or useless when trying to help your child?

[snip]

I teach grade eight English, math, history, geography, physical education, health, visual arts, and science in a JK to 8 school.

[snip]

The Gambill Method has been a rather interesting, and effective, strategy in my classroom. Needless to say, the kids have never been exposed to the idea. I really messed up the other day when I tried to combine two ideas, like terms and the distributive property, into one day. We went over Thursday's lesson again (Lesson Nine - Solving Equations in More Than One Step). [ed. note: ktm contributors have been discussing formative assessment. Smartest Tractor is using daily formative assessment, in the form of a brief quiz, to discover whether her students grasped the previous day's lesson.]

The current results for the unit (pdf file).

Smartest Tractor In a Nutshell. (pdf file)

also see:
Smartest Tractor's Solution Key (pdf file)
Algebra to date(pdf file)

Rory Donaldson at brainsarefun.com

Smartest Tractor links to Rory Donaldson, who has this to say about Carol Gambill:

In all my years of teaching I have only met one teacher, Carol Gambill, who thoroughly understood the effectiveness of "solution keys."

Solution keys are not the same as "answer keys." A real solution key does not skip any of the steps required to reach the final answer. Solution keys never try to trick the student, or force the student to fill in missing gaps, or require the student to extrapolate. Solution keys provide the student with an ideal solution, every step spelled out.

When creating solution keys the teacher must sit down, and with pencil in hand, thoroughly write down every step required to solve the problem. What ends up on the page are the steps students are required to take to successfully solve the problem, with written comments under each step, or off to the side, adding explanation.

Let me see if I can create both a good and bad example.

Problem: Jerry and Jenny have \$1.50 in cash. Jerry has twice as much as Jenny. How much does each have?

The reason that solution keys are ignored is that they require a lot of extra work on the part of the teacher. However, they are very effective when used with homework. Armed with solution keys, and problems that follow the solution keys step by step, students have a great deal of success. Little is more frustrating than the modern crop of textbooks that present no solution keys, and then a bunch of unrelated and dissimilar problems. The work is left to the teachers who really want to consider themselves "good."

Carol Gambill method in a nutshell
brainsarefun.com
Smartest Tractor's algebra class In a Nutshell
Smartest Tractor's Solution Key for students & parents
Smartest Tractor's current results for the unit

-- CarolynJohnston - 01 Feb 2006

GoodAdvice 01 Feb 2006 - 13:55 CatherineJohnson

I was just straightening up my computer files, and I came across this piece of fantastic advice on how to work word problems in algebra.

Unfortunately, I didn't record the author of this advice.

I think this is the text of an email Carolyn's husband, Bernie Johnston sent me back before we started writing ktm. But it may have been posted by Steve....(I'm inclined to think it's Bernie, not Steve, because Steve prefers 'isolate the variable' to 'undo what's been done to X,' assuming I read his response to Carolyn's post on the subject correctly.)

I'm sure one of them will recognize this. [update: Bernie wrote it]

This reminds me of a thought I had last week. For many many algebraic or calculus computations I have a phrase that runs through my head and tells me how to proceed. If I forget what to do I simply conjure up that phrase in my head. When I've tried to tutor people I've noticed that they frequently get stuck at exactly the point where the phrase would be useful but they have no phrase in their heads. When I think back upon where the phrase came from I realize that in many cases it came from my high school algebra teacher.

For example, when you start an algebra word problem, it's very difficult to know where to begin. There are a lot of words and the potential complexity of the problem is enormous. If you spend a lot of time using the front part of your brain to search for an appropriate path you may never find it. The phrase "when you don't know something, give it a name" is essentially the secret of algebra. This allows you to mentally grasp a particular thread of the problem which you can then follow through to the proper conclusion: the problem space has been cut way down in size.

Another one he gave me:

"When you have an equation with variables on the bottom, clear the denominators".

"Put the x's on one side and the numbers on the other."

"Undo whatever has been done to x."

These phrases are not singing rhymes but they are quite useful. The idea that certain procedures must be memorized or learned by rote is highly unfashionable these days but I think absolutely necessary.

words to remember

When you don't know something, give it a name.

When you have an equation with variables on the bottom, clear the denominators.

Put the x's on one side and the numbers on the other.

Undo whatever has been done to x.

words to remember from Vlorbik

Include the units.

V is right; including the units & writing word answers to word problems this is a VERY good habit to get into, right up front. I'm forcing myself to remember to do this.

Interestingly, Christopher isn't hugely resistant to including the units. I thought he would be, because he's resistant to everything.

Just goes to show how distant the middle-school brain is from the grown-up brain. Christopher seems to view 'including the units' as Obviously Something A Person Should Do.

I wonder if it's the relative hyperspecificity of the child's brain. He may feel like an answer of '5,' when what is meant is '5 cents,' really truly isn't 5 cents.

Don't know.

key words: good advice on algebra word problems good advice on how to solve algebra word problems
understanding basic algebra moves (& Comments)
good advice on solving algebra word problems

-- CatherineJohnson - 01 Feb 2006

AndyBlogDog 01 Feb 2006 - 20:40 CatherineJohnson

Andrew's been creating lots of tableaus lately, and I've been failing to record them.

At least I've captured this one, which is actually a (close) recreation of the real one he had waiting for us this morning. The only thing different here is the hat; I don't know what he did with the white baseball cap the dog was wearing in the a.m.

Maybe some other blogging animal is wearing it.

-- CatherineJohnson - 01 Feb 2006

ProductivityQuestion 01 Feb 2006 - 23:07 CatherineJohnson

I'm being so productive today that naturally I got surfing the web looking at websites about productivity

Which led me to 3 things:

• Quicksilver this appears to be a staggeringly productivity-enhanding "app" for Mac users that will change my life

gtd-php is the thing I'm really interested in, so here's my question:

Am I likely to have and/or be using already MySQL and Apache?

And how would I know?

This is supposed to be a 'Getting Things Done Lite' website for people who feel overwhelmed by the prospect of going whole hog.

Doesn't seem all that lite to me at the moment, but maybe I'm wrong.

Gantt charts & PERT charts; also some reputedly cool software for drawing Gantt charts on Macs

some books that have changed my life
the answer to all of Doug's problems
productivity question
what is an hour? Time Timers
Steve & Susan J & Doug on spiralling curricula
my Time Timer came - how long is a nap?
Time Timer says no!

-- CatherineJohnson - 01 Feb 2006

WrongAnswer 02 Feb 2006 - 00:20 CatherineJohnson

More fun with Prentice-Hall.

Find the missing measure.

8. a triangle
A = 28 m2
b = 7 m
h = 

The Teacher's edition says the answer is 8 m

[pause]

oh wow

i'm tired

he**

I have two pages left to go on the gazillionth revision of our Very-Short proposal, which in theory I ought to be able to do NOW......but if I can't tell that 1/2 of 56 is 28, I better hang it up.

This can only mean one thing.

It's time to go torture myself with today's packet of KUMON fractions.

-- CatherineJohnson - 02 Feb 2006

MilgramStatementToCongress2000 02 Feb 2006 - 00:32 CatherineJohnson

I am honored to be here today and to be able to share my observations on the state of mathematics education in this country with the distinguished members of the Committee on Education and the Workforce.

The K - 12 teachers in this country are dedicated professionals, deeply committed to teaching our children. They persevere in the face of difficult conditions and low pay. I have the utmost respect for them. But all too often, their knowledge of mathematics is extremely superficial, and when this happens they are easily swayed by trendy and unproven programs which typically offer a superficial treatment of the subject, leading to weak backgrounds in their students.

Perhaps a local parent described this situation best when she wrote me recently that the curriculum was getting fuzzier and fuzzier, and she "concluded that by and large most teachers support it because it makes them feel OK about math - they understand language, not symbols." She continues, "I cannot tell you how many times I have heard from administrators and teachers, how, if they had had "this" math when they were in school, perhaps they, too, would have been perceived as a `math person'."

I am a research mathematician, and research in esoteric areas of mathematics is essentially all I did besides teaching graduate and undergraduate classes in mathematics at Stanford until four years ago.

Two things obligated me to spend much of my time for the last three years studying issues related to K - 12 mathematics.

The first was some courses I gave in New Mexico, where I had too many bright, very highly motivated students in my mathematics classes whose third rate K - 12 educations in mathematics could not be overcome no matter how hard these students were willing to work.

The second came from the Presidential Commission designing Clinton's proposed national eighth grade mathematics exam. The commission - including many of the foremost math education specialists in the country - distributed a list of 14 proposed problems. I and my colleagues at Stanford were amazed to find that 3 of the problems had serious errors.

One was so ill posed that it could not be solved. One had an incorrect solution included with it.

We later testified to the Clinton commission about these difficulties, and it became clear that the level of mathematical understanding on the part of the mathematics educators on this panel was unimpressive.

There is a distinction between math educators who are primarily interested in questions involving education, and mathematicians who know about mathematics. While educational issues are unquestionably important there has been a tendency recently to focus on educational questions at the expense of mathematics content. I was disturbed when I realized that it is these people who are determining the mathematics that our children learn in school. I was especially disturbed in view of the dramatic drop in content knowledge that we have been seeing in the students coming to the universities in recent years.

Since 1989 the percentage of entering students in the California State University System - the largest state system in the country - that were required to take remedial courses in mathematics have increased almost 2 1/2 times from 23% in 1989 to 55% today. And CSU admission is restricted to the top 30% of California high school graduates! This failure has important consequences for the nation. Although large numbers of US students entering the universities say they are interested in majoring in technical areas, very few actually get such degrees today.

The total number of technical degrees awarded to US citizens recently is approximately 28,000 yearly, while there are currently about 100,000 new jobs in these areas each year. Last year congress had to mandate an additional 142,000 new work visas for technically trained people, and these visas were used up by June 11, 1999, so great was the demand.

A large part of the blame rests with mathematics programs of the type recommended by the Department of Education recently as exemplary or promising.

All but possibly one of the programs in the list recommended by the Department of Education, represent a single point of view towards teaching mathematics, the constructivist philosophy that the teacher is simply a facilitator. Standard algorithms for operations like multiplication and division are not taught, but students are advised to construct their own algorithms. At all stages hand held calculators are used for arithmetic calculations. There are no means for students to develop mastery of basic arithmetic operations. Algebra is short-changed as well.

These programs all are designed to closely align with the 1989 NCTM Mathematics Standards: standards which explicitly embody all the principles above, and specifically require that skills in algebra be downplayed. Indeed, the co-chairman of the Department of Education Expert Panel on Mathematics, Steven Leinwand, recently stated that the curricula endorsed by the Department of Education "create a common core of math that all students can master." Not material that all students NEED to know or SHOULD master, imply material that HE believes all students can learn. (Incidently, Department of Education statistical analysis - C. Adelman, 1999 - show that success in algebra in high school is the single most important predictor of degree attainment in college.)

The high school programs, Core-Plus and IMP, both place heavy emphasis on topics such as discrete mathematics at the expense of basic algebra, and do not come near the level indicated in e.g., the new California Standards for most of the topics there.

However, programs such as these are completely consistent with the previous California Mathematics Standards. Consequently, at least three of them, CPM, Mathland and IMP, have been in wide use in California for up to 10 or more years. (MathLand and IMP were developed in the late 1980s at the same time that the 1989 NCTM Standards were being developed, and were introduced into California Schools by 1989.)

Recent studies of the SAT mathematics scores of high schools which use IMP showed a consistent and significant decline over the last ten years.

Moreover, high schools that use IMP in California scored below the state means, and those that expressed satisfaction with the program scored, on average, 10 points lower than those which were dropping the program or otherwise were dissatisfied with it.

It was the introduction of CMP and TERC (another NSF funded curriculum published by Dale Seymour -- designed for grades K - 5) in the Palo Alto school system that sparked the initial parental revolt which became the California Mathematics Wars.

It was the introduction of Everyday Mathematics in the Princeton Township School District, which led to the parental revolt in Princeton. This led to the involvement of a number of faculty members in both mathematics and physics at Princeton University and the Institute for Advanced Study in Princeton in trying to reform mathematics teaching in the district.

It was the use of TERC in one school system in Massachusetts, which prompted numerous members of the Harvard Mathematics Department to sign the open letter to Secretary Riley.

The support for these programs in the Department of Education is ultimately the responsibility of the Education and Human Resources Department, EHR, at the National Science Foundation. EHR funded the development of at least six of the "exemplary and promising" programs.

It is also probably worth noting that at the present time there is no valid research which shows that any of the programs of this type are effective.

At least equally important are the Systemic Initiatives funded by EHR, which have the objective of pushing the districts where these initiatives are awarded to adopt curricula in mathematics which align with the 1989 NCTM Mathematics Standards.

In California, there is one systemic initiative from EHR still functioning, a grant to Los Angeles Unified School District, LAUSD, the nations second largest district with 711,000 students. The people involved in this initiative resisted attempts to change the system in place there, while similar districts such as Sacramento Unified began to make major changes.

Two years ago, the two districts had equally bad scores - around the thirtieth percentile - on the California Statewide mathematics exams. This last year LAUSD had essentially the same score as previously while the Sacramento Unified scores jumped dramatically, particularly in the lower grades, due to their shift away from whole language and constructivist math.

Incidentally, I had been told two years ago that getting a grant from EHR in a mathematics related area required that one buy into the list of ideas discussed above. As a test of this I obtained all the (over 4000) abstracts for the last 9 years from EHR for awarded grants that involved mathematics.

I tested a random sample of about 200 for a few key phrases such as NCTM Standards, group learning, and discovery learning. All but four of them contained at least one of these phrases.

In conclusion, I believe that the sad state of mathematics education among high school graduates in this country is primarily the responsibility of two agencies: the Department of Education and Human Resources at the NSF, and the Department of Education. The programs they develop and push simply set too low a standard.

Written Testimony of R. James Milgram February 2, 2000

Written Testimony of R. James Milgram February 2, 2000, summary points

• "I cannot tell you how many times I have heard from administrators and teachers, how, if they had had "this" math when they were in school, perhaps they, too, would have been perceived as a `math person'."

• Two things obligated me to spend much of my time for the last three years studying issues related to K - 12 mathematics.

• The first was some courses I gave in New Mexico, where I had too many bright, very highly motivated students in my mathematics classes whose third rate K - 12 educations in mathematics could not be overcome no matter how hard these students were willing to work.

• The second came from the Presidential Commission designing Clinton's proposed national eighth grade mathematics exam. The commission - including many of the foremost math education specialists in the country - distributed a list of 14 proposed problems. I and my colleagues at Stanford were amazed to find that 3 of the problems had serious errors.

• There is a distinction between math educators who are primarily interested in questions involving education, and mathematicians who know about mathematics

• it is [math educators, not mathematicians] who are determining the mathematics that our children learn in school.

• I was especially disturbed in view of the dramatic drop in content knowledge that we have been seeing in the students coming to the universities in recent years.

• Since 1989 the percentage of entering students in the California State University System - the largest state system in the country - that were required to take remedial courses in mathematics have increased almost 2 1/2 times from 23% in 1989 to 55% today

• Although large numbers of US students entering the universities say they are interested in majoring in technical areas, very few actually get such degrees today.

• The total number of technical degrees awarded to US citizens recently is approximately 28,000 yearly, while there are currently about 100,000 new jobs in these areas each year. Last year congress had to mandate an additional 142,000 new work visas for technically trained people, and these visas were used up by June 11, 1999, so great was the demand.

• All but possibly one of the programs in the list recommended by the Department of Education, represent a single point of view towards teaching mathematics, the constructivist philosophy that the teacher is simply a facilitator

• There are no means for students to develop mastery of basic arithmetic operations. Algebra is short-changed as well.

• These programs all are designed to closely align with the 1989 NCTM Mathematics Standards: standards which explicitly embody all the principles above, and specifically require that skills in algebra be downplayed.

• the co-chairman of the Department of Education Expert Panel on Mathematics, Steven Leinwand, recently stated that the curricula endorsed by the Department of Education "create a common core of math that all students can master." Not material that all students NEED to know or SHOULD master, imply material that HE believes all students can learn

• The support for these programs in the Department of Education is ultimately the responsibility of the Education and Human Resources Department, EHR, at the National Science Foundation. EHR funded the development of at least six of the "exemplary and promising" programs

• Recent studies of the SAT mathematics scores of high schools which use IMP showed a consistent and significant decline over the last ten years.

• I had been told two years ago that getting a grant from EHR in a mathematics related area required that one buy into the list of ideas discussed above. As a test of this I obtained all the (over 4000) abstracts for the last 9 years from EHR for awarded grants that involved mathematics.

• I tested a random sample of about 200 for a few key phrases such as NCTM Standards, group learning, and discovery learning. All but four of them contained at least one of these phrases.

On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations (2004)
National Research Council

Executive Summary, page 3

Under the auspices of the National Research Council, this committee’s charge was to evaluate the quality of the evaluations of the 13 mathematics curriculum materials supported by the National Science Foundation (NSF) (an estimated \$93 million) and 6 of the commercially generated mathematics curriculum materials (listing in Chapter 2).

The committee was charged to determine whether the currently available data are sufficient for evaluating the effectiveness of these materials and, if these data are not sufficiently robust, the committee was asked to develop recommendations about the design of a subsequent project that could result in the generation of more reliable and valid data for evaluating these materials.

[ellipsis]

These 19 curricular projects essentially have been experiments. We owe them a careful reading on their effectiveness. Demands for evaluation may be cast as a sign of failure, but we would rather stress that this examination is a sign of the success of these programs to engage a country in a scholarly debate on the question of curricular effectiveness and the essential underlying question, What is most important for our youth to learn in their studies in mathematics? To summarily blame national decline on a set of curricula whose use has a limited market share lacks credibility. At the same time, to find out if a major investment in an approach is successful and worthwhile is a prime example of responsible policy. In experimentation, success and worthiness are two different measures of experimental value. An experiment can fail and yet be worthy. The experiments that probably should not be run are those in which it is either impossible to determine if the experiment has failed or it is ensured at the start, by design, that the experiment will succeed. The contribution of the committee is intended to help us ascertain these distinctive outcomes.

[ellipsis]

The charge to the committee was “to assess the quality of studies about the effectiveness of 13 sets of mathematics curriculum materials developed through NSF support and six sets of commercially generated curriculum materials.”

[ellipsis]

In response to our charge, the committee finds that:

The corpus of evaluation studies as a whole across the 19 programs studied does not permit one to determine the effectiveness of individual programs with high degree of certainty, due to the restricted number of studies for any particular curriculum, limitations in the array of methods used, and the uneven quality of the studies.

source: On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations (2004)
Mathematical Sciences Education Board (MSEB)
Center for Education (CFE)
available online or purchase, pages 3 & 188

learning a year or more of math in 2 months
James Milgram on long division & lag time in math learning
NYU math major

-- CatherineJohnson - 02 Feb 2006

WhatIsAnHour 02 Feb 2006 - 19:32 CatherineJohnson

I saw the Time Timers when you posted about them previously, and I visited the website, but I still don't understand the purpose of a Time Timer???

I'd been seeing Time Timers in special needs catalogues forever, and they always looked cool.

They are also expensive. Just like everything else in special needs catalogues. The kind of toy you pick up for ten bucks at Toys R Us will set you back 50 when you buy its slightly adapted version from a special needs outfit.

People say it's a Market Thing, but I have my doubts.

I think it's a School Funding thing, just like textbooks. Schools have to buy stuff from these outfits & taxpayers have to pay for the stuff, so when it comes to pricing the sky's the limit.

I could be wrong.

In any case, it used to make me nuts trying to scrape together a few hundred dollars to buy the Boardmaker pictures all schools & special ed programs universally use for their 'PECS' (Picture Exchange Communication System) pictures because there wasn't anything else out there. The pictures were wretched, and had 'jaggies' all over the place ('jaggies' are the jagged edges that show up on curved lines drawn on a computer).*

Jimmy couldn't tell what they were at all.

I wish I could find the Boardmaker image for underarm. It was outrageous. An abstract jaggie-edged-computer drawing of a torso with no head and no stomach and one arm raised up (no forearms or hands, either). Very informative.

Here's a good one:

So take Jimmy, a kid with severe autism, a kid who can't read & who's squinting and not making eye contact and never looking directly at anything, and hand him one of these card, and he's supposed to see what?

No breaking things?

That's what got me off on my Great Clip Art Quest. I spent about 6 months of my life ferociously tracking down every last bit of decent, free clip art the internet had to offer, in hopes I'd have some images that actually made sense. I just wish I'd known Google Master back then.

Andrew, on the other hand, was a freaking PECS genius. He could understand any wonky jaggie-edged piece of lousy computer drawing you threw at him. I remember one time, when he was 4 & we'd just moved to Westchesteer, he went to the refrigerator where I had the PECS cards taped up and pulled off the Boardmaker picture representing 'hot tub,' because it was getting to be spring, and he wanted to go in the hot tub!

Very few adults would have known that picture represented hot tub if they hadn't been able to read the label, but he took one look at it and went: HOT TUB. I WANT IT. (Who knows. Maybe he read the label, too.)

Here's a photo of a child with his PECS system:

And here's a nice, large image of a PECS board.

back on topic

So, Time Timers.

I got thinking about the Time Timers again when I read The Organized Student by Donna Goldberg.

She has an interesting chapter on time management that struck me as probably sensible:

[In order to manage time well one must have] an ability to accurately gauge how long things take: What does an hour feel like and how much can I really accomplish in that time?

[snip]

Unfortunately, time management is not part of the school curriculum. In fact, many adults still feel like they're playing catch-up for the same reason that so many students feel left behind: no one ever taught them how to manage their time. This is a basic skill that should be taught just like reading, writing, and arithmetic....Many children can tell you that it's 12:30 and time for lunch, but they cannot gauge how long it will take them to eat or how much time they have left before the next class begins, just as many adults know what time an appointment is, but don't leave enough time to get there or forget to account for traffic. [ed.: or, umm, in my case, leave at the last possible moment and PRAY the traffic will cooperate]

Most adults actually have the skill of the average third grader when it comes to understanding time. By the age of nine, our education in the field of time is effectively over; once you can distinguish betewen the big hand and the little hand, you're on your own. You may not have the opportunity to learn time management skills until your company hires a corporate consultant to teach you and your colleagues how to increase efficiency through time management. [ed.: OBVIOUS HONKING RELEVANCE TO SPIRALLING CURRICULA ] Employers make the investment because...if they can train their employees to do more work in less time the company will profit. If we as parents and teachers are willing to make that same investment in our children, imagine how much they will profit, both in school and beyond.

The Struggle Today

There are two reasons today's students are struggling with the concept of time even more than students did in past generations. The first is that children are being taught to tell time at an earlier age. What used to be taught in the second and third grades is now being introduced as early as kindergarten. Most children, however are not developmentally ready to understand the idea of time at the age of five...but once it's taught...the class moves one.

The second reason children are struggling more now is that they've grown up in the age of the digital clock...Time appears on a digital clock as a statement of "now." It says nothing about the past or future and it doesn't place the present time in the context of the hour or the day. When time has no context, it has no appreciable meaning. Conversely, an analog clock with a numbered face and moving hands shows the present time in relation to the past and future (before the hour and after the hour) and is broken down into increments (hours, minutes, and seconds) that work together to create a whole picture...Their understanding of time has no depth or movement, and they do not see time in relative terms, which makes it hard to gauge how long things take and to plan realistically.

[snip]

Kids who don't understand time, however, are usually overlooked and don't get the help they need. All through school they have difficulty meeting deadlines and completing their work. They are constantly rushing, often late, and frequently unprepared.

in a nutshell

• kids lack time management skills because they lack time sense, period

• telling time is taught at school; time comprehension is not (call for constructivists!)

• kids today have 2 disadvantages making their time sense even worse than ours:

• 1. they're taught to tell time too early

• 2. they're surrounded by digital clocks

what is an hour?

Goldberg drew these ideas about time from the book About Dyslexia by Priscilla Vail, which apparently tracks dyslexic kids' difficulties grade by grade as they go through school.

I don't know whether Vail is right or wrong, but the idea intrigues me. One of the children I know who's most disorganized can't read an analog clock. This is a super-smart kid. Can't read analog time. Maybe it's a coincidence. Or maybe not.

As far as I know, the concept of 'hourly' time is pretty much an artificial construct; I don't think it's something we're born knowing, right.

In contrast, it does seem to me that 'day' and 'night' are built-in; probably something like winter and spring are, too.

Assuming that's true, 'what is an hour' probably ought to be taught directly like everything else.

Goldberg suggests various exercises, like having your child time one minute on a stop watch to see how long one minute actually is. (When I was a kid, we always found out how long one minute actually is by trying to hold our breath for a minute. Don't kids still do that?)

She also says kids need to learn how long various tasks take to do. That's important for a person like me who's constantly thinking she can 'whip things off.'

For instance, more than halfway through my second STUPENDOUSLY HUGE Saxon Math book, I actually do not know how long it takes me to do a full lesson.

I have a vague idea that it takes maybe 45 minutes. 45 minutes or less.

So I start doing a lesson at....10, when I'm already too tired to be doing math, including easy math.

Then at 11 I think: wow, this is taking a long time.

Pretty much the story of my life.

What I like about the Time Timer is that it 'times' time — you can actually see your allotted period of time disappearing. (ok, when I put it that way, I think: why don't we not and say we did?)

I'll probably use it for Christopher, Andrew, & me.

Time Timer website

*Now they've got smooth edges & the program costs \$300. This is very primitive software we're talking about, or it was when I had to buy it. \$300.

Yes, I'd be happy, too if I were selling a lousy software package to financially strapped parents and captive school districts for three hundred bucks a pop.

I'll probably regret writing that.

some books that have changed my life
the answer to all of Doug's problems
productivity question
what is an hour? Time Timers
Steve & Susan J & Doug on spiralling curricula
my Time Timer came - how long is a nap?
Time Timer says no!

-- CatherineJohnson - 02 Feb 2006

BoyTroublePart4 02 Feb 2006 - 21:45 CatherineJohnson

Ed finally took a census in his class on nationalism.

60% girls, 40% boys. At NYU.

We're not talking low SES here, and we're not talking 'girl subject matter.' Girls didn't used to flock to courses on nationalism.

(I'm sorry if that annoys folks; I don't mean it to. I'm glad girls are taking courses on nationalism; I've managed to learn a little something about nationalism myself since 9/11. Nevertheless, 60/40 in a history course on nationalism isn't what you'd expect.)

random factoid for the day

from It's Payback Time by Cathy Young, an article about Christina Hoff Sommer's book The War Against Boys:

More male students are "disengaged" from school, says the author, and they are pessimistic about their prospects. While boys, on average, maintain an edge on the Scholastic Assessment Test (SAT), this is largely due to the fact that more girls from disadvantaged backgrounds take the SATs, because more of them go to college. (Overall, 55 percent of bachelor's degrees awarded in 1996 -- and 64 percent for African-Americans -- went to women.) On standardized tests taken by all schoolchildren, girls are narrowing the gender gap in math and science while boys continue to lag behind, by a much wider margin, in reading and writing.

competitive versus cooperative learning

Then there's this, from an unedited preprint of SEXUAL SELECTION AND SEX DIFFERENCES IN MATHEMATICAL ABILITIES by David C. Geary:

It was also suggested that sexual selection operated to make males more competitive than females, and, as such, might influence how boys and girls perform, in mathematics and other academic areas, in competitive and cooperative classroom environments. In keeping with this view, is the finding that the mathematical achievement of girls is the highest in cooperative settings (e.g., problem solving small groups); the performance of boys, however, drops in these setting (Peterson & Fennema 1985). Similarly, the mathematical achievement of girls drops in competitive classrooms, while the achievement of boys improves slightly.

This phenomenon was on vivid display in my Singapore Math class last fall.

There were 5 boys and 1 girl, and the boys loved to compete.

The girl couldn't stand it. She would flat-out refuse to do timed worksheets. The whole idea made her super nervous. And she was a serious math brain.

I'm working with her mother & her now, because the mom loves the Singapore Math approach & wants to learn it herself. She also wants her daughter to master her math facts, and asked me to bring timed worksheets.

Turns out her daughter can't stand doing a timed worksheet even without any other kids around! It just makes her too nervous. She freezes up.

I told her just to forget about the time, and do the problems. When she calmed down enough to get started, she did great. She needs practice, of course, but she's as speedy as any of the boys were, or close to.

Time pressure just doesn't work for her.

otoh: is fuzzy math good for boys?

from Gender and Mathematics by Elizabeth Fennema, a researcher who characterizes her career thusly:

My entire professional career has been predicated on the belief that women deserve equity with men in all walks of life, and that belief has informed a significant part of my scholarly activities, particularly in the area of gender and mathematics. I have always believed that I can learn how to better facilitate the learning of mathematics by females through research.

Here she is on research she did in the 90s:

One extensive study, Cognitively Guided Instruction (CGI) [ed.: thanks to Charles for the link], was done by Tom Carpenter, me, and several others (Fennema, Carpenter, Jacobs, Franke, & Levi, 1998). In a 3-year longitudinal study we studied teachers and their students as they progressed from Grade 1 through Grade 3 (Fennema, Carpenter, et al., 1998). Once or twice each year, children who had learned their mathematics in CGI classrooms, were asked to solve a variety of problems (number facts, addition/subtraction word problems, non-routine, and extension problems) and to report how they solved the problems. We found no gender differences in correctly solving number fact, addition/subtraction, or non-routine problems throughout the three years of the study. This finding was in agreement with literature where it has been widely reported, as well as believed, that gender differences do not emerge until early adolescence. In our study, however, each year from Grade 1 to Grade 3 we found strong and consistent gender differences in the strategies used to solve problems, with girls tending to use more concrete strategies like modeling and counting and boys tending to use more abstract strategies that reflect conceptual understanding. In other words, the mental processing of boys and girls were different, and we also found some significant achievement differences in solving extension problems.

By the end of the third grade, the girls used more standard algorithms than did the boys. On the problems that required flexibility in extending one’s problem solving procedures, boys were more successful than were girls. The ability to solve the extension problems in the third grade appeared to be related to the use of invented rather than procedural algorithms in earlier grades, as both girls and boys who had used invented algorithms early were better able to solve the extension problems than those who had not.

So I guess it all comes out in the wash.

Boys do worse in all the small-group collaborative problem-solving confabs, but end up with admirably extended problem solving procedures in the 3rd grade anyway, while the girls are busy Following the Rules CGI was attempting to teach them to ignore.....6 of one, half dozen of the other.

I guess.

I haven't read either of Fennema's papers, but I've added them to The List.

USA Today report on 135:100 boys:girls ratio in college
sexism in Everyday Math
invisible boys
boy trouble (New Republic on boys)
slacker boys, middle school, & forbidden positive images of boys in textbooks
throw rocks at them
please remain seated at all times
Ann Althouse thread sums up classroom change
cooperative vs. competitive learning
the boy show (character ed)
the other boy show
Where the Boys Aren't

letter from Robert Lerner, former commissioner NCES
Tom Mortenson's research
The Boys Project board
for every 100 girls —

-- CatherineJohnson - 02 Feb 2006

NoCommentPart3 03 Feb 2006 - 00:45 CatherineJohnson

I'll Take Retention For 500, Alex

update from Janet at 'Art of Getting By'

Since I am the author of the post, I feel like I need to respond. I actually welcome questions like this to be made directly on my blog or to me because I am very open to answering them, no speculation needed.

Google Master was right. No one had to memorize anything. The test was assessing the skill of how to read a simple map. All the children had to do was count pictures. They also had to know a little bit about a compass. That was it.

As for this test itself, it might seem harsh, but this is precisely the kind of questions they need to answer on the NJ Ask and tests just like it all across the country. I'm not saying that sometimes some of the material isn't tough sometimes but this is not an example of such material. My job is to try to get them to understand stipulated grade level material as well as they possibly can.

This is where my somewhat sarcastic attitude came in. If you were in my classroom you would know I have done anything BUT give up on these children. The problem is bigger than this post alone can measure, and that is why I plan to address it in multiple posts that I'm spacing out over time. In short though, there are many contributing factors to the frustration: homogeneous grouping and low motivation just being two of them.

If there are any additional questions about my particular classroom, I would be more than happy to answer them.

Thanks, Janet!

Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Practice Makes Perfect, But Only When You Practice to the Point Beyond Perfection
Allocating Student Study Time: "Massed" versus "Distributed" Practice
Why Students Think They Understand—When They Don’t

formative assessment:
formative assessment
formative assessment in a nutshell

teaching to mastery
CA report on quality ed research
accelerating low performers
Gambill method of teaching algebra
Smartest Tractor's algebra class
Matt Goff's algebra class
TERC, KIPP, & mastery

other posts:
overlearning
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
failing algebra in Los Angeles
Yonkers middle schooler tutors a student who is failing

-- CatherineJohnson - 03 Feb 2006
StateOfTheUnion2006 03 Feb 2006 - 02:59 CarolynJohnston

From President Bush's state of the union address, a call for 30,000 new math teachers to move from math and science-based professions into teaching (hat tip to JoAnneC, who can't believe we're so late with this post):

"Third, we need to encourage children to take more math and science, and to make sure those courses are rigorous enough to compete with other nations. We've made a good start in the early grades with the No Child Left Behind Act, which is raising standards and lifting test scores across our country. Tonight I propose to train 70,000 high school teachers to lead advanced-placement courses in math and science, bring 30,000 math and science professionals to teach in classrooms, and give early help to students who struggle with math, so they have a better chance at good, high-wage jobs. If we ensure that America's children succeed in life, they will ensure that America succeeds in the world."

My question is this: will there be incentives?

And would President Bush like to pay me to develop teacher training courses?

-- CarolynJohnston - 03 Feb 2006

OmegaThreeFattyAcids 03 Feb 2006 - 22:55 CatherineJohnson

I think Carolyn & I have ESP.

I'm serious.

A few days ago I read an article on fish consumption, IQ, & pregancy in THE ECONOMIST (\$). I set it aside because I wanted to write a post about it.

Then yesterday Ed told me we're almost out of omegabrites, and today my cod liver oil for Jimmy & Andrew came in the mail.

AND: I just opened an email from Carolyn to find that she's wondering about fish oil for Ben! (Of course, Carolyn probably read the same article I did....)

My answer is: fish oil for everyone.

brain food

I found out about the Omega 3 fatty acids a few years ago, and was immediately convinced. Since then, the data has just kept coming, all of it good. On my Bayesian scale of certainty, 1 being No Clue and 7 being Death and Taxes, I'm at 7.

Fish oil is one of those 'Lost Knowledge' things....by which I mean that it belongs to the store of cultural knowledge people used to have that's gone missing. (Flash poll: how many women here can name the different cuts of meat in a side of beef? I can't. People used to know this stuff!)

My mom told me that when she was a kid, people gave cod liver oil to their kids, because they considered it 'brain food.'

Well, guess what. It is brain food. But that idea got lost somewhere along the line.

Here's the connection.

Probably everyone here knows that, at some point, the NIH funded research on fish consumption and heart health, which found that high fish consumption was good for your heart.

From there it followed directly that high fish consumption would likely be good for your brain, too, since researchers had already noticed a number of connections between heart health & mental health. For instance, people who suffered heart attacks were likely to suffer depression, too (IIRC I think the connection worked the other way around, as well).

Although people knew these correlations existed, I gather it took researchers a little while to put two and two together. But finally someone did, and the NIH funded, I believe (NOT FACT-CHECKED) an epidemiological study of fish oil consumption and depression. It turned out that there are very low rates of depression in countries and communities with high rates of fish consumption.

Andrew Stoll

I no longer remember when Andrew Stoll came on the scene, but I do remember his story.

Stoll is an expert on bipolar disorder, which meant he was prescribing a lot of lithium to patients. Lithium has numerous side effects; it's a tough drug to take, and can be quite dangerous. (It's a naturally-occurring salt.) IIRC, he and a colleague wanted to find a substance that would work like lithium with fewer side effects.

Apparently there is an enormous, multi-volume dictionary or encyclopedia of all known chemicals, so Stoll and his colleague starting searching through known chemicals to find something that might mimic lithium.

They found that the one chemical closest in structure to lithium was omega 3 fatty acid. Their study of Omega 3 fatty acid used to treat bipolar patients was published in the Archives of General Psychiatry, one of the two best journals in the field.

Three-page excerpts from every chapter of Stoll's book, The Omega-3 Connection, are posted on the omegabrites website. Terrific book.

We buy all of our fish oil from OmegaBrite, because it's manufactured by Stoll's ex-wife and because it's pharmaceutical grade, meaning it can be prescribed by physicians. This may mean nothing in terms of insurance; I don't know. I've never tried to get reimbursement. 'Pharmaceutical grade' in the case of omegabrites means the product can be used in an NIH-funded study.

