Entries from MiddleSchoolMath

A comparison of our eighth- and ninth-grade data reveals three middle grades experiences associated with students who take and succeed in higher-level courses in grade nine.

These experiences are:

• studying “something called algebra” in the middle grades;
• reading a great number of books in grade eight; and
• expecting to graduate from college.

Studying “something called algebra”

Across all schools, 62 percent of the students who said they had a course with “algebra” in its title during the middle grades were enrolled in college-preparatory mathematics in ninth-grade. Eighty-five percent of these students earned a “C” or above. High enrollment schools enrolled 82 percent of students who had algebra in the middle grades in college-preparatory mathematics courses. They had virtually the same success rates as schools with lower enrollment rates. Clearly, students who begin algebra earlier are more likely to succeed in an accelerated mathematics curriculum if high schools choose to enroll them inthis curriculum.

You can just feel how much fun it is trying to drag information out of young teenagers for the purposes of a Major Report.

Yeah, I studied something that said algebra. I think.

Hotmath.com

[Hotmath provides] explained solutions to the odd-numbered homework problems from most of the popular secondary math textbooks used in California. Thus, teachers can now assign practice problems for homework where teacher-prepared, explained solutions are instantly available, and can mix in even-numbered problems for challenges. Students who do not need to see the worked solutions needn't bother, and students who might abuse the availability of worked solutions will be tested on the even problems.

Providing students with worked out examples of math problems has been found to be more effective than simply assigning the same problems for the students to work out on their own. In one experiment (Carroll, 1994), 40 high school students were instructed in how to solve linear equations. In an “acquisition phase” the students were divided into two groups and their instruction differed in the following way: in the “conventional learning” group, students were assigned 44 unsolved problems to work out (in the classroom and at home homework), and in the “worked examples” group students were provided with the same problems, but half of the problems were accompanied by correct solutions. After completion of the assigned problems, both groups were tested on 12 related problems, 10 of which were very similar to the linear equations presented in the acquisition phase, and 2 of which were word problems, used to test whether students could transfer and extend their knowledge to a new context. No worked out examples were available during the test. The test results revealed that students in the “worked examples” group outperformed students in the “conventional learning” group on both types of the test problems. A second experiment, employed a similar methodology but focused on “low achieving” students (students with a history of failure in mathematics, and students identified as learning disabled). Here, the data revealed that students in the “worked examples” group required less acquisition time, needed less direct instruction, made fewer errors, and made fewer types of errors than students in the “conventional learning” group.

Related research (Pass & Van Merrienboer, 1994) sheds light on the cognitive underpinnings of the effects described above. In this study, 60 college-aged students were instructed in geometry concepts. As in the Carroll experiments, students were assigned un-worked problems to solve or worked out examples to review (unlike the Carroll study, the “worked examples” group was assigned no un-worked problems to solve). In this study, the researchers manipulated the nature of the problems presented to the students: within each group, some students received problems which were all similar to each other, while others received a more varied problem set. Furthermore, the researchers measured the “cognitive load” experienced by the students. This research revealed that while students in the worked examples group completed their work more quickly, they perceived the work as less demanding and displayed better transfer performance at test. The effect was most pronounced for the students given highly-variable problems. The researchers suggest that the reduced cognitive load associated with the worked examples enabled students to “take advantage of” the variability in problems by using the available cognitive resources to process the underlying similarity in the problems (i.e., the mathematical concepts being taught), and to integrate the current problem with existing knowledge (Linn, 2000).

I think it's going to be fantastic for Christopher to have an answer source that isn't His Mother.

Especially since it looks like I'm going to have to start some heavy-duty Writing Instruction this year. (That's another story.)

cognitive load

We're trying to reduce cognitive load.

update

OK, that was unkind.

Anyway, Carolyn and I have been trying to figure out WHICH Prentice-Hall middle school math textbook the state of California adopted, since we had thought we were both using the same one.

It turns out we're not. (OK, it's possible Carolyn is not obsessing about this. I, however, am losing Valuable Work Time trying to track down which text the folks at mathematically correct like, and why.....)

So far I find a positive review of Ben's text for the fall (Prentice Hall Math Course 2) at mathematically correct; then I find, on what I assume must be David Klein's web site, that Prentice Hall Pre-Algebra (Christopher's Prentice Hall book for the fall) is the one California actually adopted.

Apparently, my plan is to let this Get To Me. Who moved my cheese? And why, why, why?

(I may become calmer if Ed resolves the computer crisis that's currently unfolding upstairs in my office.....)

Here we go:

CA 2001 middle school textbook adoptions

positive review of Prentice Hall Math Course 2

severely fragmented review of Prentice Hall Pre-algebra

Prentice Hall California Mathematics
(this is probably going to be terrific for me, assuming CA is actually using Pre-Algebra, not Course 2...)

teachers' resources on Prentice Hall CA Math site

• in the STUDENT SECTION: online 'self-tests' for each of the chapters in Prentice Hall Pre-Algebra
• in the TEACHER SECTION lists of prerequisite skills for each chapter in Prentice Hall Pre-Algebra

I may be able to pick up some pedagogical content knowledge in my spare time.

prerequisites for Chapter 1: Integers and Expressions

• adding and subtracting whole numbers
• multiplying and dividing whole numbers
• comparing whole numbers
• combining whole numbers
• reading numbers on a number line
• using whole number patterns
• graphing on a number line

OK, we've got it covered.

Except maybe for the using-whole-number-patterns business.

update, update

And here is a whole big web site for middle school math that looks like fun. (Did I just say that? Have I lost my mind?)

Apparently I have become a person who SEEKS OUT Problems of the Week.

I'm going to have to get Bernie to tell me what this means.

[pause]

uh-oh

There's a whole lot of spatial stuff on the problems web site.

I have a long way to go.

They have an article about Kitchen Table Math in the latest issue! (Although so far I haven't been able to find it.....I don't think....)

Sigh.

However, I have managed to attach and display the logo they sent me!

A ktm guest left a link to an online course that is actually called Universal Algebra.

I'm going to add this link to the Favorite Math Supplements for Kids page (on the sidebar) so people can find it.

By the way, anyone who has resources to add to the list should let Carolyn or me know.

Today was Ben's first regular day at his new middle school (yesterday was officially Transition Day, for 6th-graders only). He came home pretty happy; they are helping him with his organizational stuff, he is coping with his locker, and he doesn't have any homework yet. He is enjoying feeling like a big kid. Life is pretty good.

I went to pick him up at the end of school; he wanted to give me the grand tour of his teachers and classes, but we didn't have enough time to do the whole thing. I did ask him to take me to his math teacher, so I could shake her hand and tell her that I'd chosen this middle school because I thought it had made a good choice in math curriculum (having chosen Prentice Hall's Math Courses 1 through 3), and that I'd fought like heck to get Ben into their school for just that reason, and was commuting for a half hour in the morning in order to get him there.

So Ben and I went into his math class, and I introduced myself, and stuck out my hand and smiled, and got about halfway through my spiel when I noticed that in back of her there is a stack on the floor of Connected Mathematics pamphlets. So my final sentence actually came out something like--

"... I really approve of the curricular choice you've made and -- what curriculum are you using ???"

It turns out they are using a hybrid curriculum: every unit will be taught using both Prentice-Hall and Connected Mathematics.

A little background first: Connected Mathematics is an extreme example of a constructivist mathematics curriculum that our school district has adopted (in fact, our SD was an early adopter of Connected Mathematics). I battled long and hard last year to get Ben into a middle school that used a traditional mathematics curriculum instead of Connected Math. I had tearful phone conversations and hot-tempered meetings over this issue.

Whether or not I think Connected Math is a reasonable math curriculum has not been an issue in my fight to have Ben learn math from a traditional curriculum. Ben has special needs, and won't have a lot of employment options; he will need a strong math background in order to have a trade as an adult.

In grade school, Ben did extremely well in Saxon math for the first 3 years; but for the last two, the school switched to a semi-constructivist curriculum (Everyday Math), and Ben ceased to thrive. He didn't cope well with the emphasis on verbal explanations, the games and group exercises, multiple methods for doing calculations, and constant jumping from topic to topic. He went from being completely independent in math class to requiring an aide on a daily basis (our story was mentioned in Linda Seebach's recent article on KTM in the Rocky Mountain News).

When we were discussing Ben's options for middle school, everyone agreed that he needed a traditional curriculum. I open-enrolled him into this school in order to ensure that he would get one, and battled the school district when it looked as though he would not get into it.

Now I find that the school I thought -- was in fact assured -- had a traditional math curriculum actually has a hybrid curriculum which incorporates Connected Math. Connected Math is so purely constructivist that it makes Everyday Math look tame.

Here is the Mathematically Correct review of 7th grade Connected Math (and the many reasons why it received an F).

Here are descriptions of the units in 6th grade Connected Math and 7th grade Connected Math. Read these to get a feel for what kids spend their time doing in Connected Math.

I attended a new parents session at our neighborhood middle school in which Connected Math was discussed. We were told that Connected Math was generally not well liked by parents, who found it impossible to help their kids do the problems because "the style in which it is taught is so different from the rote way in which parents have typically learned math". I have a Ph.D. in math, and taught and tutored math at the college level for ten years; this kind of prevarication doesn't impress me. I know what Connected Mathematics and similar curricula do; they leave college students weak, and utterly without math skills.

We have not yet decided what to do; fortunately we have the weekend to think this over.



worsethanyouthink

SingaporeMathPlacementExam 05 Sep 2005 - 13:33 CarolynJohnston


The last two nights, I've been giving Ben the Singapore Math 4A placement exam (all the Singapore Math placement exams can be found here). I had a look at the Singapore Math 3A and 3B tests, and decided that Ben can probably do them fairly easily; but I wasn't so sure at all about Singapore Math 4A.

I've been giving the test to him in little chunks. The first day I did it -- it was several days after school had started, and I hadn't tutored him at all, and he was having an easy time of it since all they were doing was factoring numbers into primes -- he howled as though I were slipping bamboo shoots under his fingernails. That was to be expected. We always get the worst resistance after he's had a break.

At this point, I've gone as far with him in these placement tests as I plan to go -- 4A is definitely the place for him to start. What I'm finding is that in the first part of the placement exam, where the problems are computational, he is doing fine; I've taught him well in that regard (using mostly Saxon math, with some Prentice-Hall). However, after the first ten or so problems, the placement exam starts to test a kid's problem-solving ability. In Ben's case things got ugly quickly. He fell apart emotionally in the face of these problems, of a type he'd never seen before.

The first two problems involved analyzing a figure for parallel and perpendicular lines, and determining the area of a rectangle that had had a couple of rectangular pieces removed. That last is a real-world problem, by my lights, if there ever was one.

These two problems were on the placement exam as well:

A rectangular swimming pool measures 24m by 16m. A concrete path 2m wide is paved around it. What is the area of the path?

Mary bought 1m of ribbon. She used 2/5m to tie a package, and 2/7m to make a bow. How much ribbon had she left?

Ben's reaction to the second one was especially interesting. By the time he got to that problem, he was frazzled by having had to skip a few of the earlier ones. He shouted:

"What do you expect me to do, add 2/5 and 2/7?"

"Yes," I said. "Oh," he said.

Ben's confidence crumbled fast with this placement exam. I tried to assure him that it was just a pretest, and that he should skip problems he can't do; but he's just frail these days. Perhaps all kids are.

I think the Singapore math curriculum may work for us. It's challenging, but we can do it; it's not impossible. And at least the evidence says we're on the right track with it.

And the books are cheap, to boot (check them out here).

---

MiddleSchool 08 Sep 2005 - 14:02 CatherineJohnson


Christopher started Middle School today.

I am wearing my black Govenator t-shirt in honor of the occasion.






UPDATE 11-20-06: good choice



parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

worsethanyouthink

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MiddleSchoolPart2 07 Sep 2005 - 17:55 CatherineJohnson


Ed was awakened at 6 am this morning by a violent anxiety dream that began with me shouting 'Get down!'

We all dropped to the floor and huddled below the window sill, trying not to be spotted by the TRUANT OFFICER, who was walking up to our door.

It didn't work. The officer came into our house and took Christopher away.


So this morning I ordered my copy of Not Much Just Chillin'.

Here's Kay Hymowitz:

...[middle school] classmates are like the KGB with orthodonture, surveilling the halls for unusual odors, dress, language or manners...

Then there's the inevitable How We Got Here passage:

Of course, peer pressure and sullenness have been defining traits of these school years since long before middle schools were introduced in the U.S. in the 1960s. At the time, educators hoped to shape learning around new scientific findings about the nature of pre- and early adolescent thinking.

What makes me think these new scientific findings about the nature of pre- and early adolescent thinking were hokum?

Could it be the fact that we are now in the midst of a movement to dump middle school in favor of elemiddle? (subscription may be required)

In a new review of 20 years of research on middle schools, Rand Corp., a nonprofit organizations in Santa Monica, Calif., concludes that states and school districts should "consider alternative structures that allow them to reduce multiple transitions across grades K-12" in order to capitalize on "continuity of schooling and introducing changes gradually."

A number of districts that have recently begun converting to K-8 configurations say they have already noticed fewer disciplinary problems among students, as well as an increase in test scores.