IIRC, Stoll had a lot of trouble rustling up enough pharmaceutical-grade fish oil to do the study in the first place. I think he had to get the stuff he used from the people who did the heart study....Then, because there was no pharmaceutical commercial-grade product available on the market, his wife, who is also a psychiatrist, decided she would manufacture it herself & start up a whole company. I'm glad she did, but I don't think it's been fun for them.

That reminds me.

I spent years poking holes in zillions of omegabrite capsules every morning so I could squeeze out the oil inside into grape juice & give it to Jimmy and Andrew.

Those days are over.

The last time I spoke to Andrew Stoll, who is a friend of John (Ratey)'s, he said they were going to try to make a liquid version. I'm still waiting.

A couple of months ago I finally gave up and bought some Nordic Natural Complete Omega-3.6.9 oil.

Then I remembered my mom liked Carlson Norwegian Cod Liver Oil, which is what came in the mail today.

I have no idea way of judging their quality. I could use advice.

no more asthma

Fish oil has two important properties of which I'm aware; I'm sure there are lots more:

• it is a natural antiinflammatory

• it is liquid at very low temperatures

The natural antiinflammatory characteristic means, basically, that fish oil is a cure-all.

For at least the past 10 years researchers & physicians have been focused on inflammation as the source of all evil.

Eventually people began looking into inflammation as a problem for the brain, as well, and I'm sure it is.

Fish oil is a phenomenal antiinflammatory. When we first moved to Westchester Ed, Christopher & I developed asthma. Actually, I'd already had fairly severe asthma for about 10 years, but it had never been diagnosed. People kept telling me I had bronchitis. When Christopher was 4, he spent July 4 having an asthma attack so bad he was throwing up, which, unbeknownst to me, is the Danger Point. He could barely breathe.

All three of us were using inhalers every day when we started taking omegabrites.

Within a few months, all 3 of us had stopped using inhalers.

I think there may be a cumulative effect as well, because for a few years there we'd still have to get on the inhalers every time any of us came down with a cold.

Now we don't need inhalers for colds, either.

Another miracle cure: my mom's bursitis is gone. Bursitis is an inflammatory disorder.

Andrew Stoll's dad, who was in his 70s or 80s when I met him, told me his arthritis was gone. This stuff works.

fluid brain membranes

I don't think anyone knows exactly what Omega 3 fatty acids do in the brain, but one thought has to do with membrane permeability.

Mostly, Americans eat Omega 6's. That's corn oil. We eat HUGE quantities of corn oil, which is fine by me, since my dad was a farmer who raised corn. I've got nothing against corn!

But we're almost certainly way out of whack; we're supposed to be getting a lot more Omega 3s, and a lot less Omega 6.

Here's the way I think about the brain & Omega 3s.

Why don't salmon freeze up stiff as a board when they're swimming around the North Pacific waters?

Because they're made of fish oil.

Now picture a salmon made of margarine.

He's froze-solid, isn't he?

Stoll and others (IIRC) think it's possible fish oil is good for the brain because it replaces Omega 6s in cell membranes, which are made of fat.

If you're eating margarine, your brain cell membranes are made of margarine.

If you're eating fish, your brain cell membranes are made of fish oil.

Apparently, it's good to be a fish.

I have no idea whether this hypothesis is still current, but it's highly motivating. Every time I pull up an image of a semi-sold margarine brain I get serious about sticking with my fish oil regimen.

fish oil, pregnancy, IQ

I think Terri mentioned that they hope to have one more baby, so I wanted to get this study posted.

from THE ECONOMIST story:

...the amount of omega-3 in a pregnant woman's diet helps to determine her child's intelligence, fine-motor skills (such as the ability to manipulate small objects, and hand-eye co-ordination) and also propensity to anti-social behaviour.

[snip]

That, at least, is the conclusion of Joseph Hibbeln, a researcher at America's National Institutes of Health who has been working with a set of data from the Avon Longitudinal Study of Parents and Children. The Avon study was begun 15 years ago by Jean Golding, of the University of Bristol, with the aim of unravelling the genetic and environmental pathways that predispose children to disease. It contains data on 14,000 expectant mothers and their offspring.

[snip]

...the children of those women who had consumed the smallest amounts of omega-3 fatty acids during their pregnancies had verbal IQs six points lower than average...the finding is particularly pertinent because existing dietary advice to pregnant women, at least in America, is that they should limit their consumption of seafood in order to avoid exposing their fetuses to trace amounts of brain-damaging methyl mercury.

[snip]

Dr Hibbeln, however, says his work shows that the benefits of eating such fish vastly outweigh the risks from the mercury in them. Indeed, in the Avon study, it was those children exposed to the lowest levels of methyl mercury who were at greatest risk of having low verbal IQ....at 3½ years of age, those children with the best measures of fine-motor performance were the ones whose mothers had had the highest intake of omega-3s. Their third finding was that a low intake of omega-3s during pregnancy led to higher levels of pathological social interactions such as an inability to make friends as a child grew up.

....the “frightening data” showed how 14% of those seven-year-olds whose mothers had had the lowest intake of omega-3s during pregnancy demonstrated such behaviour, compared with 8% of those born to the highest-intake group.

converging lines of evidence

more:

Studies such as this one, which rely on correlating one variable with another, are not enough to draw firm conclusions on their own, since correlation is not necessarily causation. But these results are supported by several lines of data. One is that the graphs show “dose response” curves—in other words, different levels of omega-3s have different effects. There is also a lot of experimental work showing that omega-3s have behavioural effects on adults. One of Dr Hibbeln's other studies, for example, showed that omega-3 supplements given to violent alcoholics reduced their anger levels by a third within three months

serotonin & dopamine hypothesis

more:

It also helps to have a plausible mechanism, and Dr Hibbeln thinks there is one. Research published in 2000 by a group in Canada showed that giving omega-3 supplements to piglets doubled the levels of molecules called serotonin and dopamine in the frontal cortexes of the animals' brains. One of serotonin's jobs is to show growing nerve cells how they should connect from the frontal cortex, where reasoning takes place, to the limbic system, the seat of many emotional responses

yuck

more:

there is a second way that its level might be reduced—by competition with a similar group of fatty acids called omega-6s. Indeed, it may be the ratio of omega-3 to omega-6 in the membranes of cells—particularly nerve cells—which is at the root of the problem, since this can affect the ability of messenger molecules to pass through the membrane. The average cell membrane of an American, whose diet is low in fish and high in omega-6-rich vegetable oils, contains 20% omega-3-based lipids and 80% omega-6-based ones. (Some 10% of American calories now come from linoleic acid in maize and soya oils, the principal sources of omega-6s.) In a Japanese cell membrane, by contrast, the figures are 40% and 60% respectively.

words to live by

I love this.

Here's the title of Dr. Hibbeln's talk to the McCarrison Society:

I think I'll go pour Jimmy & Andrew a slug of their yummy new Norwegian cod liver oil right this minute.

autism & bipolar disorder & fish oil

Which reminds me.

I may have mentioned that Robert DeLong believes autism is caused by the genes for bipolar disorder expressed early in life, when the brain is still developing, instead of later on.

I believe him. When I say I 'believe' him, I mean I think that's what autism IS: autism is bipolar disorder expressed at birth or sometime around there. Until someone proves DeLong wrong, autism = bipolar is my personal hypothesis.

In an article in the March 23 issue of the journal Neurology, [ed.: I think this refers to the 1998 study] DeLong presents a new hypothesis that about two-thirds of children with the most common form of infantile autism actually have a treatable, genetically linked, early-onset form of severe depression. The argument is based on recent genetic analyses, behavioral studies and brain chemistry and imaging analyses on autistic children by researchers at Duke and several other institutions.

gold strike

I've just discovered DeLong has a recent publication on this subject. I've been out of the loop; I had no idea.

wow. It's a review article. So I've got this evening's reading all picked out.

Family history studies of autism consistently reveal a large subgroup with a high incidence of major mood disorder in family members, suggesting the two entities are related clinically and genetically. This review examines this concept, comparing current clinical and biological knowledge of autism and major mood disorder, and advances the hypothesis that this subgroup of autism represents an early-life phenotype of major mood disorder. If confirmed, this hypothesis would suggest that the basic biological defects determining major mood disorders may have prominent neurodevelopmental and cognitive dimensions. Testing of the hypothesis will depend on genetic studies.

The entire text is here: Autism and Familial Major Mood Disorder: Are They Related? J Neuropsychiatry Clin Neurosci 16:199-213, May 2004

in a nutshell

• fish oil is good for the brain

• fish oil may be especially important for pregnant women

• fish oil is probably good for every aspect of brain function, including mood and cognition

• we have strong evidence that fish oil treats bipolar disorder

• we have very strong evidence (strong as in almost certainly definitive) that autism tracks with mood disorders

• since fish oil treats bipolar disorder, it may well treat autism as well

• if you're taking fish oil supplements you need to take Vitamins C & E, too. I forget why

• American brain: 20% omega-3-based lipids, 80% omega-6-based ones

• Japanese brain: 40% and 60%

No wonder we can't do math.

nix on the flax seed oil AND Vitamins C & E

A couple more factoids.

First, if you're taking fish oil supplements, you should take Vitamins E & C, too. I've forgotten why. There's some wonky mechanism where you can end up producing more free radicals (or something) & damaging brain cell membranes, etc.....obviously, I remember essentially nothing of this except that you're supposed to take E & C along with.

Second, I would skip the flax seed oil. First of all, it's different from fish oil somehow....I forget why.

But also, a psychiatrist friend of mine told me she'd heard from other psychiatrists that flax seed oil can actually cause mania.

That was interesting to hear, because I once gave Jimmy & Andrew big honking doses of flax seed oil & they were both up for the entire night, manic as all get out.

update from ktm guest

"So if flaxseed oil isn't good (and I had heard that it wasn't), then what would vegetarians take in order to get a healthy dose of Omega 3s?"

Flax is a good source of ALA, but not EPA and DHA. Fish oil is a good source of EPA and DHA. All three of these are omega-3 fatty acids. ALA can be converted to EPA and DHA, but it doesn't seem like this works very well when humans eat flax oil (according to some researchers). If you're a vegetarian then you're probably just screwed as far as finding a good source of EPA and DHA goes and you'll have to just stick with flax. Maybe there's some way of convincing the ALA to convert to EPA and DHA more readily.

"Is cod liver oil a liquid source of Omega 3?"

Yes. it is about 11% DHA, 7% EPA.

Thank you!

(This is exactly what I recall reading, btw. I also remember - NOT FACT CHECKED that grazing animals like cows can convert ALA to EPA & DHA. That's why cows don't need to eat fish.)

update from Ann

If you go back to the Omegabrite website, they now have OmegaBrite Kidz Tutti-Fruitti or Orange Cream flavor liquid omega 3 for kids. They only have to take 1/4 tsp.

I can't believe I didn't see that!

I'm thrilled.

Of course, first we're going to have to use up our two big honking bottles of Carlson's Norwegian cod liver oil.

The omegabrite website is new and improved. They seem to have posted abstracts of most or all of the psychiatric and cognitive research on the Omega 3s.

Here's where the research stands on autism and Omega 3 fatty acids:

At present, although omega-3 polyunsaturated fatty acids are considered to be a promising therapeutic for autistic children (Kidd, 2002; Richardson and Ross, 2000), the best evidence currently available to support this claim comes from research showing that autistic children have lower DHA levels in blood than children with mental retardation (Vancassel, et al 2001; Bell, et al 2000). Additional support comes from evidence that low plasma omega-3 levels in boys were associated with behavior problems, temper tantrums, and sleep disorders (Stevens, et al 1996).
I should add that I don't see any particular changes in Jimmy & Andrew thanks to fish oil.

I give it to them because it's obvious to me that Omega 3 fatty acids are critically important for the brain, period - and because I do see obvious changes in me thanks to fish oil.

Jimmy & Andrew have such severe forms of autism that I don't think it would be pretty hard to see subtle improvements.

update: Andrew & cod liver oil

Since we have some parents with autistic kids reading the site, I think I should post this.

Both Andrew and Jimmy are highly sensitive to medication changes.

I ran out of my Nordic Natural liquid fish oil a couple of months ago, and didn't get around to ordering new fish oil until last week.

I ordered Carlson's cod liver oil.

Yesterday I gave Andrew 1 tsp, and he had a horrendous half-day. Then he settled down sometime in the afternoon, and was pretty good.

This morning he's been great.

Twenty minutes ago I gave him 1 tsp of Carlson's cod liver oil, and now he's screaming & tantruming.

So.

I don't know what to make of this.

Either he's 'getting readjusted' to fish oil, or he's not supposed to be taking cod liver oil.

I don't remember problems like this with the Nordic Natural product. (Which is not to say they didn't happen. We have so much tantruming & screaming that we often miss the cause.)

Jimmy's been fine both days. But he's 18, and much more stable than Andrew at this point. (fyi: Andrew is 11. He is Christopher's twin.)

I have no idea whether Andrew's tantrums are connected to the cod liver oil.

However, I'll probably go ahead and order the new Omegabrite produce & switch him to that. Jimmy can use up the cod liver oil....

update: Andrew's fine, too

There's obviously no problem with Andrew taking Carlson's product.

update: The Omega Plan

Joseph Hibbeln recommends Artemis P. Simopoulos & Jo Robinson's book, which was the first book I read about the Omega 3s. Simopoulos also did NIH-funded research on the Omega 3 fatty acids, IIRC.

I thought it was terrific.

while we're on the subject of Jo Robinson —

I also like her book When Your Body Gets the Blues very much.

Check out her research page - wonderful stuff on light, mood, & weight (though I can't find the study they used to have posted showing weight loss from sitting in the sun....). The original 'body blues' study is here.

WHEN YOUR BODY GETS THE BLUES is the other alternative-medicine self-help book I believe absolutely.

Ever since reading the book, I try to get all 3 kids outdoors in the sun for 20 minutes every day.

These study findings suggest that a program of moderate-intensity walking, increased light exposure, and selected vitamins can improve women's mood. The high level of adherence to the intervention suggests that women could comfortably incorporate this tri-modal program into their daily lives. These findings extend the work of other studies that have demonstrated the positive influence of each independent component (light, exercise, and vitamins) on mood (Kripke 1998; Wirz-Justice et al. 1996; Blumenthal et al. 1999; Moses et al. 1989; Benton, Fordy, and Haller 1995).

Women in the intervention group improved significantly compared to those in the control group on all five dependent variables that measured mood and well-being. Not only did their depression scores decrease, they also reported greater self-esteem, improved general well-being, and greater happiness.

We were particularly interested in determining whether the intervention addressed symptoms more prevalent in women than men, such as anxiety and fatigue. The subscales of the POMS showed that the women in the intervention group experienced a significant decrease in anger and tension. Meanwhile their vitality improved, as measured by the GWB subscales.

Omega 3 fatty acids
brain food

-- CatherineJohnson - 03 Feb 2006
BoyTroublePart5 04 Feb 2006 - 15:48 CatherineJohnson

Just spotted this "Remark from the Fray" in reaction to Slate's article on self-disipline & achievement:

Any high-school teacher will tell you why boys do more poorly than girls:

Boys are jerks.

Sure, there are exceptions, the occasional aesthete or scholar...but generally speaking, boys between the ages of 13 and 22 are uncouth vulgarians interested primarily in either prodding or pounding on each other, only expanding their limited interests to include such complexities as beer and breasts as age and situations permit.

If the SAT answer sheets used more mammilary shapes instead of the current oval bubbles, or phrased their instructions in terms like "Dude, shove your fist through the best answer to this question," scores would soar.

--Robert P.
High-school teacher since 1985

yoo-hoo

Robert

It's not nice to call other people's children uncouth vulgarians interested primarily in either prodding or pounding on each other.

Don't make me come down there.

-- CatherineJohnson - 04 Feb 2006

EconomicsBlackboard 04 Feb 2006 - 18:12 CatherineJohnson

source:
Economics Round Table

-- CatherineJohnson - 04 Feb 2006

WhatYoullWishYoudKnown 04 Feb 2006 - 18:23 CatherineJohnson

Karen A left links to two articles. I'd read What You'll Wish You'd Known by Paul Graham a couple of years ago, and had forgotten all about it.

Thanks for reminding me!

excerpts:

(I wrote this talk for a high school. I never actually gave it, because the school authorities vetoed the plan to invite me.)

When I said I was speaking at a high school, my friends were curious. What will you say to high school students? So I asked them, what do you wish someone had told you in high school? Their answers were remarkably similar. So I'm going to tell you what we all wish someone had told us.

I'll start by telling you something you don't have to know in high school: what you want to do with your life.

[snip]

...there are other jobs you can't learn about, because no one is doing them yet. Most of the work I've done in the last ten years didn't exist when I was in high school. The world changes fast, and the rate at which it changes is itself speeding up. In such a world it's not a good idea to have fixed plans.

And yet every May, speakers all over the country fire up the Standard Graduation Speech, the theme of which is: don't give up on your dreams. I know what they mean, but this is a bad way to put it, because it implies you're supposed to be bound by some plan you made early on. The computer world has a name for this: premature optimization....These speakers would do better to say simply, don't give up.

What they really mean is, don't get demoralized. Don't think that you can't do what other people can.

[snip]

In fact I suspect if you had the sixteen year old Shakespeare or Einstein in school with you, they'd seem impressive, but not totally unlike your other friends.

Which is an uncomfortable thought. If they were just like us, then they had to work very hard to do what they did. And that's one reason we like to believe in genius. It gives us an excuse for being lazy. If these guys were able to do what they did only because of some magic Shakespeareness or Einsteinness, then it's not our fault if we can't do something as good.

I'm not saying there's no such thing as genius. But if you're trying to choose between two theories and one gives you an excuse for being lazy, the other one is probably right.

So far we've cut the Standard Graduation Speech down from "don't give up on your dreams" to "what someone else can do, you can do." But it needs to be cut still further. There is some variation in natural ability. Most people overestimate its role, but it does exist. If I were talking to a guy four feet tall whose ambition was to play in the NBA, I'd feel pretty stupid saying, you can do anything if you really try. [2]

We need to cut the Standard Graduation Speech down to, "what someone else with your abilities can do, you can do; and don't underestimate your abilities." But as so often happens, the closer you get to the truth, the messier your sentence gets. We've taken a nice, neat (but wrong) slogan, and churned it up like a mud puddle. It doesn't make a very good speech anymore. But worse still, it doesn't tell you what to do anymore. Someone with your abilities? What are your abilities?

Upwind

I think the solution is to work in the other direction. Instead of working back from a goal, work forward from promising situations. This is what most successful people actually do anyway.

In the graduation-speech approach, you decide where you want to be in twenty years, and then ask: what should I do now to get there? I propose instead that you don't commit to anything in the future, but just look at the options available now, and choose those that will give you the most promising range of options afterward.

It's not so important what you work on, so long as you're not wasting your time. Work on things that interest you and increase your options, and worry later about which you'll take.

Suppose you're a college freshman deciding whether to major in math or economics. Well, math will give you more options: you can go into almost any field from math. If you major in math it will be easy to get into grad school in economics, but if you major in economics it will be hard to get into grad school in math.

Flying a glider is a good metaphor here. Because a glider doesn't have an engine, you can't fly into the wind without losing a lot of altitude. If you let yourself get far downwind of good places to land, your options narrow uncomfortably. As a rule you want to stay upwind. So I propose that as a replacement for "don't give up on your dreams." Stay upwind.

How do you do that, though? Even if math is upwind of economics, how are you supposed to know that as a high school student?

Well, you don't, and that's what you need to find out.

I like this part:

The best protection is always to be working on hard problems. Writing novels is hard. Reading novels isn't. Hard means worry: if you're not worrying that something you're making will come out badly, or that you won't be able to understand something you're studying, then it isn't hard enough. There has to be suspense.

This part is foreign to me, but I get the point:

Ambition

In practice, "stay upwind" reduces to "work on hard problems." And you can start today. I wish I'd grasped that in high school.

Most people like to be good at what they do. In the so-called real world this need is a powerful force. But high school students rarely benefit from it, because they're given a fake thing to do. When I was in high school, I let myself believe that my job was to be a high school student. And so I let my need to be good at what I did be satisfied by merely doing well in school.

If you'd asked me in high school what the difference was between high school kids and adults, I'd have said it was that adults had to earn a living. Wrong. It's that adults take responsibility for themselves. Making a living is only a small part of it. Far more important is to take intellectual responsibility for oneself.

If I had to go through high school again, I'd treat it like a day job. I don't mean that I'd slack in school. Working at something as a day job doesn't mean doing it badly. It means not being defined by it. I mean I wouldn't think of myself as a high school student, just as a musician with a day job as a waiter doesn't think of himself as a waiter. [3] And when I wasn't working at my day job I'd start trying to do real work.

When I ask people what they regret most about high school, they nearly all say the same thing: that they wasted so much time. If you're wondering what you're doing now that you'll regret most later, that's probably it. [4]

nix on community service:

You may be thinking, we have to do more than get good grades. We have to have extracurricular activities. But you know perfectly well how bogus most of these are. Collecting donations for a charity is an admirable thing to do, but it's not hard. It's not getting something done. What I mean by getting something done is learning how to write well, or how to program computers, or what life was really like in preindustrial societies, or how to draw the human face from life. This sort of thing rarely translates into a line item on a college application.

We didn't have enforced community service when I went to school.

What you should not do is rebel. That's what I did, and it was a mistake. I didn't realize exactly what was happening to us, but I smelled a major rat. And so I just gave up. Obviously the world sucked, so why bother?

When I discovered that one of our teachers was herself using Cliff's Notes, it seemed par for the course. Surely it meant nothing to get a good grade in such a class.

In retrospect this was stupid. It was like someone getting fouled in a soccer game and saying, hey, you fouled me, that's against the rules, and walking off the field in indignation. Fouls happen. The thing to do when you get fouled is not to lose your cool. Just keep playing.

By putting you in this situation, society has fouled you. Yes, as you suspect, a lot of the stuff you learn in your classes is crap. And yes, as you suspect, the college admissions process is largely a charade. But like many fouls, this one was unintentional. [7] So just keep playing.

Rebellion is almost as stupid as obedience. In either case you let yourself be defined by what they tell you to do. The best plan, I think, is to step onto an orthogonal vector. Don't just do what they tell you, and don't just refuse to. Instead treat school as a day job. As day jobs go, it's pretty sweet. You're done at 3 o'clock, and you can even work on your own stuff while you're there.

I believe this:

The word "aptitude" is misleading, because it implies something innate. The most powerful sort of aptitude is a consuming interest in some question, and such interests are often acquired tastes.

I've met people whose interests were at odds with their aptitude. I always found that intriguing.

And here's good news! —

In most adults this curiosity dries up entirely. It has to: you can't get anything done if you're always asking why about everything. But in ambitious adults, instead of drying up, curiosity becomes narrow and deep. The mud flat morphs into a well.

Curiosity turns work into play. For Einstein, relativity wasn't a book full of hard stuff he had to learn for an exam. It was a mystery he was trying to solve. So it probably felt like less work to him to invent it than it would seem to someone now to learn it in a class.

One of the most dangerous illusions you get from school is the idea that doing great things requires a lot of discipline. Most subjects are taught in such a boring way that it's only by discipline that you can flog yourself through them. So I was surprised when, early in college, I read a quote by Wittgenstein saying that he had no self-discipline and had never been able to deny himself anything, not even a cup of coffee.

jeez

I wonder why this guy got dinged from delivering the h.s. graduation speech.

Personally, I've had to have QUITE A LOT of self-discipline.

Of course, probably if I'd been writing about the philosophy of language instead of animals & autism life would have been a breeze.

OK, this part is true:

Now I know a number of people who do great work, and it's the same with all of them. They have little discipline. They're all terrible procrastinators and find it almost impossible to make themselves do anything they're not interested in. One still hasn't sent out his half of the thank-you notes from his wedding, four years ago. Another has 26,000 emails in her inbox. [ed.: check]

I'm not saying you can get away with zero self-discipline. You probably need about the amount you need to go running. I'm often reluctant to go running, but once I do, I enjoy it. And if I don't run for several days, I feel ill. It's the same with people who do great things. They know they'll feel bad if they don't work, and they have enough discipline to get themselves to their desks to start working. But once they get started, interest takes over, and discipline is no longer necessary.

find a question

More synchronicity. I've been planning to write a post on questions.

If you want to do good work, what you need is a great curiosity about a promising question. The critical moment for Einstein was when he looked at Maxwell's equations and said, what the hell is going on here?

It can take years to zero in on a productive question, because it can take years to figure out what a subject is really about. To take an extreme example, consider math. Most people think they hate math, but the boring stuff you do in school under the name "mathematics" is not at all like what mathematicians do.

The great mathematician G. H. Hardy said he didn't like math in high school either. He only took it up because he was better at it than the other students. Only later did he realize math was interesting-- only later did he start to ask questions instead of merely answering them correctly.

When a friend of mine used to grumble because he had to write a paper for school, his mother would tell him: find a way to make it interesting. That's what you need to do: find a question that makes the world interesting. People who do great things look at the same world everyone else does, but notice some odd detail that's compellingly mysterious.

And not only in intellectual matters. Henry Ford's great question was, why do cars have to be a luxury item? What would happen if you treated them as a commodity? Franz Beckenbauer's was, in effect, why does everyone have to stay in his position? Why can't defenders score goals too?

I love this:

Now I have enough experience to realize that those famous writers actually sucked. Plenty of famous people do; in the short term, the quality of one's work is only a small component of fame. I should have been less worried about doing something that seemed cool, and just done something I liked. That's the actual road to coolness anyway.

It's true.

-- CatherineJohnson - 04 Feb 2006
BarModelsInKumon 04 Feb 2006 - 21:03 CatherineJohnson

I just looked ahead in this week's packet of KUMON worksheets, and found KUMON bar models!

Saxon uses bar models, too

I keep meaning to mention the fact that Saxon Math 8/7 uses bar models to teach fraction word problems. A Saxon student sees bar models in a number of lessons, then practices drawing them to mastery.

Saxon, Singapore, & KUMON.

We have a consensus.

Sybilla Beckmann's terrific article on bar models

Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4-6 Texts Used in Singapore (pdf file) by Sybilla Beckmann. (pdf file) by Sybilla Beckmann>

Sybilla Beckmann Kazaz

also by Sybilla Beckmann:

-- CatherineJohnson - 04 Feb 2006
PutOnYourBigGirlPanties 04 Feb 2006 - 22:38 CatherineJohnson

I'd noticed that eduwonk had been somewhat perseveratively quoting Margaret Spellings' line about putting on her big girl panties.....which was just odd enough not to cause me instantly to go read the article it came from....but then joannejacobs finally read the article herself, which galvanized me into action.....and let me tell you, I'm glad I got over to WAPO.

Margaret Spellings: In Her Own Class is fantastic:

Spellings is blunter than you might expect, vivid and bigger, as if her photo had been cropped and enlarged. She is a tall woman swinging an iguana-green purse, wearing edgy rectangular glasses and chewing gum. (She spits it into the garbage when you arrive, as if you were the teacher.) Spellings scanned the crowd: "Colin's the little hottie of the school."

She had her babies without pain medication. She's a tough enough manager to be called a "bulldog on details" by Rove; strong enough to raise her girls as a single mom when her first marriage ended; brave enough to admit that she dreams of being a torch singer draped over a piano; Texan enough to live by the motto (on her notepad) "Put on your big girl panties and deal with it."

the good news is —

— she's got a kid in middle school:

Middle school is tricky, Spellings said -- too many hormones and too loose a curriculum. When boys in white shirts and ties shuffled onstage, Spellings said, "They're so awkward, it cracks me up." Her own experience in seventh grade was "the low point of my life," she said. ". . . There's a lot of mush going on in middle school -- one of the nuts we haven't cracked in public education policy."

You can order the big girl doll here.

-- CatherineJohnson - 04 Feb 2006
MathematicsAtFloatingLog 05 Feb 2006 - 00:59 CatherineJohnson

the blog

-- CatherineJohnson - 05 Feb 2006

AnimalsInTranslationFebFive 05 Feb 2006 - 13:38 CatherineJohnson

February 5, 2006

Moving to number eight next week.

Animals in Translation on TIMES list
Animals in Translation 1-29-2006
Animals in Translation 2-05-2006
Animals in Translation 2-12-2006
Animals in Translation 2-19-2006
Animals in Translation 2-26-2006
Animals in Translation 3-05-2006
Animals in Translation 3-12-2006
Animals in Translation 3-19-2006
Animals in Translation 3-26-2006

-- CatherineJohnson - 05 Feb 2006
KenOnSingaporeMathInAbington 05 Feb 2006 - 14:14 CatherineJohnson

[Can I tell you how much I dislike TWiki's Change Name process? I loathe it, that's how much. As I was trying to correct a misspelling in the title of this post, the log page disappeared, as the log page is wont to do under these circumstances. So now I'm reconstructing the post here.]

from Ken

Speaking of Singapore Math ...

The Singaporeans are in town being corrupted by our local educators. I don't know whether to laugh or cry.

Students in Singapore had the top scores among 25 countries in an international math and science test. But their educators think they still have something to learn from the United States.
Giggle.

Two principals from Singapore and a representative of its education agency recently visited schools in Abington, hoping to see American students' creativity and communication skills in action.
Double Giggle.

The Singapore educators attribute their students' success in math and science to their city-state's highly structured form of instruction. But they suspect that structure keeps some students from asking questions and limits opportunity for independent learning and thinking.

[snip]

"I like the way your children are able to communicate," she said. "Maybe we need to cultivate that more - a conversation between students and teachers."

Hmmm, maybe they are on to something with their lack of critical thinking skills. [ed.: The superiority only applies to math IQ, not verbal IQ, as this article clearly demonstrates.] *

Chia, Pei Hwa Secondary School principal Hoi Neng Chong, and Mark Nivan Singh, of Singapore's Ministry of Education, came to Philadelphia for a training conference. While they were here, they wanted to see U.S. classrooms, and Chia's online research left her impressed with Abington, which has been recognized by the U.S. Department of Education as a high-achieving district.

Abington, eh. Let's see:

Median Household Income 101,951 ?Adults with a Bachelor's Degree 25.2%

Not exactly a typical school district. High Income, slightly above average parental education.

"We have a lot to learn from you guys about social and emotional learning," Singh said.
Oooookaay. Fair enough. And, we have a lot to learn from you about, you know, teaching math.

The group visited a Spanish class with about 25 students. Chia, the primary school principal, asked whether the class size was typical. When told yes, she smiled and said, "We have 40 in a class back home."
Small Classrooms, Reason for Success: Uncheck.

For Breana Brown, 14, one of three student guides, the walks between class visits gave her a chance to ask questions about student life in Singapore. Most students there use public transportation or walk to school, she learned. Public schools don't offer kindergarten. The school day has only one half-hour break for lunch. At 11th grade, some students go to a junior college-like academic program. Others go to high-level technical study.
Very Interesting. Here comes the good part, get the daubers ready.

American researchers have been visiting Singapore and other Asian countries, too, said Patrick Gonzales, a U.S. Department of Education research analyst who coordinates the Trends in International Mathematics and Science Study, or TIMSS. That's the test in which Singapore's fourth graders scored higher in math and science than students in 25 participating countries. Singapore scored first with an average of 594; the United States was 12th with an average of 518. Eighth graders in Singapore also outperformed students in 45 countries.

"There's a growing interest in the U.S. in what is termed 'Singapore Math,'" Gonzales said. "It has been published in the U.S., and school districts are beginning to use it."

But the tricky part in all of this, he said, is that Singapore's top scores are in line with other Asian countries even though they teach math differently.

"Some are very traditional, teacher-centered, with rote memorization and lots of practice," he said.

Thanks Mr. Gonzales, I hadn't realized that the reason for Singapore's success was because they have a fuzzy curriculum.

"In other, more inquiry-based models, students take more responsibility for their learning and there is more independent learning."
I wonder if he was able to keep a straight face when he said this, especially the "there is more independent learning" part. For those of you playing along at home, you should have BINGO by now, but we're going for blackout at KTM.

Researchers are now paying close attention to one characteristic that is shared by many Asian countries: a focus on teaching students the concepts behind their math lessons. But wait, the TIMMS guy, just called it rote memorization a few paragraphs up. Circuits overloading.

The people who run TIMSS have begun sending video cameras into classrooms to record how teachers around the world teach, Gonzales said.

In the United States, they have noticed, math and science are largely taught in isolation, without stressing the underlying concepts that allow connections between lessons within the same subject. "The lessons are being taught as discrete units," he said.

White is black. Black is White. Yes, that's our problem -- not enough "stressing the underlying concepts" at the expensive of learning to mastery. The solution: more fuzziness. The usual.

Students in other countries also get more advanced lessons at a younger age, he said.

In the United States, there is growing support to have all students take algebra by grade eight, Gonzales noted.

"In Hong Kong, 14 percent of students in grade eight are taking trigonometry," he said.

And, the reason why they're getting more advanced lessons? Could it be because they're not wasting an inordinate amount of time on "inquiry learning"? And...

Gonzales said that U.S. students may not be advancing in math as quickly because much more time is spent on review.

"It's harder to get to more advanced topics because we are also going back and dealing with more elementary topics that, at eighth grade, students should be beyond," he said.

But I thought Inquiry learning was so great. Are you now telling me that students aren't learning and teachers have to constantly review old topics, yet still by 8th grade kids aren't getting it. Wait a second, there's a name for this nonsense -- the spiral curriculum -- and it's supposed to be a feature not a bug. I'm really confused now.

Another issue is homework.

The videotaped lessons revealed that in the United States, students are frequently allowed to spend the last 10 minutes of class time on homework.

Chia said her elementary students have at least an hour of homework each night.

Of course when US students do get homework, it sometimes looks like this.

F. Joseph Merlino, project director of the Mathematics Science Partnership of Greater Philadelphia, ...
And well-known shill for the fuzzy math program IMP.

... said the United States' competitive edge has always come from creativity. But the most rigorous classes and best teaching that foster creativity have often been enjoyed by a small group of high achievers. That's no longer enough to stay competitive.

"We're not teaching kids to think for themselves in sufficient numbers," he said.

You should have a blackout by now.

The visiting Singapore educators said parental pressure is part of the reason why their students excel at math and science.

Parents see accomplishment in math and science as the way to success, they said. They pressure schools to offer challenging courses and pressure students to do well in them.

I did learn something after all. Singaporean parents are smarter than American parents.

* That's what I've been thinking. Where's the vaunted 1-standard-deviation IQ superiority we've been hearing about when you need it?

-- CatherineJohnson - 05 Feb 2006
AnneDwyersMathBoosters 05 Feb 2006 - 16:44 CatherineJohnson

Comment left by Anne:

BTW, my Math Booster class has seemed to strike a nerve with parents. One of the parents on the PTO at one of the elementary schools is going to speak to her principal about having the PTO sponser my class. I would love to be a fly on the wall at that meeting!!! Politics being what it is in a school district, I don't see it happening.

Excellent.

On all counts.

Irvington redux

Now that I know we have one person from Irvington reading the site, I figure I'll engage in a bit of spaced repetition on the Singapore Math in Irvington front.

personal narrative:

• I co-chaired the PTSA after-school program at the Main Street School for two years.

• During my second year as co-chair, I taught an after-school course in Singapore Math. The principal approved the course, asked me how it was going, borrowed the books to show his wife (a high school math teacher), and told me NY state was moving toward a 'Singapore' model (fewer topics taught in more depth) in state standards. Christopher's teacher helped me out with advice and materials.

• This fall I taught the course again. One teacher asked me for materials to give to the parent of an especially bright child in his/her class. Another teacher told a parent that he/she was eager to learn more about what I was doing.

• Our assistant superintendent in charge of curriculum contacted the president of the PTSA. He told her that 'teachers' and 'parents' had called to complain about the course. He said, too, that I was using my course to undermine TRAILBLAZERS.

• Our assistant superintendent in charge of curriculum did not contact me at any point. Instead, acting in his professional capacity, he chose to make anonymous charges against one parent to another parent in private.

• The PTSA president contacted me. We talked. I met with the PTSA Executive Committee.

• Last I heard, the Superintendent planned to draft a formal policy, to be submitted to and voted on by the School Board, giving her authority to approve and disapprove all parent-run courses.

micromanagement

I have been told, by a board member, that our Superintendent has a tendency to micromanage.

When Ed heard what was going on — for the uninitiated, Ed is a longtime professor and university administrator — he said, "The superintendent shouldn't even know about your course. This should be way below her level of vision. If this is what she's spending her time on, we're in trouble."