[snip]

Particularly troublesome in Philadelphia was the noticeable decline in test scores after students graduated from elementary schools, which mostly went through the fifth grade. "Sixth-grade test scores were always our lowest," Mr. Vallas says.

Now, an analysis of standardized test scores from 2000 to 2003 shows that reading and math scores are consistently higher for eighth-grade students enrolled in some of Philadelphia's new K-8 schools compared with those in traditional middle schools. The average reading score for K-8 students was 1218 in 2003 compared with 1146 for students in middle school. Also, Mr. Vallas says, K-8 schools have higher attendance rates and fewer incidents of student discipline than do their middle-school counterparts.

My own district has just spent a gazillion dollars building a brand new middle school next door to the high school. The two schools share a big, fancy Ikea-style cafeteria with a noise level roughly equivalent to that inside an airplane hangar.

Last night Christopher was lying on the floor playing with his WWE action figures; today he'll be watching teenage boys get B-Js in the bathroom.

What's the word for that?

Friends with benefits?

Is that it?

Or have I lost my mind?


OK, I'm going to Reserve Judgment.

I don't actually KNOW, for a fact, that the 6th graders will be sharing bathrooms with the high school kids.

update

I haven't lost my mind.

Friends with benefits.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

MiddleSchoolPart3 09 Sep 2005 - 02:39 CatherineJohnson


Given the fact that Middle Schools were an invention of the late 20th century, I am perfectly willing to assume they were a bad idea from the get-go.

And I've read enough about other countries' curricula to believe this observation:

"The middle school is the crux of the whole problem and really the point where we begin to lose it," says William H. Schmidt, a professor of education at Michigan State University and the U.S. research coordinator for TIMSS. "In math and science, the middle grades are an intellectual wasteland."

Still, I'm not persuaded middle schools are entirely to blame for the middle school slump, necessarily.

Everyday Math in Schaumburg, IL

(It's Schaumburg-with-a-U)

I'd been meaning to write about this for awhile now.

I met two retired teachers, a married couple, from Schaumberg, IL at the airport on my first trip to Chicago this summer.

I was working on problems from my Russian Math book, so we got to talking about school & about math, and the wife, who had been a first grade teacher, told me that Schaumberg has been using Everyday Math for 15 years.

They were one of the first districts to try it out, and their students' scores promptly went up by 3 times. So they adopted Everyday Math, and have been using it ever since.

The grade school teachers apparently love E-Math, and the parents don't seem to mind. There was a Schaumberg district mom sitting next to me, who said she couldn't help her daughter with any of her math homework because she didn't understand it. This wasn't a problem; she seemed to think it was natural not to understand anything your 4th grader is doing in math, and not to be able to help with homework. No complaints.

The middle school teachers were another story.

When I asked how the middle school kids were scoring, both grimaced & said, 'Their scores are terrible.'

Then the wife gave me the story on the middle school teachers. 'They don't want to change,' she said. 'They want to keep doing things the same way they've been doing them for 20 years.' Her husband nodded.

They were sure that if the middle school also changed curricula, those students would have high scores, too.

I started to say kids need to know fractions & long division to do algebra, but had to stop when the wife grew visibly alarmed, thrust out both her arms at me hands first, and said emphatically, 'I teach first grade. I don't know anything about that.'


Schaumberg, I learned from my brother-in-law, is the 2nd largest school district in the Chicago area, after Chicago itself.

update

We have our answer!

THE STUDENT SHOULD BE THE UNIT OF ANALYSIS!

Tomorrow I'm reading up on Cargo Cults.

update update

connecting high school scores to elementary school


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

MiddleSchoolPart4 19 Sep 2006 - 12:40 CatherineJohnson


Day 2 and we have locker trauma.

Christopher can't open his locker. He spent hours after school trying to open it until finally a teacher came by and opened it with a key.

The reason we have locker trauma, apart from the fact that lockers are apparently not easy to learn when you're 11, is that Christopher's locker was jammed on Day 1, so when they taught the kids how to open their lockers Christopher wasn't able to follow along with the moves, or practice the moves after the demonstration.

No practice, no learning.

It's a Discovery Locker.

Google has failed me

So naturally I was searching all over the web for locker opening instructions....and I came up with these, which are fine, but which apparently are not the instructions for Irvington lockers.

today's advice: before your kid goes to middle school, buy a combination lock and have him practice it 5 gazillion times.


they grow up so fast





parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

ExtendedResponse 08 Nov 2005 - 22:52 CatherineJohnson


My sister-in-law, a fantastic teacher in central Illinois, says the Big New thing in math is extended response. She's going to fill me in when she finds out what it is.

In the meantime, I found this page of released extended response items on the ISAT.

my extended response to extended response

OK, my initial reaction to extended response is: I'm against it.

Actually, make that mixed. My initial response is mixed.

Here's one of 2 released 2004 extended response gr5 items:

A company makes a wall calendar each year. The company sells ad space
around the calendar to local businesses. The cost of ad space is based on
the number of square units each ad contains. The company charges $40.00
for Ad Space D. Using this information:

Draw an Ad Space that costs exactly $60 in the gridded space on page 10 of
the answer document.


And here's the illustration:




I like this problem, although wiser heads here at ktm may give me reasons why I shouldn't, in which case I'll revise my opinion.

I like it because it's visual & spatial as well as 'numerical' (if that's the right word), and because I've found Christopher to be very challenged by any problem that asks him to combine numerical thinking or problem-solving with spatial 'thinking' or problem solving. And of course I love the Singapore bar models, and this problem reminds me of them.

I also like it because it has 2 steps: you have to figure out how much each square costs & then you have to figure out how many squares $60 would buy.

I like the open-endedness of this particular problem, too. A child could simply count the number of squares in Ad Space D (40) and then divide 40 dollars by 40 squares to get $1/square. Or he or she could notice that Ad Space D is a standard multiplication array, and multiply 4 by 10 to get 40. I'm sure a lot of kids would start out counting & then notice, mid-stream, that they could have arrived at their answer more efficiently by multiplying instead. Which is good. A little Math Object Lesson buried inside a story problem.

I like that!

Last but not least, I kind of like the fact that each square turns out to cost exactly one dollar. I don't know why. It reminds me of a genre of problems in Russian Math, in which you go through all kinds of elaborate, painstaking calculations only to end up with an answer of ONE. Or maybe TWO. Or, when things get really fancy, ONE HALF.

Interestingly, I'm finding, as I work my way through RUSSIAN MATH, that I'm becoming quite attached to the number one. Every time it crops up as an answer I think: I should have seen that coming. An answer of one always seems like a flag, a sign that there was an easier, more elegant way to do whatever it was I was doing.....but I missed it.

Russian Math has all kinds of 'surprise answers,' and I think a surprise answer in the middle of an ISAT could be slightly.....fun?

An answer of one is like a little joke.

What I don't like...

...is the injunction to Explain in words how you got your answer and why you took the steps you did to solve the problem.

That is a terrible, terrible idea for a test.

It's a good thing to do on homework once in awhile, or in the classroom. RUSSIAN MATH asks students to write out explanations, although it doesn't ask students to explain how they did a problem. It asks them to restate the definitions & explanations given in the lesson.

Items like these can't possible be graded well on tests. They are far too time-consuming, and graders will end up scoring on length or number of explanations given. When you have items like these teachers are going to end up devoting all kinds of class time to writing extended responses, as Susan H says is already happening. We're looking at a massive waste of teachers' and students' time.

Last but not least, I'd bet the ranch you learn nothing from the verbal explanation that you didn't already learn by looking at the student's work.

Being able to produce a fluent, intelligible verbal explanation of a mathematical solution is almost certainly important for math teachers.

It's not important for the rest of us.

I really don't like this one

The number of fifth-grade students going to the museum is greater than 30
but less than 50. Each student will have a partner on the bus. At the
museum, each tour group will have exactly 6 students.

How many students are going to the museum?

Show all your work. Explain in words how you got your answer and why
you took the steps you did to solve the problem.

Unless 5th graders in Illinois are doing a lot of prime factor problems, I don't see any reason to include an item like this one on a timed assessment.

First of all, no one should have to be doing discovery ON A TEST.

And second, this problem has two answers (36 & 42, right?), but the wording implies that it has just one answer, and that one answer is findable.

I am DISCOVERING the fact that I don't think red herrings belong in math classes. Certainly not in elementary school math classes.

What is the point? You are teaching children to distrust the English language at the precise moment they're learning grammar & composition. An unreliable narrator in a work of fiction can be a terrific device.

But an unreliable questioner in an examination is just wrong.

I'm against it.

update: I forgot 48!

sigh

(thank you, Dan K)

extended response in 8th grade

Here's the 2004 released 8th grade item:

Peter sold pumpkins from his farm. He sold jumbo pumpkins for $9.00
each, and he sold regular pumpkins for $4.00 each. Peter sold 80 pumpkins
and collected $395.00.

How many jumbo pumpkins and regular pumpkins did he sell?

Show all your work. Explain in words how you got your answer and why
you took the steps you did to solve the problem.


The problem is fine, assuming these kids have actually been taught some algebra.

If they haven't, this is a discovery problem on a timed assessment, and I'm against it.

So, assuming they've learned how to set up & solve equations with unknowns, the problem is good. IMO.

The demand that the student explain each step in words is not.

Russian Math rocks

Instead of writing about Russian Math, I should be downstairs (at the kitchen table!) actually doing some Russian Math.

So I think I'll sign off.

But tomorrow I'll give some examples of what a proper extended response item should be.

A proper extended response item should be a RUSSIAN MATH EXTENDED RESPONSE ITEM.

update: scoring rubric for extended response

'Student Friendly' Mathematics Scoring Rubric

Assuming I'm reading this correctly (I feel a little distrustful), students must get all computations correct in order to earn the highest possible score of 4. They can earn a score of 3 with minor mistakes in computation, which I feel is fair, though others may disagree.

What I reject absolutely is the explanation section:

• I write what I did and why I did it.
• If I use a drawing, I can explain all of it in writing.

This is wrong. I don't believe a 4 should depend upon being able to supply an explanation in any case. But here you have a child who can explain why he or she did what she did in a drawing, which is no mean feat (and I'm in a position to know) and even that isn't enough.

Pace Anne, you'll notice that it's not OK for a child to explain what he/she has done by offering a mathematical demonstration, as the teachers in Liping Ma's book do. Anne's right about that; it struck me, too. Over and over again, when Liping Ma asks a Chinese teacher why he/she teaches an idea a certain way, the teacher responds by writing out a proof-like mathematical demonstration. That's what makes the book incredibly difficult (and incredibly valuable) to read for most of us; the teachers don't translate math into words, and neither does Ma.

For Chinese teachers, math is math.


This drops you to a 3:

• I write mostly about what I did.
• I write a little about why I did it.
• If I use a drawing, I can explain most of it in writing.

A couple of years ago the head of our school board sent out an email explaining the adoption of TRAILBLAZERS that included this line (from memory): In recent years math has become language-based.

I think that would come as a surprise to actual mathematicians.


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

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MiddleSchoolPart5 18 May 2006 - 21:27 CatherineJohnson


From a paper posted on a (pro-)Middle School site:

Converting a school system to a K-8, 9-12 configuration also eliminates the transition from fifth to sixth grade that occurs when there are 6-8 middle schools. As every parent knows, whenever a young person transitions from one level of schooling to another, whether that is from fifth to sixth grade23, or eighth to ninth grade, or twelfth grade to post-secondary education, there is potential for difficulty. These transitions require developing new relationships with adults and peers, negotiating unfamiliar and unwritten social norms, and responding to expectations of higher levels of academic performance.

Particularly for young adolescents who are also experiencing a variety of developmental stresses, the transition from elementary to middle schools can be problematic. The experience of adolescent development is filled with variables and unknowns, and one can argue that a potential beneficial effect of eliminating the fifth to sixth grade transition is to reduce, or perhaps just delay, the problematic effects of some variables.24

One researcher concluded that the fewer school-to-school transitions children experience, the more likely it is they will have a positive academic experience. After analyzing passing rate data from 232 schools in a large Midwestern inner-city school system, she reported:

As grade span configuration increases so does achievement. The more grade levels that a school services, the better the students perform. The more transitions a student makes, the worse the student performs..The longer a student stays in a given school, the better the student performs.25

The K-8 configuration may also lead to unanticipated political benefits for the school system. Families of young adolescents are understandably concerned about losing influence and control over their children. While many families are quite involved in their children’s elementary schools, their participation declines dramatically when their children enter middle school. This is not entirely the responsibility of the parents; middle school leaders often make less effort to engage parents as full partners in the educational process.

source: Still Crazy After All These Years: Grade Configuration and the Education of Young Adolescents (pdf file)


Our middle school does not permit a parent-run after-school program or any other form of parent involvement that would allow parents to set foot inside the door.

This is taken to such an extreme that, I'm told, the school has a formal policy against sending notices home in backpacks about school clubs & teams. (Naturally I'll be checking this out on back to school night. I could be wrong, though seeing as how my source is the PTSA president, I don't think so.) The administration believes that, at age 11, children must become responsible for themselves, so it's up to them to decide which clubs and teams to join, and to handle the details.

This week a mom who has one child in college told me that, back when he was in middle school, she used to hang out in the parking lot so she could introduce herself to teachers walking out to their cars.

My sister has been told exactly the same thing about middle schools in CA.

not entirely the responsibility of the parents—I'll say.

When middle school starts, the doors slam shut.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

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MiddleSchoolPart6 10 Sep 2005 - 22:51 CatherineJohnson


I think Dan K wins the award for Itinerant Schoolboy:

I know that personal anecdotes don’t generalize, but, hey it’s a blooki, right? So I will share that I attended six different schools for grades K-8. My family never moved. We just lived in a rural area outside town, so we were going to be bused wherever we went. Whenever a school on our side of town got a new addition built, we got bused there. Sure I had a number of bad first days or first weeks at school, but all the kids on my bus route went through the same thing. No one treated us as transient outsiders or kids who needed to be hazed or something to join the school. We just went to school. No big deal.

That's incredible!

(btw, I think anecdotes do generalize, which is one of the reasons I put so much time into ktm. I learn huge amount from Other People's Anecdotes. Anecdotes are just the everyday form of raw data. So while I don't personally know how Dan's multi-schooled childhood generalizes to other kids, I assume it does.)

Here's the rest:

Last school year, my wife and I were both working, so we put our younger daughter in an all-day pre-school. She was four at the beginning, so there were some transitional problems. Thereafter, she was fine. This school year, she has started at the public school. We did our best to prepare her, and…guess what?...she’s doing well. Is this unusual? Of course not. If a five-year-old can go from a private pre-school to a public school with zero classmates in common, I really think the major source of middle schooler trauma—-when all their classmates transition right along with them—-is due to everybody warning them that it’s a big deal. It’s a self-fulfilling prophecy.

I can certainly see that it’s much different for parents, especially if teachers belligerently keep parents out. Even without that, the fact that there isn’t one, clear homeroom teacher with which to interface makes it harder for parents. The upside, though, is that middle school and high school accommodate more tracking and electives. So, you’ve got to take the good with the bad.

So, to me, the question is much more about when students transition away from the homeroom-centric model to the subject-oriented class model.

The one observation I take issue with here is the notion that you get more electives & tracking with middle school.

I don't know about 7th and 8th grade yet, but there are no electives in our middle school 6th grade, and no more tracking than there was in 3rd, 4th, and 5th.

In that sense it's a case of taking the bad with the bad.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

MiddleSchoolPart7 11 Sep 2005 - 17:55 CatherineJohnson


This could be fun--

Save the date! Unmuddling the Middle—September 14, 2005 American students are achieving academic success—until they reach middle school.

The Thomas B. Fordham Institute is proud to host this timely debate on why the middle grades have become "the place where achievement goes to die." Dr. Cheri Pierson Yecke (newly appointed Chancellor of K-12 Education in Florida and author of the new Fordham report, Mayhem in the Middle) will join leading middle school researchers and practitioners to discuss the necessary steps for bringing children in this age group back on track before they reach high school. Joining (and debating) Dr. Yecke will be: Dr. James Beane (Professor in the National College of Education, National Louis University), Sondra Cooney (Consultant, Making Middle Grades Work, Southern Regional Education Board), Susan Schaeffler (Executive Director and Founding Principal, KIPP DC) and moderator Richard Whitmire (USA Today). Please RSVP no later than Monday, September 12, 2005, at 5 pm via phone at 202-223-5452 or email rsvp@edexcellence.net.

When
Wednesday, September 14, 2005
9-11 am (Continental breakfast available at 8:30 am)

Where
National Press Club
Holeman Lounge (13th Floor)
529 14th Street, NW
Washington, DC

So that gives you some idea about my idea of fun.

I wonder if Middle School actually is "the place achievement goes to die"??

Do we know for a fact that our kids are achieving in elementary school?

And that they slow down and/or stop in middle school?

I finally read Stevenson & Stigler's Learning Gap over vacation; I'll check exactly what they have to say about this & post.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

TeachingSubtractionAndIntegers 18 Sep 2005 - 02:42 CatherineJohnson


click on Printable Version to print


What is subtraction?

Subtraction is the ______________ of addition.


When you subtract, you __________ ___________ ___________________ of the number you are subtracting.


An absolute value is always _________________.


1 - 2 = _________

1 - ( - 2 ) = _________

-1 - 2 = _________

-1 + -2 = _________

1 - | 2 | = _________

-1 - | 2 | = _________

-1 - | -2 | = _________


answers
study sheet for class quiz on pages 2 - 16, Prentice Hall Mathematics: Explorations & Applications & Prentice Hall Pre -Algebra

outloud sheets: integers & absolute value
answer key
notes on outloud sheets for integers & absolute values
Carolyn on introducing absolute value
keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud

---

PracticeSheetIntegersSubtractionAbsoluteValue 16 Sep 2005 - 14:38 CatherineJohnson


I wrote up a study sheet for Christopher's test (it's in the next post) & dragged him through it kicking and screaming.

I think it worked, but we'll see.


If you hit 'Printable Version' it prints out great, exactly enough space for answers in big, round middle-school handwriting.

update

Christopher said last night he doesn't like it when I tell people he screams when we do math.

I told him, Stop screaming and I'll be happy to stop telling people.

We are at an impasse.

---

StudySheetIntegersSubtractionAbsoluteValue 16 Sep 2005 - 14:45 CatherineJohnson


(study sheet is here: subtracting integers & absolute value)


Here is how Christopher does this problem:

-1 - ( - 2 )


He pencils in a vertical line across both of the minus signs in the middle, turning them into plus signs:

- 1 + ( + 2 ) =


That works for him every time, no matter what the numbers, and he isn't thrown off by the same problem written with an absolute value:

-1 - | - 2 | =


This reminds me of Carolyn's belief that you need to get math into a child's hand.


For some reason a problem like:

-1 - 2

makes sense to him. He 'sees' that he's adding two negative numbers.

Here, too, however, he does a swoop and swoop thing: he squeezes in a plus sign between the 1 and the second minus sign, like this:

-1+-2 =

Ed's explanation to Christopher that you can think of -1 - 2 as adding two debts -- first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3 -- seems to have been the ticket.

I tried that explanation on a friend of mine who is severely math phobic, and she instantly got it, too. Adding debt to debt is something everyone can grasp! It's EVERYDAY MATH FOR THE MASSES!


From one of Carolyn's first posts:

That's what the standard algorithms are: they are moves that you learn how to make. Those moves get into your fingers, just like learning the piano or the violin or typing, and eventually you can do them completely mindlessly.


swoop and swoop
the craft of math
subtraction as the difference between 2 numbers
outloud study sheet: subtracting integers & absolute value
answer key
notes on integer, subtraction, & absolute value study sheet
Carolyn on introducing absolute value

keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud

---

ILikeMathPart3 17 Sep 2005 - 02:47 CatherineJohnson


I almost forgot!

Monday or Tuesday night, when Christopher was doing one of his first homework assignments from Prentice Hall Mathematics: Explorations & Applications, he saw an illustration on the side of the page with the caption:

The early Egypticans drew pairs of legs walking in different directions to stand for addition and subtraction.

He looked up at me and said happily, "I like math. I just don't like math when you make me do it."


BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
BonusPreTeenPost
fun with Saxon Math in the summer
SundaySchool
I like math
I like math, part 2
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids
Christopher on his 39
I like math, part 3

---

GlencoePreAlgebra 18 Sep 2005 - 00:05 CatherineJohnson


Glencoe Pre-Algebra is supposed to be one of the two decent not-completely-fuzzy Pre-Algebra texts out there....but I just found this review, by an Amazon reader calling himself wiredweird that I thought was so funny I'm posting it here. (No idea whether he's right or wrong, though I'd bet money he's right about the page splatter):

It is hard to imagine a worse math book, except maybe the earlier editions of this title. This book demonstrates just about every bad teaching and typographic practice I know. Every page is splattered with colored text in a menagerie of fonts. Most pages feature irrelevant or misleading photos, perhaps several. There are dozens of distracting sidebars, many full of errors in fact. Just looking at a typical page, I feel my attention batted about in a pinball trajectory. Holding a thought for the length of a Glencoe page is quite a challenge.

Math skills are cumulative; each new technique is founded on the earlier one. I can't think of a case where this book seems to sustain an idea for more than a few pages. Some students, through chance or a teacher's skill, may manage to glean some mathematical fact from this book. It will do them little good, though. The book's complete lack of continuity gives no reward for that success, measured in skills used later in the course.

Students who can't squeeze understanding from this book - the ones it calls "alternative assessment" students - are very nearly abandoned, as far as any real education goes. Instead of being offered meaningful help, they are invited to draw pictures and write essays about their feelings. Such students are not only left in the dust, they are patronized and insulted in the process.

I have examined earlier editions of this book, back to 1997. The only thing I can say in favor of it is that, in preparing the 2001 edition, some of the worst errors and blatant commercialism were removed. It improved, but its basic flaws remain.

Do yourself and your math student a favor: find a different title. A little web searching will point you to sites that review and recommend better books, as well as more detailed analyses of this one. Or just pick another title at random - this is so bad that almost anything would be an improvement.

(based on the 2001 edition)

I've just given wiredweird an honorary entry on Wit and Wisdom of Kitchen Table Math.

He's also written a review of an interesting-looking book called Four Colors Suffice: How the Map Problem Was Solved by Robin Wilson.

update

I had no idea there even was a Four Color Map Problem. Lucky for me there've been mathematicians around for lo these many years figuring this stuff out.

page splatter

I'm going to be using that one again.


Glencoe page splatter
Doug Sundseth on ransom note typography
Tom Friedman piles on
distance tutors & mathematicallycorrect review Glencoe
page splatter and the frontal lobes
page splatter redux
pagesplatter

---

GlencoePreAlgebraPart2 21 Sep 2005 - 11:03 CatherineJohnson



Susan has Googled up the Mathematically Correct review of Glencoe Pre-Algebra. (Thank you, Susan)

I had remembered it as being good, but didn't have the patience to go find it again for the gazillionth time.

They give Glencoe an A.

Pretty amazing.

I found it

While I was on vacation, USA Today ran a fabulous photo of a Distance Tutor chained to his terminal in India. There was a copy of Glencoe Pre-Algebra in the foreground that was so huge it was bigger than the tutor.





I love it.

That photo alone should be worth another billion or two in sales.


source: Overseas tutors help U.S. students online By Greg Toppo

hmm

OK, here is a picture of Glencoe Pre-Algebra.

This textbook cover & the Distance Tutor textbook cover are two different things.

mystery solved

This is the one, right?





Glencoe Pre-Algebra on Amazon.


Glencoe page splatter
Doug Sundseth on ransom note typography
Tom Friedman piles on
distance tutors & mathematicallycorrect review Glencoe
page splatter and the frontal lobes
page splatter redux
pagesplatter

---

DecisionMadeIThink 20 Sep 2005 - 01:45 CarolynJohnston


I've finally decided what to do about Ben's middle school math situation, which started out with a nasty shock and has been declining ever since.

We can't go on like this. I've been struggling with constructivist math in vain for three years, because I wanted to try to keep Ben in the mainstream math classes. I think, though, that something I wrote in this post has really taken root in my mind over the last few days; Ben may need to work on his social skills, but I don't want him doing it during math class.

And so it hardly seems worth keeping him in the regular class. What's the point? He can work on social skills in English, Social Studies, and Science, where the knowledge base isn't as relentlessly cumulative.

So now, at least, I know what I want to ask for. They've got an aide following Ben around a good part of the day anyway, so she might as well just take Ben out of the class and sit with him while he does a Saxon section a day. If she can't help him learn the day's lesson, that doesn't matter; I can do that. I just want him getting the bulk of it done during regular math time.

If he works through Saxon 8/7 successfully, he'll be way ahead of the other kids in his class. While I'd rather he did Singapore Math, I believe Saxon will be easier to do for everyone; Ben, me, the teacher, the aide. Plus, my major rule of thumb regarding Saxon -- that it's the curriculum of choice if a kid has lost confidence -- applies to Ben at this point. He needs to get his confidence back; he's had two-going-on-three difficult, confusing years. I can, and will, supplement from Singapore.

I agree with the commenters here that it's too bad that every kid can't have an IEP, and that (looking at it from a slightly different perspective) it's a shame that, in spite of IEPs, parents still have to take their school districts to court to get what they need for their kids. I am hoping that my request is simple enough that it just goes through, without my having to generate a big fuss; but if I have to, I will. The meeting is later this week.

Stay tuned though -- after I go to bat on math, I get to go ask sharp questions about why Ben, in his intensive reading and writing clinic, is doing less reading and writing than he did in elementary school.

---

KumonMathInDetroit 17 Nov 2005 - 13:28 CatherineJohnson



fyi:
KUMON math program
KUMON reading program


I've had an amazing email from an engineering professor who learned of Kitchen Table Math while she was in China (!)

(Apparently, not being listed on Google isn't a problem in China.)

She also sent me a copy of her paper on Kumon supplementation in Detroit schools (the results were incredible), and I'm waiting to see whether it's OK to post. In the meantime, she says it's fine to post her email:

I'm sure you must have come across Kumon mathematics? I'm a professor of engineering at Oakland University, and so mathematics is obviously very important to me. As a consequence, to make up for the problems with the American school system I've had my own daughters in the Kumon program for about ten years each--between the ages of three and thirteen. Their math skills are far better as a result. I was so impressed with the ideas behind Kumon (it is an outstanding supplement that provides the additional practice missing from K-12 math), that I started a program using the Kumon method in a local inner urban school district, Pontiac. The results are described in the attached paper.