I'm sure he's right.

some questions

• This is a small community. I wonder whether my reputation has been harmed by the assistant superintendent's decision to make anonymous accusations against me, in private, to another parent.

• This is a small community. I wonder whether the assistant superintendent has talked to other parents, administrators, teachers, and community members about me.

• This is a small community. I wonder whether the assistant superintendent maybe ought to pick up the phone and give us a call. We're in the book.

one more question

The administration's thinking, I gather, is that under the new policy the PTSA cannot offer after-school courses that cover the same material taught in Irvington schools.

The PTSA can offer enrichment courses — knitting, cooking, all-sports.

The PTSA can offer academic courses not offered by the district — Chinese, for instance. The PTSA is free to offer after-school courses in Chinese.

This means that I cannot teach a writing course in the after-school program.

Irvington parents are actively distressed by the quality of writing instruction in the middle school, and the district acknowledges the problem.

I taught writing to middle-school students for Johns Hopkins CYO; I have a Distinguished Teaching award from the University of Iowa for my teaching. I am a professional writer, author of a well-reviewed book that spent 6 weeks on the New York Times bestseller list. [3-31-2006: 10 weeks on the paperback list and counting]

I would probably agree to teach writing to middle-schoolers in an after-school PTSA program as a service to the community.

Is the administration acting in the interests of Irvington children?

I can think of a dozen parents from whom I'd want Christopher to be able to take an after-school course, and that's just off the top of my head.

All of these parents would be teaching core academic subjects. Math, English, history, science.

I would like to see our administration foster such opportunities for our kids.

Irvington mission statement: The mission of the Irvington School District is to create a challenging and supportive learning environment in which each student attains his or her highest potential for academic achievement, critical thinking and life-long learning.

-- CatherineJohnson - 05 Feb 2006

LetterToLosAngelesTimes 05 Feb 2006 - 20:02 CatherineJohnson

My AlphaSmart is back in action, so I may try to bash out a letter to the LA Times while we're watching the Super Bowl.

My AlphaSmart wasn't out of action, fyi. I was. After I switched from PCs to Macs I dragged my feet figuring out how to switch the AlphaSmart to the Mac. That was dumb. AlphaSmarts were designed by the folks who designed Macs, and it turns out that the only thing I had to do was plug the AlphaSmart into the Mac the exact same way I used to plug it into the PC, i.e. via USB cord.

The AlphaSmart did the rest.

not a paid announcement

AlphaSmarts may be the single best piece of kid (and adult) technology ever invented. They're indestructible, cheap (\$139), as easy to use as an old-fashioned dial telephone, and they run 700 hours on 3 double-A batteries. I got interested in them when I read a mom's story on a writers' forum. She said her daughter's AlphaSmart had gone flying out the door of their still-moving station wagon & skidded all the way down the driveway to the curb without suffering the slightest slowdown in functioning.

Now that I've had my own AlphaSmart for awhile, I believe her.

These things are indestructible.

I'm going to start using it with Andrew & his math. I'll have him type answers on the AlphaSmart. We can do the same thing with KUMON reading if I start him in that program this summer.

Ed bought the first Dana to hit the market (larger screen & internet hook-up) but it's been glitchy. Don't know whether they've got all the bugs out by now. They may have.

back on topic

Ben Calvin suggested these points:

• The false rigor of adding Algebra req. without math foundation.

• Failure begins w/ basic K-8 math.

• Math education is cumulative

• Spiral vs Teach to Mastery

• Lack of Formative Assesment

That sounds right to me, but if anyone else has thoughts, I'd like to hear.

same story in Sacramento

Last week joannejacobs linked to a similar story that appeared in the Sacramento Bee: Test's moment of truth painful for some: With chances to pass dwindling, students feel the heat.

This prompted the usual round of condemnations in Comments threads and letters to the editor. Lazy, no-good students and their lazy, no-good grammar; throw the bums out.

Here's one, from an educator:

Re "Test's moment of truth painful for some," Jan. 25: It's about time our students were held accountable for their academic performance. An educator for the past decade, I have seen our state, districts and educators held accountable for what is taught in classrooms and the performance of students. To have this start coming full circle and encompass students is progress for the future.

If student accountability were placed upon middle school students, it would create an early emphasis on the importance of being successful. This accountability would lead to students who could rise above the standards and cut down on the behavior issues that middle school educators must deal with.

Ideally, the accountability will also have to be shouldered by parents. Will they accept being held accountable?

The era of accountability is here, and everyone needs to play their part.

Colby Franklin, Sacramento

OK, Colby, here's how it shakes out.

I'm happy to shoulder accountability.

What I'm not happy to do is shoulder accountability and pay your salary.

One more thing.

I know a number of parents who've shouldered accountability. These parents are on the line for their children's educational success or failure.

They are called homeschoolers.

A dejected Juan Calderon, a senior at Hiram Johnson High School, has just
learned that he failed to pass the math portion of the California High School Exit Exam.

Juan crumpled [the test results] in his fist and threw it in the trash.
He growled in frustration and kicked a nearby garbage can with his
bright white sneakers. Then tears began to run down his flushed cheeks.

Gee. I wonder if lousy schools have anything to do with this situation?

...the head of one of the stronger LAUSD high school math departments lamented: "The mandatory 40-hour algebra training was worthless. We had to teach the trainers how to do algebra … the people in charge of making final decisions on math [in the LAUSD] don't know math!"

I agree with Colby on one thing.

If parents were fully accountable — if parents knew they were fully accountable — pass rates would soar.

failing algebra in Los Angeles

AlphaSmart
AlphaSmart reviews
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
AlphaSmart to the rescue
the joys of primitive computing

-- CatherineJohnson - 05 Feb 2006

SecretBallot 05 Feb 2006 - 23:04 CatherineJohnson

I'd never heard this:

It is especially noteworthy that San Antonio dropped Everyday Math shortly after [Diana] Lam departed, following a secret ballot by the city’s teachers, 80% of whom voted against it.

source:
Mathematics in the NYC Children First Initiative
Fred Greenleaf
Professor of Mathematics
New York University
Prepared for the Courant Initiative for Mathematical Sciences in Education Forum:
“Delivery on the Promise of Mayoral Control”
Courant Institute of Mathematical Sciences
New York University
October 2, 2005

Our assistant superintendent for curriculum has told me that our teachers like TRAILBLAZERS very much.

He's heard no complaints at all.

Of course, he says the same thing about the parents.

-- CatherineJohnson - 05 Feb 2006

JohnnyAndKarin 05 Feb 2006 - 23:20 CatherineJohnson

This is so beautiful, I'm posting the whole essay.

From the Los Angeles Times
X = Karin (Johnny) {gt} 95%
What does it take to learn algebra? First you have to master the fundamentals.
By Karin Klein
KARIN KLEIN is an editorial writer for The Times.

February 4, 2006

JOHNNY PATRELLO was a greaser. I was a dork. And yet, despite our rigidly stratified school culture, we came together in the spring of 1968 at Walt Whitman Junior High School, where I tutored Johnny in algebra.

I thought about Johnny again as I read The Times' series this week on L.A.'s dropout problem. Algebra, the reporters found, is an insurmountable stumbling block for many high school students.

What struck me was that the reasons why Johnny can't do algebra in L.A. today are remarkably similar to why Johnny Patrello couldn't do algebra almost four decades ago in Yonkers, N.Y.

Johnny and I were brought together by Mrs. Elizabeth Bukanz, the algebra teacher. Mrs. Bukanz wore her sandy hair in a frizzy French twist and her glasses on a chain. But she was gentle and smiling, and she had passion — at least for what she called "the beauty of algebra." I, too, loved its perfect logic and tidy solutions, so unlike my messy teenage life.

But Johnny was deaf to algebra's siren song. He was flunking, and Mrs. Bukanz hoped that if I used my study halls to tutor him, he might score at least 65% on the New York State Regents exam. Passing the exam allowed even failing students to move on to high school, which started in 10th grade; otherwise, Johnny would be left behind.

Johnny wore his leather jacket in class despite the spring warmth, and he habitually tilted his face toward the floor so that when he looked up at me, he seemed embarrassed. Yet for such a cool guy, he was surprisingly friendly and committed to giving this a try.

Things looked pretty hopeless to both of us those first couple of sessions, as Johnny stumbled through algebra problems while I tried to figure out exactly what he didn't understand. Then, as we took it down to each step of each little calculation, the trouble became clear: Johnny somehow had reached ninth grade without learning the multiplication tables.

Because he was shaky on those, his long multiplication was error prone and his long division a mess. As Johnny tried to work algebraic equations, his arithmetic kept bringing up weird results. He'd figure he was on the wrong track and make up an answer.

This discovery should have made us feel worse. How could we possibly make up for a dearth of third-grade skills and cover algebra too?

But at least we knew where to start.

We spent about half of those early sessions on multiplication drills. Seven times eight, eight times seven — Johnny could never remember. As an adult, in memory of Johnny's struggles, I would rehearse my kids at an early age in that one math fact. Get that 56 down, I would tell them, and the rest of multiplication is a snap.

Today's failing high school students, though plagued by more poverty and upheaval than Johnny or I ever knew, bring the same scanty skills to algebra class, according to The Times' series. They never quite grasped multiplication tables, but still they moved on to more complicated math.

Who can focus on the step-by-step logic of peeling back an equation until "x" is bared when it involves arithmetic that comes slow and slippery, always giving a different answer to the same calculation?

Yet in all these decades, the same school structure that failed Johnny goes on, dragging kids through the grades even if they don't master the material from the year before. This especially makes no sense for math, which is almost entirely sequential.

Leaving children back isn't a solution; it simply makes them feel stupid. They learn, like Johnny, to look at the floor. The floor can't embarrass them.

What I learned from Johnny — aside from the fact that greasers could be sweet-natured and very, very smart — is that schools are structured to help administrators feel organized, not to help children learn.

Young children's skills are all over the map, yet we corral them into second grade, third grade and so forth, where everyone moves at one pace in all subjects. Better to group them according to their skills in each subject, without the "grade" labels, and let them move on to the next skill when they have mastered the one they were on. If they're not getting it, give them extra tutoring, but don't push them forward until they're ready. This way, there is no failure — only progress.

It requires a sea change in thinking, but it's not impossible or even all that hard. Back before standardized tests put classes in lockstep, some progressive schools already were using team teaching to do this in math as well as reading and writing.

Johnny finally nailed seven times eight, then with amazing quickness worked his way through basic "x" problems up to multiple variables and beyond. Still, I couldn't quite catch him up to a year's worth of work in a couple of months. And on a sweltering June day, with humidity that neared 100%, the regents exam came, faster than we felt ready for it.

A couple of weeks later, I saw Johnny in the hall. He shot me a dazed look and broke the news — 95%! That moment has wiped from memory my own regents score. But I won the algebra award at the graduation ceremony. Johnny cheered, apparently undaunted by the fear of appearing uncool.

We lost touch in high school. I was college-prep, he was voc-ed. We would pass occasionally in the halls, and he would glance up from the floor and say, "Hi, teach!"

I know he received his diploma because I see his picture in my old yearbook, wearing a suit and tie instead of his leather jacket. His eyes still look up cautiously from his slightly downcast face, as though he is a bit surprised to be there.

BEFORE I USED Johnny's full name in a story that would reach more than a million readers, it was only right to try to contact him for permission. Directory assistance found one John Patrello, not too far from Yonkers.

The phone was answered by his wife, Joann. It was the same Johnny, but he had died a year and a half ago of a massive stroke, leaving behind Joann and four children.

As she and I talked, both of us in tears at times, it was amazing how much of what I remembered about Johnny continued throughout his life — the tough outer look, the sweetness a millimeter underneath, the quick mind, the habit of tilting his face toward the floor. His eldest is a doctor; the second, a teacher. His teenage daughter wants to be a journalist, and I'll see what I can do to help her along the way.

Johnny became an auto mechanic. ("He loved math, and you know auto repair involves a lot of math," Joann said. Yes, it does.)

Another thing Joann told me about Johnny: He was incredibly fast at multiplication.

-- CatherineJohnson - 05 Feb 2006

SandraStotskyOnReadingAndEdSchools 06 Feb 2006 - 13:04 CatherineJohnson

Abstract: Reading instruction is one of the very few areas where it is not the case that “more research is needed.” Educational policy makers already have the theory and the evidence supporting it to guide the implementation of effective reading programs from K-12. In fact, they have had the theory and the evidence for decades. The central problem they face in providing effective reading instruction and a sound reading curriculum stems not from an absence of a research base but from willful indifference to what the research has consistently shown and to a theory that has been repeatedly confirmed. Using Jeanne Chall’s The Academic Achievement Challenge as a point of departure, I suggest why our education schools, through their influence on teachers, administrators, textbook publishers, and state and national assessments of students and teachers, have come to be the major obstacle to closing the “gap” in student achievement.

source:
Why Reading Teachers Are Not Trained to Use a Research-Based Pedagogy:
Is Institutional Reform Possible?
Sandra Stotsky
Research Scholar
Northeastern University
Prepared for the Courant Initiative for the Mathematical Sciences in Education Forum:
“Delivery on the Promise of Mayoral Control”
Courant Institute of Mathematical Sciences
New York University
October 2, 2005

David Klein on Bennet-Kew

Not all teachers can accept the kind of environment one finds at Bennett-Kew. Newly credentialled teachers from prestigious universities are sometimes turned away after a semester or two. Education college doctrine is often at odds with what works at Bennett-Kew, and Mrs. Ichinaga has found that in some cases noncredentialled teachers provide better instruction than credentialled ones.

source:
High Achievement in Mathematics:
Lessons from Three Los Angeles Elementary Schools
by
David Klein
Commissioned by the Brookings Institution
August 2000

I have never heard of it

Notices [of the American Mathematical Society]: Starting in 1968, the government funded a huge study called Project Follow-Through. It cost a billion dollars and ran almost thirty years. The purpose was to examine how different teaching methods or philosophies affected student performance. What they found was that the traditional, “direct instruction” method was the most effective. Are you familiar with this study?

[President of NCTM,] Gail Burrill: I have never heard of it.

source:
Interview with Gail Burrill by Allyn Jackson

Project Follow-Through — what happened?

I've barely skimmed the surface of writing about what happend and why.

However, out of my very small sample of articles on the subject, Cathy L. Watkins' piece is the first thing I'll read in full.

excerpts:

The history of Follow Through and its effects constitute a case study of how the educational establishment functions. As in other bureaucracies, it is composed of parochial vested interests that work to either maintain the status quo or to advance a self-serving agenda. As a result, the largest educational experiment in history (costing almost one billion tax payer dollars) has been effectively prevented from having the impact on daily classroom practices that its results clearly warranted. Let's look at some factors that operate at each level of the educational establishment to influence decisions about teaching methods and materials.

Policymakers. Follow Through demonstrated that public policy is based on public support, not on empirical evidence....Because the Direct Instruction model represents a minority view in education, it was not surprising that policymakers failed to take a strong position in support of the Follow Through results.

Although some policymakers may have some formal training in areas of education, they typically rely on input from education professionals when developing and supporting programs. The influence of stakeholders in traditional educational practices can be seen throughout the history of Project Follow Through....For example, the chairman of the Follow Through National Advisory Committee was the dean of the Bank Street College of Education, whose model was ineffective in improving academic achievement or affective measures.

....In fact, some social policy analysts assert that in situations where administrators are strongly convinced of the effectiveness of a program, it is likely that an evaluation will be disregarded. This is tragically illustrated in California where policy makers enamored with Whole Language were seemingly incapable of attending to data showing serious declines in students' reading performance, including a national assessment on which California students placed last.

[snip]

Colleges of Education. Project Follow Through was unique because it examined not only instructional programs, but the educational philosophies from which they were developed....The majority of models were based on philosophies of "natural growth" (Becker and Carnine, 1981) or what Bijou (1977) referred to as "unfolding." According to these models, learning involves changes in cognitive structures that are believed to develop and mature in the same manner as biological organs. Whole Language is an example of instruction derived from this philosophy. It is based on the belief that reading develops naturally given sufficient exposure to a print-rich environment.

The second philosophical position is concerned with principles of learning or "changing behavior" (Becker and Carnine, 1981). From this perspective, teaching involves specifying what is to be taught and arranging the environment in such a way that the desired change in behavior results.

Although the data from Follow Through support the latter position, the majority of colleges of education espouse a philosophy of cognitive restructuring. Thus, the data from Follow Through fail to support the philosophy that dominates colleges of education. This obviously made it difficult for educators to accept the Follow Through findings and they responded by discrediting the evaluation as well as by voicing specific objections about the Direct Instruction model or questioning the values of the model. For example, educators are fond of accusing direct teaching approaches of ignoring the "whole child" by emphasizing academic achievement at the expense of affective development. The Follow Through data clearly show that no such trade-off occurs. The Direct Instruction model was more effective than any other model on measures of self-esteem. A second objection is that this Direct instruction is reductionistic and results in only rote learning of non-essential skills. Yet, the data show that students in the Direct Instruction model demonstrated superior performance on measures of complex cognitive skills. In contrast, not a single model that set out to improve these cognitive skills was able to do so.

[snip]

The training paradigm underlying most teacher training programs has little to recommend it, with students spending the majority of their time listening to lectures about theory and method. Sponsors of Follow Through models found that lectures about teaching had little impact upon actual teaching practices. Training was most successful when it included modeling of the desired behaviors, opportunities for teachers to practice, and feedback about their performance (Bushell, 1978)....

Teachers. Probably the biggest obstacle is the fact that the instructional methods a teacher uses are most likely to be those taught during his or her own training....there are currently thousands of teachers in classrooms who do not know how to teach beginning reading, because the professors who "taught" them adhered to a philosophy of "natural growth." One teacher confided to me, "I do not know how to teach reading to someone who doesn't already know how to read"!

Teachers may not seek out empirically validated methods, such as Direct Instruction, because they fail to recognize that their current methods are not effective. [ed.: self-assessment is difficult for everyone, not just for students] Student failure is more likely to be attributed to deficits within the child or to external factors such as the child's home life, than to ineffective instruction. ...even if teacher did know there was a better way to teach, how would they acquire the necessary skills? Surely not by returning to the schools where they received their initial teacher training.

Teachers who are motivated to look for and use effective methods, often run into opposition....

School Districts. The fact that effective teaching methods are available does not mean that they will be adopted. According to Alan Cohen (personal communication, 1992), "We know how to teach kids, what we don't know is how to get the public schools to do it!"

....One way that Follow Through differed from other federally funded programs was that in exchange for funding, particular instructional practices were specified and monitored. This system of supervision resulted in a higher degree of fidelity of implementation of the model than might otherwise be expected. However, schools are generally not organized to provide the level of supervision that Follow Through model sponsors found necessary to ensure fidelity of implementation.

Publishers. Much, perhaps most, of what a teacher does is determined by the materials he or she uses....materials are not field tested to ensure their effectiveness with children. The publishing industry does not initiate the development of instructional materials, but instead reacts to the demands of the educational marketplace....In California the state adopts an instructional framework. Criteria for instructional materials are then derived from the framework. Publishers are provided these criteria and busily get to work developing instructional materials that conform to them. They submit their materials during the textbook adoption process and panels evaluate the extent to which the materials correspond to the specified criteria. Noticeably absent from these criteria is any mention of measured effectiveness. ...field tests are expensive, and the prevailing contingencies provide absolutely no incentive for publishers to conduct them in order to provide learner verification data because such data are not considered in textbook selection and adoption. (See "Why I sued California, Engelmann, ADI News, Winter, 1991).

The Public. What the public has supported is a system which has continued to neglect effective methods of instruction....Parents and others have been led to accept that the failure of a great many students to learn is due to deficits in the children. The general public has no way of knowing that children's achievements are largely a function of how they are taught.

source:
Project Follow-Through: Why Didn't We? (full text of Cathy L. Watkins' article)

teaching to crammery

I've attended many CSE meetings, and until recently it hadn't occurred to me that our definition of 'learning disabilities' is entirely a function of public school curricula and teaching practices — which is not to say children don't have biological differences in learning ability. They do. But the definition of LD is comparative. You don't diagnose a learning disability with a brain scan or a blood test. In fact, I don't think learning disabilities are actually 'diagnosed' at all, are they? [please fill me in — I remember my neighbor, who is a clinical psychologist, explaining this to me a couple of years ago...]

IIRC, a child's problems in school 'qualify' as a learning disability when he or she has a normal IQ, but performs two years below grade level.

The possibility that the child may be two years below grade level because of a problem in the school, not the child, is never raised — and, in fact, can't be raised. It's not on the menu.

Once you let this fact sink in for a bit.....you're midway into a paradigm shift. A big one.

At ktm, we've talked about kids who do OK in spiral curricula.

I was one of those kids; probably many or most of you were, too.

Lately I've been wondering what it is about some children that allows them to do OK in courses that aren't taught to mastery.

I've called Christopher's accelerated math class a Death March to Algebra.

It is a Death March to Algebra, but there are going to be a bunch of kids still standing at the end. If I have anything to do with it, Christopher will be one of them.

How are they doing it?

And how normal is it that they are doing it?

Lately I've been realizing......we've based our concept of normal learning on these kids.

Learning disabilities are defined in relation to these children. Christopher's class is mostly populated by 'high-achievers,' by which I mean kids who do OK in spiral curricula. I'm starting to see this particular group of kids as a group, as a specific sub-population within any larger population of children. There's 'something about them' — something different. (I'm thinking it has to do with speedy memory; these are kids who can be taught to crammery. But I don't know.)

A child who's two years behind the kids who 'do OK' in a spiral curriculum is diagnosed with LD.

At the moment, I've got only one word to say about this realization and what it implies, or may imply:

yikes

update: from Charles

The indispensable Fordham Institute had a big report on why the big Follow-Through study was ignored.

If you're interested in Project Follow-Through, Carnine's article is probably the place to start.

Washington Times article on Project Follow-Through
Effective Educational Practices (issue devoted to Project Follow-Through]]
Project Follow-Through: Why Didn't We? (brief summary Watkins' article)
Project Follow-Through: Why Didn't We? (full text of Cathy L. Watkins' article)
Sciencephobia (EDUCATION NEXT)
Illinois LOOP page on Project Follow-Through

CarolynOnMasteryLearning 06 Feb 2006 - 16:33 CatherineJohnson

I was just doing some Librarian work on ktm (linking like posts with like, dropping 'back doors' into existing posts, posting links in the book-style index) — and I discovered that Carolyn wrote a post on mastery learning back in May!

How good is mastery learning? Two of the review studies looked at mastery learning by itself and with combinations of other curricula, and found that mastery learning by itself produces better results than what was termed 'conventional instruction'. However, mastery learning got its best results when used with other teaching techniques. One study got decent results for "mastery learning with corrective feedback" (meaning -- electric shock? The review didn't say), but got its best results from mastery learning with 'enhanced cues' -- extremely detailed instructions to the students on how to do problems.

Another study found that mastery learning and cooperative learning strongly enhanced each other (note: cooperative learning is structured working-together among students, as opposed to simply being stuck in groups to do your homework together: see part two of this series).

It's interesting, reading this post now, not least because I recognize one of the author's names: Doug Carnine.

Report to the California State Board of Education

-- CatherineJohnson - 06 Feb 2006

SpirallingStories 06 Feb 2006 - 17:25 CatherineJohnson

I'm pulling parents' experiences together into one post.

Math Trailblazers

A parent here told Ed that in 2nd grade TRAILBLAZERS teaches kids how to construct graphs.

Then, in 3rd grade, TRAILBLAZERS teaches kids how to construct graphs again — the exact same lesson — except that, this time around, they teach the kids TO LABEL THE AXES. (fyi: She wasn't sure what the grade span was; it could have been 3rd to 4th.)

Everyday Math

My cousin describes her experience with Everyday Math:

Chicago Math gives you advanced math problems sprinkled in with the elementary math your child is learning. They slip it in.

They would have you guess at the answers for the advanced problems, but then they never gave you the answers so you didn’t know if you guessed right or not. You’re always a work in progress with Chicago Math. So you never get a definite answer. And you never had a sense of completion or success on a day-to-day basis.

But my pet peeve was that it sped you along at a rapid pace and you never mastered the material that you left the page before. When my daughter was in the 2nd grade one work page would be coins; the next day you’d be dealing with weather; the next day you’d be dealing with problem solving. My daughter had no sense of what a quarter or a dime was.

When I was taught math, each day you built on what you knew. When you did the coins you learned a penny, a nickel, a quarter. You kept going. Telling time, same thing. You work on time until you get it. You don’t just have a flash of it one day.

In Chicago Math you had one page on one topic, then you went on to something completely different on the next page. There was no repetition. It was irresponsible, very ungrounded.

Mike Feinberg of KIPP on spiral curricula
Steve and Susan J on spiral curricula
acceleration versus remediation

-- CatherineJohnson - 06 Feb 2006

DougOnDeadlines 07 Feb 2006 - 16:29 CatherineJohnson

A couple of weeks ago I mentioned the term guillotine deadline.

Here's Doug:

When I was a periodicals editor, the term was "drop-deadline". 8-)

I did that job for long enough to develop a real defense-in-depth approach to deadlines:

"I'd like to get all your new information in by ...."

"I need your information by ... to make sure it gets in the next issue."

"I know I said that I need your information by ..., but you know we build in a little bit of slop in the schedule to handle the occasional late arrival."

"I've had a few other people late this issue, so I still have a little bit of time. Can you overnight it to me today?"

"I'm sending the book off to the printer tomorrow; if you can fax me the new stuff today, I should still be able to get it in."

"Don't worry, I can insert it at blueline. Of course, I'll have to charge you for the blueline change."

"I'm sending the bluelines back to the printer today. If you send it direct to the printer, we can still get it in. But you'll have to pay for all the printer's extra work."

"Nope, it's too late for this issue, but send it anyway; the next issue's deadline is tomorrow."

file under: it can always be worse, and it will be

So for the past couple of weeks I've been flogging myself to meet a self-imposed deadline, and then, of course, not meeting it, then setting a new deadline, then not meeting that one, and so on.

All in all, a wretched experience. I was glad to be done.

But now today I'm sitting around biting my nails waiting for everyone involved to figure out how I'm going to revise this project, which means I don't have to try to Write Anything today, i.e. I have some Free Time I could use productively to, say, Clean Up My Desk (& Surrounding Floor Area) ......and waiting around for other people to get back to me with loads of new work is even worse than doing loads of work & missing self-imposed deadlines in the first place.

Apparently, the fish oil isn't working.

-- CatherineJohnson - 07 Feb 2006

SchmidtInLosAngelesTimes 07 Feb 2006 - 17:48 CatherineJohnson

The LA Times series on Los Angeles high schools includes a terrific interview with William Schmidt, U.S. TIMSS NATIONAL RESEARCH COORDINATOR 1998.

I love this line:

...we know that by the end of eighth grade, U.S. students are probably some two years behind their counterparts in most of the rest of the world…. Middle school in the rest of the world is about algebra, geometry, chemistry, physics. In this country it's still about a lot of arithmetic and what I call "rocks and body parts."

rocks and body parts

Never heard that one.

elementary school & fractions

A: Studies show that middle school is where we lose a great deal of ground, at least internationally. The middle school in these other countries in mathematics is much more demanding. And it's much more of a transition into what we in this country first do in high school. So when our kids come into high school, they're a couple of years behind already. And our high schools just can't make it up.

Basically, the middle school is not preparing kids adequately. But it actually goes all the way back even into primary school, where, again, the kids are not being prepared well, don't understand and aren't able to do the computations associated with simple arithmetic.

Q: So it starts in elementary school?

A: We need to really start a much more serious, clearly defined, coherent curriculum all the way back there, and then we'd have a better shot at doing better with our kids. A lot of mathematics in this country is not designed very coherently. It doesn't progress from the simple to the more complex in ways that are reflective of the mathematics discipline. There's a sequence of things that make the most sense. And very typically in American schools, these sequences are not very clearly laid out.

Q: What do you mean?

A: Fractions, for example, are very difficult for students. Instead of introducing the concept clearly enough so that they understand fractions as numbers on the number line, we oftentimes try to move too quickly to other parts of fractions, such as the operations, before they really have a clear understanding of what fractions are and how they fit into the broader number system.

So kids are trying to learn how to operate on these things, and at the same time they really don't understand what they are, so things get very muddled in their minds.

For me, this is very helpful.

I have yet to meet a mathematician, engineer, or applied-math professional who didn't tell me that fractions are the bottleneck.

I believe it, but I don't quite understand what it means. That's due, in part, to the fact that I haven't begun to re-learn algebra. (Algebra starts in April.)

But I'm also confused, at this stage of the game, over what exactly K-6 kids should be learning about fractions in order not to fall apart later on.

The idea that kids need to understand fractions as numbers on a number line before performing the four operations on them is extremely helpful.

I tend to think he's right about this, though not in quite as literal a sense as this passage implies. Based entirely in my experience of teaching math to Christopehr & re-teaching math to myself, I wouldn't say you need to nail down fractions are numbers before here's how fractions are added & subtracted.

I'd say that fractions-are-numbers can be illustrated and taught via fractions-are-numbers-that-can-be-added-and-subtracted.

My sense is that you want to spend a great deal of time using the number line and using rulers to show both that fractions are numbers and that fractions are numbers that can be added and subtracted.

Saxon Math & fractions

Saxon Math has a number of interesting approaches to fractions:

• kids are asked to count in fractions: 1/4; 1/2; 3/4; 2; 2 1/4; 2 1/2; 2 3/4; 3

• kids do mental math with fractions

• I believe kids are asked to do some skip-counting with fractions as well (not sure)

• fractions, especially fractions of groups, are taught via bar models

is there one perfect method?

Q: Are the nations throughout the world using a different curriculum? Do they have different teaching methods?

A: That's actually a point I want to make very clearly. There doesn't seem to be one perfect method for doing this across the world. Different countries have different methods, just like we do here in the United States.

The real issue is the what. What it is that they're studying, in what grade levels in what sequence and at what level of rigor. Those are the issues that become important, not the how. It's more the what.

Q: We're just not being hard enough.

A: Yes. That's it, in a certain sense. As we move through the grades, we keep repeating topics year after year. We try to do too many topics at each grade level. We coined the phrase the "mile-wide, inch-deep curriculum" as a characteristic of the U.S., which means they just keep repeating these topics and as a result they have so much every year that it's too much for the kids to try to learn.

In these other countries it's a more focused attention on a smaller number of topics that progress across the grades in a logical fashion, leading to higher levels of expectation as you get up in the grades, like in the middle grades. And that's what we need.

Here's where I suspect he's missed — or perhaps slighted — a key issue, which is teaching to mastery.

I'd put money on it that in fact there is one 'perfect method' of teaching math, which is to make sure students learn to mastery.

I also suspect that in some (or perhaps many?) countries parents, not schools, are responsible for seeing to it their children learn to mastery. I'd almost bet the ranch that's the case in Singapore.

If this is so, classrooms could in fact look very different to researchers. Once parents take on the job of formative assessment, schools gain a great deal of leeway, to put it mildly.

Wherever the learning-to-mastery is actually taking place, whether at school, at home, or in both locations, you're going to see the same things. You're going to see massed practice, you're going to see distributed practice, and you're going to see overlearning.

Assuming I understand the findings of cognitive science correctly, and I think I do, there is no other way.

mile-wide, inch-deep

....As we move through the grades, we keep repeating topics year after year. We try to do too many topics at each grade level. We coined the phrase the "mile-wide, inch-deep curriculum" as a characteristic of the U.S., which means they just keep repeating these topics and as a result they have so much every year that it's too much for the kids to try to learn.

In these other countries it's a more focused attention on a smaller number of topics that progress across the grades in a logical fashion, leading to higher levels of expectation as you get up in the grades, like in the middle grades. And that's what we need.

Again, why is it we 'keep repeating topics,' and why is it that as a result our kids have 'too much to learn'?

Kids in other countries end up learning far more than our kids do.

This is a perfect description of Christopher's accelerated math class, I must say. They're covering a zillion topics; it's far too much to learn in the time they have.

What he's not mentioning is the fact that when you cram too many topics into one school year, the kids end up learning nothing well.

Easy prediction: 'mile-wide, inch-deep' is going to be interpreted, in the next cycle of math reform, to mean we should teach fewer math topics, period. Teach fewer topics and continue not teaching to mastery.

teacher prep

Q: In Los Angeles, some educators say they have a hard time finding qualified teachers. Is that a problem for other nations?

A: For some. In the elementary grades, everybody struggles with this, because elementary teachers have to teach all the subjects. But once you get into about middle school, this is more of a problem in the United States, where our teachers are not as well prepared as the teachers in these other countries.

We are doing a study right now across six countries in which we very clearly find that U.S. teachers — U.S. teachers from middle school — are not being … required to take the same level of mathematics that is true in other countries. Teachers that are going to teach middle school mathematics have to have a stronger background.

IIRC, in Asian countries teachers begin to specialize as early as the 4th grade. I'd like to see that in our schools. Teaching both English language arts and math well in 5th grade is a huge undertaking.

By the numbers

A 2003 study found that U.S. 15-year-olds scored low among industrialized nations on the PISA* mathematics test.

 Rank Country Score 1. Hong Kong (region) 550 2. Netherlands 538 3. Japan 534 4. Belgium 529 5. Australia 524 6. New Zealand 523 7. Norway 495 8. Hungary 490 9. Latvia 483 (tie) United States 483 11. Russia 468 12. Italy 466

* Program for International Student Assessment -
Source: American Institutes for Research

Chapter 1 Why Schools Matter (pdf file)

-- CatherineJohnson - 07 Feb 2006

CollegePrep 07 Feb 2006 - 23:01 CatherineJohnson

via eduwonk, a link to an Ed Sector anaylsis, High Schools Failing to Prepare Many College-Bound Students for Science Careers.

factoids

• science, technology, engineering, and mathematics = STEM

• 82 percent of high school kids say they plan to go to college, but only 51% are in college prep [ed.: awhile back I read some material from Roy Ohrbach, of U.C. Riverside, showing that often Hispanic parents have no idea their kids aren't in college prep — Ohrbach's been traveling around CA, IIRC, giving parents papers in Spanish explaining what the college track is & how to find out if your child is in it]

• definition of college prep: 4 years of English, 3 years of math, science, and social studies, 2 years of foreign language, and 1 semester of computers — 31 percent of high school graduates complete this basic college preparatory curriculum

• 14 percent earn math or science credit in Advanced Placement (AP) or International Baccalaureate (IB) programs

• about 60 percent of students who take AP tests in Biology, Chemistry, and AB Calculus get a score of "3" or better

• 12 percent of h.s. kids take calculus

• 40 percent take trig (this includes the 12% of all h.s. kids who go on to take calculus)

I wouldn't think these figures were so bad, if it weren't for the charts below. Forty percent of all h.s. kids making it through trigonometry sounds OK to me (not that I would know...)

But when you look at how many of these kids take no math at all in college — around 70 percent — that seems pretty bad to me.

Because of poor middle school preparation, tracking, inadequate guidance counseling, low-quality instruction, or a simple absence of available courses, too many students are permanently knocked off the pathway to a STEM career early in high school or even before. This is particularly true for low-income and minority students. No one tells them or their parents that by failing to enroll in a rigorous, math-oriented college prep curriculum, they're effectively making a life decision to forgo the opportunity to pursue a career as a scientist or engineer.

This isn't just a problem for low-income & minority students. It's a problem for just about anyone who majored in the social sciences or humanities.

I had no idea, when Christopher was tracked into Phase 3 math in 3rd grade, that he'd been tracked out of calculus in high school. None. (spaced repetition, I know) I had no idea that a) there is a 'math track' and b) it starts young. People with jobs like mine naturally assume that math works like everything else. You go to high school, you graduate, you go to college, you choose a major — and the major can be anything you decide you're interested in. All doors are open.

update: Tracy & Matt Goff weigh in below

from Tracy

On the topic of the importance of doing maths, I know two girls who were tracked out of what they wanted to do by not doing maths.

One was told by her guidance councillor that she didn't need Maths With Calculus to get into engineering, only Maths With Statistics. (You could take two maths courses in the last year of high school).

Another was told by the Head of Chemistry that she didn't need to do another maths course at uni for her chemistry degree. Then she couldn't do an advanced organic chemistry course because she didn't have enough of a calculus background and had to change the topic of her PhD.

here's Matt G

I would not say that it is not possible to get a degree in a STEM field without having had calculus in High School. One of my math major classmates as an undergraduate had not had calculus in High School and he did fine starting in Calculus in college (which many students need to do anyway, even if they have already had Calculus in High School). I knew at least one person while I was at graduate school who had started in the basic algebra class and worked her way up through the math program (she was a non-traditional/adult student).