Kumon provides the easiest, smartest way I've ever seen for a Mom to help her kids with math. I couldn't recommend it more highly.

One last thought. I've taught in China as well as the US. The US is definitely way ahead on the "creativity" side. But we are so far behind in math that it is ridiculous--and it is potentially crippling for our source of engineers and other professionals. There are many aspects involved in good engineering, for example, where a good math background is critical. Most of the engineering professors where I work now (Oakland University), are foreign born. Although I greatly respect my foreign-born colleagues, it's really an indictment of the American system that we can so rarely grow our own any more.

Thanks for your blooki, which I have bookmarked and will be following!

Kumon for children with severe disabilities, too?

And, in a follow-up:

Actually, the woman who ran one of the Kumon centers I brought my children to originally got into Kumon because she saw how much it was helping a profoundly mentally disabled child who she was working with. So I suspect it may be surprisingly beneficial for Andrew. I couldn't have done the outreach in my local inner-urban outreach without the incredible help I got from Doreen Lawrence, the Vice President of Research for Kumon, North America. Her phone number is 248-755-2587, and her email is dlawrence@kumon.com. Doreen is a wonderful person who is deeply oriented towards helping children. I'm sure she'd be glad to answer any questions you might have about Kumon (she knows EVERYTHING about the program).

You can feel free to post anything from my letter that might help. I just apologize for the poor writing. I just got back from China and am still jet-lagged.

Over the next week or two I'll read through your website more carefully and get a better feel for what's going on (I just found out about your website while I was in China, but scarcely had any time available while I was there). I've a lot of thoughts and background information related to what you're doing, and have some interesting and relevent experience with national policy setters in academia on this topic, but am a little bogged down now working on a book, research papers, experiments, and grant proposals. You know, the usual academic stuff! So I will try posting some once I feel I understand more fully what you are doing and how you are doing it.

Thank you ever so much for providing a forum for something that is so important to our children!

Her name is Barbara Oakley & she has had an amazing life (e.g., she met her husband at the South Pole.....)

Plus--and I MUST post this--she's started a page of things she finds funny, which, thus far, has one link to a pdf file of what looks to be a PowerPoint presentation: Yours is a Very Bad Hotel.

All you World Traveling Kitchen Table Math denizens will relate.

it's getting clearer now

Back when Carolyn and I started Kitchen Table Math, my one question was: Why?

Why exactly, in the middle of my life, am I spending 18 hours a day WRITING A MATH BLOG? Excuse me, a MATH BLOOKI.

This was my husband's question as well.

I'm just coming off a newyorktimesbestseller, the goal nonfiction writers spend their careers aspiring to reach.....shouldn't I be Following Up with another book? (I will follow up with another book; Temple and I are working up steam. But still. Kitchen Table Math is a detour.)

So what was I thinking?

Somehow, it seemed like I was supposed to be writing a math blooki.

That reason turns out to be, in large part, the people who write comments and set up pages and create dimensional dominoes and, now, send me an email out of the blue telling me I need to take Andrew to Kumon.

That is exactly what I need to do. I need to take Andrew to Kumon.

Andrew is my little locked-in boy; he's bright--so bright, it's there, you can see it--and I don't know how to reach him.

The folks at Kumon may not know how to reach him, either, but it's obvious to me I'm supposed to give it a shot. If they don't know, something there will give me a new idea. It's a lead.

I wasn't going to figure this out on my own.

I was telling my neighbor about this today, complaining that I can't think of these things myself. I have to have complete strangers tell me: take your severely autistic son to Kumon Math.

My neighbor said, 'You can never think what you're supposed to do about your own life.'

---

OakleyPapersOnline 19 Sep 2005 - 17:20 CatherineJohnson


Chris Adams found all of Barbara Oakley's research papers posted at her web site (something I probably could have done if I hadn't gotten sidelined by the humor page.....)

This is why it's a bad idea for me to try to learn math from textbooks with pictures of diving penguins.

Thank you, Chris!

update

Oh, boy.

I'm gonna be reading all of her stuff.

Check out this title: IT TAKES TWO TO TANGO: HOW ‘GOOD’ STUDENTS ENABLE PROBLEMATIC BEHAVIOR IN TEAMS

This paper was written to describe a successful program developed to forestall non-cooperative behavior in team-related activities, and to provide an explicit guide for students on how to handle such problematic behavior if it does arise. The program involves creating self-awareness of the deleterious effects of typical, seemingly ‘nice’ behavior in a dysfunctional team situation. Indeed, it has proven to be a revelation to many students to find that their ethical, industrious, and well-meaning responses to non-cooperative behavior can often enable such unacceptable behavior to continue and even escalate.

I myself have Personally Experienced the deleterious effects of seemingly nice behavior in a Dysfunctional Team Situation, and I've never had the first clue how to deal with it.

Mostly I just fume and glare and fire off furiously angry body language in all directions, & end up looking like a lunatic.

I once did this on cable TV, trying to speak my piece at a school board discussion of TRAILBLAZERS.

update update

OK, this paper is not going to solve my looks-like-a-lunatic-at-school-board-meetings problem.

It's about dealing with Hitchhikers & Couch Potatoes.

More t/k.....

---

MiddleSchoolPart8 20 Sep 2005 - 15:33 CatherineJohnson


One of the commenters on Instructivist links to this Fordham study: Mayhem in the Middle: How middle schools have failed America—and how to make them work (pdf file)

Middle schoolism (definition): An approach to educating children in the middle grades (usually grades 5-8), popularized in the latter half of the 20th century, that contributed to a precipitous decline in academic achievement among American early adolescents.

brain periodization

Middle schoolism is partially based on the now-discredited theory of “brain periodization,” which holds that “the brain virtually ceases to grow” in children ages 12 to 14 and that teaching complex material during that period will have damaging effects.

Of course, we now know that the truth is precisely the opposite.

The middle school years are the second window for explosive brain growth.

Jay Giedd on brain development

interviewer: Tell me a little bit about how the brain develops.

Giedd: How does the brain -- arguably the most complicated three-pound mass of matter in the known universe -- how does the brain become the brain? It does so through two simple but powerful processes.

The first one is over-production. The brain produces way more cells and connections than can possibly survive. There's only so many nutrients, there's only so many growth factors, there's only so much room in the skull. After this vast over-production, there is a fierce, competitive elimination, in which the brain cells and connections fight it out for survival. Only a small percentage of the cells and connections make it.

This is a process that we knew happened in the womb, maybe even the first 18 months of life. But it was only when we started following the same children by scanning their brains at two-year intervals that we detected a second wave of over-production. This second wave of over-production is manifest by an actual thickening in the gray matter, or the thinking part, in the front part of the brain.

As this second wave of over-production is occurring, it prepares the adolescent brain for the challenges of entering the next stage of life, the adult years. There's enormous potential at that time. People can take many different life directions. But about around that time of puberty, people start specializing, so to speak. They start deciding, "This is what I'm going to be good at, whether it be sports or academics or art or music." All the life choices, even though they are still there, start getting whittled away, and we have to start sort of focusing in on what makes us unique and special.

As to timing, "this process of thickening of the gray matter peaks at about age 11 in girls and age 12 in boys, roughly about the same time as puberty."

And:

interviewer: And what do you think this might mean, this exuberant growth of those early adolescent years?

Giedd: I think the exuberant growth during the pre-puberty years gives the brain enormous potential. The capacity to be skilled in many different areas is building up during those times. What the influences are of parenting or teachers, society, nutrition, bacterial and viral infections -- all these factors -- on this building-up phase, we're just beginning to try to understand.

Yup, definitely the stage of brain development where you'd want your local middle school to reject academics.

back to the Fordham report

Still, our main point isn’t grade structure. It is education philosophy and effectiveness. And on that front there’s been evidence for years that U.S. middle schools haven’t been pulling their weight—and that something needs to change. Generalizing, one can say that American students do reasonably well in grades K-4; that their performance falters in grades 5-8; and that (with splendid exceptions) it is dismal in high school.

This is what we call red meat.

The War Against Excellence

Oh!

The report is written by Cheri Pierson Yecke, author of The War Against Excellence: The Rising Tide of Mediocrity in America's Middle Schools (My copy has yet to arrive):

[Yecke] is superbly qualified to tackle this topic, having served, among other things, as a senior federal Education Department official, as Secretary of Education in Virginia—a state widely praised for the quality of its academic standards—and, for a brief but astonishingly fruitful period, as Commissioner of Education in Minnesota. As we go to press, Florida Governor Jeb Bush has just named her that state’s new chancellor for K-12 education. She also authored the fine 2003 book, The War Against Excellence, which simultaneously exposed the shortcomings of U.S. middle school education and the country’s strange and dysfunctional animus toward “giftedness.” (Information about that book can be found at www.waragain stexcellence.com.) As expected, her book was condemned by reviewers for the National Middle School Association....

Lucky for us, the middle schoolists had bad timing:

Ironically, the radical middle school concept reached its zenith in 1989, the same year the Charlottesville education summit convened by President George H.W. Bush set in motion a reform sequence that would doom that very concept. This summit famously launched the nationwide standards and accountability movement that put an unprecedented premium on student academic achievement, the very thing that radical middle schools activists spurned.

it's always worse than you think

I had no idea this was going on:

A “scientific theory” known as “brain periodization” or the “plateau learning theory” was introduced to the education world in the late 1970s. It claimed that brain growth in children ages 12 to 14 reaches a plateau, at which time “the brain virtually ceases to grow,” and that teaching complex material during that period will have damaging effects on children.21 Thus, middle school advocates now had a “scientific” reason to dilute the rigor of the academic offerings at the middle school.

According to biophysics professor Herman Epstein and education professor Conrad Toepfer:

With virtually no increase of brain size and mass in the large majority of 12- to 14-year-olds, there is no growth in the capacity of the brain to handle more complex thinking processes usually introduced in grades seven and eight. This continued demand for the youngster’s brain to handle increasingly complex input, which he or she cannot comprehend during this period, may result in the rejection of these inputs and the possible development of negative neural networks to dissipate the energy of the inputs. Thus, it is possible that even when the subsequent growth of the brain between the ages of 14 and 16 could support the development of more complex cognitive skills, the untold numbers of individuals who have developed such negative networks have been so “turned off ” that they literally can no longer develop novel cognitive skills....

Negative neural networks.

That's a new one.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
Dan K on middle school transition middle school math teacher blogs
Fordham debate on middle school
middle schoolism (Fordham report)

---

CongruentAnglesInRussianMath 21 Sep 2005 - 01:45 CatherineJohnson


I can't answer this question from Mathematics 6:

Explain why the angles formed by the intersection of two lines consist of two pairs of congruent angles.

I'm tongue-tied.

To me, it's 'self-evident' that the angles formed by the intersection of two lines are congruent.....and that's it. That's as far as I get.

I started writing something about how all lines are straight angles and all straight angles are 180 degrees, and then I stopped. I couldn't see what the next step was (assuming that's the correct first step.)

Smartest Tractor has the answer

They are supplementary angles (Two angles with measures whose sum is 180 degrees.)

If two angles are supplements of the same angle or congruent angles, then the angles are congruent.


Thank you!

I have one question left, though, which is that this seems slightly circular to me.

Is this a chicken and an egg question?

What would the formal proof be?


fyi....I did do proofs in high school geometry; at least I think I did.

Last night I read my first geometry proof since high school in the famous SMSG Geometry by Moise and Downs and I understood it.

Not only did I understand it, I liked it. So that's good.


geometry vocabulary
projective geometry web page
Math League geometry page

---

PrenticeHallPreAlgebraQuestion 21 Sep 2005 - 10:24 CatherineJohnson


Well, Christopher managed an 85 on his first math quiz.....but we're gonna need to step up the pace around here.

Ed checked his homework tonight, which prompted vast quantities of screaming and yelling (maybe there's something to that brain periodization business after all), and now reports that Christopher has essentially zero comprehension of how to solve a story problem involving negative numbers. He's just looking at the problem and trying to figure out which operations to do. Ed says he's more or less guessing.

The good news is he got points off for mechanics, failing to put in the degree sign and the like. He would have had an 89 if he'd LABELED EVERYTHING CORRECTLY. So from now on he will label everything correctly.

The bad news is that the teacher is doing what she did last year, which is putting problems on the test they've never done before or even seen in class or on homework. He had two story problems like this one:

The boiling point of oxygen is -297 and the boiling point of nitrogen is -320. How much higher is the boiling point of oxygen?

Here's my question.

Distance, I know, is always expressed as an absolute value.

Is 'distance' on a thermometer the same thing?

Say the question had been written as, How much lower is the boiling point of nitrogen than the boiling point of oxygen?

Would the answer still be 23?

anyone know of a good source of story problems?

To get Christopher through this course, I'm going to need two things:

• LOTS of practice computation problems (integers, fractions, the works)
• LOTS of practice word problems

Does anyone know of good supplies of either?

I am also going to need vast supplies of Iron Will.

teach kids good handwriting in school

Christopher's handwriting was so bad in Kindergarten that his teacher told us he was considered 'at risk' for dyslexia. (Kids with learning disabilities often (usually?) have bad handwriting.)