It is, however, my impression that if you have (barely) made it through algebra in High School, the chances are pretty decent that in some way for some reason you have been turned off to math (and likely science). At that point it seems very unlikely that you would choose to major in a STEM related field. That is to say, I think the barrier to students entering STEM fields is mostly a matter of perception and/or expectation, rather than something fundamental and insurmountable. It may take a year or more extra, and you probably won't get your degree form Cal Tech or MIT, but there are plenty of schools where the motivated student can work through the math/science curriculum (and whatever prerequisites might be necessary) and enter a STEM field.

That makes sense to me (based in extremely limited knowledge of what it takes to succeed in college math, obviously.)

It's never struck me as likely that not taking AP calculus would knock a kid out of any kind of math at all in college. And based in Ed's view of AP history (not especially positive) I assume most AP students are going to have to repeat calculus in college.

My AP calculus goal for Christopher is almost entirely pragmatic.

I'm assuming that if Christopher sets AP calculus as his goal (which, at this point, he has) he'll work hard in lower level courses, and learn more.

I also assume that taking calculus twice is a good thing. (Maybe it's not, but for me it's been good to do basic math twice.)

Rudbeckia Hirta on taking calculus twice

Bad calculus is worse than no calculus. I'd much rather have students in my class with a solid algebra background + no calculus than those who took a purely algorithmic high school calculus classes. Just this week one of my students (in Calculus 1) told me, "I already know calculus. It's when you take the number up top and put it down in front and lower it."

But perhaps I say this because this week I am teaching the limit definition of the derivative.

[snip]

I would say that a bad calculus course would be one that emphasized the easy, algorithmic calculations while minimizing the historical context, the applications, the technical details that make it all work, and the importance of mathematical precision in phrasing and justifying statements.

A crude analogy would be a history class that was only about dates and places and names (bad) and one that involved analysis of the issues involved and their context (in addition to the dates and places and names) (good).

You can probably teach a BIRD how to take the derivative of a polynomial function. Knowing when to do it, why you can, and what it means requires a person (who probably has taken a good calculus course).

The problem that I face is that my students (who are at the dualistic thinking stage of the Perry Model) believe that their high school teacher's point of view ("Calculus is about computing derivatives and integrals") is the right one and that mine ("Calculus is a subject in which mathematical techniques were developed to solve problems relating to areas and tangents.") is not. If they came to me thinking, "In my high school calculus course, I learned a little bit about part of calculus," then it would be OK. But instead they tend to think, "In my high school calculus course, I learned calculus. And my college is SO MEAN AND UNFAIR by making me take this so-called calculus course that ISN'T REALLY CALCULUS because it contains all sorts of stupid and unimportant stuff like proofs and limits and word problems!"

I had never heard of the Perry model - it's terrific.

Ed is constantly trying to talk college undergraduates out of stage 2.

-- CatherineJohnson - 07 Feb 2006

TheGap 08 Feb 2006 - 00:27 CatherineJohnson

This is starting to be funny.

I mentioned a couple of days ago that Christopher went into his Chapter 10 quiz knowing the material cold.

He could find:

• area of a square

• area of a rectangle

• area of a triangle

• area of a parallelogram

• area of a trapezoid

• area of a circle

He had learned all this stuff in about 3 days (YAY!), AND he could do it the KUMON way, with speed and accuracy (DOUBLE-YAY!)

source:
Bitter Single Guy

So what does the test look like?

This:

do we see the problem here?

Christopher has never, in his life, ever, figured the area of a complex figure.

He would never even have seen a complex figure if I hadn't shown him a few and bugged him about how he maybe ought to learn how to figure the area of a complex figure because "It might be on the test."

IT'S NOT GOING TO BE ON THE TEST! NO! IT'S NOT ON THE TEST! WE DIDN'T DO THAT IN CLASS! SHE DIDN'T TEACH US THAT! IT'S NOT ON THE TEST!

etc.

So now, the good news is: Christopher thinks I have Top Secret Mom Knowledge of WHAT'S GOING TO BE ON THE TEST.

That's a Good Thing.

update: Old Grouch says the drawing is wrong

I love this drawing Old Grouch left!

I love it so much I'm completely distracted from the question Old Grouch is raising — (in my next life I may have to be an artist who paints paintings of MATH)

Which dimensions on the drawing are Christopher's, and which were given as part of the test? If the (3cm+6cm) and the center 9cm lines are really parallel, the hypotenuse of the "one triangle" on the left CAN'T be 12cm... it has to be greater than 14cm.

Here's Anne:

If you use the marked numbers on the test of 4cm for the height and 13cm for the base, the hypotenuse of the triangle on the left is the square root of 185 which is between 13 and 14. But the base of the triangle on the left marked 10cm cannot be correct. If you draw a line parallel to this 10 cm base with its start at the right hand corner where the circle is and drop it to the bottom, you get a right triangle with a hypotenuse of 14 and sides 3 and 10. This is not possible since 32 + 102 does not equal 142.

Also, since the horizontal line marked 6 cm is parallel to the horzonal line marked 9 cm, the two vertical sides of the resulting parallogram have to be parallel and the same length. But, as I've pointed out, the length cannot be 14 cm because the sides are 3 and 10.

So the student who said he couldn't do this problem was absolutely right. You can't do this problem if you try to get all the number right because they don't come out right.

The funny thing is, when I put in my original post about this being a problem for high school geometry students, I believe it was because my intuitive brain recognized the problems, but didn't articulate the words to my verbal brain.

Thanks to Old Grouch for pointing out all the errors.

update: Ed and I just looked at this —

This drawing is wrong, no question.

Ed and I see that if the (3cm + 6cm) line is parallel to the 9cm line, then the left line labelled 12cm has to be 14cm.

We don't remember our high school geometry well enough to pick up on Anne's observation.

I do think this is a case of Anne's cognitive unconscious knowing something Anne's conscious mind didn't. To wit: this problem is way too hard for an 11 year old.

Ed just said this problem might be good for a sophomore, if the assignment is to explain what's wrong with the figure. (Yes?)

update: the test was 'easy'

Christopher just told me that when he went in for extra help on Thursday (he sees the math teacher once a week for extra help) she told him the test was easy.

I just told Ed, and he said, 'Then you have to bring this to her attention.'

I guess so!

I have this t-shirt.

The X-rated version is here. I figure if eduwonk can perseverate on big-girl panties, I can post x-rated tourist-wear.

-- CatherineJohnson - 08 Feb 2006

ILoveGoogle 08 Feb 2006 - 01:35 CatherineJohnson

I found this image while searching for "good things."

fellow math brain?

from unkemptwoman:

Graphic Designer (rubbish)
Barmaid (brilliant)
Meat Packer (now that was FUN)
Software consultant (hahahahahaha)

-- CatherineJohnson - 08 Feb 2006
CoffeeAtCaffeSole2Part2 08 Feb 2006 - 03:35 CarolynJohnston

At Caffe Sole this morning, while I was swilling my coffee, (yes, Caffe Sole again), I happened to sit within earshot of the mother of a very bright kid that Ben went to grade school with (or rather, she sat near me -- I swear I wasn't stalking her). This kid was one of your classically bright Math Kids -- by 5th grade, he was traveling up to the middle school every day to do honors 6th grade pre-algebra (which is the same course Christopher is doing this year, I think). He's one of those kids who was left standing at the end of it.

I don't know if this kid ever had to do Everyday Math himself at all. If so, it was for one year at most, and he never even broke stride.

Anyway, this mom was talking to her friend about the constructivist math class her younger daughter was in. It was driving her nuts trying to keep her daughter up to speed in it, for all the same reasons it drove me nuts when Ben was in it. It jumps around too much; it teaches too many algorithms for some things and too few (like, none), for other less important things, like, oh, long division. New problems are introduced without their ever having been taught.

And it teaches too, too much about stem-and-leaf plots.

So I, of course, turned and smiled broadly at her (I approve of complaining about Everyday Math!) and we got into a conversation. I told her about KTM and gave her my card; she asked me how Ben was doing now; I asked her how her son was doing now. She told me that she was having to afterschool her daughter, more and more, in mathematics (there is a swelling crowd of us afterschoolers, isn't there?).

She told me that at her son's middle school, there is a group of kids coming from Ben's old grade school who, in spite of having always done well in school, are having a hard time finishing math tests in time because they can't compute as fast as they need to. Like Ben, they learned the lattice method of multiplication and the forgiving division 'algorithm'; unlike Ben, they weren't then made to unlearn them and replace them with the standard algorithms.

It takes time to draw those silly lattices, and time to muddle around looking for 'friendly numbers' to try to divide by, and sooner or later you are going to be expected to do those computations faster than these nonstandard algorithms allow. At this local charter school (Greta's former school), the piper is being paid this year; for schools being fed by Ben's middle school, the crunch will come in high school, after these kids have had 3 years of Connected Math on top of their Everyday Math.

She is talking to her daughter's teacher about Everyday Math. It just doesn't give enough practice, she says (and this is true; homework sets consist of perhaps 6 different problems, at most, a night, selected from all over the board; often problems the kids have never seen before). The teacher is responding well, and giving extra practice sheets -- cheating, in other words, as many experienced teachers stuck with constructivist texts end up doing.

"They're starting to figure it out; good. I complained a lot about Everyday Math when Ben was there," I said. "But, you know how it is; they could always say that Ben was a special case."

"They said the same thing whenever I complained about something that was going on with my kid," she told me.

I hope she makes it here. This is where the goods are, if you're afterschooling in math. And if you do make it here (you know who you are!) -- welcome! Here's a starting point.

I spoke to the Colorado Saxon rep on the phone today for a bit -- he's based in Denver (a very busy guy, too). While charter schools and academies and private schools have been his bread and butter for a while, he is seeing increasing interest from district schools that are starting to get into trouble (i.e., that are on NCLB probation) and have to get their scores up.

He also tells me that Saxon physics texts are out of print and as scarce as hen's teeth -- he's got his feelers out, but hasn't been able to get one for his own son yet. So if you have one -- hang on to it! (Either that, or sell it to me.)

-- CarolynJohnston - 08 Feb 2006

WholeSchoolReform 08 Feb 2006 - 18:01 CatherineJohnson

A series of links, starting with Carnival of Education, then moving to Jenny B & on to Foundations of Teaching and Learning brought me to a professor's notes taken on a lecture about bringing "research-based practices to scale in school."

I'm out of my depth here. I've begun reading books & articles on 'whole school reform'.....and that's about it.

Translating the findings of cognitive science on the nature & process of learning, which I do understand, into public policy and systemic institutional reform — I can't make that jump.

This lecture, and the study to which it refers, appear to come out at least moderately in favor of very early grades scripting, which I know sets a lot of people's teeth on edge —

As far as I can tell, it appears that scripting was effective in Kindergarten, but not in grade 3 (please correct me if I'm wrong).

I think I've mentioned that the Saxon books are scripted early on. I know the Kindergarten book is scripted, because I have it. I know the 1st grade book is scripted because my sister-in-law uses it in IL.

I don't know when Saxon stops scripting lessons, but I'll bet it's somewhere around 2nd or 3rd grade. (Again, if anyone knows for sure, chime in.)

Although I don't understand public policy well, this passage doesn't surprise me:

ASP - focused on "cultural control" aimed at promoting "powerful learning" that schools needed to define themselves. Instruction is not specified in any centralized way.

AC - focused on "professional control" in which the emphasis is adhering to standards of teaching and learning. A key feature was a very aggressive leadership training program focusing on principals and coaches.

SFA - focused on "procedural control" in which instruction is highly scripted. What students should learn and how they should be taught are quite clear, particularly given the scripting. Coaches and leaders teach the design and monitor fidelity of implementation.

Teachers report that SFA and AC (compared with controls) have greater design specificity and consistency, and more interaction with leaders, but ASP has more support for teacher autonomy.

[snip]

Effects on achievement (using the TerraNova test).

SFA had a 1.5 month grown effect at K but not at grade 3.

AC had a positive effect of 2 months at grade 3, but not at K

ASP didn't have any significant effects.

As far as I can tell, for years researchers have been saying that strong principals are the key.

Until someone proves that to be wrong, I believe it. 'The person at the top sets the tone.'

It doesn't surprise me that a reform focusing only on 'culture' or on 'teacher autonomy' would produce no results. Schools need strong educational leadership.

question

Ken may know the answer to this.

What is the difference between Success for All & Engelmann's Direct Instruction?

update: Vlorbik on SFA

i'll take that one after barely glancing
at "success for all": engelmann is clearly
a human being with actual opinions of his own
but "s.f.a" is a committee of mushmouth obfuscators
with nothing in the world to say but feel-good cliches.

-- CatherineJohnson - 08 Feb 2006

TimeTimer 08 Feb 2006 - 20:01 CatherineJohnson

My Time Timer came today.

So far, I love it.

I ordered it because I've always been drawn to Time Timers in special needs catalogues, and because The Organized Student, by Donna Goldberg, says students need to be directly taught what time is.

That struck a chord. Like your basic middle schooler, I don't really know how much time any given task takes to do, either.

my problems and welcome to them

One of the Stupid Things I've been doing for — oh, the last year or so — is going to bed too late because I start doing math too late, and can't stop.

Many people would look at this problem and say, "Why don't you start doing your math earlier?"

Good question.

For some reason, I always plan to start doing my math earlier.....and sometimes I do do my math earlier.

But then, somehow, even when I do start my math earlier, I still end up going to bed too late.

This is why I need a Time Timer.

how long is a nap?

OK, so there I am, sleep-deprived & sitting at my desk facing massive piles of Stuff that needs managing.

And I'm tired.

I'm so tired I obviously need to take a nap, BUT I don't take a nap because I DON'T HAVE TIME TO TAKE A NAP....

And so, tragically, I remained rooted at my desk, getting nothing done, because I'm too tired to get things done but I don't have enough time to take a nap because I have too much stuff to get done, etc.

So today, contemplating my groovy new Time Timer, I decided: let's just SEE how long it takes to take a nap.

I took it upstairs with me, set the dial for 30 minutes, got in bed & went to sleep.

Fifteen minutes later I woke up.

Fifteen minutes.

That's not very long.

I can easily spare 15 minutes to take a nap when I'M NOT GETTING ANYTHING DONE ANYWAY.

why do I need a Time Timer for this?

In theory, I could use an ordinary analog kitchen timer, as Google Master pointed out.

Sure, a Time Timer has obvious advantages.

A Time Timer is almost silent; a kitchen timer ticks loudly.

A Time Timer has no alarm when time runs out; a kitchen timer is designed to blast you out of your skin.

Still, these are details. There's no logical reason I have to have a Time Timer instead of a kitchen timer.

Except: the very fact that I have not been able to bring myself to use a kitchen timer as a Time Timer is undoubtedly evidence that I belong to the class of persons who would benefit from the purchase of a Time Timer.

(key words: environmental dependency; frontal lobe function; ADHD ... in case you were wondering)

snippets from the Time Timer materials:

"Since using the Time Timer, my meetings have never been more efficient or effective. People actually want to attend because I don't waste their time."

"...perfect idea for people with alzheimers disease who constantly ask their caregivers 'how much longer' type questions..."
- Family Member/Caregiver

"I have seven students (six with autism and one who has Downs Syndrome.) I like using the Time Timer with my students because it does not disturb the others, some of whom are extremely noise sensitive."
- Special Education Classroom Teacher

"The Time Timer really helped me keep track of time at my AP tests."
- High School Student

The booklet says Time Timers are good for timing time-outs, transitions, and 'how much play-time is left.'

Time Timer and motivation

I think the Time Timer is going to help.

Christopher definitely has no concept how much time things take. He'll tell us he has 'nothing' for homework, when it's really 'something'; he just has no clue. I have no clue, either, but I'm at a higher level of cluelessness, to paraphrase Charles. THE ORGANIZED STUDENT suggests using the Time Timer to teach kids how long homework takes, and that's what I'll do, for Christopher as well as for me.

So far today I've seen that the Time Timer has a useful anti-procrastination effect.

I'm in 'waiting' mode at the moment — waiting for phone calls, waiting for feedback, waiting to see what comes next — it stinks.

While I'm always inclined to do what I want to do instead of what I'm supposed to do, Waiting Mode makes everything much, much worse. Waiting Mode makes even structured procrastination hard to do. Since half my productivity is based on Structured Procrastination, this is bad.

So this morning, I set the Time Timer for half an hour.....and then I did productive stuff for half an hour.

The reason I could do productive stuff for half an hour, instead of spinning my wheels NOT thinking about the telephone, was that I could see how fast that half hour was passing me by.

I didn't want to lose it.

My Time Timer isn't nearly this beautiful.

some books that have changed my life
the answer to all of Doug's problems
productivity question
what is an hour? Time Timers
my Time Timer came - how long is a nap?
Time Timer says no!

-- CatherineJohnson - 08 Feb 2006

TimeTimerPart2 09 Feb 2006 - 17:24 CatherineJohnson

I love my new Timer Timer.

Thanks to Time Timer, I now know that in 25 minutes I can:

• do 4 KUMON worksheets

• NOT read kausfiles (Time Timer says No!)

• pick up office floor

• take out office trash

• figure out a logical filing location for Edmark reading program originals AND RECORD

• figure out a logical storage place for metronome AND RECORD

• finish last of Cape Cod potato chips

At this rate I'll have my desk cleared by spring at the latest.

some books that have changed my life
the answer to all of Doug's problems
productivity question
what is an hour? Time Timers
my Time Timer came - how long is a nap?
Time Timer says no!

-- CatherineJohnson - 09 Feb 2006

RobertDeLongReviewArticle 09 Feb 2006 - 20:55 CatherineJohnson

(section on bipolar disorder & math below)

Robert DeLong is one of the greats.

I invited him to an autism conference a few years back, and did a long interview with him.....and have now misplaced the notes. (Time Timer & David Allen are going to fix all that.)

Quite by accident I discovered the other day that DeLong published a review article in 2004. I'll post bits of it as I read through.

In a nutshell, DeLong believes that autism is caused by the gene or genes for bipolar disorder expressed early in life instead of later on.

Until this is proved wrong, I believe it.

Here's the abstract:

Family history studies of autism consistently reveal a large subgroup with a high incidence of major mood disorder in family members, suggesting the two entities are related clinically and genetically. This review examines this concept, comparing current clinical and biological knowledge of autism and major mood disorder, and advances the hypothesis that this subgroup of autism represents an early-life phenotype of major mood disorder. If confirmed, this hypothesis would suggest that the basic biological defects determining major mood disorders may have prominent neurodevelopmental and cognitive dimensions. Testing of the hypothesis will depend on genetic studies. (The Journal of Neuropsychiatry and Clinical Neurosciences 2004; 16:199–213)

Autism and Familial Major Mood Disorder: Are They Related? (pdf file)
Robert DeLong, M.D., D.S.

As I understand it, a similar line of thought is being developed in schizophrenia research. Where we once understood schizophrenia to be a mental illness, it's looking more like a 'neurodevelopmental disorder.'

At least, it was last I checked.

By the way, some of these 'cognitive dimensions' will be good.

I like this part:

I am inclined to agree that idiopathic autism can be divided conveniently into two “taxa,” as some have designated.9 One is higher functioning, often with preserved islands of skills and prominent anxiety, obsessiveness, mood disorder, positive family history of major mood disorder, and frequently a family history of unusual intellectual ability/achievement.

Hah!

This is self-evidently true!

bipolar disorder and math

I suspect we'll find that the line between 'cognitive' disorders and 'emotional' disorders isn't really a line.

Here's a report from SCIENCE NEWS \$:

Dalhousie researchers had previously noted a link between math problems and bipolar disorder. Their 1996 review of medical and academic records for 44 teenagers with the illness found that they had performed well in school until the onset of psychiatric symptoms. While the students received treatment for bipolar disorder over the next 4 years, their school performance deteriorated far more in math than in any other subject.

In the new study, the scientists administered academic and intelligence tests to three groups of teens: 44 taking prescribed medications for bipolar disorder and whose symptoms had largely diminished, 30 who had responded well to treatments for major depression, and 45 who had no past or current psychiatric ailment.

The teenagers with bipolar disorder scored much lower on a broad range of math problems than those in the other two groups did, the researchers say. This math deficit appeared regardless of whether the participants had a limited or unlimited amount of time to solve each problem. Girls with bipolar disorder scored much lower on math tests than their male counterparts. A less pronounced sex disparity in math scores appeared in the other two groups.

In contrast, the three groups of teen participants displayed no differences in scores on reading, spelling, and nonverbal intelligence tests.

Intriguingly, school records for the teens with bipolar disorder show that their math grades dropped noticeably beginning about 1 year before their psychiatric condition was diagnosed, says Dalhousie psychiatrist Stanley P. Kutcher, a study coauthor. The onset of math troubles long before exposure to psychoactive medication underscores Kutcher's suspicion that brain changes associated with bipolar illness disturb math reasoning.

I have no idea whether this finding will be replicated. It's intriguing.

Of course, now I'm going to have to spend mental energy NOT panicking every time Christopher hoses a math test in high school.

Thank God I've got my Time Timer.

Searching for the Genetic Link to Autism
Robert DeLong review article
you can say that again

-- CatherineJohnson - 09 Feb 2006

YouCanSayThatAgain 09 Feb 2006 - 21:24 CatherineJohnson

Autism is the most mysterious disorder I know of in medicine.

- Dr. Robert DeLong, Duke University Medical Center pediatric neurologist

source:
Searching for the Genetic Link to Autism

Robert DeLong review article
you can say that again

-- CatherineJohnson - 09 Feb 2006

HelpDeskPart2 10 Feb 2006 - 15:58 CatherineJohnson

I mentioned that I've gotten my AlphaSmart back in gear.*

I love it!

I used it with Andrew for the first time this morning. He's doing KUMON sheets that ask him to write in the missing number in a sequence, and he's reached the numbers 100 - 110.

I had printed out a 1-100 chart for him, and was having him point to the missing number before helping him write it on the KUMON worksheet. That way I know he knows the answer; I'm not just moving the pencil for him.

But now we're past 100, which means I need a second chart with smaller figures, and it seems slightly silly just to keep making up larger and larger number charts with smaller and smaller font size as we go along.

Also, I don't really want to be using a chart, I don't think.

Andrew has incredibly strong 'visual patterning' abilities, for want of a better term, so I'm not sure whether he's finding the correct number because it's the correct number in the sequence, or whether he's finding the correct number because it's in the right square on the chart.

I also have no idea whether 'finding the correct square on the chart' actually is the same thing as 'finding the correct number in the sequence.' It may be! I don't know enough about math or neuropsychiatry even to make an educated guess.

In any case, my feeling is: we're ready to move on to, or perhaps simply to add, the AlphaSmart.

So we got started.

It was so cool, watching him figure out how to type numbers like 112.

help desk

Here's my question.

I haven't used the AlphaSmart in at least a year; it could be two years or even more.

So it's been sitting around gathering dust (and I do mean gathering dust. It was filthy when I finally pulled it off its shelf, poor baby).

The keyboard doesn't work the way I remember it working. It's very stiff; some keys are actively hard to press down, and the 'u' key actually got stuck in the down position last night.

I feel like a schmuck; obviously I've failed to provide even the most minimal care & maintenance.....

But it's too late for that now, so the question is: What can I do now?

The tops of the keys all pop off, so I'm popping them off and using an air duster to clean the keyboard. So far that seems to be helping, but I'm not sure.

Is there something else I can be doing?

I'm going to call the folks at AlphaSmart, but if you have any advice, I'd like to hear.

NY Times article on AlphaSmart

I tracked down the article that originally made me want to buy an AlphaSmart:

Smart keyboards start up and shut off instantly, are apparently crash-proof, save your work automatically and preserve your files when the batteries are removed. Because there is no hard drive or other moving parts inside, these machines withstand youthful handling that would shatter a real laptop (and its owner).

When compared with the Palm-and-folding-keyboard setup that is increasingly popular among journalists, writers and researchers, a smart keyboard offers considerable savings, more rugged construction, greater typing comfort and dramatically improved battery life. And beaming the resulting plain-text files to a Macintosh or PC by infrared or cable is simpler than a Palm synchronization; the smart keyboard pours your text directly into whatever document is on your computer's screen (Word, Note Pad, an e-mail program, whatever).

International frequent flyers, too, are discovering these products; one set of AA batteries could take you around the world for 80 days. (One smart-keyboard owner told me how, on a transoceanic flight, a desperate seatmate with a dead ThinkPad battery offered to buy her smart keyboard on the spot for several times its price.)

The best-known smart keyboard is the AlphaSmart 3000, a compact two-pound \$230 device [ed.: price is down to \$139] created by a pair of former Apple engineers (www .alphasmart.com). Its Macintosh heritage is obvious; its translucent dark blue sculptured curves make it look like an iMac's house pet. On the AlphaSmart, you can't, or never have to, name or file your documents. In the name of idiotproof simplicity, its inventors have limited you to eight files, each no more than 12 1/2 pages long. You open each by pressing a key on the top row; they're labeled File 1, File 2 and so on. Technophobes adore this one-key-per-file system; technophiles are likely to roll their eyes.

The AlphaSmart is the only model reviewed here that can accept files from your desktop computer for on-the-road editing, courtesy of a \$20 add-on program called Get. Other exclusives include an optional Dvorak keyboard layout (the keys themselves easily pop off for rearrangement); the ability to download new programs like a typing tutor and quiz-taking program; and what the company says is 700 hours of battery life per set.

source :
State of the Art; Less than a Laptop and More \$
by David Pogue
Published: July 5, 2001

If the air duster doesn't do it, then you want something like an Electronic Contact Cleaner.

* In fact, I used it to write a letter to the Los Angeles Times last while waiting for Beauty and the Beast to start. And, umm, No, I don't normally haul a portable keyboard with me to Broadway musicals. That's because a) I almost never see Broadway musicals, and b) in this case I had the AlphaSmart with me only because I forgot it was in my backpack with my Saxon Math books, which I do take to Broadway musicals. I take my Saxon Math books everywhere. Christopher says, 'You would do math at a wedding! You would do math at a funeral!' As a matter of fact, I wouldn't do math at a wedding or a funeral, but I can see why he thinks I would.

AlphaSmart
AlphaSmart reviews
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
AlphaSmart to the rescue
the joys of primitive computing

-- CatherineJohnson - 10 Feb 2006
AlphaSmartReducedPrice 10 Feb 2006 - 23:01 CatherineJohnson

I talked to the folks at AlphaSmart today & learned that the price has been reduced 30%. \$199 (which is what I paid for mine years ago) down to \$139.

The price is reduced because the company may discontinue AlphaSmarts; the woman on the phone wasn't sure.

This news prompted me to buy one for Andrew on the spot. (Impulse purchase alert.)

I hope they don't discontinue the AlphaSmart, but the possibility that they might is reason to buy one before they do, not reason to move on to the new, improved Neo or Dana (though the Neo probably is an improvement).

Ed bought a Dana as soon as it came out and has had problems. I can't remember now whether his problems — losing his research notes from a trip to France — were the machine's fault, or his, but I have a memory the problem was in the machine...

UPDATE 7-23-2006: The original AlphaSmart is no longer shown on the site. Now they're just selling the Neo for \$249 and the Dana for \$429. I should have bought another AlphaSmart while I had the chance.

When I turned on my AlphaSmart for the first time in at least 2 years last weekend, everything was still there where I left it.

I'd guess that whatever bugs the Dana had at first have been worked out, but I know the AlphaSmarts can live in a backpack.

I also got a new keypad for 25 bucks, AND — once you get going with a completely un-thought-through semi-major purchase, you may as well go for broke — I also purchased two 10-dollar cloth slip covers so as to avoid a repeat of the gummy keyboard mishap.

I'm thrilled Andrew will have his own machine. He can be liberated from doing his addition problems at school with stamps and inkpad. Talk about inefficient.

Neo

from the website:

Features:

Neo is a rugged and lightweight tool that can be used anywhere, with 700 hours or more of operation on 3 AA alkaline batteries or 200 hours on a charge. Instant on/off and autosave eliminate startup delays and accidental data loss.

Affordable and expandable.

Neo offers the lowest cost of ownership compared to other computing technology. Plus, with the extensible SmartApplet architecture, new functionality can easily be added so you can get more from your Neo investment.

Connectable.

Easily synchronize data with a home, classroom or office PC.

Built-in word processor.

Easily synchronize data with a home, classroom or office.

AlphaWord Plus, a full-featured word processor that provides:

• Eight active file spaces for one-key file access
• Named files for convenient file management
• Spell-Checking and Thesaurus
• Linked files for rubrics, homework instructions, or reference materials
• Find/replace and word count
• Spanish-English word lookup

The large screen and new font technology display up to twice as much text as the AlphaSmart 3000. Students can save hundreds of pages of text with room for SmartApplets “ software programs extending classroom versatility.

prices

• AlphaSmart \$139
• Neo by AlphaSmart \$249
• Neo Rechargeable \$269
• Dana by AlphaSmart \$379 new price: \$429
• Dana Wireless \$429

AlphaSmart
AlphaSmart reviews
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
AlphaSmart to the rescue
the joys of primitive computing
the joys of primitive computing

-- CatherineJohnson - 10 Feb 2006
RichardRothsteinReportCardForEverything 11 Feb 2006 - 00:05 CatherineJohnson

via eduwonk, a link to Joe William's new blog for New York Charter School Association, The Chalkboard.

Horrifying:

The Economic Policy Institute's Richard Rothstein, in a lecture this week at Amy Stuart Wells' Columbia University, complained that focusing too much attention on reading and math under the federal No Child Left Behind law will make kids better in reading and math, but at the detriment of other subject areas.

Rothstein, according to this news item from Teachers College, is now calling for schools to be held accountable for even more subject areas, including basic academic skills; critical thinking; social skills and work ethic; citizenship; physical health; emotional health;* the arts and literature; and vocational education.

Apparently Rothstein is working on a report.

Richard Rothstein in a nutshell

Rothstein is the enemy of eduwonk-Jenny D-Joe Williams-type reformers everywhere.

Rothstein:

But even if lawsuits demanding an "adequate education" could produce more money, class differences will continue to ensure an achievement gap because schools alone, no matter how well financed, can't by themselves overcome the cultural, social, and economic causes of the differences in academic achievement. The drive for "adequacy" is bound to be seen, when someday it has played itself out, as only another failed education crusade.

source: Must Schools Fail? by Richard Rothstein
New York Review of Books \$
Volume 51, Number 19 · December 2, 2004

That's Rothstein. Academic adequacy, inside quotes or out, is a pipe dream.

First we need to fix everything else.

This is the kind of thing I find particularly hard to take:

...the Thernstroms praise a chain of middle schools called the KIPP Academies, which try to enforce an academic culture that the Thernstroms say most black families lack: strict discipline, constant talk of college plans, and a focus on basic skills.[13] But these charter schools do not enroll black children from typical low-income families....Parents who send their children to such schools are already unusually interested in their education; children are accepted only if parents agree to monitor their homework, enforce approved disciplinary measures, and limit television-watching. If children or their parents violate these agreements, the children can be expelled—a rare occurrence, but a threat nevertheless.

Talk about your soft bigotry of low expectations. The typical low-income parent isn't "unusually" interested in his or her child's education, can't or won't monitor homework, & can't or won't enforce approve disciplinary measures or limit television-watching. With friends like Rothstein, who needs enemies?

nerd celebrity death match

Meanwhile, Rothstein's son is involved in a nasty fight with Caroline Hoxby, who's behaved none too well herself, I'm sorry to say. Of course, she didn't start the fight.

Five years ago Harvard's Caroline Hoxby, a rising star in economics, wrote a paper that reached an unusual conclusion: Cities with more streams tended to have schools with higher test scores.

Today her work is a widely cited landmark in the fierce national debate over free-market competition in public schools. And it's at the center of a bitter dispute with another economist that is riveting social scientists across the country.

Her adversary is Jesse Rothstein, a young professor at Princeton, who says her study is full of flaws. In a rebuttal to her critic, Dr. Hoxby wrote of his work: "Every claim is wrong." She has also accused him of ideological bias. Dr. Rothstein, in turn, says she resorts to "name-calling" and "ad hominem attacks" on him.

[snip]

Dr. Rothstein, 31, is the son of Richard Rothstein, a former textile-union organizer who's now a lecturer at Columbia. Father and son have both worked closely with the left-leaning Economic Policy Institute in Washington. The son got interested in the streams paper while studying for his doctorate at the University of California, Berkeley. He is now an assistant professor at Princeton, not yet eligible for tenure. His Berkeley thesis adviser, David Card, describes Dr. Rothstein, who had majored in math as a Harvard undergraduate, as "tenacious" and having "very good technical skills."

[snip]

In July, Harvard's student newspaper, the Crimson, quoted Dr. Hoxby, whose father is African-American, as saying that "there is a lot of race and gender bias going on here."

In an email, Dr. Hoxby says that the paper misrepresented her views and that she had made no allegation of racial or gender bias. The Crimson's president, Harvard senior Lauren Schuker, says the paper stands by "a fair story (that) covered all sides."

[snip]

An economics Web log called "The Lowest Deep" sums up the squabble as a "nerdy Celebrity Death Match."

The fight is over Hoxby's method of counting streams inside a city — the entire article is worth reading for insight into the kind of 'found experiments' economists like Hoxby perform.

I love that stuff.

*If schools were to begin 'measuring' mental health & citizenship, I'd be marching in the streets. I'd have plenty of company, too.

-- CatherineJohnson - 11 Feb 2006

MathOnBroadway 11 Feb 2006 - 15:34 CatherineJohnson

Ed and I went to see Beauty & the Beast Thursday night (NYU had discount tickets on sale). The first act was so boring we almost left at intermission, but the second act was great. There were a zillion little kids in the theater having the time of their life, so that was fun, too.

Seeing as how I had my AlphaSmart with me, I was able to record, almost verbatim, the conversation behind me. The person speaking is female:

He said, Why are you going to be gone for 6 weeks?

I said, Well 6 weeks divided by 3.

He said, 5?

I said, Divided by 3.

He said, 3?

I said, 2. Six divided by 3 is 2. I’ll be gone 2 weeks. And what do you care anyway? You’re not even in my group.

True story.

-- CatherineJohnson - 11 Feb 2006
RenaissanceLearningAndAcceleratedMath 11 Feb 2006 - 16:19 CatherineJohnson

ok, I am now officially too sick to carry on. (head cold; bad one)

I'll drop in these links, and come back later:

• STAR Math 12-minute assessment program (part of Accelerated Math)

This sounds like a good idea, especially seeing as how a parent invented it. I almost always like teaching systems and ideas parents come up with.

Does anyone have experience with Accelerated Math?

The 'wiki' page is excellent — seems to be written by a teacher actually using the program.

can formative assessment be done by software?

Offhand, it strikes me that formative assessment is the area of math ed most compatible with software & programming...

"I am thoroughly convinced that Accelerated Math can do things for students in math that are almost impossible to accomplish otherwise. The instant feedback and the emphasis on mastery ensure that students do not just coast through the program without truly learning the material. While the teacher (or someone) still has to do much of the teaching, students can be much more independent much of the time, and can cruise quickly through objectives that come easily to them. I have never made it through the end of the math book with any of my classes - I'm lucky to get past the halfway point with some of them. But with AM, motivated students can master EVERY SINGLE objective for the grade level library they work through, eliminating the gaps I see in the math skills of most of my students."

"The true power of AM is its ability to collect data about each student and to report that information to the teacher so he/she can act upon it. AM will notify a teacher whether a student is struggling in any given topic. It is then the teacher's job to act accordingly. The teacher may re-teach a lesson to the whole class, assign a peer-tutor to a struggling student, or to meet with the struggling student himself/herself. AM notifies the teacher of a struggling student much faster than the teacher ever could have figured it out if left to his/her own devices. I could continue singing the praises of this wonderful teaching tool, but I fear I've gone on long enough."

One last thing: Joanne Cobasko, of SOCMM, had a horrific experience with a software math-teaching program her school used with her son. I'll get her story posted at some point. The school wouldn't let her son advance, because the software, which was broken (IIRC, the headphones may have been defective...?) said he wasn't ready.

Apparently they put Hal in charge of math.

Fairfax County, VA Evaluation of SuccessMaker Computer Curriculum Corporation (CCC) SuccessMaker Program Final Evaluation Report (pdf file)

From page 5 of the pdf file above under the heading Findings then sub heading of Student Achievement comes the following:

"For the most part, no significant differences were found between the performance of students at the CCC [SuccessMaker] program and comparison schools on the Stanford 9 mathematics tests. In all three years of the evaluation, students at both groups of schools demonstrated significant growth over the course of the year, and not many differences were found in terms of the rate of growth. Student gains from fall to spring on the Stanford 9 showed modest correlations with the gains made on SuccessMaker's own assessments, but did not show direct correlations with time spent on the system. In several instances....Students who spent under 20 hours on the program outperformed those who spent more than 20 hours on the program..." [bold emphasis is mine]

To put these findings in plain language there were only SMALL correlations with actual standardized test outcomes and the SuccessMaker reports teachers print out which show glowing results in student achievement. The students who spent the least amount of time on the SuccessMaker program scored better on standardized tests.