That was one of those four-star fun-with-childbearing moments. Two autistic kids, and this one's gonna be dyslexic!

Ed pooh-poohed the whole thing (he is the pooh-pooher in the family), and in fact Christopher began reading on his own literally 2 weeks later (THANK YOU, GOD).....and that was the last any of his teachers had to say about handwriting until he had Ms. Duque in 5th grade last year.

So tonight he missed at least one problem on his homework because his handwriting is still so bad he can't read it himself. His test is a mess; I don't know how he managed to do as well as he did given what a visual morass it is.

Two summers ago I researched handwriting programs, and we spent one summer working on handwriting....and then Ms. Duque pushed him on it last year, though she didn't teach it. When my parents went to school, handwriting was taught in formal handwriting-practice programs that worked. (Ever noticed that ALL members of the greatest generation have beautiful handwriting?)

Today there are schools on Long Island that don't even teach cursive anymore, or maybe it's the other way around.

Anyway, handwriting is one of those ROTE NON-CONCEPTUAL NON-CRITICAL-THINKING SKILLS that have been drop-kicked right out of the curriculum. Replaced by character education. Last year the school spent 20 minutes each and every morning for six months doing their No Put Downs program. This year the program's even bigger as far as I can tell. The teachers are all being trained, and one of Christopher's teachers told us on back-to-school night that, thanks to all the character education she would be doing during class time, 'your children will be better people.' [update: This teacher was Mrs. R. 3-25-2006]

The point is, if Christopher is going to speed through these tests, he's going to have to develop fluency not just in math facts & computation, but in handwriting, too.

Well, at least he had those couple of months with me. I have a couple of cursive practice books sitting in his homework file, so maybe I'll pull those out and get started again. One more thing to brawl over.

I feel a rant about character education coming on.

That stuff I just wrote?

That wasn't it.


keywords: character education bullying no putdowns


keywords: good handwriting Write Now

---

MathClassWarmUp 26 Sep 2005 - 19:40 CatherineJohnson


For their warm-up in math class yesterday, the kids penciled in all the odd numbers on a worksheet to see what word they spelled.

They spelled the word odd.

Clearly, ed schools do not teach the concept of opportunity costs.

---

MathLessonRepeatingDecimals 22 Sep 2005 - 20:01 CatherineJohnson




My neighbor showed me this yesterday. Naturally no one had ever taught me how to do this, which is par for the course. But she's a statistician & she'd never learned it, either.

I love this. It reminds me of the shenanigans I go through trying to force Microsoft Word to do graphic design.






I've entered this on the Math Lessons page.


other resources

Purple Math

Math Wizz on converting repeating decimal to fraction




update: Saxon meltdown (3-2-06)

Maybe I'm just tired, but I practically had a nervous breakdown tonight trying to convert 0.013333....(repeating decimal) to a fraction.

I just could not get it.

Finally Math Wizz saved me. Of all the websites I looked at, Math Wizz had the simplest, cleanest, & most follow-able explanation.

Math Wizz also has gigantic gifs.

---

CommentsThreadIntegerProblems 21 Sep 2005 - 20:37 CatherineJohnson


Check out the Comments thread on the Prentice Hall Pre-Algebra problem.


First of all, here's an important resource Dan K has posted before: Mathcounts - a site entirely dedicated to middle school math.

Dan, thanks for re-posting that source. I remember your mentioning it the first time, but it didn't register.


Second, Lone Ranger has advice on improving handwriting. We're just going to HAVE to do this, and it sounds like her idea is less time-consuming than the one I was using. (I was using the book Write Now: The Complete Program For Better Handwriting by Barbara Getty, Inga Dubay. It's a terrific book - I highly recommend it - but it's more than I can deal with at the moment. fyi, the authors give workshops to physicians, teaching them to improve their handwriting sufficiently in just a couple of hours that they can write decipherable prescriptions. I improved my handwriting quite a bit working with the book, and hope to get back to it someday before I'm dead. Their web site: Getty-Dubay Productions)


Third, I think Carolyn & Barry may have given me opposite advice (but I'm too time-crunched at the moment to figure it out...)


Fourth, I'm with J.D. when he says, It peeves me that texts still use the "higher" and "lower" terminology here. To be accurate, they should use "greater" and "lesser."


Fifth, WOW!

J.D. has a lesson on fractions!

---

MathLessonsPage 21 Sep 2005 - 15:48 CatherineJohnson


I've started to get the Math Lessons page pulled together. I'm sure I've forgotten posts that should be indexed there, so if you know of any, let me know. (Any lessons you especially like from other people's sites, like MathandText, for instance, should also be added.)

There's a link to 'Math Lessons' on the sidebar.

---

TeachnologyFreeWorksheets 21 Sep 2005 - 20:07 CatherineJohnson


Teachnology seems like a useful site.

Here are free online word problem worksheets.

And here are lots of free math worksheets.

I like this addition and subtract equations worksheet.

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IntegerWorksheetsAndWordProblems 22 Sep 2005 - 23:07 CatherineJohnson


The internet is amazing.

Here are 3 worksheets for problems with integers. The last sheet has some good word problems, which I desperately need.

integer addition & subtraction
integer expressions & word problems (pdf file)
sample page of multiplication and division integer problems from Math-U-See (pdf file)

are community colleges an important resource for us?

Math Worksheets with Answers from Central Lakes College looks like a wonderful web site. It has free, printable worksheets on quadratic equations, on 'foiling,' on finding the slope--amazing. Community Colleges, which probably do a huge amount of the math remediation in this country, may be a terrific resource for us. These people are doing the heavy lifting.


Check out this sheet of Number and Consecutive integer problems (pdf file) from a course called Elementary Algebra at Broward.

keywords: community college free worksheets online

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FunBrainNumberLine 22 Sep 2005 - 19:26 CatherineJohnson


Line Jumper, an online number-line competition at FunBrain.

The kids in my Singapore Math class LOVED the FunBrain site. They especially liked the Math Baseball game.

Normally I'm skeptical of online activities (because Christopher seemed to learn nothing from software math facts programs) but the kids I've known really did like these math facts games, and could play them for a lot longer than they'd do a worksheet.

You can also use Math Baseball to teach mental math, because the kids have to do the calculations in their heads, unless they pull out a pad of paper & a pencil.


I had Christopher do the integers worksheet from Saxon Math 8/7 last night. I'm going to have him keep doing it until he can finish it in 5 minutes & get everything right. That will help.

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OnlineMathResources 22 Sep 2005 - 22:30 CatherineJohnson


I came across all kinds of interesting-looking math web sites last night while looking for:

• integers worksheets
• downloadable number line worksheets

I didn't find either of the things I wanted (and almost spent $29.95 to join some teacher site linked to by FunBrain just to be able to printout their number line sheet...).

But I found all of these:

• AAA Math (resources listed by grade thru gr8)
  also has a potentially interesting page called World Education Levels. Unfortunately, I can't tell what 'world education levels' are without spending a lot more time on the site than I want to spend. LOTS of online quizzes that are corrected by the site, and they seem to be selling a software program on arithmetic.

• Computer Lab: Math, Numbers, and Counting HUGE survey of 163 different online math sites for kids. Terrific collection.
  Item number 163: Disaster Math for Kids
  From FEMA! Interactive word problems graded by the FEMA site.

• the aforementioned FunBrain Math Baseball is a classic.

• FunBrain's teacher site, the page that almost sold me a $30 sheet of number lines. Has articles on behaviormanagement in the classroom that look good.

• Harcourt School Publishers' number line express Blecch. But maybe little kids would enjoy it. There's a talking lion railroad engineer.

• MacTutor History of Mathematics

• Math Cats how-to for teachers Definitely worth looking at.

• math clip art! possibly for autistic kids (I was on a major clip art tear a few years ago, when Andrew was in his PECS genius phase...)

• Maths Dictionary (British?)

• Mathsurf teacher's site word problems from Pearson Scott Foresman. If you're looking for story problems with multiple answers, this is the spot. Possibly (probably?) a good site to visit for problems your child may encounter in constructivist math courses -- worthwhile problems, as far as I can tell on cursory inspection.

• Mathsurf telling time worksheet (to print)

• NCTM Illuminations Looks decent. Lots of interactive 'tools': affine recurrence plotter and--Yay! nets!! I've been looking for nets!

• National Library of Virtual Manipulatives for Interactives Mathematics I've visited this site several times before. It's pretty good, as I recall. (If I'm remembering correctly, the pan balance problems are kind of cute & potentially useful.)

• Room 108 Looks decent. You can create online Mad Minute pages (must be answered & graded online)

• odd & even numbers possibly good for autistic kids? this site speaks the directions, although I don't think the directions are also written out in words. But any time an autistic child can hear the same words spoken by the same recorded voice it's a good thing, I believe. Site is simple and graphically compelling. Has a HUGE cursor (also great for autistic kids.)

• Primary Games good for autism? I have a feeling this might work with Andrew at some point in the near future. Very simple, has ONE moving image--'Squigly,' a little worm inside one of 10 apples who pops out of his apple and then disappears back inside every couple of seconds. The child has to tell which apple Squigly is in (first, third, fifth, and so on). The only bad part is that there's a lot of advertising crud at the top and the bottom of the page.

• Primary Games 'Diamond Mines' knock-off I spent a couple of years as a Diamond Mine addict.

• Primary Games fishy counting game good for autism? terrific. Very, very simple counting game (as nice as the counting game they used to have on the Barney web site....

• Primary Games Tetris bubbles Great! I've been meaning to post a TIME MAGAZINE article saying girls improve their spatial-visualization skills when they play Tetris. This is, I think, a somewhat slower version of a Tetris game. (Slower is always good for me....) Stupid music, though.

• Primary Games time clock Terrific! Very simple & cute. You have to be able to use a mouse (Andrew & Jimmy both have huge MOUSE difficulties, unfortunately.)

eureka

I will never, ever speak ill of the NCTM again.

They have FREE NUMBER LINES, 8 to a page!

Unfortunately, all 8 number lines start at 0 and contain only positive numbers....

update

I take it back.

I will carry on saying bad things about the NCTM.

They do not appear to have posted a single number line on their web site that includes negative numbers as well as positive numbers and 0.

keywords: online interactive math resources tools nets manipulatives

---

MathsurfStoryProblem 27 Sep 2005 - 21:25 CatherineJohnson







The folks at Illinois LOOP are none too happy with Scott Foresman Addison Wesley Math.

We dealt with SFAW Math's nightly visual assault of colors, graphics, fonts, and wildly irrelevant detail, a powerful set of distractors when all our kid was trying to do was master subtraction.

and:

The layout of fourth grade Scott Foresman Addison Wesley "Math" is best described as "Tokyo By Night", a visual assault of MTV style, with literally thousands of cluttering photos, cheezy graphics, cartoons, splotches of bright colors, marginal notes and decorative slugs, adding nothing to the task of learning math. To the contrary, this fusillade of distractions can only impede your child's focus on learning math.

Speaking of distractions, your child's fourth grade math book will tell him or her that "Abwenzi" is the word for "friends" in the Chichewa language of Malawi, Africa, that small family farms in Massachusetts produce about half of the world's cranberries, that bicycle racing began in France in 1869, and that Pong was one of the first popular video games. He or she will read about cliff climbers in Nepal retrieving honey, will learn an assortment of words for cowrie shells in the Yoruba language of west Africa, and will be asked "Why do you think the Anasazi chose to built on cliffs?" and "Why do you think they chose to build dwellings with more than one story?" (despite a total lack of context).

Sounds like maximum page splatter to me!


no one-answer math problems

keywords: no one-answer math multiple answer math multiple-answer math poor word problems bad word problems bad story problems

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DougSundsethNumberLine 23 Sep 2005 - 19:09 CatherineJohnson


Fantastic!

Here's Doug Sundseth:

Would it be helpful to you to have a sheet of number lines (with whatever arbitrary endpoints you wish) as a .jpg file? It might be as much as a 10-minute task for me to make one and send it to you (though I doubt it would take that long), and I'd be happy to be of assistance.

If so, let me know what you'd like (number of lines per page, end points, title, name line, file resolution, whatever), and I should be able to get to it in a day or two.

This is great!

I'm thrilled!

Thank you!

OK, what do you guys think?

How many number lines should be on the page, and with what kinds of distances between the ticks?

Should there be any numbers associated with the ticks, or should everything be left open so parents, teachers, and students can write in whichever number scale they need? (I'm thinking no numbers except for maybe a 0 in the middle....)

Should some of the ticks be longer than others?

Do I sound like a complete nut?

Don't answer that!


Doug's downloadable number lines

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SaxonItWillBe 23 Sep 2005 - 19:17 CarolynJohnston


I had my meeting this morning with B's special ed teacher, his math teacher, and an unexpected guest -- the principal. Perhaps they were a little nervous because of this letter I had sent them, in which I mentioned that I have a math Ph.D. and I'm a Powerful Math Ed Blogger (be afraid: be very afraid).

I asked them if they would have a teacher's aide work with Ben on his math, one-on-one, using the Saxon Math curriculum. The special ed teacher, bless him, said that he could make it work; that he thought he could spare a teacher's aide during that last period of the school day, and it would just be an (easier) matter of finding them a quiet place to work. I was so relieved I could have hugged him.