To further illustrate the lack of effectiveness of this program, Aspen Elementary has been using SuccessMaker since December of 2003 and their API scores have not shown ANY improvement. 2003 and 2004 API reports on the CA SBE web site (posted before 2004-2005 adjustments took place, show a 5 point drop from 879 down to 875, then a one point increase to 876) California Department of Education Academic Performance Index (API) Report

Why on earth is the administration requesting that the district finance this ineffective intervention? It is expensive and shows little in the way of results.

The IES has indicated there is NO VALID RESEARCH to show this program is effective: What Works Clearinghouse.

The district is further crippling CVUSD math education by using this program as it's sole intervention for students who are struggling with math.

If all students are required to spend 20min twice a week in the computer lab on this program you must add in the time necessary to line up and walk to and from the computer lab. There is probably 1.5 hours per week taken out of classroom instruction time to accommodate this intervention. THESE ISSUES MUST BE ADDRESSED BEFORE APPROVING GENERAL FUNDING FOR SUCCESSMAKER At the very least the district needs to perform a scientific evaluation of standardized test scores from the CVUSD schools that have been using SuccessMaker and the ones that have not. A teacher survey of their perception regarding outcomes will NOT be sufficient. The board members have a responsibility to protect taxpayers by insisting on a cost benefit analysis of this intervention.

Scarce funding would be better spent on tutors for after school Math and Reading programs staffed with human instructors, not computers.

-- CatherineJohnson - 11 Feb 2006

FundingForTheDOE 11 Feb 2006 - 17:22 CarolynJohnston

From the desk of JoAnneCobasko, budget highlights related to the President's education proposals in his State of the Union address:

Among the highlights of the FY 2007 budget request are: Preparing America's Students for Global Competition.

\$380 million under the American Competitiveness Initiative will strengthen math and science instruction in our elementary and secondary schools, including:

• \$125 million for the Math Now for Elementary School Students initiative, modeled after Reading First, to prepare K-7 students for more rigorous courses in later years;

• \$125 million for a new Math Now for Middle School Students initiative, based on the principles of the Striving Readers program, to support research-based math interventions in middle schools;

• \$10 million for a National Mathematics Panel to identify key mathematics content and instructional principles to create a research base for teachers and guide the implementation of the Math Now programs;

• \$5 million for an Evaluation of Mathematics and Science Programs that would determine which federal education programs are the most effective in raising achievement in math and science and how they can be coordinated to save taxpayer money;

• A \$90 million increase for Advanced Placement to train 70,000 additional teachers for math, science and foreign language AP-IB courses and increase the number of students taking and passing AP-IB tests in those subjects; and

• \$25 million for the Adjunct Teacher Corps to encourage qualified professionals to teach high school courses with an emphasis on math and science.

As usual, this raises more questions than it answers. The first being: what the heck are Reading First and Striving Readers, and why should we base expensive math improvement initiatives on them?? I'm not hostile, I just don't know anything about them.

And the second: just how do they plan to encourage qualified professionals to teach high school math and science courses with \$25M? Billboards? I can see it now. "Having a midlife crisis? Sick of that high-paying job at Microsoft? Feeling like you need more meaning in your life? Come teach public school!"

-- CarolynJohnston - 11 Feb 2006

AlphaSmartToTheRescue 11 Feb 2006 - 21:26 CatherineJohnson

I'm still sick as a dog.

I'm sick as a dog, BUT I'm not in bed because Ed decided to go for a run. A 'short one.'

That was awhile ago.

Five seconds after Ed left, Andrew began tantruming so severely he knocked the kitchen clock off the wall.

When he tantrums, Andrew jumps as high into the air as he can, slaps temples with his hands as hard as he can, then lands as hard as he can, screaming at the top of his lungs throughout. There aren't words to describe it. 'Jump-slam' is the best I can come up with.

The sound is nerveshattering, even more so when you're sick. The house shakes.

This went on for what seemed like hours, until Andrew finally came downstairs, sobbing.

I got the AlphaSmart.

'What do you want?' I said. I didn't expect him to answer, but since the AlphaSmart was there, I thought I'd try.

This is what he typed. The two lines below are my answer.

After he read what I'd typed, he stopped crying and ate some 'cheese toast.' Cheese toast is one of Andrew's only foods. He has a severe autistic eating disorder. He lives on cheese toast, pizza, grape juice, and Starburst candies. Sometimes he eats peanut butter, too, and he goes through phases when he likes bacon.

And that's it.

Now he's calm and happy.

We've been telling the school for perhaps the past year that Andrew needs a keyboard.

What he has is the Dynamo, an assistive tech device that's so confusing only Andrew knows how to use it. The school is constantly telling us to use the Dynamo, that we have to have Andrew be 'responsible' for his Dynamo, he has to carry it around the house, etc. We should never allow him to communicate with us in any way at all apart from the Dynamo.

So, if he goes to the refrigerator & gets out hot dog rolls & 2 Kraft cheese slices & then goes to the pantry and gets a paper plate, and hands the lot to us, we are to do nothing until he puts down his food and plate and presses the 'Cheese toast' button on the Dynamo.

We don't do it.

The Dynamo doesn't work for us; there's nothing remotely normal or normalizing about this device for us.

instructions for the Dynamo — exactly what you want to be reading
every time you have something to say to your child

Plus it's been obvious for years now that Andrew can read; he doesn't need all the pictures. We've been saying, 'Get rid of the pictures, he can read.'

Lately, that's what they've been doing; a lot of the pictures are gone. Still, because the speech therapist is programming it, not us, we have no clue where the 'pages' of Andrew-words are (each screen is a page), what's on them, or how they're linked. When we do try to use it, we get lost in the information architecture, and then we're trapped inside the Dynamo, trying to find our way back to the home page — and all this is going on while Andrew is screaming.

After we'd lived with the Dynamo for a couple of months we felt about it the way those high school kids in Los Angeles feel about algebra: we have learned helplessness.

So we've been telling the school Andrew needs a keyboard.

They're just now getting around to 'scheduling an assessment,' which, of course, will consume many months more.

So it turns out we were right.

Andrew needs a keyboard.

Now he's got one.

AlphaSmart
AlphaSmart reviews
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
AlphaSmart to the rescue
the joys of primitive computing

-- CatherineJohnson - 11 Feb 2006

CognitiveUnconscious 12 Feb 2006 - 16:53 CatherineJohnson

Ed and I were just going over Old Grouch's drawing & Anne Dwyer's notes....whoa nelly.

They're right.

The figure can't be 'solved' as drawn.

what did your C.U. know and when did it know it?

Anne also had this to say:

If you use the marked numbers on the test of 4cm for the height and 13cm for the base, the hypotenuse of the triangle on the left is the square root of 185 which is between 13 and 14. But the base of the triangle on the left marked 10cm cannot be correct. If you draw a line parallel to this 10 cm base with its start at the right hand corner where the circle is and drop it to the bottom, you get a right triangle with a hypotenuse of 14 and sides 3 and 10. This is not possible since 32 + 102 does not equal 142.

Also, since the horizontal line marked 6 cm is parallel to the horzonal line marked 9 cm, the two vertical sides of the resulting parallogram have to be parallel and the same length. But, as I've pointed out, the length cannot be 14 cm because the sides are 3 and 10.

So the student who said he couldn't do this problem was absolutely right. You can't do this problem if you try to get all the numbers right because they don't come out right.

The funny thing is, when I put in my original post about this being a problem for high school geometry students, I believe it was because my intuitive brain recognized the problems, but didn't articulate the words to my verbal brain.

I think Anne is right.

I've pulled out my copy of Arthur Reber's Implicit Learning and Tacit Knowledge: An Essay on the Cognitive Unconscious (Oxford Psychology Series, No 19, and will try to get around to posting some of the key passages from the book shortly.

In the meantime, I'm sure Anne is right.

As I understand it — and I'm still learning this area — the cognitive unconscious does most of the heavy lifting. This is one reason why I feel it's wrong to 'privilege' the 'verbal mind,' as constructivist math curricula do.

The verbal mind, as I understand it is the conscious mind, and the conscious mind is the last to know anything about anything.

I think. (Irony intended)

Here's an abstract of a 1987 article in Science:

Contemporary research in cognitive psychology reveals the impact of nonconscious mental structures and processes on the individual's conscious experience, thought, and action. Research on perceptual-cognitive and motoric skills indicates that they are automatized through experience, and thus rendered unconscious. In addition, research on subliminal perception, implicit memory, and hypnosis indicates that events can affect mental functions even though they cannot be consciously perceived or remembered. These findings suggest a tripartite division of the cognitive unconscious into truly unconscious mental processes operating on knowledge structures that may themselves be preconscious or subconscious.

source:
SCIENCE 1987 Sep 18;237(4821):1445-52

the death of implicit memory?

As I say, I'm still working my way through this field.

The next article I'll read will be Willingham on The Death of Implicit Memory:

Abstract

The thesis of this article is that implicit memory does not exist. Implicit memory phenomena are distinct from explicit memory phenomena at a neural and information processing level, but there is such variety among the implicit memory phenomena that nothing holds them together in a common category. Other researchers have distinguished among different types of implicit memory, but have retained the superordinate category. Extant data is evaluated in light of how classification systems should be developed, and it is concluded that there is currently not a reason to retain the construct "implicit memory."

I suspect that Willingham's & Preuss's article doesn't contradict Reber's book, but I don't know.

Here's Willingham in a passage from Malcolm Gladwell's article on The Art of Failure 'The Art of Failure':

"Choking" sounds like a vague and all-encompassing term, yet it describes a very specific kind of failure. For example, psychologists often use a primitive video game to test motor skills. They'll sit you in front of a computer with a screen that shows four boxes in a row, and a keyboard that has four corresponding buttons in a row. One at a time, x's start to appear in the boxes on the screen, and you are told that every time this happens you are to push the key corresponding to the box. According to Daniel Willingham, a psychologist at the University of Virginia, if you're told ahead of time about the pattern in which those x's will appear, your reaction time in hitting the right key will improve dramatically. You'll play the game very carefully for a few rounds, until you've learned the sequence, and then you'll get faster and faster. Willingham calls this "explicit learning." But suppose you're not told that the x's appear in a regular sequence, and even after playing the game for a while you're not aware that there is a pattern. You'll still get faster: you'll learn the sequence unconsciously. Willingham calls that "implicit learning"--learning that takes place outside of awareness. These two learning systems are quite separate, based in different parts of the brain. Willingham says that when you are first taught something--say, how to hit a backhand or an overhead forehand--you think it through in a very deliberate, mechanical manner. But as you get better the implicit system takes over: you start to hit a backhand fluidly, without thinking. The basal ganglia, where implicit learning partially resides, are concerned with force and timing, and when that system kicks in you begin to develop touch and accuracy, the ability to hit a drop shot or place a serve at a hundred miles per hour. "This is something that is going to happen gradually," Willingham says. "You hit several thousand forehands, after a while you may still be attending to it. But not very much. In the end, you don't really notice what your hand is doing at all."

Under conditions of stress, however, the explicit system sometimes takes over. That's what it means to choke. When Jana Novotna faltered at Wimbledon, it was because she began thinking about her shots again. She lost her fluidity, her touch...

I'm still confused about the relationship of the conscious, verbal mind to 'knowing,' 'understanding,' and 'expertise."

However, I'm not confused about the fact that expertise means you've reached automaticity — and automaticity means you can do something without thinking about it.

Again, this is why I'm uncomfortable — very uncomfortable — with the constant demand that math students explain their answers in words.

On the one hand, it's true that I discover gaps in my knowledge when I force myself to put things in words.

So....having to explain an answer, I think, functions as formative assessment.

At this point, I think Feynman's aphorism — unless you can show how to arrive at an answer through 5 different paths, you don't know it — (NOT FACT-CHECKED) describes true conceptual understanding for me. (Personally, I'm not shooting for 5. Two will do. Two or perhaps 3.)

I have the strongest feeling that, in forcing children who are just learning math to 'back up' into words every time they learn how to solve a particular kind of problem, constructivists are pulling these kids back out of real mathematical learning and comprehension — back out of implicit memory into explicit memory.

-- CatherineJohnson - 12 Feb 2006

SnowPlowDrama 12 Feb 2006 - 17:28 CatherineJohnson

Good Lord.

The guys are out trying to plow our drive, and there's so much snow the main driver almost ran over his men. They had to jump out of the way when the truck skidded downhill towards them.

Now one of them fell down.

This is harrowing.

I've got some pictures of Christopher buried in snow....

help desk

We got a new camera for Christmas.

The old camera is taking blue pictures.

Would that happen because the battery is dying? (The battery is at least 3 years old, maybe more.)

deep

It's impossible to get a shot of Andrew in focus.

oops, I lied

-- CatherineJohnson - 12 Feb 2006

LindaSchrockTaylorOnMathAtSchool 12 Feb 2006 - 18:32 CatherineJohnson

I was just trying to de-code the mysteries of Saxon Physics, when I came across this observation from Linda Schrock Taylor:

Frequently we are asked, "When do you end the school year in homeschooling?" My answer is always, "When the last math lesson has been completed and the final exam passed with flying colors." I think it is important that students complete books, especially math books. Each year I would note that even the best math teachers in the public school where I taught were only completing about 42% of each math book prior to the start of summer vacation. The students then went home for eleven weeks, and returned to face the next book in the sequence—even though they were never taught the last 58% of the material in the prerequisite class! Still people wonder why American students fall ever further behind in math!

update: more on not finishing the book

I am thoroughly convinced that Accelerated Math can do things for students in math that are almost impossible to accomplish otherwise. The instant feedback and the emphasis on mastery ensure that students do not just coast through the program without truly learning the material. While the teacher (or someone) still has to do much of the teaching, students can be much more independent much of the time, and can cruise quickly through objectives that come easily to them. I have never made it through the end of the math book with any of my classes - I'm lucky to get past the halfway point with some of them. But with AM, motivated students can master EVERY SINGLE objective for the grade level library they work through, eliminating the gaps I see in the math skills of most of my students.

update: question

I remember reading somewhere — and posting — that math textbooks have approximately 23% new content each year....the rest being review of content taught in years before.

I have no idea where I read this, or where I posted it — and am now wondering whether I dreamed the whole thing up.

Does this factoid sound familiar to anyone?

Saxon Physics mystery

Charles found a site selling Saxon Physics, which a Saxon rep told Carolyn is out of print, at a nice price....but I can't figure out what comes with.

The same site also offers the Solutions Manual (\$27.99) and Saxon Physics, Answer Key Booklet & Test Forms (99 cents!)

Maybe I've gone blind or lost my capacity to read, but I simply cannot tell whether the Saxon Physics Home Study Kit — "Offering 100 physics lessons, tests, answers, periodic table, charts, and more: all you need to teach a complete physics course" — also includes a Solutions Manual and an Answer Key & Test Forms.

I'm guessing it does not include a Solutions Manual (but why would that be?) & does include an answer key & tests, seeing as how it says it includes an answer key & tests, & does not mention a Solutions Manual.

Nevertheless, I'm confused.

Megawords 14% off

The site offers Megawords at 14% off the regular price.

I love this

Linda Schrock Taylor...is a free-lance writer and the owner of "The Learning Clinic," where real reading, and real math, are taught effectively and efficiently.

I'm going to have to get in touch with her.

-- CatherineJohnson - 12 Feb 2006
SnowDay2 13 Feb 2006 - 14:32 CatherineJohnson

source:
Life, Unscripted

-- CatherineJohnson - 13 Feb 2006

WhyDoWeHavePerCent 13 Feb 2006 - 22:27 CatherineJohnson

I was teaching Christopher Lesson 77 in Saxon 8/7 today: "Percent of a Number, Part 2."

Saxon does something incredibly cool.

He gets kids started on writing equations to solve very simple fraction & percent problems by using WP, WN, WD, and WF to mean "What percent?" "What number?" "What decimal?" and "What fraction?"

Take the question:
What percent of 40 is 25?

The 'of' translates easily & directly to x; the 'is' translates easily and directly to =; the 'what number' translates to WN: WP x 40 = 25

What number is twenty-five percent of 80?
WN = .25 x 80

Fifteen percent of what number is 45?
.15 x WN = 45?

Seventy-five is what decimal part of 20?
75 = WD x 20

What fraction of 56 is 42?
WF x 56 = 42

This system allows Saxon to teach percent, decimal, and fraction problems close together, without students getting lost mid-stream. (At least, I assume this system works....it worked with Christopher today, so he's my 'n of 1.')

more Saxon subscripts

While I'm on the subject of Saxon's painstaking efforts to support the student, 8/7 also uses subscripts to set up proportions.

In the town of Centerville, 261 of the 300 working people do not carpool. What percent of the people carpool?

Saxon uses PC ('percent who carpool) and PN (percent who don't carpool) in the 'ratio box' he teaches students to construct.

PC/100 = 39/300

When I was a kid, everything was X.

I don't actually remember that being a problem for me.....but having everything be X today would sure be a problem now that I'm trying to teach this stuff.

so why do we have percents?

I wanted to tell Christopher why we're doing percent & proportion problems.....and I realized I don't necessarily know why.

I assume that percents were invented, or 'agreed upon,' to give everyone a common & efficient standard of comparison.

In other words, percents are another kind of 'math machine,' an invention that makes things go faster.

Is that right?

Are there other reasons?

And: when did people start using percents?

Saxon 8/7 a remedial book?

This is something I don't quite fathom.

Linda Schrock Taylor sees 8/7 as a remedial book.

But I love this book....and certainly don't experience it as remedial. (I finished Lesson 84 last night, out of 130. Saxon books have 120 lessons plus 12 'Investigations' plus an appendix or two. There are 133 lessons in Saxon 8/7 altogether; I've done 91.)

Any thoughts?

I'm thinking Saxon 8/7 must repeat a great deal of 7/6, which I haven't used beyond the first 20 lessons.....

But I don't know.

Percents, derived from per centum, or "per hundred", give you a common denominator with which to compare ratios.

So, instead of having to compare 3/4 with 7/9 with 2/3, you can compare 75% with 77.8% with 66.7%.

— and from Old Grouch:

And my Webster's Collegiate gives that derivation and first use of "percent" as French "per" + Latin "centum" in 1568.

— and from Steve:
Why percents? Because it's nicer to have some numbers to the left of the decimal point. Notice that scientific notation always puts one number to the left of the decimal point. Actually, I think I might prefer two digits to the left, rather than one.

Thanks!

Christopher learns how to do proportion/percent problem from Saxon Math

-- CatherineJohnson - 13 Feb 2006
APoemAboutAutomaticity 13 Feb 2006 - 23:49 CatherineJohnson

Old Grouch found this at "The Centipede Who Went to School" !

```A centipede was happy, quite,
Until an ant, in fun,
Said "Pray, which leg comes after which?"
Which raised his doubts to such a pitch,
He fell befuddled in the ditch,
Not knowing how to run.
```

cognitive unconscious

-- CatherineJohnson - 13 Feb 2006
TheLimitsOfScientificResearch 14 Feb 2006 - 00:06 CatherineJohnson

From a terrific short essay by Chester Finn, warning of an almost-certain-to-occur (IMO) Unintended Consequence. It's worth reading the whole thing.

Science and nonscience: The limits of scientific research

American education research has turned a corner. The 2002 creation of the Institute of Education Sciences (IES), the ascendance of accountability, and the No Child Left Behind act's demand for "scientifically based research" have radically altered an educational research culture that just a few years ago bridled at the "medical model" and too often championed ethnographies, action research, "critical narrative," "discourse analysis," and other approaches that provided parents, practitioners, or policy makers with little useful information.

Together, both NCLB and IES represent a demand that rigorous scientific principles be used to assess programs. This development did not "happen" and it was not an inevitable evolution embraced by the education research community. Rather, this change was the consequence of prodigious efforts by proponents like Congressman Michael Castle, reading expert Reid Lyon, and IES head Russ Whitehurst. For their efforts, they have met with fierce resistance from some quarters of the education research community, as well as professional discourtesy, bizarre conspiracy theories, and ad hominem attacks.

[snip]

Amidst this good news, however, lurks the risk that the pendulum will swing too far, that the lure of "scientifically based research" will cause certain methods of study—especially randomized field trials—to be demanded even when ill-suited for the issue at hand.

[snip]

...we risk stifling sensible and promising structural reforms in schooling. This risk is posed when we start to imagine that reforms to personnel, management, or financial systems need to be subjected to these scientific standards. In such cases, a premature or unyielding application of the tenets of "scientific research" could insulate ineffective and dysfunctional arrangements from needed and attainable reform.

How does this danger arise? In large part, it occurs from an imperfect understanding of how the "medical research model" works in medicine and how and when to import it into education. It's vital to recognize that there are really two kinds of "reforms" in medicine or education—and that the proper role of science and scientifically-based research is very different from one to the other. One kind of reform relates to specialized knowledge of how the mind or body works, and the other relates to the manner in which we design and operate organizations, governments and social institutions.

In education, the former category deals with the science of learning and with behaviors and programs that induce it....Such interventions are readily susceptible to field trials, and findings on effectiveness can reasonably be extrapolated to other populations.

[snip]

The second category of reform entails governance, management, or policy innovations intended to improve organizational effectiveness. It includes such innovations as permitting mayors to appoint school boards, permitting schools to operate free of some regulations, paying employees based on performance, and so on. None of these changes is unique to education. They draw upon a mass of experience gained in other sectors—and their effects are consistent enough and understood well enough across a broad swath of human experience that it's neither useful nor appropriate to use the scientific method to determine whether, for example, initiatives to reward excellence, increase managerial flexibility, or ensure accountability may hold promise in schooling. Such interventions are rarely precise, do not take place in controlled circumstances, and generally are administered to classes of people rather than discrete clients. Since the results of these structural reforms will be contingent on the context and manner in which they are implemented, even well-designed studies will find it problematic to draw lessons from isolated experiments that trump our broader body of knowledge regarding the use of incentives or markets. Of course, we should welcome inquiry and take new findings into account when reflecting on policy or program design. However, it's vital to remember that we've got a vast store of knowledge on these questions, and that whatever the results of small-scale experiments with merit pay or educational competition, this existing body of knowledge ought to weigh more heavily than the results of one or another context-specific study.

[snip]

....in medicine, while we deem it appropriate for the Food and Drug Administration to monitor and approve drug therapies and treatments, we don't require FDA approval before we permit doctors, hospitals, or health care firms to change their management practices, compensation strategies, accountability metrics, or work routines.

In truth, charter schooling, accountability systems, school vouchers, alternative certification, and merit pay are not really "educational" innovations in any meaningful sense. They don't rest on conceptions of teaching or learning processes or practices in the way that decisions about literacy or math programs do. They are decisions about how to arrange and deliver services, similar to those made in social welfare, library management, higher education, or private enterprise. Such decisions draw upon our experience across a wide range of human endeavors and organizations. They apply practical wisdom and experience about human behavior from a wealth of sectors. We should welcome research on the effects and efficacy of such reforms and use them in debating and crafting policy. But we also need to understand the limits of science.

The notion that rewarding performance ought to be subject to scientific validation before adoption is akin to suggesting that the National Institutes of Health should determine permissible compensation systems for doctors.

in a nutshell

• there are two kinds of reforms in education: roughly, 'educational' reform (curriculum & teaching) and 'management' reform (mayoral control, vouchers, pay scale, etc.)

• educational reform is the proper subject of scientific research

• management reform can be studied, and has been studied, but management reform is always context-specific and thus not susceptible to random-assignment controlled studies

• we possess a wide and deep body of knowledge concerning effective management practices, which transcends particular institutions and can be generalized

• there is a danger that in embracing 'science' as the arbiter of all reform, needed management reforms will be held hostage to context-specific studies that will be many years in the making and won't give us as much information as we already have about good management

-- CatherineJohnson - 14 Feb 2006
NyuMathMajor 14 Feb 2006 - 02:26 CatherineJohnson

Ed talked to an undergraduate majoring in math today.

I guess the kid spontaneously told Ed that, "Calculators are the worst thing that ever happened to math students."

Ed said he almost burst out laughing, because next this student went on to say that nobody who used calculators as a kid can do fractions, and if you can't do fractions you can't do calculus.

Ed said this guy could have been channelling me.

The student also said that, in high school, his calculus teacher had told the students who were having trouble, "You're having trouble because you used calculators in grade school and you never learned to do fractions." It was obvious to her. He spent quite a lot of time describing automaticity to Ed, and how important it is.

Ed asked why he hadn't used calculators as a child, when everyone else was, and the answer was chilling: he hadn't used calculators because he 'was into' math, he liked it, and he wanted to do the calculations by hand.

What that tells me is that only the natural born Math Brains are going to make it through these days — natural born Math Brains who know they're natural born Math Brains.

Your basic kid is going to use the calculator if the teacher hands it to him.

Then he's going to regret it later on.

That's what happened to the other kids in his high school calculus class.

Ed asked him whether the kids who'd used calculators could catch up.

The kid didn't think so. At least, he hadn't seen it happen.

Math is hard, he said. It's hard, it takes a long time to learn, and he didn't think a high school student who'd lost that much time could make it up.

That's what James Milgram said, too.

no calculators in Irvington

I don't think any of the grade school kids here are using calculators.

One of main criterion for choosing a new math curriculum was (paraphrasing) 'constructivist approach.'

One of the other main criterion was emphasis on math facts & computation.

TRAILBLAZERS was the only constructivist curriculum they considered that stressed fluency in math facts.

(I assume they're teaching the traditional long division algorithm in spite of the fact that TRAILBLAZERS teaches 'forgiving division,' but I don't know. Nevertheless, nobody's passing out baskets of calculators.)

Good for them.

which reminds me

I had to buy Christopher an expensive graphing calculator (or something) last fall, for Middle School.

He never used it once, and then finally lost the thing.

Good riddance!

His teacher is letting them use calculators for the first time this year, to calculate circumference & area of circles. I'm not even sure that's such a good idea.

Since he's doing KUMON, though, I figure it's OK. He's incredibly fast & accurate on the KUMON sheets.

Of course, the two "Fraction Levels" - E & F - are killers.

-- CatherineJohnson - 14 Feb 2006

QuestionForSmartestTractor 14 Feb 2006 - 15:32 CatherineJohnson

First of all, I may have forgotten to mention that Matt Goff's post about teaching algebra is linked in last week's Carnival of Education.

I'm sending Smartest Tractor's material to this week's Carnival, and have managed to round it up. (I have a sinking feeling that Anne Dwyer material, which I plan to send in next week, is scattered to the four corners of ktm...)

I have one question for Smartest Tractor (or anyone else): I don't understand her box and whisker chart, 'Algebra to date.' (pdf file)

-- CatherineJohnson - 14 Feb 2006

PrimitiveComputing 14 Feb 2006 - 17:43 CatherineJohnson

At least 2 ktm Contributors have ordered AlphaSmarts since I started obsessing about the things last week.

No question I missed my calling in life. I was supposed to be a Travelling Salesman.

This reminds me of the time my mom and I interviewed her Uncle George, who was the patriarch of the family, to the extent that we had a patriarch, which we didn't.

Uncle George was an engineer. He worked all over the world, in Saudi Arabia, South America — everywhere. He has incredible stories of his wife giving birth in the middle of South American revolutions.

Anyways, we were talking about his father, my Grandad McCammon, a Methodist minister who was president of the first Methodist college in Illinois.

Uncle George said (paraphrasing), 'Dad wasn't really a religious man. He was a salesman.'

I just about fell out of my chair.

I like religion myself, and try to 'be religious,' but it doesn't come naturally. It's something I have to work at (and it tends to be something I put off working at.)

Tearing around the internet grabbing folks' arms and urging them to BUY THIS REDUCED-PRICE ALPHASMART NOW! is what comes naturally.

Blood will out.

In case you're wondering, the reason my Granddad McCammon became president of the first Methodist college in IL was that he'd raised enough money to build a Methodist Fellowship Center (I think that's what it's called) at the U. of Ill. Folks had been trying to raise the funds for awhile without much luck. When my Granddad took over, he got the money.

That's selling.

His reward was to be named president of the Methodist College.

On the Joys of Primitive Computing: The AlphaSmart Neo

While I was hopping from one AlphaSmart website to the next, I found this terrific essay on the joys of primitive computing by Kendall Clark.

I agree with every word that a) applies to me and b) I understand.

Part of being a savvy technologist includes staying on the perpetual hardware upgrade habitrail -- or so people too often assume.

Some of us, however, are done with hardware. I put myself through college, back in the day when Intel' 80386 CPU was a big deal, by building computers for aeronautical engineering students at the University of Texas, where I wasn't a student.

I am so over hardware, and I have been for more than a decade. I take pride in making my living from technology and doing so with very old, even decrepit hardware. My main server for five years has been an IBM Thinkpad I found in a dumpster. My only extravagance was to max out its RAM at 512 MB. My everyday system is a nice 15" Powerbook supplied by UMD. While OSX is nice, it's not exactly Linux on an Opteron.

I'm bored by hardware and a bit cheap about it, too.

All of which makes the fact that I've fallen in love with a new box (and a new kind of box) all the more curious. I'm talking about my new Neo by AlphaSmart, upon which I'm typing this weblog entry. Before saying more, thanks to Paul Ford for telling me about the Neo. Paul rocks.

Oddly enough, the Neo is basically a computer for school children. It's stunningly stupid and, well, primitive. I'm enjoying it so much, and being so productive with it, that it's got me thinking about what I'll call Primtive Computing and Power User Devolution.

The Neo is interesting not because of what it does or what features it has, but what it can't do and the features it's missing. It's all about one thing and one thing only: writing. [ed.: I wrote a huge part of the ANIMALS IN TRANSLATION proposal on my AlphaSmart, sitting at the picnic table outside the kitchen.] I'm most comfortable turning any task into a writing task (when all you have is a hammer...), which means I'm super comfortable with a primitive device that's really only good for writing.

Specs? I don't even know what kind of CPU this thing has, and I couldn't care less. The OS is some homegrown thing, apparently, I think the OS is some variant of PalmOS, but I don't really know. Or care -- cultivating ignorance about irrelevant details is part of the ethic here, I think. The word processor, the only app it has, is brain dead. Which means no distractions; it gets out of my way as well as venerable Word Perfect 5.1 for DOS used to -- a writerly experience I've only come close to replicating with Emacs.

The keyboard action is passable; not great, but no impediment. The screen is a measly six lines, and I'm finding it perfectly acceptable. Especially when it meaans that battery life -- powered by 3 AA batts -- is a remarkable 700 hours. Yes, 700 hours! The damn thing weighs all of 2 lbs, though it feels lighter. It's the ultimate road warrior's tool, at least if you think of a road warrior as a writer.

My joy at the sheer utlity of the Neo -- even at the rather inflated price of \$250 [ed.: the original AlphaSmart is on sale for \$139! Not \$250!] -- leads me to wonder whether Primitive Computing is a trend of larger significance. Maybe the sign of a real power user is someone who's happy to get by with less, rather than ever insisting on more. Using the Neo is of a piece with the Hipster PDA and with Danny O'Brien's ethnographic observations about the ubiquity among the power set of text files as a first class organizational tool. [ed.: no idea what he's talking about]

The Neo is the closest I'm going to get to the kind of intentional simplicity that could lead to something like Walden on the job. (A chimerical goal, to be sure, since Walden was mostly about not working for The Man, rather than doing so sanely. Oh well!) ....

[snip]

As the man used to say back in the day: Highly Recommended.

The best thing about the AlphaSmart & the AlphaSmart Neo?

You can't hook them up to the internet.

Kendall Hunt
Mind Swap - Maryland Information and Network Dynamics Lab Semantic Web Agents Project
(Kendall Hunt is part of this)

AlphaSmart
AlphaSmart reviews
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
AlphaSmart to the rescue

-- CatherineJohnson - 14 Feb 2006

HappyValentinesDay 15 Feb 2006 - 01:02 CatherineJohnson

Valentine's stroll : A couple walks by heart-shaped balloon street vendor in downtown Sofia.
(AFP/Valentina Petrova)

A milestone.

Christopher gave his first Valentine's gift to a girl today.

I'm not giving away secrets, because apparently the entire 6th grade class is ONE with Christopher and his quest to win this girl's heart. He's being massively egged on.

Meanwhile I got an email from his new English teacher today saying she asked him to bring in a marble-cover composition notebook last week, and he didn't.

Fortunately, I have TWO marble-covered composition notebooks on hand, and had already given him one tonight.

-- CatherineJohnson - 15 Feb 2006

AnimalsInTranslationFebruaryTwelve 15 Feb 2006 - 18:07 CatherineJohnson

February 12, 2006

Animals in Translation on TIMES list
Animals in Translation 1-29-2006
Animals in Translation 2-05-2006
Animals in Translation 2-12-2006
Animals in Translation 2-19-2006
Animals in Translation 2-26-2006
Animals in Translation 3-05-2006
Animals in Translation 3-12-2006
Animals in Translation 3-19-2006
Animals in Translation 3-26-2006

-- CatherineJohnson - 15 Feb 2006
CalculusAdviceFromRudbeckiaHirta 15 Feb 2006 - 18:19 CatherineJohnson

Rudbeckia Hirta left this piece of advice yesterday:
Slightly off topic, for Catherine to tuck away for future reference:

If you want Christopher to be a successful calculus student down the road, when his math class covers slope (probably next year?) (probably in the context of graphing lines), make sure he understands every detail that is included.

Calculus is (roughly speaking) the study of finding areas, finding slopes, looking at tiny pieces of things, and how all these ideas are related.

I'm taking this to heart.

Incidentally, I hope I have most of the calculus advice ktm Contributors have offered logged in the Book-style index. Most or all of the book recommendations are here.

speaking of Rudbeckia...

I love this!

A brilliant idea.

R H's calculus students

I have a pretty good mental model of the typical student in my calculus class. Specifically, they can compute derivatives of polynomial functions (even though I haven't taught that yet), they wish to use this skill as often as possible (even if the problem doesn't call for it), and they are absolutely helpless when faced with a graph without its equation (insert snarky comment of your choice about graphing calculators).

OK, I relate to this!

As far as I can tell, the ONE concept that I really, truly GOT in my 12 years of math ed was: RATIOS & PROPORTIONS.

I've spent my entire life solving every conceivable math problem that's come my way via ratios & proportions. You Math Brains out there probably wouldn't believe how much you can do WITH RATIO & PROPORTION & NOTHING ELSE. I could probably write a book about it. When it comes to RATIO & PROPORTION I'm like those Frugal Housewife people who can make a hat out of a Clorox bleach container. (Seriously. I once appeared on a talk show just before a guest who was going to demonstrate how to make a hat out of a Liquid Clorox bleach container.)

The funny thing about my RATIO & PROPORTION life is that my neighbor, who is a statistician, by which I mean she earns her living doing the statistics on things like genetic research, has also spent her life relying on ratio and proportion for everything else. I find that hard to believe, but that's what she says.

This part is interesting:

In one activity there are graphs of eight functions, and the students are supposed to sketch the graph of the derivative of each function. It's amazing how resistant they are to following the directions, estimating the slope of the function at several points, and visualizing the derivative as the slope of the tangent line. Instead, they try to guess the equations of the graphs and to calculate the derivative and then graph the result with their calculators. Unfortunately, my students can't recognize classic graphs. They misidentified the graph of natural log as square root; for them everything U-shaped is a parabola. This is one activity where the students that haven't had calculus before do much better than the ones who have had calculus before.

I wish I knew more about calculus. Scratch that: I wish I knew anything at all about calculus.

Soon.

[pause]

umm....

'Soon' is perhaps not the correct term.

'Later' might be the word I'm looking for. Or: 'all in good time.'

I took my Saxon book with me to my brother-in-law's house for Thanksgiving, and Ed's dad, who substitute teaches, said to me, 'Are you still doing pre-algebra?'

I said, 'Yes.'

He said, 'You've got a long way to go.'

Everyone burst out laughing. Because, of course, that's what everyone was thinking.

I'll show them.....

-- CatherineJohnson - 15 Feb 2006

RetirementBombsAway 15 Feb 2006 - 19:03 CatherineJohnson

via Education Wonks, Schools face 'death spiral', a USA Today article on the cost of lifetime health insurance for retired teachers.

random factoid:

Los Angeles sets aside \$1,000 of its \$5,500-per-student budget to cover health care costs for current and retired teachers. To cover the newly estimated \$10 billion liability would require \$2,087 per student.

Well, I guess the good news is they won't have a lot of money left over for purchasing fancy-shmancy manipulatives or hiring math consultants who don't know any math.

(just kidding)

N Y Times on 'pension bomb' (free link)

Since 1983, the city of Duluth, Minn., has been promising free lifetime health care to all of its retired workers, their spouses and their children up to age 26. No one really knew how much it would cost. Three years ago, the city decided to find out.

It took an actuary about three months to identify all the past and current city workers who qualified for the benefits. She tallied their data by age, sex, previous insurance claims and other factors. Then she estimated how much it would cost to provide free lifetime care to such a group. The total came to about \$178 million, or more than double the city's operating budget.

My understanding is that many or most public employee pension contracts have the force of law, which I take to mean that citizens can't vote to revise the terms:

...the public pension morass is bigger, more wide ranging, and ultimately more costly than anything you've seen in the corporate world. The practices, quietly approved by elected officials, allow workers to dramatically spike their pre-retirement compensation, to retire on more than 100 percent of their pay, and to draw both their salaries and pensions, with guaranteed market returns, simultaneously.

[snip]

...for almost a decade now, while it has been continually sweetening the pension plan, the [San Diego] city council has also voted to give the pension system far less money than its actuary recommended. But those pension benefits must be paid -- they're protected by California law, just as public pensions are constitutionally guaranteed or protected in 40 other states.

[snip]

A corporation, under federal law, typically must start pumping money into its pension plan once the value of the plan's assets sinks below 80 percent of its liabilities. But there is no such law governing state and local plans -- the decision to pump additional money into a pension plan lies with the individual discretion of state and local governments.

Thanks to this discretionary funding system, shortsighted politicians can simultaneously dole out rich pensions to their heavily unionized workforces (thereby presumably currying favor with a powerful group of voters and avoiding nasty strikes) and keep the rest of their constituents at bay by shoving the liability for those increased benefits onto future taxpayers. "The next generation of taxpayers is not sitting at the table," says Jeremy Gold, a New YorkÐbased pension consultant. "In fact, the money is going from our children's pockets to today's municipal employees."

[snip]

...government plans are generally much richer than those offered by corporations. The average public sector employee now collects an annual pension benefit of 60 percent after 30 years on the job, or 75 percent if he is one of the one-fifth or so of workers who are not eligible to collect Social Security benefits. Of the corporate employers that still offer traditional pensions, the average benefit is equal to 45 percent of salary after 30 years. Just as important, about 80 percent of government retirees receive pensions that are increased each year to keep pace with the cost of living, a feature which protects pensions against the effects of inflation and that can increase the value of a typical pension by hundreds of thousands of dollars over a person's retirement. But such inflation protection is nonexistent in corporate plans.

[snip]

In March [San Diego] agreed to a tentative settlement that would require it to increase its annual payments to the pension plan dramatically, starting with \$130 million in 2005 (a 40 percent increase over the prior year) and gradually rising in subsequent years. To put that amount in context, San Diego's total general revenue fund for 2004 is \$742 million. No matter what, San Diego residents are now facing some drastic cutbacks in city services or unwanted tax hikes. As for the latest round of pension increases, they can't be reduced because -- you guessed it -- they're protected by law.

[snip]

Governments will probably continue to offset rising pension costs by slashing services and, in the process, laying off workers -- not a pleasant alternative for either the workers or the citizens of the community.

source:
The \$366 billion outrage (Wall Street Week with Fortune)

update

Joe Williams links to an AFT response:

This might come as a surprise to many readers, but in the 25 years that I negotiated contracts with school districts for affiliates of the American Federation of Teachers, no one ever threw money at me.

Hey!

Me, neither!

Actually, that's not true.

People threw money at Temple and me for ANIMALS IN TRANSLATION.

Unfortunately, they didn't throw pensions and/or health care.

-- CatherineJohnson - 15 Feb 2006

CarnivalOfEducation 15 Feb 2006 - 19:21 CatherineJohnson

54th Carnival of Education

I think I've got most of Smartest Tractor's pdf files attached to this post. She has also been adding material to the User page on teaching writing.

I would kill to have Christopher in Smartest Tractor's class. Ed read her 'in a nutshell' course description last night & felt the same way. I'm hitting my friend Kris with a copy tonight!

In fact, I'm giving Smartest Tractor's work to everyone who'll read.

I'm very eager to hear how Smartest Tractor's students are faring. (I'm also interested in how Smartest Tractor organizes larger tests, such as Chapter Tests & the like...)

One more thing: Smartest Tractor must be working 18 hours a day on her teaching. Has to be.

Carol Gambill method in a nutshell
brainsarefun.com
Brains are fun: examples of good & bad solution keys

formative assessment: Black & Wiliam recommendations
formative assessment: summary of principles

-- CatherineJohnson - 15 Feb 2006

TotallyOffTopic 16 Feb 2006 - 02:01 CatherineJohnson

priceless

-- CatherineJohnson - 16 Feb 2006

AnApproachToReadingThatWorks 16 Feb 2006 - 03:20 CarolynJohnston

Catherine pointed me (pointed us all) to a book, a while ago, called How To Double Your Child's Grades In School, by Eugene Schwartz. I bought it, because I always do what Catherine tells me to do, especially if it's inexpensive (this book costs only \$10.00 new).

I'd love to double my child's grades in school (although I'm not clear on how you would double a B or a C). I'd just as much love to double my own -- that is, I'd like to learn anything I can that will help me be a better reader and learner. Learning is hard for me; I'm curious about a million things, and I can't take them in as fast as I want to, so things end up going by the wayside. This will be true in spades for Ben, if we can't find ways to help him maximize his time spent reading and learning while he's young.

I've tried other books that purport to tell me how to read better -- and in fact most of them say pretty much what this book says. But there's something about this book. It tells you exactly what to do, step by step; you follow the steps, and they work. Or, that is, you get your child to follow the steps, and they work for your child. The whole book is written in that format -- make your child do this and do that, and watch his grades double.

But of course, the parent needs to learn how to do it first if she's going to teach it to her child. Right?

Here's the reading method Schwartz teaches, in a nutshell.

First, pre-read the book, and make mental note of:

• the title
• the index
• the introduction

This will help you understand the main theme of the book as a whole, which in turn will improve your understanding of it.

This seems obvious... but for some reason, when I pick up a book and start reading it, I usually begin at page 1 and start reading -- anything else seems like cheating. Perhaps that's because I began my reading career reading a lot of fiction, like everyone else.

Next step: pre-read the individual chapter, and look for signposts that indicate what the main ideas are.

There are eight signposts of every chapter:

• the chapter title
• the paragraph headings (if any)
• the introductory paragraphs
• the summary paragraphs
• the first sentence of each paragraph
• the figures (if any)
• any marginal titles (if any -- not likely)

If you write these out, you will have an outline of the main ideas of each chapter.

A side comment -- I often find illustrations and figures in textbooks annoying and distracting. This is more true for lower-grade texts than for upper-grade texts and adult nonfiction. So I would give permission to ignore illustrations on the first pass through at least, for what it's worth.

The next trick sounds kind of stupid -- but it's the coolest thing.

turn the chapter's main ideas into questions

Any idea, phrase or sentence can be turned into a question by putting what, when, where, why, or how in front of it.

Take your reading assignment outline, extracted from your chapter signposts, and turn them into questions. The chapter title the background sources of Greek Civilization becomes what are the background sources of Greek Civilization?. A chapter title of The human body: a living machine becomes how is the human body like a living machine?.

You can see immediately what this technique does. It forces your attention on the main points, and prevents your being distracted by minor details.

But his method doesn't stop there. It goes on to tell you how to teach your child (yourself) how to power through the text fast, and retain it. I'll post more on that tomorrow.

my own applied research on this reading method

Years ago, I taught post-calculus probability and statistics, and really loved it. In grad school it seemed too grubby for me; but now it seems cool to me, to use math to quantify the unknowable.

I've been meaning to buckle down for quite a while, and brush up on prob and stat; particularly the statistics side, which I had to race through too quickly when I taught it.

A while ago, someone pointed me to the MIT Open Courseware website. The contents of this site are spotty -- not every professor sees fit to upload his course notes and materials - but there is really a lot of good stuff there. I found a math department course on Statistics for applications. The professor uploaded his notes, which are sketchy -- but they provide a good outline, and even fill in some details here and there.

I want to 'take' that course, and really benefit from and absorb the material as though I were there (yes! at MIT! But without the pressure and definitely without the tuition!).

But simply charging in and starting to read will cause me to get bogged down. I know this; I've been teaching myself things for years, but not as effectively as I could have been. I tried teaching myself Kalman filtering last year, got bogged down in minutiae and confusion, and let myself be distracted by something else that was more important. Same thing with my attempts to teach myself Bayesian decision theory and Bayesian inference and a whole host of other things. I work hard, but in the end it doesn't add up; in the long run I don't benefit from my own work as much as I could.

So I thought I'd try this reading technique -- since if it works, I want to start teaching it to Ben.

It seems lame on the surface to simply go through each chapter, reading the paragraph and section headings, and converting them into questions. But there is something about it; it converts the reading into a much more active, aggressive process.

As it is, we tend to skip over section headings, especially if they are as fascinating as 'the hypergeometric distribution'. But when you convert that heading to 'what is the hypergeometric distribution?', it becomes something else. It becomes a question that you must answer before you move on, one of the questions you must know the answer to if you are going to be able to say you've learned that section.

It gives you permission, too, to skip the things in that section that don't relate to the question -- the history of the distribution's derivation by some statistician, or how it derives from some other distribution through some funny trick. If it doesn't answer the question at hand, you can skip it.

I'm not just using the MIT open courseware notes as a source for answering all my questions -- for one thing, it doesn't have all the answers; they're just notes. I have a whole pile of ten statistics books (cheap, used books) that I can go through to look for the answers to the questions the MIT notes raise. I'm mainly getting the benefit of knowing what Dr. Dmitry Panchenko of the MIT math department thinks constitutes a course in applied statistics; a list of the questions I need to know the answers to, in order to say I've learned the material he covers.

More to come.

-- CarolynJohnston - 16 Feb 2006

ScaryTeachersToBe 17 Feb 2006 - 17:36 CarolynJohnston

Thanks to SusanS for passing on this tidbit from Profgrrrl at Playing School, Irreverently.

Let's hope these ladies don't make the cut.

-- CarolynJohnston - 17 Feb 2006

AnApproachToReadingThatWorksPart2 18 Feb 2006 - 04:29 CarolynJohnston

This is part 2 of a post about Eugene Schwartz' book, How to Double Your Child's Grades in School.

The first part of Schwartz's reading technique teaches you to power through a reading assignment, looking for clues to help you construct an outline of what you will learn from that assignment, in question form. The outline-in-question-form part of his technique is crucial, I think; it makes reading an active sport. You end up tearing through the reading assignment looking for answers to your question, rather than passively reading the book, one sentence after the other. I think the latter approach is absolutely the right one for reading fiction for pleasure -- but not nonfiction. Not homework assignments, technical papers, newspaper articles, or textbooks. Or math books, for that matter.

The second part of Schwartz's method teaches you how to fill in the outline you've created, and how to remember it.

Interestingly, the first thing Schwartz recommends is that you ruthlessly expunge your kid's bad reading habits. Reading with a finger under the words, reading with your lips moving, reading with your head moving -- all are just habits to be broken. The only thing that should be moving is the child's eyes.

And then he suggests that your child start training now to make every reading assignment a search for main ideas, through a "forest of less important details". In short, he recommends teaching skimming-with-a-purpose.

• When you find the answers, highlight or underline them.

This deliberate physical act -- this aggressive underlining or highlighting of the answers in the book as they are read -- is the Golden Rule that makes your child's concentration automatic.

It's interesting to me that Schwartz points out the physical act of highlighting or underlining as being important. I actually take in a lot more in the process of reading when I'm underlining, making notes in the margin -- even if they are as simple as my saying 'yeah' or 'no way'. Of course, this is a problem with textbooks -- I personally prefer highlighter, but you're not supposed to highlight in the school district's textbooks. I wish they'd invent an erasable highlighter; how hard can it be? In the meantime there is always pencil. Or Schwartz recommends that you copy the chapter.

The next step is for the child to 'make the chapter his own', by rewriting it in condensed form, in his own language.

How to take notes

Your child should take a blank sheet of paper -- not in his notebook-to-keep -- and from memory write down each of the main thoughts of the chapter. Your child will forget some, and will get others wrong, and won't clearly understand a lot of the rest of it; that doesn't matter. What matters is that he or she will have taken the first self-test on the material.

He should then go back to the text and correct the outline, adding omissions and corrections right onto his scratch outline, and boiling down the material where appropriate.

He should then put the outline away, go to his permanent notebook, and write an outline again -- again from memory. He is freeing himself, step by step, from the crutch of the textbook.

If there are one or two errors or omissions, he should write them in to the notebook outline. If there are more than that, he should go to a new page in the notebook, and do it again.

When he has the outline of the chapter's reading completed to his satisfaction, he is done for the night. He has the material down cold, and has his notes ready in his notebook if a refresher is needed.

There is a lot in his book, obviously, that I haven't transcribed; tips for improving your child's outlines, for power-reading certain types of text, and for helping your kid hold himself to higher standards by doing a 5-minute "achievement check" when the reading assignment is over.

But all of this is beside the main point, which is to aggressively seek out the main points of a reading assignment, and to play a few tricks on yourself (let's admit it, most of us need to start doing this stuff ourselves before teaching it to our kids) to get yourself reading more aggressively and wasting less time in the act of reading.

I like the notion of actively tearing through the text with a list of specific questions at hand, looking for answers. And the need to underline the answers -- and to form an outline of the answers to your main-thought questions -- fits well with my perception that in order to retain anything I read, I have to somehow write it out; I have to actively get it into my hand through writing. (I've talked about this before with respect to math -- 'practicing to automaticity' means getting the math into your hand, the way that the knowledge of how to ride a bicycle gets into your body).

All of this is an elaborate recommendation that you buy the book. It's terrific. And while it blithely ignores the truth about most of us -- that we may not have the frontal lobe development to learn and apply these reading techniques until we're in our forties -- any one of these tricks that we can successfully teach our kids will benefit them.

Perhaps even just the realization that reading fiction and nonfiction are different will benefit them.

An Approach to reading that really works, part 1

Catherine here — I ran across a product called Highlighting Tape just the other day, on an assistive technology site.

Highlighter tape can be used for temporary marking of books, calendars, word lists, maps, etc. It comes off easily without damaging the paper and can be stored on a sheet of plastic for repeated use. It includes a plastic dispenser and is available an assortment of colours – yellow, green, orange, pink, blue, or purple.

-- CarolynJohnston - 18 Feb 2006

RealityCheck2006 19 Feb 2006 - 04:33 CarolynJohnston

A KtmGuest pointed us to a really interesting article posted at publicagenda.org, Reality Check 2006 Issue #1: Are parents and students ready for more math and science? (thanks, KtmGuest!).

It's worth a read, if only because it will add to your understanding of How Funny People Are.

Nearly everyone agrees that America as a whole needs more emphasis on math and science education -- except when it comes down to their, or their children's, having to take more math and science. Because any one individual you ask is getting plenty of math and science, thank you.

I guess it's a corollary of the Your Congressman Needs Term Limitations, But Mine is Just Fine theorem.

P.S. It looks as though there's a lot more interesting stuff at publicagenda.org.

-- CarolynJohnston - 19 Feb 2006

NewYorkStateMathTestGrade6Part2 19 Feb 2006 - 16:41 CatherineJohnson

update: oops

Ms. Kahl did send home state test prep material (see below). Apparently, Christopher has a PACKET.

Good!

He and his dad are working on the scale drawing right now. (see below) They're having a blast.

fyi, I think scale drawing is a fabulous assignment. Christopher is finally getting some extended practice using a ruler, and of course a scale drawing means fractions, ratios, & proportions.

It's true Christopher couldn't do this assignment on his own. (I'm feeling smug today because my fiercest competitor-mom, aka the 'Homework Nazi,' could not do this assignment. She told Ed, 'I didn't even know where to start.' Hah! I say Hah! because this woman is good. She's blowing me out of the water.)

However, Ed isn't doing this assignment for Christopher. He's helping.

update update

Ed is grumpy.

The scale drawing was fun for the first two hours.

The last two hours weren't fun at all.

"This is vacation."

"I don't see why they're giving this much homework on vacation."

"I have a huge amount of work to do myself; this took 4 hours."

"Christopher doesn't know anything about ratio."

"He doesn't have any conceptual understanding at all."

"He kept looking for formulas to do things."

"He didn't even know where to begin."

"He doesn't have a lot of natural ability in math." [ed.: Any assignment that ends with the parent deciding his child doesn't have any natural ability in math is the wrong assignment a far as I'm concerned]

"She has no idea how to structure an assignment." [ed.: ditto]

Over dinner Ed was pondering the 'packet,' which turns out to be a special Glencoe-produced 58-page booklet called "Mastering the Intermediate Level Mathematics Test: Diagnose — Prescribe — Practice Workbook."

Fifty-eight pages of items aligned to the New York state test, with no answers or solutions.

Apparently our job over 'break' is to Diagnose — Prescribe — Practice and also create our own answer key.

Well, thank God I've got Smartest Tractor lighting the way (pdf file).

back again

I've been off doing Career Stuff that's actually been quasi-fun.

I say quasi because my particular career seems to involve heaping loads of crapola* (not a nice word on Sunday!), not to mention the occasional bolt from the blue.

The other day I called my agent and, when her assistant answered the telephone, said, 'Hi, this is Catherine.'

The assistant said, 'Who?'

That's the crapola aspect; I'll spare you & me both an extended account of the bolt from the blue part (though poor Caroline is slated to get an earful today....)

Anyway, I've been off because I was doing Career Stuff that was actually a blast.

This involved going into the city to meet with our kids' psychiatrist, Eric Hollander (that was the fun part), after which I decided to surprise Ed in his lair. (What is that woman in white doing in the picture?)

It had to be a surprise, because I didn't have my cel phone with me. I didn't have my cel phone with me, because I forgot my cel phone.

I need WAY more exercise.

So I decided to drop in unannounced.

Naturally that didn't work out; Ed wasn't there, and when he finally did get there he had five minutes to get to a faculty meeting.

So there was nothing left to do but visit the NYU bookstore and look at every single education title on both floors.

Nothing by Diane Ravitch, that's for sure.

It was all constructivism all the time. Every last textbook.

That and feel-good books about heroic white teachers teaching poor black children — books like Small Victories: The Real World of a Teacher, Her Students, and Their High School. (I'm thinking a 'small' victory probably doesn't include teaching kids enough algebra to graduate from high school, but I don't know.) There were many of these books.

Until that visit, I hadn't realized that heroic white teacher saving poor black children must be an important fantasy element in ed schools today. I say fantasy element, because I'm pretty sure all of the teachers in all of the books were white, while all of the kids were black. Certainly Jaime Escalante was nowhere to be seen. (Of course, neither was Rafe Esquith, and I don't expect to see Our School turn up on the assigned reading lists any time soon, either.)

Perusing the offerings, you wouldn't know teachers teach math. Everything was about 'literacy' and 'authentic assessments' of literacy and the like. Which is probably just as well, considering.

There was one book that stuck out like a sore thumb: Techniques for Managing Verbally and Physically Aggressive Students. I think that was the title. This book was so unadorned by photos of Beaming White Teachers surrounded by Adoring Black Children that it was refreshing.

Leafing through the pages I found instructions on what a teacher should do when he is being strangled by a student.

The 2 or 3 books that did address math were constructivist all the way. Liping Ma was absent; John Van de Walle's now-classic hundred-dollar tome Elementary and Middle School Mathematics: Teaching Developmentally, Fifth Edition was present in abundance.

The funny thing was, the store management had stocked a bunch of food business textbooks just across the aisle from the ed books. There was a book on restaurant math — I think it was Math Principles for Food Service — that was pure direct instruction. No photos of smiling white teachers surrounded by black students yearning to succeed in food services, just stuff you need to know. Chapters on 'weights and measures,' 'portion control,' 'converting and yielding recipes,' 'production and baking formulas,' and 'using the metric system of measure.' If you're going to make it in food service, you're going to need some math. Seeing as how the first chapters cover addition, subtraction, multiplication, and division, apparently you're not going to learn any of this math in grade school.

Part 1 is titled: Using the Calculator.

upstairs, downstairs

So those were the texbooks, which are housed downstairs in the basement.

Upstairs, in the 'commercial' section, I found:

AND

A clean sweep.

New York state tests coming right up

In March.

Christopher's class took a sample test (pdf file) this week; only 2 kids scored a 4. Christopher thinks he got a 3. Apparently the teacher told them that any kids scoring a 1 or 2 would be moved down to Phase 2-3.

This is the Highly Accelerated, Algebra-in-the-6th-grade, Death March to Algebra-in-the-Eighth Grade Phase 4 extravaganza I've been banging on about. Only two of 19 children can score a 4 on the sample test and apparently there are enough kids in danger of scoring 1s and 2s that the teacher is talking about it in class.

So here's the scoop.

Christopher is studying algebra in the 6th grade, but he can't do percent. I pulled the Sample Test, which turned out to be the test Christopher's class took this week, and asked him about problem number 26:

On Friday and Saturday, there were a total of 200 cars in the parking lot of a movie theater. On Friday, 120 cars were in the parking lot.

Part A

What percent of the total number of cars were in the parking lot on Friday?

Part B

What percent of the total number of cars were in the parking lot on Saturday?

Christopher has no idea how to do this problem, in spite of the fact that he's just 'finished' the chapter on ratio, proportion, and percent in Prentice-Hall. (Says he 'froze up' on the test; expecting another D; etc.)

my vacation and welcome to it

We are on mid-winter vacation this week.

For my vacation, I will be teaching Christopher how to do percent.

I know how I'm going to do it. I'm going to use the Singapore-Saxon bar models and the Saxon-Dolciani percent charts.

I think I'm starting to get a feel for teaching-to-crammery, which is the skill middle school parents need most. If I've got 5 days to teach percent word problems to proto-mastery, I'm going to need bar models & charts (& possibly Saxon's brilliant starter WP variables to boot).

If that were all I had to do this week, I'd be cool.

It's not.

I'm also going to have to figure out what's on the freaking test.

I read some guy last week complaining that Most Parents don't have the Sense of Responsibility it takes to find out what the state standards are.

Sure, sure; we all know about those Parents who don't have a Sense of Responsibility as defined by the people who write state standards.

How many parents fall in this category?

I'd estimate, conservatively, that perhaps 99% of all parents have zero interest in what the State Standards are.

The reason 99% of all parents have zero interest in what the State Standards are is that their Bayesian priors are telling them the State Standards are likely to be:

a) impossible to find

b) bunk

Given my household's limited common sense-y, my own attitude can be characterized as: 'Damn the Bayesian priors, I want those standards!'

Thus, I have now attempted to a) locate and b) comprehend my state standards.

Which means I am now qualified to tell you that all those irresponsible parents are correct. Spending your Sunday morning tracking down New York state standards (pdf file) is what Carolyn calls a FWOT.

See?

a visit to the mathematical reasoning strand!

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

Students:

• apply a variety of reasoning strategies.
• make and evaluate conjectures and arguments using appropriate language.
• make conclusions based on inductive reasoning.
• justify conclusions involving simple and compound (i.e., and/or) statements.

This is evident, for example, when students:

• use trial and error and work backwards to solve a problem.
• identify patterns in a number sequence.
• are asked to find numbers that satisfy two conditions, such as
n > -4 and
n < 6.

That certainly clarifies things.

source:
New York state standards

the return of common sense-y

So forget about the New York state standards. If I need standards — and I do — I'll use California's.

My job now is to go through every page of the Sample New York state test, pull out the problem genres, and teach them to crammery.

I have one week to do this.

We're going to have to pedal, because we also have to help Christopher with the massive scale drawing exercise Ms. Kahl has sent home for the kids to do over vacation:

This project requires you to be creative and draw up the floor plans of your ideal bedroom. Will you have a big screen television, a walk in closet, or even a king sized bed? You will map out the blueprint for your room and show the furniture and items contained in our room from an aerial view in the form of a scaled blueprint.

The blueprints must contain at least two of each of the following geometrical figures:

• square

• rectangle

• triangle

• trapezoid

• paralleleogram

• circle

Oookaaaayyy!

Two trapezoids coming right up!

And two parallelograms!

In a 6th grader's dream bedroom!

Making those real world connections!

my vacation and welcome to it, part 2

Getting Things Done:

• analyze sample state test

• find out if Christopher can do any of the problems on it

• teach to crammery

• re-vamp book proposal, deal with inevitable assorted mishegoss sp?

• help Christopher construct highly complex scale drawing he can't possibly do on his own

question

You are teaching accelerated 6th grade math.

You give your class of 19 students a sample New York state standards test.

Only two children score a 4, 'exceeds state standards.'

Many of the children, who have just taken a test on ratio, proportions and percent, miss the percent question.

For mid-winter vacation you assign:

• daily 20-item problem sets of percent, ratio, and proportion problems ranging from simple calculations to word problem applications

or

• a complicated scale drawing requiring two trapezoids and two parallelograms

Alright. It's 2:28, and I must go for my 45-minute aerobic walk-run. If I do this 6 days a week until I'm dead I'll be younger next year and, even better, I'll stop screaming at my kids.

So I'm going to do it.

Because I am a responsible parent!

When I get back I'll analyze the test. Then I'll break the news to Christopher that we're going to spend mid-winter break cramming math.

Farewell, Ms. Kahl! We who are about to die salute you!

update, update, update: Verghis speaks!

For the blueprint, why not have a square study desk whose top is decorated with (a) 2 trapezoids, (b) 2 parallellograms, (c)....

This should (1) satisfy Ms. Kahl's requirements and (b) blend nicely with the surrealism that pervades the math curriculum.

Don't you think?

Yes! I do think!

* heaping loads of cr***** probably doesn't distinguish my job from most other people's jobs, I realize

pre-algebra is bunk
death march to algebra
NYU ed textbooks; NY math test
state test impending doom

teachtocrammery

-- CatherineJohnson - 19 Feb 2006

AdviceFromATopHighSchoolStudent 19 Feb 2006 - 21:17 CatherineJohnson

Ed struck gold today.

He's interviewing students from Westchester County who are applying to Princeton.

Today he interviewed two amazing students, both of whom are headed for math-related careers.

Both students have Math Brain parents, and both are Chinese-heritage immigrants, which I think is OK to say, given articles like this one. (\$) They went to school abroad during their early years.

One of them gave Ed an amazing piece of advice.

He said his dad had complained all the way throughout his school years here in the U.S. that math was not being taught conceptually.

He countered this by having his son derive every formula he used.

The boy said this had helped tremendously, that he now has a great deal of conceptual understanding of math. (He's in BC calculus.)

I think that's brilliant.

My challenge, now, is figuring out how to teach math in the tiny pockets of time we have that aren't devoted to school.

Grade school was easy. I taught my own separate curriculum. Saxon Math: every lesson, every problem in every problem set.

We had the time, and we did it.

There's no time now. Christopher goes to school all day, then has homework to do at night, and his brain is consumed by thoughts of girls and lunchroom rivalries with his friends and he's rebellious, resistant, and emotional. (Apparently, middle school means mood swings, something I didn't know going in.)

Carolyn and I started writing this blooki nearly a year ago saying reactive teaching was a bad thing.

Now I have to figure out how to do reactive teaching that works.

This may be the way to go.

update: an example from Saxon

I'm not certain I know, but I think I can give an example from pre-algebra.

Saxon 8/7 teaches the 'formula' for finding the area of a trapezoid thusly:

To me — and let me know if I'm wrong — that's 'deriving a formula,' or close to. The student has to know that a trapezoid can be divided into two triangles, and that you can add the areas of the two triangles together to get the area of the trapezoid.

In contrast, Prentice-Hall teaches the formula this way:

To us this is the same thing, but to an 11-year old just starting out it's not.

Saxon gives kids a lot of practice with the un-simplified version before anyone moves on to the standard, simplified expression.

advice from a top high school student
rote knowledge in Everyday Math

-- CatherineJohnson - 19 Feb 2006

RoteKnowledgeInEverydayMath 20 Feb 2006 - 18:16 CatherineJohnson

Great comments on the advice from a top high school student thread. (This was the student whose father countered his son's rote learning of math by having him derive every formula he used.)

from Steve:

Perhaps you don't have to derive everything, but you do have to be able to understand and explain why you can do something using basic definitions and rules. And don't forget mastery. There is linkage.

The biggest fallacy of the latest fad math is that it teaches conceptual understanding. It does no such thing. My son is taking 4th grade Everyday Math, which is supposed to be one of the better fad math curricula. One of its rapid spiral "Home Link" assignments lately was a "Fraction of" sheet with problems like:

4/5 of 25 is _

This is before they know anything about multiplying fractions. How does the teacher explain how to do this problem? You take the whole number (25), divide it by the number on the bottom of the fraction (5) (notice that it is evenly divisible), and then multiply it by the number on top of the fraction. All rote understanding. Perhaps the students have to try and get a Zen-like understanding of four-fifths of 25. But then what do they do with a problem like:

4/5 of 7/8 ?

or

4/5 of 2.3 ?

Another Home Link spiral sheet talked about something like "Part of One" ?!? which is supposed to be the opposite of the example above:

20 is 4/5 of _

Once again, my son was taught a rote procedure for solving this problem.

I am getting really sick of this modern math conceptual understanding rubbish. Can anyone give an example of teaching real mathematical understanding in MathLand, TERC, Everyday Math, CMP, or their cronies? The so-called problem with traditional math was that it was all about drill and kill and no understanding. Well, nowadays, modern fad math does neither.

One of our school committee members told me that her younger daughter (in 6th grade, I think) doesn't have the math skills that her older brothers had at her age, but she has better conceptual understanding because of MathLand and CMP. I honestly don't have a clue what that means.

from Susan:

Exactly. Problems like these show up in Saxon in the form of word problems with the aim being to "see" the numerator and denominator in the form of a bar model, or to practice and clarify unerstanding the role of the numerator (3/8's of the girls had blonde hair, what fraction of the girls did not have blonde hair.) There are several problems like that, but I there is no rote procedure to solve them except in drawing out the vertical bar model to see the segments.

The Saxon version seems to be shooting for conceptual understanding without anyone locking in the procedure of dividing by the denominator, then multiplying by the numerator as the most efficient way of doing it.

Multiplying fractions as a procedure comes quite a bit later. While using the word "of" in previous chapters as another word for "times," this chapter is where they first bring it to learn and practice in a straightforward, rote way. The timing, I think, makes a big difference and is probably less confusing. My son has learned all of this with no bumps in understanding. One piece just fits into the next.

Cancelling is not mentioned at this point. Reducing, at this point, only happens in the answer. I'm dying to just teach this to him, but I'm sure I'd be piling on too much, too soon, and I've learned my lessons the hard way about doing that. A couple of chapters later is the GCF chapter, so I know that's why that next step is postponed a bit.

It's just hard to be an adult and go backwards. I want to show him the easy way when he needs to soak in the new stuff a little at a time.

aside from Catherine:

I am ONE with Susan on this point.

I've mentioned that I worked every single problem in Primary Mathematics Challenging Word Problems Book 3, and that I'm doing every problem in Saxon 8/7 as well.

That's a lot of bar models.

As a direct result, my brain has changed. When I read a fraction problem, bar models pop into my mind's eye unbidden.

I imagine some of you will feel skeptical about this, but for me that's a good thing.

Also, Steve's question — But then what do they do with a problem like: 4/5 of 7/8 ? or 4/5 of 2.3? — has an answer. In Singapore & Saxon the sequence of fraction problems is such that you 'see' that you need a common denominator — that is, you need a bar model divided into 40 segments.

I can't remember whether either Saxon or Singapore asks students to draw bar models of a problem like 4/5 x 7/8 — judging by the fraction problems I just did in KUMON Level F, for god's sake, Singapore may.

Saxon would, I think, use bar models to have kids do a problem like 2/3 x 3/5.

You see from what you've drawn that 2/3 'of' 3/5 is 6/15 which equals 2/5.

The funny thing is that, because I'd learned the multiplication operation with zero conceptual understanding attached (zero conceptual understanding of how the algorithm worked, I mean) I spent quite a long time being befuddled by the computation itself.

I just couldn't 'get' why you multiply the numerators and the denominators. You guys all tried to teach me & I still didn't get it! (I should rustle up those posts. Rudbeckia sent me a wonderful explanation; Dan created a graphic that everyone loved & I was the only person who didn't understand - - - )

Finally, the idea that 'clicked' for me came to me in the car.

This will sound incredibly unschooled & dumb....but tant pis. (French for t**** s***.)

I'd always sort of 'gotten' the idea that you multiply the numerators for the same reason you always multiply; you're finding '2 of 3' or '2 sets of 3' which is six.

But I couldn't put that together with why you multiplied the denominators.

Finally I realized that the denominators are divisors. 2/3 of 3/5 means you are successively dividing 3/5 by 3; you're doing two divisions in a row.

Two divisions in a row means you're dividing by 2 x the factor. (If you divide 12 by 2 and then divide the quotient by 2 again, you're dividing 12 by 2 x 2.)

I don't think this works as a verbal explanation for somebody still trying to figure this out, but it probably makes sense to all of you.

I have NO idea why I was so stumped by this.

I'm guessing I spent too many years overlearning the algorithm without the faintest idea why the algorithm worked. But I don't know.

conceptual understanding without skills

I think I do know what conceptual understanding without skills may be.

I think it would be quite possible to gain conceptual understanding of fraction multiplication — including conceptual understanding of problems like 4/5 x 7/8 — without acquiring procedural fluency in the multiplication algorithm.

It might even be possible to gain conceptual understanding of fraction multiplication with very limited understanding of factors.

I think it's the same observation Ken made a little while ago, after giving his son a Rubik's cube for Christmas.

It's possible to understand the directions for how to solve a Rubik's cube.

Actually solving the Rubik's cube is a different story.

from Kathy:

The biggest fallacy of the latest fad math is that it teaches conceptual understanding. It does no such thing.

Good-I was looking for an excuse to post my latest rant. My daughter is also in 4th grade Everyday Math. Tomorrow is her Unit 6 test, which covers long division, coordinate grids, something called "turns", map coordinates, angle measuring and drawing with a protractor, and word problems where you have to interpret a remainder. And all these topics relate to each other in what way??? With Meg's issues, all this jumping around is very confusing. She has figured out long division, thanks to much practice and tons of supplementation, but all this other stuff is causing much confusion.

Just for "fun" I was able to find the 4th and 5th grade Math texts I used back in the mid-70's and started to do a quick comparison to Everyday Math.

The thing that jumps out immediately is the sheer number of practice problems from my old books. For example, there are over 300 long division problems in the 4th grade 1970's text, just in the division chapter. They return to previously taught concepts in "Keeping Fit" sections which appear at least twice in every chapter.

How many practice division problems in EM's division unit? 20.

Measuring angles with a protractor wasn't introduced until 5th grade, and there's just 1 lesson on it, logically in the Geometry chapter. And decimals didn't appear until the very end of the 5th grade book; in EM they appear in 3rd grade, often through the introduction of problems which the kids are never taught to do.

from Carolyn:

Oh, Kathy, you're bringing it all back to me. 4th grade Everyday Math was the absolute worst, perhaps mostly because it was new and horrible to me, but also because 4th grade is a year when you have to learn and master so many critical things -- fractions, long division, multidigit multiplication. And there is all the jumping around in topics, and never never enough practice, and topics introduced in advance of their being taught.

I have to go lie down now.

a fraction problem from Intensive Practice 3B

Ms. Martinez ordered a pizza. The boys ate 2/5 of the pizza while the girls ate 1/2 of it. One of the boys, Mike, said that all of them ate 3/7 of the whole pizza. Was Mike correct?

3B is second semester, third grade; this problem comes from the 'Take the Challenge' section, so it's considered difficult.

Unfortunately, I sold my copy of 3B, so I can't look to see how kids are taught to solve such problems.

I'd put money on it they draw bar models along with using the addition algorithm, however.

advice from a top high school student
rote knowledge in Everyday Math

-- CatherineJohnson - 20 Feb 2006

TheLowGirlTrack 20 Feb 2006 - 21:15 CatherineJohnson

Ed told me this story.

Someone's been putting together an anthology of personal essays by French historians writing about what drew them to the study of France.

One historian talked about having spent a year in France when he was in high school, IIRC.