It's been two years of struggle for me and Ben, supplementing from Saxon and trying to work around the vagaries and inconsistencies of Everyday Math; and here we were, once again, facing another year of it, after having worked so hard last year to find a school that offered a traditional math class, and then fighting the open enrollment system to get him into it, and then committing to the 45-minute-per-morning commute that it entails. I wanted so much for this year to be the end of it. I never really wanted Ben to have to do two math curricula, especially when one of them seemed to be a total waste of time for him.

And then I found on the first day of school that Ben's math class would be using Connected Math after all. I just about despaired. I've had to give up my dream of having Ben mainstreamed in math -- I always thought it was the one class in which he could hope to really hold his own and have a Typical Kid Experience. But I don't care any more -- math education is a mess in this country, and we're perversely fortunate to be able to opt out.

I got some insight into why Ben's new middle school had chosen to go 50-50 with Prentice Hall and Connected Math this year, following many years during which they had a reputation for doing solid traditional math classes (and for having the best math department in the city). It's not ideology; it's fear.

The special ed teacher told me that if I wanted Ben to be taught from a traditional math class, that I would have to just 'ignore the CSAP' (the CSAP is Colorado's assessment test for students, given in compliance with NCLB). "He'll do badly on it," he told me. "The test is very applications-oriented. You can't hold us responsible for that."

"If he does poorly on the CSAP," I told him, "I'll hold myself entirely responsible." No way will he do poorly on the CSAP. He didn't this last year -- except in those sections, data representation and probability, that I chose not to supplement.

Apparently, on the CSAP, kids are frequently asked to give verbal explanations for what they did on a problem. Math CSAP scores for students at Ben's school have been getting worse and worse over the last few years, and the teachers and principal don't know why, and don't know what to do about it. This adoption of Connected Math is therefore, I conclude, their attempt to grasp at straws. There is no way for them to know in advance whether Connected Math is going to solve their problem; I doubt they even know what the cause of the problem is.

An even deeper question is whether the CSAP itself -- or any other state assessment -- is worth a hoot. Who's vetting the CSAP to check whether kids who do well on it in 5th grade have the skills, on average, to go into calculus in college?

I believe in the value of assessment -- it provides a minimal benchmark of proficiency and keeps people accountable. But the assessment has to be good, and we have to know what to do about the weaknesses it reveals. If it leads good schools astray, I call that backfiring in a big way. I've been assuming that the metrics, at least, are good; now I wonder. The more deeply I look at the problem of math education in our country, the more I realize that there are "unknown unknowns" all the way down to its foundations.

---

DougsNumberLines 25 Sep 2005 - 14:03 CatherineJohnson


I can't thank Doug enough for his number lines--and ALL OF YOU SHOULD USE THEM, TOO!

Adding & subtracting positive & negative numbers is one of those areas that can be severely procedural if you have a good memory, which most children do as far as I can tell.

Christopher was already becoming entirely 'procedural' with his integer problems: if he saw two minus signs in a row he automatically penciled in little vertical lines and turned them into two plus signs. Then he added.

ooops--must take Christopher to his playdate

will finish this when I get back

I love these number lines.

back again

Well, I'm back from my Excellent Adventure at Barnes & Noble with Andrew, who is obsessed with pulling Arthur books off of their shelves and lining them up on the floor, while I apologize to clerks & customers.

Now he's shrieking at the top of his lungs & jumping as hard as can on his bedroom floor upstairs, which has shaken loose all the lightbulbs in the kitchen light fixture, which means someone will have to climb up on a ladder, take down the fixture, and screw the bulbs back in.

I'm in a nuts-to-autism mood.

back on topic

as I was saying.....Christopher's memory is good enough that he's reaching the point of procedural fluency with integer computations, and that's got its bad side as well as its good side, because I'm sure he still has no idea how to do the problem I posted a couple of days ago, the one asking what the difference was between the boiling point of oxygen and the boiling point of nitrogen.


[pause]


This is grueling. I've just spent 15 minutes trying to deal with Andrew, who has slapped himself on both sides of the head so hard that he'll be bruised again. We're both trembling. I loathe this disorder.


I'm going to make one more stab at writing about Doug's number lines before I go have my own nervous breakdown.

What I'm trying to say is that it's clear Christopher is reaching the point where he's going to have procedural fluency with virtually no conceptual understanding, and Doug's number lines are the answer.

Number lines are to integer problems what bar models are to story problems. Perfect.

I'm going to have Christopher do a page of Doug's number lines every day for a few weeks, and I'm going to do them myself.

I was telling Ed about all of this, and he said number lines were essential in the GED math course he taught to high school drop-outs in Newark years ago. He was pretty successful with those kids, and number lines were a big part of it. These kids--young adults, actually--were years and years behind in math; they'd never, ever gotten it. Ed had to have visual ways of teaching math to them, he said, or he couldn't have done it.

I haven't got all of the number lines posted yet, but will get to it soon. Right now one page is here, at the top of the Comments thread.

number lines in your head

I'll have to track this down, but one of the neuroscientists who studies math argues that we have number lines--a kind of number line, though not a formal visual image of a number line--in our heads; number lines are essentially there already, along with basic counting & very simple fractions such as 1/2. (I'll have to see whether this particular researcher thinks animals have number lines, too.)

This is all the more reason to use number lines frequently, I think. Any time you can hook a new concept to something a child already has inside his head you've got an advantage.

Vision in Elementary Mathematics by W. W. Sawyer

While we're on the subject of visual models, I've been reading Sawyer's book, which my neighbor gave me for my birthday. It's challenging, but incredibly useful & rich.

Andrew is better

Lately Andrew seems to be having low blood sugar crises. Either that, or dehydration, or both. He has an autistic eating disorder on top of everything else, and won't drink water or milk, etc....and eats only a couple of foods. So he's chronically low on calories, nutrients, and fluids.

I forced grape juice down him 10 minutes ago, and now he's making cheerful noises. His face is bruised, and he's urinated all over his TV stand, videos, and whichever of my books he'd lined up as part of the still life.

BUT, he's OK.

I feel like Annie Sullivan after breakfast.

He folded his napkin.


(So is Kumon Math sounding like just the ticket for Andrew?? I say yes!)

---

AlgebraicSymbolsHardForStudents 27 Sep 2005 - 21:22 CatherineJohnson


Another interesting comment from a joannejacobs thread on new research about children's abstract understanding of math:

Imagine what a man like Archimedes could have accomplished if he had had the benefits of Saxon math. It is true that we all have some mathematical aptitude and that certain simple skills develop naturally, but this is far from enough mathematics to function at even the minimum wage level in our world.

I have never met a student who could flawlessly manipulate symbols according to the rules of algebra but had trouble with the deeper concepts of mathematics. Most of my students find poor algebra skills to be an almost insurmountable barrier to deep understanding.

Of course the foundations for success in algebra are those tedious skill sheets we "abuse" our children with in primary school.

Posted by: CRW at September 27, 2005 03:42 AM

hmm.

Now that I re-read this, I'm not sure what he or she is saying....is the point that a student who excels at writing & interpreting algebraic expressions can always also understand algebra?

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WickelgrenOnPrealgebra 16 Jul 2006 - 20:48 CatherineJohnson




Gulp.

A student can learn a year of pre-algebra math in three to six months studying three to ten hours per week, depending on the child's math aptitutde.

I'm gonna have to pick up the pace around here.

I've been working my way through Mathematics 6 since the beginning of June.

It is now the beginning of October.

RUSSIAN MATH has, estimating conservatively, 10,000 problems. At least 10,000. I have now worked 8000. In the process, I've learned a huge amount, although, sadly, even Enn Nurk & Aksel Telgmaa have not been able to dissuade me from the conviction that 7 x 6 = 43. If they can't do it, probably no one can.

I've just begun the last of RM's six chapters, and I was getting excited about starting algebra next. I can't wait.

So last night I took Saxon Math's placement test (pdf file) for algebra 1.

I got a 72.

conclusion number one:

I am going to stop expressing reservations about the Saxon math series until I can actually take and pass a Saxon math test.

conclusion number two:

wow

There are a boatload of topics I still don't know after doing 8000 complicated Russian computation, geometry, & word problems.

They are:

• using four 'unit multipliers' to convert 630 square yards to square inches: I have no idea what a unit multiplier is, or how to use it
• what a decimal part of a number is (I got the answer right, but only because I made a blind guess as to what a decimal part would be)
• negative exponents
• how to find the volume of a cylinder
• 'the method of cut and try' to find the square root of 20: to my knowledge, I have never heard the words 'cut and try' in my lifetime
• how to use a straightedge (what's a straightedge? I still don't know) and a compass to copy an angle
• how to find the area of a triangle (all I remember is: hypotenuse)
• how to find the probability that a die will first roll a 6 and then roll a 2, in that sequence
• base 2
• update 7-16-2006: I know all these things now, and will finish Lesson 81 (of 120) in Saxon Algebra 1 today.

So my first reaction, in Western polarizing fashion, was: I know nothing.

I know nothing, and I need to work through all 857 pages of Saxon Math 8/7 with Pre-Algebra before I can even think about setting foot inside a real algebra textbook.

I was depressed.

But then I calmed down a little and thought, mmmmm....maybe not.

Maybe I can just go through Saxon 8/7 and do every single lesson & every single problem related to these 9 topics.

Is that wrong?

update 7-16-2006: I ended up working through the entire book. Every lesson, every problem, every test. Then I took the Saxon placement test and placed into Algebra 2, but decided to start with Algebra 1. I'm glad I did.

Christopher began teaching himself Saxon Algebra 1/2 this summer (he starts 7th grade in th fall) so I'm reading through those lessons to make sure I didn't skip anything I need to practice - and just for the joy of encountering John Saxon's take on topics I already know.

Algebra 1 integrates algebra and geometry, though without proofs. I'll start Algebra 2 in September.

In one year I will have worked through:

• final chapter of Russian Math
• all of Saxon Math 8/7
• all of Saxon Algebra 1

That pace seems OK to me.

---

AnyNumberCanBeAFraction 01 Oct 2005 - 05:52 CatherineJohnson









Steve, on the thread need for speed thread, pointed out that any number can be a fraction, and when I said I ought to put together a worksheet on this subject for Christopher, Dan directed me to this frame, DimWksheet010.ppt. of his dimensional dominoes!

It's wonderful.

I'm going to have Christopher do it.

Which reminds me, yet again, I have got to get Doug Sundseth's number lines attached. I've used them two nights in a row, and today I sent a bunch in to Christopher's teacher, in case she wants to use them with the kids.

math ed is a riveting subject

Obviously, I've become obsessed with math education. I'm constantly trying to figure out what it is about math that makes it confusing, and what one can do to make it less confusing.

Liping Ma talks a lot about fragmented knowledge, and cognitive scientists all wrestle with the problem of expertise, which means the ability to generalize what you know to novel problems and solve them.

I've noticed (I may be quoting others without realizing it) that one of the problems with the 'novice' stage of learning is a kind of over-solidity of numbers, a thingness.

Doesn't Freud talk about children first playing with words as if they were things?

Does he say the same of numbers?

I don't remember.

In any case, what I've seen in myself, and in Christopher, is that numbers are too-solid. Both Saxon & Singapore spend a great deal of time conveying the idea that numbers are fluid, in a away, blinking constellations that can be one thing one moment (-10, say) and another in the next (-5 + -5, or -20/2, or any of an infinite number of combinations & expressions).

The Everyday Math article called this 'number partition theory,' and I haven't been able to figure out whether it is or is not number partition theory, but for my purposes, at the moment, it doesn't matter. Just knowing that the number 10 doesn't have the stability of a chair or a tree or a car is a big help.

So I've been trying to convey this to Christopher.

Dolciani's classic algebra text, btw, opens with this idea. '6 + 4' is another expression for '10.' Ten is not the answer to '6 + 4,' but another expression of '6 + 4'. The difference is huge.

Saxon 8/7 constantly uses the word 'Simplify' to mean 'Find the answer,' which I think is excellent. One day Christopher actually said, 'When he says simplify, he means find the answer.' And I thought that was fine. He's getting the idea that simplify and answer are synonyms.

generalizing knowledge

I'm wondering whether making numbers less thing-y for a child might help him or her to generalize a bit more easily, or a bit sooner -- or at least help him to generalize when he's practiced enough that he/she ought to be generalizing.

---

DougSundsethNumberLines 30 Sep 2005 - 21:37 CatherineJohnson





blank number lines (pdf file)

symmetric number lines (positive numbers, negatives numbers, 0 (pdf file)

number lines: all positive numbers (pdf file)

number lines: all negative numbers (pdf file)

update

If anyone is interested in, or has time to, critique these study sheets, that would great. (There's no pressing need for this; I'm reasonably certain these are accurate, especially since the second document came straight from the pages of Mathematics 6.

addition & subtractions of integers review sheet

integers problems from RUSSIAN MATH

---

MathmanOnPractice 01 Oct 2005 - 15:03 CatherineJohnson


from mathman:

So how many exercises should I assign? I can't possibly grade them all. This is not an easy question to answer.