He was one of the top students in his school, but when he got to France he was placed in the 'low girl track' in mathematics.

"Low girl" meant that not only was this the math track for students who wouldn't be taking any math at all in college, but this was the lower-low.....this was the math class girls took! (Girls and boys weren't tracked separately; this was a process of self-selection.)

Until that moment, this fellow hadn't seen himself as being either low or slow in math.

-- CatherineJohnson - 20 Feb 2006

WhyDontSchoolsTeachDimensionalAnalysis 20 Feb 2006 - 21:44 CatherineJohnson

Does anyone know?

Can't remember if I've mentioned that last summer Ed and I spent some time with his cousin, who began life as a Ph.D. researcher in chemistry and is now a chemistry teacher at Evanston High School.

About five seconds after we'd started talking he told me the Big Problem with his students was that — ALL TOGETHER NOW — THEY CAN'T DO FRACTIONS.

He also said, more specifically, that they don't understand ratio and proportion.

His solution is to teach them unit multipliers.

Which brings me to my question: why don't middle school textbooks teach dimensional analysis?

If unit multipliers are so easy that a chemistry teacher can teach them to incoming students and still have enough time left over to teach chemistry, that's a strong recommendation.

I just taught Christopher unit multipliers (Lesson 50 in Saxon 8/7) for the second time. He's obviously forgotten our first go-round, which is to be expected.

I taught them again today, because he had just missed this question on his GLENCOE MATHEMATICS Grade 6 Mastering the Intermediate Level Mathematics: Test Diagnose - Prescribe - Practice Workbook:

Esther was traveling down the highway at the rate of 75 miles per hour. How far would she travel in 3 hours?

Christopher showed his work.

He divided 75 by 3 and got an answer of 25.

This is one of the consequences of never, ever assigning word problems....the kids fail to develop the habit of asking themselves whether the answer they just got makes a lick of sense.

Still, even if he had spent some time this year developing good habits, questions like these are confusing for kids.

I've always been able to figure questions like this easily, but I've discovered that there are certain questions that confuse me....like Christopher, I can't tell which number I'm supposed to be dividing into which. I wish I could remember the problems (the next time I see one, I'll write it down). In any case, I'm sympathetic.

So I pulled out Lesson 50.

Christopher was ticked off. He'd already done his KUMON pages, one page of Megawords, corrections to his other pages in Megawords, and two pages in the Glencoe test practice book. He was in no mood to do a 'lengthy' Saxon lesson on unit multipliers.

I told him I'd truncate the lesson.

Then I asked him if he knew what 'truncate' means. (No.)

unit multipliers, short and sweet

I can really see the Big Deal with choral response.

It's way faster, and it does tend to 'pull' a resistant kid's attention, or at least it did today, with Christopher.

1

I started by reminding him that any number other than zero, divided by itself, equals 1:

Me: What is 2 divided by 2?

Chris: 1

Me: What is 3 divided by 3?

Chris: 1

Me: What is 1,000,231 divided by 1,000,231?

Chris 1

2

Then I reminded him that anything multiplied by 1 remains the same number.

More choral response:

Me: What is 2/3 times 3/3?

Chris: 2/3

Me: What is 1/6 times 5/5?

Chris: 1/6

Me: What is 100 times 100/100?

Chris: 100.

3

Next up: 12" divided by 1' is also 1.

He was kind of taken with that idea (and I bet he had a glimmer of memory that he'd seen this before....) In any case, he instantly got the idea that 1 foot divided by 12 inches is 1.

I wrote all of these down on paper, so he could see them while he was giving his answer.

Me: What is 12" divided by 1'?

Chris: 1

Me: What is 36" divided by 3'?

Chris: 1

Me: What is 24" divided by 2'?

Chris: 1

Me: What is 1.5' divided by 18"?

Chris: 1.

4

Then we came to the idea that you can divide the unit by the unit, without dividing the number of units.

Naturally this led to the question of whether you could divide body parts by body parts, especially super-private body parts.

I said, yes you could, just so long as you were using those body parts as a unit of measurement.

Hysterical laughing, etc.

Then I pointed out that:

a) multiplying a number by 3'/1 yard is the same thing as multipying a number by 3/3

and

b) 3'/1 yd is the same value as 1 yd/3'

At this point I had him tell me 'reverse unit multipliers,' as Saxon does.

Me: How do you write a unit multiplier for feet and yards?

Chris: 3'/1 yd

Me: And?

Chris: 1 yd/3'

Me: How to you write a unit multiplier for feet and inches?

Chris: 1'/12"

Me: And?

Chris: 12"/1'

and so on

5

At this point the lesson became purely procedural, but that's the best I can do under the circumstances. I'll try to fill in conceptual understanding.....at some point.

The beauty of unit multipliers for a student just learning unit conversions is that you never have to think about Do I need to multiply or divide?, which is where Christopher went wrong on the practice test question.

With unit multipliers you're always multiplying; it's just that some kinds of multiplication, i.e. multiplication by a fraction, are actually division.

This was the final 'script':

I started with 'Twelve inches equals how many feet?''

[ed.: oops, I left out a step. I also had him tell me, several times, where you would put the units so as to cancel out the 'unwanted' unit - in the numerator or the denominator? He got every one right.]

tomorrow & the next day

I don't think he'll be able to set up a unit multiplier and do a unit conversion start to finish tomorrow, though I'll check to see if he can, just out of curiosity.

We'll use this same script (or a new, improved version — whatever occurs to me on the spot) and we'll do maybe 5 problems tomorrow, including the problem he missed on the practice test.

I'll stress tomorrow that using unit multipliers protects you against choosing the wrong operation.

I didn't stress that today, and I should have.

I'm also going to show him how to use two unit multipliers in a row, and how to use unit multipliers to find out how many square inches there are in one square foot.

I don't know whether I'll have him practice those two uses tomorrow, but I want him to see them because he'll realize how much easier his life is going to be once he's mastered unit multipliers.

update

I'll show Christopher this problem from Math Forum:

I'm also going to tell him Caroline's line about the guy who realized that a fraction is a division problem you don't have to do.

update: Google Master reminded me of this example of a dimensional analysis from Elements of Physics, edited by Alpheus W. Smith and John N. Cooper, McGraw-Hill 1979. ISBN 0070586349.

a section of Donna Young's lesson

This is cool: note: you may have to go to her homepage & search for the lesson on unit multipliers)

udpate: article on unit conversions

Haven't read a word of this, but thought I'd post it: Unit Conversions by Ben Logan (pdf file)

Abstract

Conversion between different units of measurement is one of the first concepts covered at the start of a course in chemistry or physics. Unfortunately, unit conversions are also one of the most confusing concepts to many students. Because unit conversions are used throughout the sciences, it is crucial to understand them from the start. Hopefully, I can help clear up some of the confusion surrounding this topic. Please email me with questions, comments, or corrections.

dimensional dominoes - announcing Dan's dimensional dominoes
Dan K's "dimensional dominoes" (PowerPoint worksheets)
dimensional analysis at Math Forum (includes other links at Math Forum)
Dr. Ian talks about fractions & units
dimensional analysis from Elements of Physics, edited by Alpheus W. Smith and John N. Cooper, McGraw-Hill 1979. ISBN 0070586349
Donna Young's online lesson in unit multipliers (you may need to start at her homepage and search)
a way to teach dimensional analysis
why & how to use dimensional analysis
rough script for teaching dimensional analysis
another triumph for dimensional analysis
dimensional dominoes emergency
report from the unit conversion wars

-- CatherineJohnson - 20 Feb 2006
RaysArithmetic 21 Feb 2006 - 14:02 CatherineJohnson

I've just discovered a series of arithmetic textbooks from the 1800s while cruising geometry workbooks at christianbooks.com. (fyi, Charles put me on to christianbooks, which has the apparently-out-of-print Saxon Physics for a good price. I'm still mulling that one.)

According to the publisher, Ray's Arithmetic was the most popular arithmetic series in the 1800s, selling more than 120,000,000 copies.

Does anyone know anything about these books? Have you used them? Seen them? Read them?

The books have glowing reviews at Amazon. My ADD TO BOOKBAG finger is starting to twitch.

The 8-volume set is \$100, but you can buy individual titles as well.

Christianbooks has posted 14 pages of Ray's New Practical Arithmetic online.

titles
Ray's New Primary Arithmetic
Ray's New Intellectual Arithmetic
Ray's New Practical Arithmetic
Key to Ray's New Arithmetics (Primary, Intellectual)
Ray's New Test Examples in Arithmetic
Ray's New Higher Arithmetic
Key to Ray's New Higher Arithmetic
Ray's New Arithmetics-Parent Teacher Guide

uh-oh

I'm going to get myself in serious trouble.

Fortunately, the listing appears to be closed.

I've sent an email to the seller just to make sure.

sources:
Amazon
Biblical Worldview Learning Center
Farm Country General Store
Homeschoolingbooks.com
Mott Media

-- CatherineJohnson - 21 Feb 2006

TodayInTheTimes 21 Feb 2006 - 20:32 CatherineJohnson

The New York Times has identified a Whole New Problem: college students who send inappropriate email to their professors.

Jim Wilson/The New York Times

Jennifer Schultens [associate professor of mathematics at UC Davis]

Monica Almeida/The New York Times

Meg Worley, an assistant professor of English at Pomona College,
has rules for student e-mail...."One of the rules that I teach my students is,
the less powerful person always has to write back," Professor Worley said.

Various hypotheses are offered for the advent of this phenomenon, including this observation, from a professor of education:

Christopher J. Dede, a professor at the Harvard Graduate School of Education who has studied technology in education, said these e-mail messages showed how students no longer deferred to their professors, perhaps because they realized that professors' expertise could rapidly become outdated.

"The deference was probably driven more by the notion that professors were infallible sources of deep knowledge," Professor Dede said, and that notion has weakened.

I'm sure that's it.

-- CatherineJohnson - 21 Feb 2006
AsiansInGreatNeck 21 Feb 2006 - 20:50 CatherineJohnson

The TIMES was chock-full of interesting items pertaining to education today.

College students sending inappropriate email to their professors, and Asians in Great Neck.

GREAT NECK, N.Y. — In the annals of American newcomers, there must be relatively few immigrants like the Shins. They are an affluent couple in their 40's with two teenage children. They were well established in their careers in Seoul. And then, last July, Maria Shin came to the United States for her first visit, carrying a pocket translator, a laptop and a map on which she had marked out the best American schools with sizable Asian populations.

She visited Scarsdale. "A little bit too much," she said, meaning it was a little too expensive.

She visited the suburbs of Los Angeles. "Too much fun," she said, referring to what she perceived as California goofiness.

Then she came to this community on the North Shore of Long Then she came to this community on the North Shore of Long Island, where houses cost \$1 million and the schools are known for producing Ivy League-bound graduates.

"Great Neck is where we chose," she said in halting English, which she works to improve in conversation classes two or three times a week at the Adult Education Center here. "Here are many Asians. And here my children have more ... more ... chance to live normal."

The chance to live normal is a relative value and might mean many different things to different people. But among a growing group of monied Chinese and South Korean newcomers arriving in this community of 40,000 in Nassau County, there is a strong feeling of what it means: the chance to spare their children the grinding competition and unrelieved pressure of scholastic life in their homelands.

[snip]

"Too much pressure, the children," said Fu Hong, 34, whose 5-year-old son was born in Shanghai just before she and her husband, a manufacturer's representative with interests in several factories, moved to a house in Great Neck. Their daughter was born here in 2002. "A lot of pressure. Here, he has fun. Skate. Swim. Aikido."

Just wait 'til these folks find out that in Great Neck skating, swimming, and aikido are not fun.

In Great Neck skating, swimming, and aikido are mandatory activities for entrance into Ivy League universities.

slave parents in Singapore

-- CatherineJohnson - 21 Feb 2006

RichardCohenAgainstAlgebra 21 Feb 2006 - 20:59 CatherineJohnson

In case you've missed it, here's the link to Richard Cohen's column on algebra.

If I had the energy (and the attention span) I'd go back through Cohen's archive and dig out the columns where he tosses statistics around like that's something a person who can't do percents ought to be doing in a major newspaper.

Richard Cohen has almost certainly drawn the wrong conclusion from his life to date.

Cohen thinks the fact that he's a well-known columnist for the Washington Post proves you don't need algebra to succeed.

What it actually proves, if anything, is: this guy got away with murder.

Along those lines, probably the best response is from Matthew Yglesias. A number of the comments there are good, too.

Eduwonk points out that Cohen's column appeared at almost the exact moment the new Toolbox report came out. I've begun reading this second Toolbox report. It's fascinating.

The Toolbox studies — these are longitudinal studies following the same group of kids for many years — look at the question of what it takes for a student to attain a college degree.

One answer: you better know your algebra. Otherwise you're sunk. The odds of a high school student making it through 4 years of college and getting his degree plummet if he or she doesn't succeed in Algebra 1 & 2:

The highest level of mathematics reached in high school continues to be a key marker in precollegiate momentum, with the tipping point of momentum toward a bachelor's degree now firmly above Algebra 2. But in order for that momentum to pay off, earning credits in truly college-level mathematics on the postsecondary side is de rigeur.

[snip]

By the end of the second calendar year of enrollment, the gap in credit generation in college-level mathematics between those who eventually earned bachelor's degrees and those who didn't is 71 to 38 percent (table 21). In a previous study, the author found the same magnitude of disparity among community college students in relation to earning a terminal associate degree (Adelman 2005a). The math gap is something we definitely have to fix.

I haven't read the whole report, but from what I gather so many fields now require so much math that not having learned algebra in high school is a significant handicap.

The Toolbox Revisited: Paths to Degree Completion from High School Through College

update from Rudbeckia

At my institution, students majoring in journalism don't need to take math that is much above algebra. However, students majoring in advertising and public relations need to take calculus -- as a prereq for calculus-based statistics.

This jogs my memory. I'd been planning to post an excerpt from a Hugh Hewitt article on journalism — I'll go track it down now.

[pause]

Here it is: The Media's Ancien Regime (\$)

Hewitt's subject is Nicholas Lemann's plans to re-vamp the Columbia J school. (personal narrative: we had dinner with Nick Lemann and his wife about a year ago. He was fantastic. For my money, he's exactly the person you want running the J school or anything else having to do with major journalism.)

[Lemann created] a year-long Masters of Arts program open only to practicing journalists, aiming to enhance and deepen their skills....

My ['my' meaning Hewitt's] second classroom experience is in an M.A. class, "Evidence and Inference," which includes all 27 students. It is the meta-class for the new track, and is co-taught by Lemann and associate dean Evan Cornog, as well as a series of academic and media guest-lecturers. Today marks the third in three lectures by the former director of the U.S. Census Bureau, Columbia's Carnegie Professor of Public Affairs Kenneth Prewitt, on the use of race as a classifying device. Prewitt's lecture is a fascinating look at the introduction of racial categories into the census and the evolution of those categories, as well as the limits of the utility of that data. An interesting and provocative 90 minutes later, though, I am left wondering how much the Prewitt lecture will do for these students unless they are fortuitously assigned some future story on the census or a related topic having to do with, say, racial classifications in university admissions. [ed.: hmm....to me, this observation reads a shade Richard Cohenish...]

Lemann's hope for this course is to cultivate in his students a capacity to discover and analyze data. He repeatedly uses the term "power skills," and he has in mind a deeper appreciation, and use, of more sophisticated research and analytical skills than most journalists bring to the table. "Regression analysis is the best example," he tells me. " Every social science study in the United States depends upon regression analysis, but almost no reporters understand it. You can't read and understand these studies if you don't know how regression analysis works. I taught myself how to do it, and we are going to teach the M.A. students, equipping them to go beyond their ordinary reliance on dueling experts interpreting studies."

That, in a nutshell, is Lemann's grand plan for salvaging the profession: Teaching reporters new skills that will make them more competent amateurs in the worlds of other professionals.

Brilliant.

I've been a science writer for years. But I can't do regression analysis myself; nor can I evaluate regression analysis in a report. The huge, gaping hole in my skill as a writer is the field of statistics.

When you spend a lot of years writing nonfiction, you learn to cess out and interpret fields you don't know much about — and to do it quickly. It wasn't until recently that I realized I have such a skill, and that other people don't. I thought everyone could read a couple of books or articles and 'get the hang of' a field or a debate; I thought that's what reading was.

It's not!

I've told this story before, but I'll repeat it in this post, because it's relevant.

A couple of years ago I was bugging my sister about some diet book, telling her she had to read it.

She was resisting, and I was pushing, and finally she said, 'I don't want to read the book. I want you to read the book and tell me what's in it.'

I thought she was being lazy.

Then I realized what she meant was that I would read the book and come up with some angle on what it had to say; she wanted to run the book through my brain. (That's what my editor at Scribner's says. 'I want to run it through your brain.')

So that's what I do for a living. I run other people's work through my brain.

But I can't run other people's statistics through my brain.

That has to change.

If Nicholas Lemann leads the way, and I hope he does, it will change for writers getting their educations today.

-- CatherineJohnson - 21 Feb 2006

DimensionalAnalysisTestimonials 22 Feb 2006 - 04:52 CarolynJohnston

A frequent KTM visitor wrote to direct me to this website , which contains important information about how the failure to learn dimensional analysis can negatively impact your life.

Just listen to this; the pathos is heart-rending:

"I was a Wilton High School student who dozed off while Mr. Laptick taught us dimensional analysis in physical science. I never quite got the hang of it. It irritated me... all of those fractions. I never really liked fractions. Although my grades had been pretty high, I got a D in physical science and subsequently dropped out of chemistry in the first quarter of my junior year. It was not long before I started on drugs, and then crime to support my drug habit. I have recently learned dimensional analysis and realize how simply it could have solved all of my problems. Alas, it is too late. I won't get out of prison until 2008 and even then, my self image is permanently damaged. I attribute all of my problems to my unwillingness to learn dimensional analysis." -- Jane

I was shocked. I think given the seriousness of these testimonials, we should redouble our efforts here at KTM to ensure that every child is taught dimensional analysis at the earliest opportunity.

(One more amusing little sidenote: the hit counter at the bottom of the page never increments.)

-- CarolynJohnston - 22 Feb 2006

PitBulls 22 Feb 2006 - 15:06 CatherineJohnson

They are incredible dogs.

Here's Vicki Hearne:

“There are a lot of pit bulls these days who are licensed therapy dogs,” the writer Vicki Hearne points out. “Their stability and resoluteness make them excellent for work with people who might not like a more bouncy, flibbertigibbet sort of dog. When pit bulls set out to provide comfort, they are as resolute as they are when they fight, but what they are resolute about is being gentle. And, because they are fearless, they can be gentle with anybody.”

It's true.

-- CatherineJohnson - 22 Feb 2006
WhatKindOfWeatherAreYou 22 Feb 2006 - 22:57 CatherineJohnson

 You Are a Rainbow Breathtaking and rare You are totally enchanting and intriguing But you usually don't stick around long! You are best known for: your beauty Your dominant state: seducing

This has nothing whatsoever to do with me.

This one, on the other hand, sounds exactly like me:

 You Are 4% Abnormal You are at low risk for being a psychopath. It is unlikely that you have no soul. You are at low risk for having a borderline personality. It is unlikely that you are a chaotic mess. You are at low risk for having a narcissistic personality. It is unlikely that you are in love with your own reflection. You are at low risk for having a social phobia. It is unlikely that you feel most comfortable in your mom's basement. You are at low risk for obsessive compulsive disorder. It is unlikely that you are addicted to hand sanitizer.

-- CatherineJohnson - 22 Feb 2006

SampleExamQuestionsFromHell 23 Feb 2006 - 00:01 CatherineJohnson

Economics: Describe in four hundred words or less what you would have done to prevent the Great Depression.

Political Science: There is a red telephone on the desk beside you. Start World War III. Report at length on its socio-political effects, if any.

Mathematics: Derive the Cauchy-Euler equations using only a straightedge and compass. Discuss in detail the role these equations had on mathematical analysis in Europe during the 1800s.

Computer Science: Write a fifth-generation computer language. Using this language, write a computer program to finish the rest of this exam for you.

Extra Credit: Define the universe, and give three examples.

source: Sample Exam Questions from Hell

Here's a real one:

My exams this semester are going horrible. I just love that feeling in which you leave an exam and you have no clue of how well you did. In fact, I feel as if I just wasted 13 weeks of my life studying, because my exams questions generally have nothing to do with the topic that I am studying. Our Con Law exam for instance wanted us to analogize an insignificant comment that Justice Breyer made in an interview about form and functionalism and how that relates to Supreme Court Commerce Clause decisions of the past 25 years. This is a least what I thought it said.

Thanks everybody I feel better now.

Sorry about the typos. I am a little stressed.

hoo boy

That is an exam question from hell.

-- CatherineJohnson - 23 Feb 2006

EisenhowerOnDewey 23 Feb 2006 - 00:14 CatherineJohnson

Educators, parents and students . . . must be induced to abandon the educational path that, rather blindly, they have been following as a result of John Dewey's teachings.

— President Dwight D. Eisenhower

source:
John Dewey & the Decline of American Education: How the Patron Saint of schools Has Corrupted Teaching and Learning
by Henry T. Edmondson III

Martin Davis isn't crazy about the book...

And here is a pre-written college term paper on John Dewey!

Don't say I never did anything for you.

Meanwhile, somewhere inside a parallel universe . . .

The education of engaged citizens, according to [Dewey's] perspective, involves two essential elements: (1). Respect for diversity, meaning that each individual should be recognized for his or her own abilities, interests, ideas, needs, and cultural identity, and (2). the development of critical, socially engaged intelligence, which enables individuals to understand and participate effectively in the affairs of their community in a collaborative effort to achieve a common good. These elements of progressive education have been termed "child-centered" and "social reconstructionist" approaches, and while in extreme forms they have sometimes been separated, in the thought of John Dewey and other major theorists they are seen as being necessarily related to each other.

These progressive principles have never been the predominant philosophy in American education.

-- CatherineJohnson - 23 Feb 2006
TheNightlyHomeworkBattle 23 Feb 2006 - 04:16 CarolynJohnston

Is anyone else finding that evening life with their middle schooler has become a desperate, pitched battle to get them to do their homework?

I've had friends with older kids go through this. I have one friend who was talking about cleaning out his child's bedroom of all distractors, including the bed, so that there was nothing left but him, his desk, his book and his pencil. He suspected that even with such sensory deprivation, his child would be unable to settle down and get his homework done.

It's been 5 years since then, and the same kid is now a senior in high school doing very well and accepted to the (engineering) college of his choice. But 5 years ago, that kid was having as much trouble with his homework as could be imagined. Now he and his friends have study groups at his house, and sit around and speak French to each other. I cling to his example; perhaps there is hope for us as well.

Another one of Ben's friends in 6th grade also has fits and rages when it's time to do homework. His mother has to take him down in a tackle to get him to do his homework, every night. He never wins the fight, never never never; she knows her behavioral theory; it doesn't matter. I suppose the fight simply delays the onset of homework; that's what's reinforcing about it.

Another friend with a slightly older child (8th grade) doesn't fight with him to get him to do his homework, and he doesn't do it. His grades aren't up to snuff. She asks why he can't simply take responsibility for himself and do what he's supposed to do, when he knows perfectly well what it is; I tell her I don't know why, but he can't -- no executive function, that's just how it is -- so she's just going to have to ride him. He'd much rather argue than work, so it won't be fun for her, I'm afraid.

It wasn't the same in elementary school. Yes, Ben fought to avoid having to do homework, but he's suddenly become much more vociferous and strong-willed and rude about it. The difference is exponential; Ben this year is the T-Rex of homework avoiders.

I can't help but note that all of my data points are boys. Are girls, too, fighting at this middle school age to avoid having to do homework? Please tell me they are. I know I'm not alone in fighting the nightly fight, but I'd hate to think that the whole country is full of angry boys every night, and of girls getting down to work with sharpened pencils, their highlighters, and a good attitude.

Not that I wish ill on those of you with girls, but I just couldn't take it.

-- CarolynJohnston - 23 Feb 2006

FreeTeachToCrammeryClipArt 23 Feb 2006 - 22:49 CatherineJohnson

from the School Discovery Zone

if you prefer black and white:

cram school
teaching to crammery in middle school
the kind of kids who can be taught to crammery
free teach to crammery clip art

teachtocrammery

-- CatherineJohnson - 23 Feb 2006

DimensionalAnalysisWordProblemsAndAnswers 23 Feb 2006 - 23:06 CatherineJohnson

I spent some time yesterday cruising the internet looking for dimensional analysis problems for Christopher.

They're hard to come by.

Here's a pretty good selection for kids in the 4th to maybe 8th grade range. (Actually, you could use these problems with any beginner.)

I've included everything inside this post, but I've also created separate pages that ought to be easy to print out, using the 'printable' tab at the top of the screen. (I think these two pages are editable by everyone, so you ought to be able to add your own problems, take problems away, increase or decrease the space between items, etc.

For future reference, all of these pages can be found in math lessons and in the Book-Style Index.

dimensional analysis word problems to print
answers to Gisele Glosser's problems only

10 problems by Gisele Glosser

1 kilometer = 0.6 miles
1 mile = 1.6 km
1 fathom = 6 feet
1 meter = 3.3 feet
1 kilogram = 2.2 pounds
1 mile = 5280 ft
C = 5/9 • (F – 32)
1 m = 100 cm

1. A dolphin dives to 24 feet. How many fathoms is this below the surface of the water?

2. The deepest part of the ocean is the Marianas Trench; its depth is 11.03 km. How many feet is that?

3. The largest whale measured 33.27 meters in length. How many feet is this?

4. The average temperature of the oceans is 3.9° C. What is this in Fahrenheit?

5. The highest tides on planet Earth occur near Wolfville, in Nova Scotia’s Minas Basin. The water level at high tide can be as much as 16 meters higher than at low tide! How many feet is this?

6. Sunlight only reaches 30 to 120 meters under the waves. Convert this to feet.

7. A blue whale can weight up to 280, 000 pounds. That’s larger than the largest dinosaur. How many kilograms is that? (Round your answer to the nearest whole kg.)

8. Previous studies suggest that the expected global warming from the greenhouse effect could raise sea level approximately 100 centimeters in the next century or two. What is this in feet?

9. If all the ice in glaciers and ice sheets melted, the sea level would rise by about 80 meters, or how many feet?

10. The longest river is the Nile River, in Egypt, Africa. It is 4,160 miles long and flows northward into the Mediterranean Sea. How long is it in km?

copyright © 2001 Gisele Glosser (from Math Goodies - can’t find URL, but Gisel Glosser seems to have worksheets posted at schoolhousetech)

2 problems by Donna Young

1. Convert 640 ounces into pints.

2. If 20 shillings equal 1 pound, how many shillings does 1000 pounds equal?

2 problems from Chemistry 192

1. How many seconds are there in 1.2 weeks?

2. If a recipe calls for 37 grams of sugar, how many pounds does that correspond to?

Carolyn's real-life problem

Carolyn & Bernie are going to buy a new car, which they will drive 13,000 miles a year.
They've narrowed their choices down to a Honda Civic or a Dodge Caravan.
The Honda gets 35 miles per gallon.
The Caravan gets 25 miles per gallon.
If gas is \$4 per gallon, how much money will they save on gasoline each year driving the Civic?

problem from Lesley Stevens

An example of the kind of math my job requires:

2.2 pounds = 1 kilogram
1 gram = 1000 milograms
1 liter = 1000 milliliters

You need to administer an IV drug to a dog.

Part 1:

The dosage is 20mg per kg of body weight. The drug is in a solution of 5g per 1 Liter. The dog weighs 66lbs. How many mL of solution do you need?

Part 2:

IV drugs can be administered using a drip set which delivers a set quanity of liquid at an adjustable rate.

You need to administer the drug over a period of 4 hours. Your drip set delivers 1mL of liquid per 8 drips. At what rate (in drips per minute) do you need to set your drip set?

problem #3 from Saxon 8/7 Lesson 96

The Adams' car has a 16-gallon gas tank. How many tanks of gas will the car use on a 2000-mile trip if the car averages 25 miles per gallon?

1.Convert 640 ounces into pints.
640 oz/1 x 1 pt/16 oz
40 pts

2. If 20 shillings equal 1 pound, how many shillings does 1000 pounds equal?
1000 pounds/1 x 20 shillings/1 pound
20,000

1. How many seconds are there in 1.2 weeks?

1 week = 7 days
1 day = 24 hours
1 hour = 60 min
1 min = 60 seconds
1.2 weeks x 7 days/1 week x 24 hrs/1 day x 60 min/1 hr x 60 s/1 min = 7.3 x 105 seconds

2. If a recipe calls for 37 grams of sugar, how many pounds does that correspond to?
Given: 37 grams
Want: lbs
Know: 453.59 g = 1 lb

37 g x 1 lb/453.59 g = 8.2 x 10-2 lb

Chem 192 problems:
Chemistry 192 Worksheets
Chemistry 192 worksheet

problem #3 from Saxon 8/7 Lesson 96

The Adams' car has a 16-gallon gas tank. How many tanks of gas will the car use on a 2000-mile trip if the car averages 25 miles per gallon?
2000 miles x 1 gal/25 miles x 1 tank/16 gal
5 tanks

dimensional analysis word problems & answers
dimensional analysis word problems to print
dimensional analysis word problems answer key only for Gisele Glosser's problems

-- CatherineJohnson - 23 Feb 2006

AnimalsInTranslationFebruaryNineteen 24 Feb 2006 - 01:26 CatherineJohnson

February 19, 2006

Animals in Translation on TIMES list
Animals in Translation 1-29-2006
Animals in Translation 2-05-2006
Animals in Translation 2-12-2006
Animals in Translation 2-19-2006
Animals in Translation 2-26-2006
Animals in Translation 3-05-2006
Animals in Translation 3-12-2006
Animals in Translation 3-19-2006
Animals in Translation 3-26-2006

-- CatherineJohnson - 24 Feb 2006
SummersGetsFired 24 Feb 2006 - 04:24 CarolynJohnston

Remember the furor Larry Summers, the president of Harvard, set off when he publicly theorized about some politically incorrect reasons why there aren't as many women as men in the highest reaches of academia?

Well, offended women everywhere can rest easier now, because he's been canned.

From the Economist:

It is tempting to present Mr Summers as a neo-conservative fallen among liberals. In fact, ideologically he is something of an old-time liberal himself (he devoted a great deal of energy to boosting the number of poor students at Harvard). His problem has always been that his affection for any agenda is less than his love of a good debate. Political correctness depends on self-censorship, especially over group differences, and Mr Summers is constitutionally incapable of not examining people's premises.

In the end, though, character was less important than power. There was a set of much more basic tensions between Mr Summers and his critics. These tensions might be dressed up as ideological, but they were really about the privileges and perks of academic life.

The most obvious was undergraduate teaching. Undergraduates get a raw deal for their \$40,000 a year. The core curriculum is an antiquated mess. Star professors palm their pupils off on graduate students and then give them top grades to keep them happy (one survey found that 91% of Harvard graduates get honours compared with just 51% at Yale). Mr Summers tried to use the bully pulpit to force professors to teach more seriously; hence his attack on Mr West.

The second was a tension between science and the humanities, or between hard and soft subjects. Mr Summers made no secret of his personal enthusiasm for the hard sciences; he was scathing about squishy "ologies". Some Harvard types speculated bitterly that he wanted to turn Harvard into an Ivy-clad version of the nearby Massachusetts Institute of Technology, the university that accepted the young Larry when Harvard turned him down.

Sounds like they've turned him down again. Imagine, requiring that Harvard professors teach. Sheesh.

-- CarolynJohnston - 24 Feb 2006

QuestionForKitchenTableMathBrainTrust 24 Feb 2006 - 13:23 CatherineJohnson

That's what Jo Anne Cobasko calls you guys — the ktm brain trust!

It's true.

Jo Anne's having trouble with her site, and the new software her husband, a computer programmer, bought for her is too complicated to deal with.

Here's her question:

I need to know the name(s) of an easy to use software which allows you to create your own website. I don't know any programming languages, and don't really want to have to learn them either. I need something that is idiot proof, and really easy to navigate and understand. I just want something basic. that can handle aproximately 20 pages.

If anyone's got any ideas, I'd like to hear, too.

Thanks!

-- CatherineJohnson - 24 Feb 2006

YourPtsaMoneyAtWork 24 Feb 2006 - 21:41 CatherineJohnson

from today's Wall Street Journal:

...the PTA has been losing members steadily for almost a half-century now, from a high point of more than 12 million in the early 1960s to a current membership of about half that. Today only about a quarter of K-12 schools in the U.S. have a PTA chapter. The reasons for this decline are familiar ones: money and politics.

[snip]

In 1897, the members of the first National Congress of Mothers -- the name of the group that would eventually become the PTA -- saw their mission as fostering "a love of humanity and of country...and the advantages to follow from a closer relation between the influence of the home and that of the school." The president of the national PTA declared at a recent convention: "We simply must change the country." What happened?

In "The Politics of the PTA" (2002), Charlene Haar explains that the PTA shifted its focus mainly because of its longstanding alliance with the National Education Association. Formed in 1857, the NEA once shared the parent group's concern for schoolchildren in such matters as school curriculum and the qualifications of public-school teachers. Indeed, in 1920, the National Congress felt so much in line with the NEA that it moved into the association's impressive Washington headquarters. Already allied with the teachers group on support for a "progressive" curriculum that would emphasize "life skills," the PTA would from then on curb its more general social programs and limit itself to matters directly affecting education.

Ms. Haar chronicles the major policies on which the two groups cooperated throughout the 20th century. Having begun as equals, the PTA gradually became the subservient partner. Both organizations refused to support the National Defense Education Act -- passed in 1958 in the wake of the Soviet's launch of Sputnik -- because, as Ms. Haar explains, it "provided funds for mathematics, science and other defense-related curricula but could not be used for teacher salaries." By the 1960s, the PTA was known as "a coffee-and-cookies organization" -- unquestioningly offering its seal of approval to the newly unionized NEA. It was the issue of teacher strikes, though, that dealt the reputation of the PTA its final blow. In 1961 the AFT, representing New York City's teachers, staged the nation's first citywide strike, and in 1968 Florida teachers followed with the first statewide strike. To avoid conflict, the PTA abandoned any pretense of independence and supported the walkouts. A few years later, the PTA tagged along with the NEA, lobbying for a cabinet-level federal department of education. What followed were a series of legislative victories for the teachers unions. Among their outstanding lobbying successes, backed by the PTA, was the defeat of a bill co-sponsored by Sen. Patrick Moynihan in 1978 proposing a tax credit for as much as half of private-school tuition. In the aftermath, many parents began their exodus from the PTA, including a large number of Catholics whose tuition fees for parochial schools would have become less burdensome under the plan.

Today the PTA supports all of the union's positions, including increased federal funding for education and opposition to independent charter schools, to vouchers and to tuition tax credits for private and religious schools. This "parent" group lobbies for teachers to spend less time in the classroom and to have fewer supervisory responsibilities like lunchroom duty. Moreover, they want a pay scale for teachers that is based on seniority, not merit. In November, the PTA even helped to defeat California's Proposition 74, which called for limiting teacher tenure by extending the probation period for new teachers from two to five years, a proposal designed to give administrators more time to weed out bad instructors.

With polls indicating that the union label is a liability with the public, an arrangement has developed whereby the NEA provides needed financial support for the PTA, which in turn bolsters union positions at the grass-roots level. As one union official put it: "[T]he PTA has credibility...we always use the PTA as a front."

PTO?

Tim Sullivan, a Massachusetts entrepreneur and former New York City public-school teacher, saw the need among the independent groups forming around the country for the kind of information and services once provided by the PTA. In 1999 he founded a company for independent parent-teacher groups. PTO Today publishes a magazine and maintains a Web site that provides opportunities for parent networking on its message boards. Both in print and online, PTO Today answers the kind of questions that parents of public-school children ask -- how to organize a family night, how to raise money for extras like arts-and-crafts supplies and what kind of insurance is necessary for field trips. With any luck, the PTOs will put the PTA out of business entirely.

source:
Losing the 'P' in PTA (\$)

I've heard of "PTO's," but I didn't realize PTO was a differen organization.

in a nutshell

• PTA membership is down from a high of 12,000,000 in the early 1960s to roughly half that today

• approximately one quarter of K-12 schools in the U.S. have a PTA chapter

• PTA housed in NEA headquarters since 1920

• PTA supports all NEA positions:
- supports decreased classroom hours for teachers
- supports decreased 'supervisory duties' for teachers
- opposes independent charter schools
- opposes vouchers
- opposes tuition tax credits for private and religious schools
- opposes merit pay
- opposed Proposition 74
- "[T]he PTA has credibility...we always use the PTA as a front." (NEA official)

PTO Today (PTO website)
PTO versus PTA by Tom Sullivan

The Politics of the PTA (Studies in Social Philosophy and Policy) by Charlene K. Haar
interview with Charlene K. Haar

update: it's always worse than you think

from the Heartland Institute interview with Haar:

When Charlene K. Haar made what she thought was a routine request to the National PTA, the reaction she received was so surprising it piqued the former public school teacher’s curiosity to learn more about the century-old Parent-Teacher Association.