It's much easier to say how many exercises the student should do although most students won't care for what I have to say. The student should work as many exercises as it takes to be able to do them correctly most of the time as fast as he can physically write out a complete solution. When informed that he has made a mistake, he should be able to find and correct his error quickly. When it counts, given time to review his work carefully, he should be able come up with the correct solution every time.

This level of mastery opens the door to calculus, differential equations, linear algebra and the quantitative elements of any science.

I'm going to print this out, ask Christopher to read it out loud to me, and then post it above the dining room table. (We're still waiting on delivery of the Ikea desk I ordered a couple of week ago.)

Willingham on overlearning

I re-read Practice Makes Perfect--But Only If You Practice Beyond the Point of Perfection every few months.

---

RussianMathProblem961 05 Oct 2005 - 17:19 CatherineJohnson


961.

A point with a coordinate of -3 moves along the number line in the following manner: First, it goes 5 units in the positive direction; Then it goes 7 units in the negative direction followed by 10 units in the positive direction and 8 units in the negative direction; Then it goes 3 more units in the negative direction and, lastly, 13 units in the positive direction.

Question: What is the final location of the point on the number line?

source:
Mathematics 6 by Enn R. Nurk and Aksel E. Telgmaa, page 255

---

ExtendedProblem1 09 Oct 2005 - 03:12 CatherineJohnson


Find all the numbers that satisfy all of the following conditions:

1. Positive whole numbers less than 100,
2. Four more than each number is a multiple of 6
3. The sum of the digits of each number is a multiple of 4.

and what is the best way to do this problem?

We used Doug's number lines (WHICH ARE GOING TO BE GETTING A WORKOUT THIS YEAR, IT'S OBVIOUS). We labeled one number line with multiples of 4, and the other with multiples of 6. We didn't need the multiples of 6, but it made things easier to have all the multiples of 6 sitting there, where we could see them.

How does a person who knows what she's doing do this problem?




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

---

JayMathewsMiddleSchoolsMoreRigorous 18 Nov 2005 - 18:58 CatherineJohnson


I hope he's right about this: Traditional Social Focus Yielding to Academics: Instead of a Year to Adjust to Puberty, 13-Year-Olds Now Given Algebra and Other Demanding Coursework

Much of the seventh-grade achievement pressure is focused on mathematics, and Kenmore math teacher Emily Henry is preparing many students for what used to be a high school course: Algebra I.

Word said he expects more than 55 percent of this year's seventh-graders to have completed first-year algebra when they finish eighth grade, compared with 25 percent nationally. At Kenmore, 16 seventh-graders are taking algebra. The push to accelerate math instruction seems to have had a national effect. The National Assessment of Educational Progress test, a common measure of academic performance, shows that 13-year-olds had an average math score of 281 in 2004, up from 270 in 1990. English scores, on the other hand, are almost unchanged, from 257 in 1990 to 259 in 2004.

I'll remain skeptical about the increase in math scores until such time as Tom Loveless tells me the NAEP tests are assessing math skills above the 1st & second grades (pdf file).

via: joannejacobs

Irvington Middle School

I've mentioned before that, last year, our middle school's stated goal was to cut the number of students placed in Phase 4 math, the only course in which students take and master algebra in the 8th grade.

They didn't say how many students they planned to cut, and soon rumors were flying that 25% of the kids would be 'demoted' to Phase 3. Ed sent an email to the middle school math chair asking her about the figure; her reply was noncommittal, as I recall.

Subsequently I was present at a meeting in which parents directly asked the principal about his plans to cut students from Phase 4. His response—almost verbatim—was, 'I don't know where these rumors come from.'

So how many kids did they cut?

35% ^*

(It's always worse than you think.)

Here are my figures on the cuts to Phase 4, based on conversations with school personnel:

school year: 2004-2005
grade 5 class size: 155 students
phase 4 placement: 60 students
number of students moved from phase 4 to phase 3 at end of school year: 21 ^*
percent of children cut: 35% ^*

So here you have a highly affluent suburban school district, a district that spends roughly $18,000 a year per pupil, devoting time, energy, and a portion of that $18,000 to decreasing the number of students who master algebra in 8th grade.

what happened?

But here's the interesting development, and this is something parents have no idea also took place.

It's not just that 21 kids moved down.^*

Another seven kids moved up.

That's 7 kids not including Christopher, who moved to phase 4 in February. Add him to the total, and you've got 8 phase 3 kids swapping places with 21 phase 4 kids. If you had to choose just one factoid to illustrate the folly of assessing math talent in the third grade, that would be it.

To my knowledge, Irvington has never had 8 kids move from phase 3 to phase 4 in one school year. Never.

I happen to know this because, when I first raised the subject of Christopher changing tracks, I had teachers & guidance counselors saying things like, 'I can only think of one student who's moved up this year.'

Or: 'A student can always move up! It's never too late. We had one phase 3 student who just blossomed this year, all of a sudden.'

Two different people made these statements. One thought he was telling me 'No chance'; the other thought she was telling me, 'There's always a chance!'

But they were saying the same thing.

Question: How many phase 3 math students move to phase 4 in a year?

Answer: One.

down to 30%

So here's how things shape up this year, roughly speaking (there are some new kids in the district; I don't know their placements):

155 6th graders, approximately
est. 47 students in Phase 4
apprx. 30% of '05-06 IMS 6th graders on track to master algebra in 8th grade

UPDATE 9-18-2006: in school year 05/06 there were
3 sections of Phase 4 math, grade 6,
apprx 17 - 18 students per class

Meanwhile the KIPP Academy in the Bronx is reporting as many as 80% of its student body mastering algebra in the 8th grade, and passing the Regents A exam. Per pupil spending: $9,900.

I assume our new Superintendent in charge of curriculum will be taking a look at this.

salt in the wound

Last year, 80 percent of our eighth graders passed the high school level exit exam in math here in New York, the Regents, the math A (ph). Eighty percent of our eighth graders passed the high school level exam, exit exam and less than 40 percent of our kids who are coming in in fifth grade on level.

-- David Levin, Knowledge is Power Program (KIPP), Co-Founder; interview with Brian Lamb, C-span

back to NAEP

Here's Loveless:

The failures are even more alarming at the eighth grade. Almost four out of ten items (39.6%) address arithmetic skills taught at the first and second grade – six years below the grade level of eighth graders taking the test. More than three-fourths of the items are at least four years below grade level – taught in the fourth grade or lower. Yet, the percentage of eighth graders answering items correctly is an unimpressive 41.4%.

[snip]

Algebra items lack rigor at both the fourth and eighth grades. On the eighth grade assessment, the arithmetic demands of algebra items are pitched at only the mid-second grade level.

[snip]

“Really knowing algebra means being able to solve equations that contain more sophisticated forms of numbers than whole numbers. Calling these items algebra is conveying a false sense of rigor, making very simple math seem more sophisticated than it actually is,” noted Loveless.

“If students do not possess the tools to solve problems involving fractions, decimals, and percents – if students do not grasp forms of numbers other than whole numbers – then the only problems they will ever be able to solve will be mathematically trivial,” the report warns.

source:
New Study Finds That Math Items on the Nation’s Benchmark Exam Are Too Easy, Don’t Adequately Assess Skills-Eighth Graders Asked to Solve Problems Using First Grade Arithmetic

keywords: Irvington math


^* My figures are a headcount of how many students did not pass the placement test. To my knowledge, the administration approached all of these parents and expressed an intention to move the child to Phase 3. Some parents refused the move, and those parents, again to my knowledge, were accommodated; their children remained in Phase 4. I know of two such cases; there may be more.

---

NAEPPanBalance 08 Oct 2005 - 02:01 CatherineJohnson








Does anyone know how to find out the percentage pass rate for particular NAEP items?

never mind

This is exactly the kind of real-world problem that Turns Kids On, and helps them Make Connections To Their World.

---

NaepNumberLine 07 Oct 2005 - 23:52 CatherineJohnson







Yes, it is a NAEP number line!


sigh

Christopher just got this problem severely wrong.

I'm gonna be using a LOT of number lines this year.


(From the 8th grade test)

---

NaepFindAPattern 09 Oct 2005 - 03:29 CatherineJohnson

---

NaepFractionProblem 08 Oct 2005 - 02:16 CatherineJohnson

---

NAEPScaleProblem 08 Oct 2005 - 00:29 CatherineJohnson













I just want to know how many kids used their calculators.

---

NaepWordProblemMultiplyAndDivide 08 Oct 2005 - 16:49 CatherineJohnson

---

NaepDrawSquare 08 Oct 2005 - 12:52 CatherineJohnson

how old is an 8th grader?

13, right?

---

ExtendedProblem2 09 Oct 2005 - 23:45 CatherineJohnson



You guys are going to have to pace yourselves.

Yes, sure, you've stomped Extended Problem Number 1 into teensy tiny little bits; Extended Problem Number 1 is no more. Extended Problem Number 1 has expired and gone to meet its maker; it has kicked the bucket, shuffled off its mortal coil, run down the curtain and joined the choir invisible.

Extended Problem Number 1, thanks to you, is an ex-parrot.

But guess what?

There's more.

Extended Problem Number 2

(Christopher's done with his answer, so here it is.)




keywords: dead parrot
to be filed under our forthcoming what fresh hell is this category thread





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

---

TeachingUnitConversions 11 Oct 2005 - 16:31 CarolynJohnston


Tonight's story is drawn, not from Ben's math class, but from his science class. The kids are doing a big unit on measurement the last few weeks, and his test is on Wednesday. Some of the material is on unit conversions, a topic relevant to both math and science.

The kids are doing tables of unit conversions, converting from meters to decimeters to centimeters to millimeters, and from meters to decameters to hectometers to kilometers (who uses hectometers, anyway?).

Well, Ben has been consistently getting his unit conversions backward. He'll convert, say, 13 meters to .013 millimeters, or 12 meters to 12000 kilometers.

"You're going backward!" I was pleading. "Millimeters are littler than meters, so you always have more millimeters than meters."

"But millimeters are supposed to be little," he said, "and kilometers are big!"

It was stuck in his head that way, all backward. I am afraid I understand this backwardness problem all too well, myself. But I was getting worried. Ben was getting lots and lots of practice doing these problems the wrong way. He was drilling, I feared, a rut into his brain that would be hard to fill in.

I tried a visual aid. I taught Ben to draw a picture of a little short bar for a millimeter, a medium bar for a meter, and a big bar for a kilometer. I thought the visual aid would help, but it didn't; he already knew that millimeters were little, and kilometers were big. More precisely, it didn't help him get problems consistently right. What you really want for this sort of task is a procedure that gives a kid the right answer every time, so that he learns to trust himself to do it correctly.

So I decided to teach him unit conversions. Unit conversion is a special case of dimensional analysis. We've talked a bit about dimensional analysis at KTM, and at the bottom of this post I'll put some pointers to the previous blog posts and user posts we've had about dimensional analysis. But here, I'll just show step-by-step how I taught Ben (who is in 6th grade) the unit conversion technique.

Keep in mind as you follow that the Main Trick of dimensional analysis is to realize that units, such as feet, meters, grams, pounds, and so forth, can be manipulated just like numbers.

Step 1. I began by reminding Ben how canceling works when multiplying fractions. For example, 6/5 x 5/4 = 6/4. He already knew that -- but I wanted to convince myself he had that down before going any farther, because that's essential.

Step 2. I showed him a little bit about how units, like centimeters or grams or feet or what-have-you, are manipulated in expressions just like numbers. For example, in calculating the area of a rectangle that is x cm by y cm, you get:

A = (x cm) x (y cm) = xy cm^2

because the centimeter units multiply (that little ^2 symbol means 'squared'). Another example: if you want to calculate how fast you're driving if you drive 60 miles in an hour, then you would write:

rate = (60 miles)/(1 hour) = 60 miles/hour,

and your units would come out in miles per hour.

Step 3. I showed him the fractional expression: (1 cm)/(1 cm) = 1.

"Do you see why that's 1?" I said.

"Yes."

"One what?" I said. "Is it one centimeter?"

He thought for a second and said, "I don't think so."

"That's right," I said. "It's just 1, without any units, because the centimeters on the top and bottom canceled."

Step 4: I showed him the following expression:

(1 m)/(100 cm) = 1.

"Do you see why that's one?" I said. "It's one because 1 meter and 100 centimeters are exactly the same, so they cancel".

We did a few more of those. We did 1000 mm/1 m = 1, 1 km/1000 m = 1, and so forth.

Step 5: Remind your student that multiplying anything by 1 (and that's 1 by itself -- dimensionless, not 1 centimeter or 1 gram) leaves it unchanged.

So, for example, you can multiply by 15/15, because it's 1. You can also multiply by 1 cm/1 cm, because this is also just 1.

You can even multiply by 1000 mm/1 m, or 1 km/1000 m, because we showed in step 5 that these are also 1.

Step 6: This was the final step, where I showed him how to use the trick to do conversions.

"Here's an example," I said. "Suppose I want to convert 24 meters to centimeters."

I wrote down: 24 m = ____ cm.

Then I wrote: 24 m x ((____ cm)/(____ m)).

"We're going to fill in those blanks so the expression on the right is equal to 1," I told him. "Then the meters will cancel on the bottom and the top, and we'll be left with the centimeters."

He knows the conversions for meters and centimeters, so we wrote:

(24 m) x ( 100 cm)/(1 m) = 24 x 100 cm.