Instead of a parent organization dedicated to the enhancement of the nation’s schools, Haar discovered a group dominated by teacher unions and little attuned to the interests of parents and their children. Her findings are detailed in the book, The Politics of the PTA (Transaction Publishers), published last fall.

Haar had been looking up information at the PTA headquarters in Chicago for a research project and asked for a copy of the PTA’s nonprofit tax return, Form 990. She was told it would be sent to her, but what she also received was an accusatory letter from a PTA finance official, who suggested her intentions for asking questions and visiting the headquarters were suspicious, and that she was misrepresenting herself.

“If I hadn’t received that letter, I would have completed my study of the PTA as a 10- or 12-page article for Capital Research Center, and that would have been it,” said Haar. “But because I received this very curious letter, I decided there must be something they were hiding, that they didn’t want their members to find out about, and that they didn’t want to have publicized. That encouraged me to go ahead with a larger study that ended up in The Politics of the PTA.”

-- CatherineJohnson - 24 Feb 2006
IntlHeraldTribuneSaysStudyMathNotChinese 24 Feb 2006 - 22:16 CatherineJohnson

The United States can find many other uses for the \$1.3 billion the Senate committee wants to allocate for Mandarin education. One priority may be to train math teachers to calculate the value of 1 3/4 divided by a half.

Ma Liping [sic] describes that particular problem in her 1999 book "Knowing and Teaching Elementary Mathematics."

More than half of U.S. math teachers to whom Ma had given the problem got the computation wrong. Not only did all the teachers in China get the answer right, 90 percent came up with a valid "story" to explain the solution to children so they got the correct figure of 3 ½.

In a Senate Banking Committee hearing in 2004, Alan Greenspan said the lack of math education threatened U.S. competitiveness. The Federal Reserve chairman's concerns were validated in a Bloomberg News article last week about the Chartered Financial Analyst exams.

Chinese students, the article said, had the highest pass rate in the world in last month's CFA Level I test, followed by Germany and India. The United States was fourth.

Kindergarten students in Portland, Oregon, are learning that a triangle is san jiao in Mandarin, according to the Associated Press.

They might learn something more useful by playing with an abacus.

source:
Commentary: U.S. students need more math, not Mandarin By Andy Mukherjee Bloomberg News

from the Dept of Silver Linings: fourth is better than we're doing on TIMSS & PISA.

(hmm.....skimming the 2nd article.....they're comparing apples to oranges, almost certainly.)

and see:
Finance test draws more Chinese and Indians by Samantha Zee Bloomberg News

-- CatherineJohnson - 24 Feb 2006

JimmyCarter 25 Feb 2006 - 18:13 CatherineJohnson

in today's Wall Street Journal:

Since leaving office, Mr. Carter has written 18 books. The most recent, "Our Endangered Values," debuted Nov. 20 on the New York Times best-seller list at No. 1. Five of his last six titles have also hit the list. One, his memoir of growing up in rural Georgia, "An Hour Before Daylight," was one of three finalists for the 2002 Pulitzer Prize in biography/autobiography.

Like other successful scribes in today's publishing world, Mr. Carter has learned how to play the game. Book retailers love him, in part because he works so hard at book signings and understands the "retail politics" of the publishing business. Disdainful of "handlers," the former president is all business and insists on sticking to a tight schedule. Once, he almost left a late-running publicist behind in a store.

At book signings, where thousands of fans often turn up, some stores distribute wristbands for crowd control. Mr. Carter autographs as many as 800 books an hour. He'll occasionally sign his full name when asked, but tries to "conceal that from the next guy in line" to avoid similar requests. He speaks to everybody who comes through, making contact with his friendly blue eyes. "I tell the little girls they're pretty and ask the little boys how old they are," he says.

source:
I, Jimmy \$
Wall Street Journal
2-25-2006 page one

taking issue with the cover art

I love this:

Like many authors and presidents, Mr. Carter is usually convinced he knows best. For example, he dismissed the original cover art for his novel "The Hornet's Nest," about the American Revolution, as unacceptable. His publisher, Simon & Schuster, initially suggested an image by the artist N.C. Wyeth. Mr. Carter gave it a look and then rejected it.

"The painting they picked turned out to be of Daniel Boone," says Mr. Carter. The problem? In Mr. Wyeth's work, Mr. Boone had black hair and was posed next to a canoe. Mr. Carter's hero, by contrast, has a blond pigtail, and there isn't anything in the book about canoes. In addition, Mr. Carter, who owns a muzzle-loading rifle, saw that Mr. Wyeth had portrayed Mr. Boone holding the rifle awkwardly.

Mr. Carter subsequently asked his wife to take a photograph of himself aiming a rifle properly. He then used the photo to paint an illustration much more to his liking. It ultimately graced the cover of his novel.

getting things done

He rises at 5 a.m., as he has done all his life. After answering his email on his laptop and reading several newspapers online that aren't available in Plains, he starts to write in his study. He works at an old table once owned by his father, surrounded by crammed bookshelves, fly fishing gear, fishing flies that he ties himself, and a couple of cardboard boxes into which he piles books for which he no longer has room. On a recent day, he was dressed in blue jeans, an open-neck shirt and moccasins.

The former president usually takes a break at 8 a.m. to share breakfast with his wife, Rosalynn, and then goes back to his laptop for several hours. By 11 a.m. or so he says he's tired of the computer and moves on to other things.

I gather Jimmy Carter has no need of a Time Timer.

Mr. Carter applied the same discipline to becoming a published poet. Recognizing in the early 1990s that his poems needed work, he got in touch with Miller Williams, the inauguration poet for Bill Clinton's second swearing-in. "I told him that I'd written poems on and off all my life, very amateurish poems, and I would really like to write poetry more seriously," says Mr. Carter. "He volunteered to take me on as a student."

Mr. Williams gave him some advice: He should read anything by Richard Wilbur, Robert Lowell or Emily Dickinson. "They are formalists and yet their work is so relaxed it sounds almost like a living room conversation."

Later, Mr. Williams hosted Mr. Carter in Fayetteville, Ark., for a weekend to work on his manuscript. Mr. Carter, famously strong-willed, says he listened to criticism, but made it clear to his tutors -- even Mr. Williams -- that they "could never give me a word, never suggest a word to go into a line."

Selling his poems proved more difficult than he expected. Peter Osnos, Mr. Carter's publisher at the time, rejected his original effort after asking three poetry experts to review his work. Instead, he suggested that Mr. Carter turn his poetry into a collection of homilies. Mr. Carter sent back a terse response: "Thanks but no thanks."

Months passed. Then Mr. Osnos received a copy of a poem that Mr. Carter had torn from the pages of the New Yorker magazine. At the bottom, the former president had written a bit of doggerel mocking the work. His point was clear.

"I looked at it and said to myself, 'The man wants to publish his poetry,' " says Mr. Osnos. "We did so, and the book, 'Always a Reckoning,' hit the best-seller lists for seven weeks in 1995 and sold 70,000 copies."

Last summer I was trying to figure out how to teach Christopher to write.

My mom suggested I have him memorize poems, and in fact I've had a book of poems for precisely this purpose sitting in my Amazon cart for months. (She got us a copy of The Best-Loved Poems of Jacqueline Kennedy Onassis for Christmas, but it hasn't arrived yet.)

My mom used to write funny rhyming poems for all occasions at our house — birthdays especially — and I'm thinking about reviving the tradition.

-- CatherineJohnson - 25 Feb 2006

SingaporeMathInWisconsin 25 Feb 2006 - 21:21 CatherineJohnson

Charles left a link to a story in Milwaukee's Journal Sentinel, via Education News, Less may be more when it comes to math.

Students in Singapore are introduced to roughly half the number of new math topics a year as students in the United States are. Experts and policy analysts say Singapore's emphasis on depth over breadth is a formula for success.

The thicker the textbooks and the greater the volume of math topics introduced a year, the less likely American students and teachers are to achieve similar results, says Alan Ginsburg, director of the policy and program studies service at the U.S. Department of Education.

"There's no way you can teach twice the amount of mathematics to the same depth that Singapore does," says Ginsburg, co-author of a 2005 report called "What the United States Can Learn From Singapore's World-Class Mathematics System," published by the American Institutes for Research.

He says the Singapore method of teaching math also puts a bigger emphasis on understanding instead of "mechanical" memory, and on visualization of the problems.

"I feel like the biggest difference is the visualization," says Julia Rothacher, 12, a sixth-grader at University School.

Previously, she says, she attended Cumberland Elementary School in Whitefish Bay, where her class used the mathematical reasoning-based curriculum known as Everyday Math.

To appreciate what visualization can do, consider a problem that Neuwirth gave her class. It was considered the hardest question on a Massachusetts state assessment for 10th-graders, based on data that showed that more than half of the 72,000 test-takers got the question wrong, according to The Boston Globe, which published the problem.

Of the people in attendance at a recent baseball game, one-third had grandstand tickets, one-fourth had bleacher tickets, and the remaining 11,250 people in attendance had other tickets. What was the total number of people in attendance at the game?

The four choices were: A) 27,000, B) 20,000, C) 16,000 or D) 18,000.

Neuwirth's sixth-graders - without using the calculators that Massachusetts' 10th-graders could use - went to work.

Alexis Block, 12, did the problem on the board.

She drew 12 boxes of the same size, because 12 is the lowest common denominator of the denominators 3 and 4 in one-third and one-fourth, respectively.

She wrote "GS" for grandstand tickets above four - or one-third - of the 12 boxes, and "B" for bleachers above three - or one-fourth - of the 12 boxes.

She wrote 11,250 below the remaining five boxes, then divided 11,250 by five to get the value for each box - 2,250.

She multiplied the value of each box by 12 and got the correct answer for the total number of people in attendance: 27,000.

[ed.: Unfortunately, the reporter didn't ask Julia whether her classmates at Cumberland could do this problem.]

• one-fourth of audience had bleacher tickets
• one-third of audience had grandstand tickets
• the remaining 11,250 people in attendance had other tickets
• QUESTION: how many people in the audience altogether?

spaced repetition: more than half of Massachusetts 10th graders missed this problem

Singapore's bar models are gold. Saxon Math uses them, too; students draw bar models in virtually every problem set in Saxon Math 8/7. I'm going to have Christopher doing them all summer.

using bar models to prep for the state test

I used a bar model to show Christopher how to do this problem from the Glencoe test prep booklet he brought home over break:

6.N.17 Multiply and divide fractions with unlike denominators

Pizza Pizzaz was running a special on their 1/2 pepperoni and 1/2 cheese pizza. Mary, Jorge, and Shaun wanted to share a pizza, but they only liked the cheese half. If they shared equally, what fraction of the total pizza would they each be able to eat?

I fault Christopher's teacher for assigning virtually no story problems all year long.

Word problems are the true manipulatives.

Every concept she's teaching should be illustrated & practiced through extremely simple word problems to start — word problems so simple the kids can do them in their heads.

Christopher had no idea — zero — that this problem called for division of a fraction.

If you tell him to divide 1/2 by 3 he can do it in 2 seconds flat.

But his procedural knowledge is completely divorced from any actual situation in which one would divide 1/2 by 3.

So I drew a bar model, and of course he saw right away that this problem requires you to divide 1/2 into 3 parts.

At the beginning of the year I was having him do 2 or 3 bar models a day. I'm going to have to get back to that.

what does the AIR study of Singapore Math find?

The conclusion of the story is quite misleading:

But it's not certain that Singapore Math is making a difference in U.S. test scores.

[snip]

In his study of Singapore's math system, Ginsburg, of the U.S. Department of Education, looked at four sites in the U.S. where the Singapore approach had been adopted. Only two of those sites achieved results superior to control groups, and those two sites got additional staff development.

"It's not magic," Ginsburg says. "You can't just give out textbooks."

I've read most of the AIR report (pdf file), and I'd say that the impression it leaves is that the Singapore textbooks are as close to magic as it gets.

Here is the actual conclusion of the report:

The two pilot sites (out of four) that had both a stable population of higher performing students and a clear staff commitment to support the introduction of the Singapore mathematics textbooks produced sizeable improvements in student outcomes.

As far as I'm concerned, that's two out of two.

In North Middlesex, Massachusetts, the school system of about 5,000 was selected by the state education agency to pilot the Singapore textbooks. Over two years, the percentage of those students who participated in the Singapore pilot and scored at the advanced level on the grade 4 Massachusetts assessment increased by 32 percent over two years. The pilot schools had strong district and staff support. Over two years, Baltimore’s Ingenuity Project increased the proportion of its students who scored at the 97th percentile or above by 17 percent. The Ingenuity Project serves gifted Baltimore students and can select highly skilled teachers capable of teaching the mathematical reasoning underlying the challenging Singapore problems.

The two other Singapore pilot sites, which in one case had uneven staff commitment to the project and in the other case had a more transient, lower income population, produced uneven or disappointing results.

• The Montgomery County outcomes were positively correlated with the amount of professional training the staff received. Two Singapore pilot schools availed themselves of extensive professional development and outperformed the controls; two other pilot schools had low staff commitment coupled with low exposure to professional training and were actually outperformed by the controls. Professional training is important in helping teachers understand and explain the nonroutine, multistep problems in the Singapore textbooks. Teachers also need preparation to explain solutions to Singapore problems, which often require students to draw on previously taught mathematics topics, which the Singapore textbook, in contrast to U.S. textbooks, does not reteach.

• The Paterson, New Jersey, school, with an annual student turnover of about 40 percent, fared no better on the New Jersey grade 4 test than the district average over two years. Having such a high student turnover meant that many 4th graders were exposed to the Singapore mathematics textbook for the first time - by definition, not a fair test of the cumulative effects of exposure to the textbook.

Offhand, I don't see where this is a triumph of professional development. None of these teachers went back to college or took additional courses in advanced mathematics. They spent a fair amount of time learning how to teach the Primary Mathematics series, and their commitment was high.

It seems extremely unlikely to me — again, having read the report — that the same degree of professional development focused on teaching EVERYDAY MATH would have produced results like these.

update: from the AIR report

This is funny:

The most serious mismatch occurred in Paterson, where grade 4 teachers supplemented the Singapore mathematics textbook with their U.S. textbook to cover a few topics, notably statistics and probability, that were on their grade 4 state assessment but not in the Singapore grade 4 textbook. Unfamiliar with the pedagogy laid out in Singaporean Teachers’ Guides, several sites were also concerned that the Singapore textbooks did not stress written communication skills by requiring students to explain their answers.

OK, that's not funny ha-ha.

Speaking of funny ha-ha, I'm going to have to find the email our school board president sent to parents explaining the adoption of TRAILBLAZERS by saying - and I think I'm quoting - 'math has become language-based.'

if you want to teach bar models to your child

I'm afraid the simplest and quickest - but not the least expensive - approach is to buy the four PRIMARY MATHEMATICS books for grade 3 & just work through all the story problems, start to finish:

• Primary Mathematics 3A Textbook (\$8.00)
• Primary Mathematics 3A Workbook (\$8.00)
• Primary Mathematics 3B Textbook (\$8.00)
• Primary Mathematics 3B Workbook (\$8.00)

I say this because last summer I tried to have Christopher do the problems in Challenging Word Problems Book 3 (3rd grade), and it was just too hard. [update 3-23-2006: I've misspoken. The only difficult problems in Book 3 are those in the "Challenging Problems" sections. The problems were too hard for Christopher to do while also learning to construct his first bar models.]

Both KUMON & DI advocate backing kids up to a point before their level of expertise, and that's what I needed to do with Christopher. He was annoyed that the bar model problems in 3A were too easy, but in fact he hadn't learned the 'core' bar models representing addition, subtraction, multiplication, and division & he kept getting tripped up.

Finally even Christopher agreed to go back and start from the beginning.

the principle: when you're learning a new skill, start at the beginning

You might be able to start at the beginning by purchasing the 2nd grade Challenging Word Problems book, but unfortunately I don't have a copy, so I can't say.

UPDATE - THERE ARE SAMPLE PAGES ONLINE!

Looking at these pages, Challenging Word Problems Book 2 (\$7.80) might be a good way to go.

Basically, you need to teach your child the 'core' bar models corresponding to the 4 operations. There are essentially 5 'core bar models' (I think):

• subtraction as diminution ('take away')
• subtraction as comparison ('difference')
• multiplication
• division

If you're more math-savvy than I was when I first started working with PRIMARY MATHEMATICS, you might just want to have your child practice these 5 forms using whatever very simple word problems you happen to have around - including 'number problems,' such as 'What number is the difference between 9 and 7?' (I'll get samples posted.)

Come to think of it, that's probably what I'll do this summer: massed practice on the 5 models.

I'll figure out the core fraction-percent-ratio-proportion bar models & teach those, too.

the bar model for subtraction as comparison

This is from Challenging Word Problems Book 2 (second grade):

bar models for parents

I like The Essential Parents' Guide to Primary Maths (\$10.50) quite a bit. As luck would have it, the 3 sample pages on bar models cover the 'Comparison Concept":

subtraction as the difference between 2 numbers
study sheet: subtracting integers & absolute value
notes on integer, subtraction, & absolute value study sheet
subtraction has two meanings - Word document

-- CatherineJohnson - 25 Feb 2006

RichardAskeyOnMiddleSchoolTeachers 25 Feb 2006 - 22:48 CatherineJohnson

Richard Askey, a professor emeritus of mathematics at the University of Wisconsin-Madison, notes that Singapore math standards are so high that "their sixth-grade students are expected to know more than we ask of our prospective middle-school teachers."

source:
Less May Be More When It Comes to Math

Singapore Math in Wisconsin
Richard Askey on middle school math teachers

-- CatherineJohnson - 25 Feb 2006
ComingOfAge 26 Feb 2006 - 03:24 CarolynJohnston

Lately, Ben has been very disturbed that he has a helper in his classes.

"Why do I have to have someone stand over me in my classes?" he says.

"Because it's really hard for you to pay attention," I say.

"It's like a walking advertisement that I'm retarded! It's like being up on stage with a sign that says I'm retarded!"

"You are not retarded," I say. I've said it multiple times. The other day I told him that retarded people, by definition, have IQs of 70 or less; and his IQ is in the 100s. That gave him pause for a minute, but not for long; "retarded" is the epithet he most fears. In spite of all the growth in understanding of people with disabilities that has come about since I was in school, kids still call each other 'retards' in middle school. If it keeps up, I'll pull out his test results, and the DSM-IV, and kill this notion once and for all.

But it probably won't do any good. All his life, he's been surrounded by kids who don't find it as easy to do math and reading as he does. He knows he's not retarded -- but he's scared to death that he might be a 'retard' (the accent is on the 're').

Today, while doing his reading, he said out of nowhere, "Mom, do I have autism?"

Pause for thought on my part. "You have Asperger's Syndrome," I said.

"But do I have autism?"

"Asperger's Syndrome is an autism spectrum disorder," I said. "That means it's like autism in many ways."

"Oh, God, Mom!" he said, and started crying. "I just want to be like the other kids!"

I held him while he cried. I've been waiting for this moment for years. I knew it would be awful, and wonderful. Wonderful, because it had to happen in order for him to begin to acquire the knowledge of himself that he'll need to be a self-sufficient adult; awful, because it's obvious why it's awful. It's heartbreaking.

It's not the first time I've mentioned Asperger's or autism spectrum disorders to Ben. I told him he has Asperger's once or twice before, and it didn't stick (if you've got a kid, you know what it's like to tell your kid something important and difficult, and have it 'not stick').

Apparently, it came up today because he was talking about autism with his friend from the neighborhood, and she mentioned that she's heard that having autism is like having 'flashlights repeatedly flashing in your eyes'. God knows where the heck she heard that.

"I don't have flashlights in my eyes," he said. I'm thinking, this is great. I've been standing by for years, ready with calibrated doses of meaningful information about his condition, testing the waters periodically, waiting to introduce it in just the right way. And what happens? The first person to get through to him about his condition is another kid, with crummy information.

But it probably doesn't matter. When the moment came, I wasn't ready and thinking clearly anyway. I was wanting to cry myself. I had to ditch my script and wing it.

-- CarolynJohnston - 26 Feb 2006

MyDreamCar 26 Feb 2006 - 05:32 CarolynJohnston

I have found it

More pictures here, here, here, and here.

-- CarolynJohnston - 26 Feb 2006

RedeemerPresbyterianInManhattan 26 Feb 2006 - 18:01 CatherineJohnson

This is interesting.

Today's TIMES (front page headline: 'Miller's Last Olympic Stumble Is Final Blow to U.S. Swagger') has an article in the METRO section about a large and growing Presbyterian Church in Manhattan.

In the twilight of the biggest snowstorm in New York City's history, the pews of a rented Baptist church on the Upper West Side of Manhattan were packed for the Rev. Timothy J. Keller's fourth sermon of the day.

The 600 or so who braved the snow for the evening service got what they had come to expect — a compelling discourse by Dr. Keller, this time on Jesus' healing of the paralytic, that quoted such varied sources as C. S. Lewis, The Village Voice and the George MacDonald fairy tale "The Princess and the Goblin." It was the kind of cogent, literary sermon that has helped turn Dr. Keller, a former seminary professor whose only previous pulpit experience was at a small blue-collar church in rural Virginia, into the pastor many call Manhattan's leading evangelist.

Over the last 16 years, Dr. Keller's church, Redeemer Presbyterian, has swelled to 4,400 attendees, mostly young professionals and artists who do not fit the prototypical evangelical mold, spread out across four different services on Sundays. Although Dr. Keller, 55, is hardly a household name among believers outside New York — in part because he has avoided the Christian speaking circuit — his renown is growing in pastoral circles and in the movement to establish or "plant" new churches, a trend among evangelicals these days.

Pastors from around the world are beginning to come in a steady stream to New York City to glean what they can from Dr. Keller and Redeemer. Their goal is to learn how to create similarly effective churches in cosmopolitan cities like New York, which exert outsize influence on the prevailing culture but have traditionally been neglected by evangelicals in favor of the suburbs.

[snip]

Since 2000, when it established its own training center for "church planters," as they are called in evangelical parlance, Redeemer has helped start more than 50 churches in the city, from faith traditions and denominations as diverse as Assemblies of God, Lutheran and Southern Baptist. In addition, it has helped found 17 "daughter churches" of its own Presbyterian denomination in communities like Williamsburg and Park Slope, Brooklyn; Astoria, Queens; and Hoboken, N.J.

[snip]

Unlike most suburban megachurches, much of Redeemer is remarkably traditional — there is no loud rock band or flashy video. What is not traditional is Dr. Keller's skill in speaking the language of his urbane audience. On the day of the snowstorm, Dr. Keller tackled a passage from the Gospel of Mark in which the friends of a paralyzed man carry him to Jesus. At least initially, however, Jesus does not heal the man but offers him a puzzling line about his sins being forgiven.

Part of the point, said Dr. Keller, is people do not realize that their deepest desires often do not match up with their deepest needs.

[snip]

Sept. 11 proved to be a defining moment for the church. On the Sunday after the terrorist attack, more than 5,000 people showed up.

So many people packed the church's Sunday morning service that Dr. Keller called another service on the spot, and 700 people came back to attend. While attendance returned to normal in other churches after several weeks, Redeemer kept attracting about 800 more people a week than it had drawn before the attack.

"For the next five years, I would talk to people about when they joined the church, and they said right after 9/11," Dr. Keller said.

[snip]

After the attack, the church also began to increase its training for those working to found churches. His church's main goal, Dr. Keller said, is to teach pastors how to truly love the city, rather than fear its worldly influences. Unlike many evangelicals, Dr. Keller advocates an indirect approach to change. "If you seek power before service, you'll neither get power, nor serve," he said. "If you seek to serve people more than to gain power, you will not only serve people, you will gain influence. That's very much the way Jesus did it."

As a result, one of Redeemer's hallmarks has always been its focus on charity, something it emphasizes in its training of urban pastors. It operates a program called Hope for New York that arranges volunteer opportunities for people from Redeemer with 35 different partner organizations. Last year, 3,300 people from the church volunteered their time.

[snip]

On the night of the snowstorm, Dr. Keller closed his monologue with a moving riff on Jesus' love in spite of humanity's flaws, and a quote from C. S. Lewis, one of his favorite writers: "The hardness of God is kinder than the softness of men, and his compulsion is our liberation."

source:
Preaching the Word and Quoting the Voice by Michael Luo
New York Times Sunday 2-26-2005 Metro p. 29

There's a slide show here. The congregants are incredibly young, and there are no children anywhere. (No mention of a Sunday School, either.) For me, it's strange.

I'm going to have to go hear him preach.

-- CatherineJohnson - 26 Feb 2006

DanKOnRightAnswersAndPleasureInMath 27 Feb 2006 - 00:29 CatherineJohnson

This is something I've been thinking about for awhile now, but hadn't gotten around to bringing up.

How do you get a kid to like math?

I didn't worry about it much when Christopher was in grade school, because I was boss; Christopher had to do what I said.

I'm still boss here in middle school - the boss of last resort at least - but it's a fight to the death, and the day when Christopher makes his own decisions about what he likes and doesn't like, and will and won't pursue, isn't far off.

Is he going to graduate high school with a superb grasp of K-12 mathematics?

If his father and I have anything to say about it, the answer is yes.

But I'm not sure how much we will have to say about it 4 years from now.

Another thing: as the British report on the UK's dwindling supply of mathematicians and applied math types points out, if we hope to increase the number of people who are good at math, we have to increase the number of students who want to be good at math. We don't have a math draft, after all.

from the report:

At this point we should perhaps comment on an apparent contradiction underlying our analysis.

(i) We know that many students find mathematics hard.
(ii) Yet our goal is to attract more students to the study of mathematics.

A crude “consumerist” model of education might lead one to conclude that one has no choice but to “drop the price” – that is, to concentrate on making mathematics “easier”. Yet we have repeatedly emphasised both (a) the need to strengthen basic technique and to expect more students to integrate one-step routines into multi-step wholes, and (b) the urgent need for a massive increase in the number of students taking A level Mathematics. How can such talk be realistic? And how can it be achieved?

These are serious questions – provided they are not merely rhetorical. Resolving the present crisis will not be easy; but, as we shall try to indicate, there is no essential contradiction in the analysis.

First, one has to understand that the long term challenge of ensuring a natural flow of home-grown mathematically competent graduates is quite different form the short term goal of selling off an unfashionable product simply by “dropping the price”.

Second, one has to recognise that a modern economy is mathematical in so many ways that we really have no choice but to find ways of producing a reliable flow of mathematically competent graduates – unless, that is, we are content to become a dependency of those countries that do appreciate the essentially “mathematical” character of a modern economy.

Third, we need to remember that the number taking A level Mathematics as recently as 1989 was more than 50% larger than at present, so there is no obvious logical reason why the goal is unrealistic.

So the question of motivating or inspiring kids to like math, and to want to pursue it, is important.

Constructivists seem to have given this question thought, and I've seen at least two real-live kids around here who love TRAILBLAZERS, and are having the time of their life with it. (I've seen more a few more who dislike it...)

Even so, if I had to bet, I'd bet that the answers constructivists have come up with are wrong, for the reason Dan K points out:

My daughter threw a (minor) fit today about having to do an extended response math homework problem. "I got the right answer," she wailed. "I did it in my head. Why do I have to write a paragraph about it?" I know I would have been as least as whiny back in my youth. I'm a mature adult now, so I enjoy learning stuff just to learn it. I can remember, though, wanting to get by with as little work as possible back in school (I still don't like working too much). To me, some of the best things about math, as opposed to other subjects, were 1) there's a right answer; 2) no term papers; and 3) no essay questions. Modern educators have eroded those benefits.

I agree.

I agree, because people who are good at math so often say that the thing they loved about math when they were kids was that there was a right answer.

For a particularly spectacular example, consider Lisa Randall (\$?)

There used to be an ice cream parlor in the student center at the Massachusetts Institute of Technology. And it was there, in the summer of 1998, that Lisa Randall, now a professor of physics at Harvard and a bit of a chocoholic, and Raman Sundrum, a professor at Johns Hopkins, took an imaginary trip right out of this earthly plane into a science fiction realm of parallel universes, warped space and otherworldly laws of physics.

They came back with a possible answer to a question that has tormented scientists for decades, namely why gravity is so weak compared with the other forces of nature: in effect, we are borrowing it from another universe. In so doing, Dr. Randall and Dr. Sundrum helped foment a revolution in the way scientists think about string theory - the vaunted "theory of everything" - raising a glimmer of hope that coming experiments may actually test some of its ineffable sounding concepts.

Their work undermined well-worn concepts like the idea that we can even know how many dimensions of space we live in, or the reality of gravity, space and time. The work has also made a star and an icon of Dr. Randall. The attention has been increased by the recent publication to laudatory reviews of her new book, "Warped Passages, Unraveling the Mysteries of the Universe's Hidden Dimensions," A debate broke out on the physics blog Cosmic Variance a few weeks ago about whether it was appropriate, as a commentator on NPR had said, to say she looked like Jodi Foster.

"How do we know we live in a four-dimensional universe?" she asked a crowd who filled the Hayden Planetarium on a stormy night last week.

"You think gravity is what you see. We're always just looking at the tail of things."

Although it is the unanswerable questions that most appeal to her now, it was the answerable ones that drew her to science, especially math, as a child, the middle of three daughters of a salesman for an engineering firm, and a teacher, in Fresh Meadows, Queens. "I really liked the fact that it had definite answers," Dr. Randall said.

source:
Scientist At Work | Lisa Randall: On Gravity, Oreos and a Theory of Everything by Dennis Overbye
NEW YORK TIMES
November 1, 2005, Tuesday

So here we have the Holy Grail, the object of millions of dollars of NSF-funded curriculum-building and conference-hosting, a Woman in Physics - at Harvard, no less!

What got her interested in math?

Lisa Randall

update: more from Dan

I'll also add that math is not the only realm in which there are right answers. Some kids of all ages enjoy playing games like Trivial Pursuit or the home version of Who Wants to be A Millioinaire? It's not because you're going to get rich winning the home edition. It's because it's fun to get the right answer. That's the whole point of the game.

And don't forget variable reinforcement!

maths in England
maths in England, part 2
more maths in England, part 2
top students in England, US, & Singapore
why do kids like math?
another brilliant person who liked getting right answers (scroll down)
Catherine's cousin talks about Everyday Math

Call for national debate on maths teaching GUARDIAN
Where will the next generation of UK mathematicians come from? (GOVT REPORT: pdf file)

The Beauty of Branes SCI AMER
On Gravity, Oreos and a Theory of Everything NYTIMES (possibly \$)
On Gravity, Oreos and a Theory of Everything NYTIMES (pdf file)

extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal

-- CatherineJohnson - 27 Feb 2006

CreativeProblemSolving 27 Feb 2006 - 18:50 CatherineJohnson

Illinois Loop has a terrific page of book reviews, which includes Creative Problem Solving in Mathematics by George Lenchner, a book published by Math Olympiads (though I'm not finding it on their website):

This book is highly recommend by math teachers as a source for specific problem solving strategies with example problems applicable to each strategy.

I have Dr. Lenchner's Math Olympiad Contest Problems for Elementary and Middle Schools. I think it's terrific, although I haven't spent much time with it. I suspect my brainy Singapore Math kids would have liked it.

The problems are quite challenging, and there are usually two methods given for solving them, which is great for a person who wants to wrestle with these things. I'm guessing this may be good for teachers or parents like me who are trying to acquire 'PUFM' (Liping Ma's 'profound understanding of fundamental mathematics'). I spent a few weeks working with Lenchner's book, making sure I could follow both methods of solution, not just the method of solution I'd come up with on my own.

I was surprised by how hard it was for me to follow an alternative Method for a problem I'd been able to solve.

Am I just ancient and cognitively rigid?

Or is this a common experience?

Whatever the answer, my rule now is always to teach myself the 'other method.' If Saxon gives two methods for solving a problem I practice both.

I'd love to take a look at Creative Problem Solving.

creative problem solving

Happy July Fourth (Moise & Downs)

-- CatherineJohnson - 27 Feb 2006

ProportionChapterTest 28 Feb 2006 - 00:40 CatherineJohnson

OK, it's the coldest day of the year & the heat is out. It's 63º in here. I got home 10 minutes ago and am just now starting to register exactly how cold 63º is indoors at night.

It's cold.

I'll post this quick, then get under the covers and do Lesson 95 in Saxon 8/7.

Christopher got his Chapter 6 test back today. Ratio, proportion, & percent. This is the test he 'broke down' in.

Turns out 'broke down' means he started crying in class, while taking the test.

He started crying because there were 14 questions on the test, and it took him half an hour to do the first 3. He panicked and started crying.

That's the bad news. I now have a kid crying in math. (What were we saying yesterday about getting kids to like math?)

The good news is he got an 80.

80 is a sucky grade, but it's not a 70 or a 60. To get an 80 on this particular test means he has some basic, starter knowledge of ratio, proportion, and percent. He might have a little more than that; this was a serious test, not to mention a LONG one. Plug and chug.

Plus the test was almost all story problems, and of course the teacher rarely assigns story problems for homework. I had him do as many word problems as I could fit in; plus we studied the Saxon 8/7 lesson on proportion. But still. Eleven word problems on a 40-minute test when your teacher almost never has you do word problems — that's big.

Last but not least I'm thinking that answering 11 questions in 15 minutes when your rate is 1 question/10 minutes and you're crying.....that's good! Bode Miller would have just quit!

I told him, Getting an 80 while you're crying is good.

Next time don't cry & get a 90.

-- CatherineJohnson - 28 Feb 2006

HenryDavidThoreau 28 Feb 2006 - 14:31 CatherineJohnson

What does this mean? (I don't understand the line about 'steering within the fewest points of the wind.)

He is the best sailor who can steer within fewest points of the wind, and exact a motive power out of the greatest obstacles.

- Henry David Thoreau

-- CatherineJohnson - 28 Feb 2006

MathOlympiadProblems 28 Feb 2006 - 14:42 CatherineJohnson

source:
Math Olympiad Contest Problems for Elementary and Middle Schools
Dr. George Lenchner

the solutions

creative problem solving

Happy July Fourth (Moise & Downs)

-- CatherineJohnson - 28 Feb 2006

RatioProblemFromTheBbc 28 Feb 2006 - 16:10 CatherineJohnson

What is ratio?

Ratio is a way of comparing amounts of something. It shows how much bigger one thing is than another. For example:

• Use 1 measure screen wash to 10 measures water
• Use 1 shovel of cement to 3 shovels of sand
• Use 3 parts blue paint to 1 part white

Ratio is the number of parts to a mix. The paint mix is 4 parts, with 3 parts blue and 1 part white.

The order in which a ratio is stated is important. For example, the ratio of screenwash to water is 1:10. This means for every 1 measure of screenwash there are 10 measures of water.

Mixing paint in the ratio 3:1 (3 parts blue paint to 1 part white paint) means 3 + 1 = 4 parts in all.

3 parts blue paint to 1 part white paint = is ¾ blue paint to ¼ white paint.

If the mix is in the right proportions, we can say that it is in the correct ratio.

This mission - improving the basic skills of adults - probably means Skillwise is going to be a good resource for math problems real people use in the real world: the kinds of problems you can show a child - or a Washington Post columnist - who's wondering out loud whether he'll ever 'use math' once he's out of school.

more real-world math

from the Delta College Teaching/Learning Center:

Ratio and Proportion in Nursing Math

Proportion is often used to calculate a dosage. Suppose a drug comes in tablets of 150mg. The dosage ordered is 375mg. How many tablets are needed? Here is the problem:

To Solve for x, we have to cross-multiply:

x = 2.5 tablets

I don't know about you, but I would like any nursing staff taking care of me & mine to know this stuff cold.

Ratio And Proportion in Nursing Math: Sample Problems & Answers

more Nursing Math

-- CatherineJohnson - 28 Feb 2006

CoolDimensionalAnalysisProblemFromSaxon87 28 Feb 2006 - 23:25 CatherineJohnson

The Adams' car has a 16-gallon gas tank. How many tanks of gas will the car use on a 2000-mile trip if the car averages 25 miles per gallon?
(source: Saxon 8/7 Lesson 96 page 660 #3)

printable version

keywords: dimensional analysis unit multipliers