"Now, the meters cancel each other," I said, "and we get left with 24x100, or 2400 centimeters."

Step 7: I did a few conversion problems with him, guiding him through the procedure. The last one he did successfully on his own.

I don't want to say that he had a Eureka moment, but this is a reliable procedure that will get him through these problems, and hopefully work around that rut that was forming. We're going to practice it to automaticity.

And as he goes through school, tricks like this -- using dimensional analysis -- will get him through a lot more than unit conversions, too.

Other stuff about dimensional analysis

dimensional analysis: why and how to use it

Our first discussion of dimensional analysis was in the comments section in this thread.

DanK invented a game called "Dimensional Dominoes" for teaching kids and grownups dimensional analysis, and posted it here.


Dan's dimensional dominoes (manipulatives)
unit conversion (in Comments thread)
Carolyn on teaching unit conversions

---

UnitConversionsPart2 13 Oct 2005 - 01:33 CarolynJohnston


Tonight Ben achieved what I would call near-mastery of the process of unit conversions, which I taught him only last night. My reason for thinking so is that he was incredibly spacy tonight -- and for Ben that's really saying something; an onlooker might think Ben, being typically spacy, was actually stoned -- but he managed to crank through a boatload of practice conversions anyway, and get them mostly correct.

In order to achieve permanent mastery, though, he'll have to practice it more, and in a more distributed way. Getting a crash course in dimensional analysis from Mom is what you might call "massed practice", and distributed practice is more effective for long-range learning. And I want him to retain this knowledge, since unit conversions are a 'hook' on which he can hang all sorts of other useful math and science knowledge.

Catherine and I had some email dialog today about unit conversions and dimensional analysis, following my post last night about teaching unit conversions.

Between the two of us, we hammered out what I think is a good intuitive explanation of dimensional analysis, and how and why it works.

Catherine: I was completely stunned to think a word (like, um, meter) could cancel out!!

Carolyn: But it's not just a word. It's a thing. It's a UNIT!

A unit is like the denominator part of a fraction. Many of the rules regarding their manipulation are the same.

The correct way to think of fractions is as a unit -- of the form 1/3, 1/4, 1/5, 1/8, etc. -- occurring some number of times, where that number is given by the numerator.

So you should think of 3/4 as being "the unit 1/4, occurring 3 times".

Why doesn't it make sense to add 3/4 + 1/3? Because the units 1/3 and 1/4 are different, and incompatible. You have to convert them to a COMMON unit (1/12) before you can add them directly.

Analogously, you can't directly add incompatible units: for example, 1 cm + 3 km makes no sense until you express them in the same unit, using a conversion to a common unit. For example,

1 cm + 3 km = .01 m + 3000 m = 3000.01 m.

Catherine: Thinking of the denominator as the unit works.....

I've probably thought of it that way implicitly, since I've never had trouble understanding or accepting that you can't add denominators.

To me, if you ask, what is 1/3 and 1/4? The answer is 1/3 and 1/4. It's like apples and oranges; if you add 2 apples and 3 oranges you have ------ 2 apples and 3 oranges.

You don't have 5 unless you change apples and oranges to fruit.

Catherine's insight into the need to convert incompatible units (apples and oranges) to a common unit (fruit) applies both to adding fractions, and adding units. It's brilliantly easy to understand. I hope some elementary school teachers will get wind of it!

One more tidbit to report

Ben's science class is only learning metric units! It's different from my own 6th grade science classes, where we kind of paid lip service to the metric system but really learned the English system.

It is to be hoped that this will prevent him from any costly unit conversion screwups that might be in his future.

---

DimensionalAnalysisMathForum 27 Nov 2005 - 16:07 CatherineJohnson

also at Math Forum

Dimensional Analysis and Unit Conversions
Dimensional Analysis and Temperature Conversion
Does My Fraction 1/1 Story Work?

---

DistributiveProperty 13 Oct 2005 - 17:57 CatherineJohnson




I keep forgetting to post this story.

A couple of nights ago I was doing my Russian Math on too-little sleep plus a glass of wine, and I found myself drawing a blank when the text asked me to multiply 24 by 7. I was sitting there complaining, '7 x 24, what's 7 x 24, oooohhhhhhh' (More Sleep, More Exercise, Less Wine coming right up) when I heard, from within my fog, Christopher calling out, "Distributive property! Distributive property!"

I was really tired.

So I kept moaning about What is 7 x 24, and Christopher kept calling out Distributive property! until finally I said, 'What are you talking about?"

Christopher said, 'It's 168! Use the distributive property! 7 x 20 is 140, 7 x 4 is 28!'

I've spent practically a whole year trying to teach Christopher the distributive property.

I had no idea he'd learned it.

---

TheMastersSchool 27 Oct 2005 - 18:13 CatherineJohnson



The Masters School is a couple of miles from my house, and a number of Irvington kids go to school there.

I've talked to four different parents who pulled their kids from the public school to send them to The Masters School, and in each case, when I asked whether The Masters School has a constructivist curriculum, the parent had no idea. It had never occurred to him or her even to ask.

One parent actually told me, with an air of pride, 'The school told me, your daughter is in the 5th grade. Not you.'

My feeling was: And you sat down and wrote out a check for $26,000 for that? ($26,000 is apparently the total cost, at least according to a mom I know who just sent her own daughter to The Masters School, which happens to be a big tragedy in my life, because her daughter is the girl I want Christopher to marry.)


This is from The Masters School curriculum guide (pdf file):

MATHEMATICS
The Middle School math program challenges students to channel their innate curiosity into meaningful and creative projects that relate math to their world. Students explore how math relates to their lives using realistic examples.

During class, experiential and exploratory activities foster open communication. Different problem solving strategies are discussed, each unique learner contributing ideas, and putting them into practice. This cooperative atmosphere encourages students to share ideas openly and to propose solutions. Through the solving of word problems, students connect concepts to the "real" world. As a result, they become strong problem solvers and critical thinkers, gaining confidence in their mathematical abilities.

In addition, technology is a vital component of the math curriculum. Each math class visits the computer lab weekly to research, explore, and practice skills. The use of technology enhances the learning experience, providing additional opportunities to challenge our students.

Fifth Grade
Fifth grade mathematics challenges students to integrate their understanding of fractions, decimals, and percents by solving investigative problems. They also explore measurement and coordinate geometry, and they design creative solutions to complex problems by working cooperatively. In addition, manipulatives give them a concrete understanding of the topics, preparing them to use these concepts in their lives.

Sixth Grade
Students in the sixth grade explore concepts in geometry, fractions, decimals, ratio, proportion and percent, and perimeter and area. The curriculum "spirals," continually reinforcing each skill so that students can make connections between topics and solidify their understanding of concepts. They use their skills to carry out critical thinking projects using statistics, which they will use in the future. Students improve their confidence so that they can successfully and creatively use their new skills.

Seventh Grade
Seventh grade mathematics introduces students to pre-algebra topics, including integers, rational numbers, expressions, equations, geometry, ratio, proportion, and percent. In addition, students research and write about the lives and work of different mathematicians. They thereby develop a deeper understanding of how mathematics evolved and why it is an important discipline.

Eighth Grade
Eighth grade mathematics introduces students to algebra (honors algebra for the strongest math students) and focuses on strengthening skills with integers and rational numbers, polynomials, inequalities, and parabolas, as well as solving equations and graphing lines. This course emphasizes independent thinking, preparing students for the challenge of high school.

Masters School high schooler

On the other hand, I also found this Comment, from a graduate of The Masters School, at joannejacobs:

A high school senior named Matthew Paul Dollar sent me a long letter detailing his experiences in public and private schools. (His family moved a lot, and he went back and forth between various schools.) I agree with this part:

Two buzzword concepts in modern mis-education are "subjective" and objective" thought. The trend in not teaching students the dates of historical events is a huge mistake. "Educators" claim that they want to encourage creative, "subjective" thought instead of "objective" fact regurgitation. But I have found that without dates, I cannot fit historical events into context or recognize their relationships with each other. Without a strong foundation of factual objectivity, I am not capable of formulating rational, creative and subjective thoughts. If I do not know the facts for myself, but am just taught to interpret subjectively, then I will always be subjected to regurgitating somebody else's subjective interpretation, and will interpret nothing in a "subjective" way. (If I have misused the word "subjective", it is because the word has been so overused that it barely has any distinct meaning.)

He left public schools in Rye, New York to attend a boarding school, The Masters School, in Dobbs Ferry, NY.

Being at Masters has been a wonderfully refreshing experience. The teachers are experts in the material, and there is a mutual respect between teacher and student. In Rye, the teachers fought me tooth and nail to keep me out of advanced courses, but I have since been able to see that there is nothing special about AP courses; there is no danger of bruising your brain from taking one of these classes. The danger comes from not taking advanced classes.

. . . The reason people say "everything I need to know I learned in kindergarten" is because the public school system barely teaches anything beyond a kindergarten level. They avoid the introduction of new topics, and drag out kindergarten through all of elementary school. . . Right now, our schools function more as minimum security prisons, than institutions of education.

He'll be an aeronautical engineering major at UC-Irvine in the fall.

The Masters School has the reputation of being the more liberal or progressive of the two local private schools. But this student's experience, along with the fact that he is now studying aeronautical engineering, makes me think there may be a shift in educational philosophy from the middle school at The Masters School to its high school.

Still, upwards of $30,000 a year for your child to spiral through math.

Hard to believe.

---

KippAcademy 18 Oct 2005 - 02:04 CatherineJohnson



beautiful





And we know what Michael Feinberg has to say about spiraling.

---

InterimReportCard 25 Oct 2005 - 17:23 CatherineJohnson



So Christopher's interim report card arrived today without fanfare, stuck inside a bunch of fundraising appeals from the Irvington Education Foundation. Good thing I forced myself to go through all the papers; otherwise I would have missed it.


Math 6-4:       Doing "B" level work.
                      Effort is good.


Well that's a thrill.

I'm working on 6th grade pre-algebra morning, noon, and night; I'm gutting my way through Total Household Math Meltdowns; I've figured out reciprocals.

And I have "B" level work to show for it.

Make that: "B" level work in quotes.


Also included in today's Paper Chase, an invitation to Coffee with Principal Fried!

Stay involved!


Yes, thank you, I believe I will stay involved!

I believe I will attend the upcoming Coffee with Principal Fried, at which event I believe I will ask Principal Fried what a "B" in quotation marks actually means.

Is a B inside quotation marks a B?

Or not?

Is it sort of like a B, but not exactly a B?

Is it an ironic B?

A tentative B?

Is it a warning B? A there's-still-time-to-turn-this-thing-around kind of B?

Or what?

Obviously, it's time for me to enroll in Community College, take calculus (OK, precalculus first; oops, I mean algebra 1, geometry, and algebra 2; then precalculus), and get my own "B"s. Inside quotes or out.


ok, what else have we got
Ah.


Science 6:       Does good work.
                       Shows positive effort/attitude


question:
What does this mean?


a) Does good work & Shows positive effort/attitude

or

b) Does lousy work, but I don't want a barrage of testy emails from parents


I'm especially curious in light of—


Reading 6                Making satisfactory progress

and

Language Arts 6     Making satisfactory progress



That sounds bad.

"Making satisfactory progress" sounds especially bad in light of the fact that English language arts is the class in which Christopher failed a test on subject and predicate, and the teacher has been out with pneumonia ever since.


possibilities:

a) Making satisfactory progress means making unsatisfactory progress

b) Making satisfactory progress means I've been out with pneumonia for 4 weeks and I have no clue

c) Making satisfactory progress means I've had tenure so long I don't need to screw around with this stuff if I don't want to


At the bottom of the interim report we have this:

Questions about Interim Reports? Call 591-9592.

If I choose to call 591.9592 I will be speaking to Griffin Murray, guidance counselor, the person who last year told me, and I quote, 'Christopher is a 3.'

I think I'm going to give Griffin a call.


p.s.
C. is doing great in drama.


update

All these Interim Comments?

Making satisfactory progress

Does good work

Shows positive effort/attitude

They're canned.

Teachers have a list of 25 canned comments, and they check off the ones they want sent home to parents.

When Ed read Christopher's Interim Report he said it sounded exactly like Jimmy's Interim Report. Jimmy, you will recall, is severely autistic.

Turns out he's right. Jimmy's Interim Report sounds exactly like Christopher's Interim Report because it's the same Interim Report. It's canned; it's been pre-written for teachers by people who are not teachers.

We're spending $18,000 per pupil and we're sending parents canned comments checked off on a website somewhere.

---

AaaMathRecommendationFromDan 25 Oct 2005 - 18:44 CatherineJohnson



Dan left a recommendation for a site I'd seen before, but hadn't spent much time on:

aaa Know Math

I'd glossed over it, because it has online math 'worksheets,' the kind of thing where the web site gives you a question to answer, then tells you whether your answer is right.

I'd glossed over this because Christopher did so poorly learning math facts online.

But this is exactly what I need today, let me tell you.

Christopher is going to be having a test on the properties of multiplication & addition in short order, and so far I haven't been able to find print worksheets anywhere.

I'm going to have him spent time doing these pages:


properties of multiplication

and

properties of additions

Here's the 6th grade page

Thanks, Dan!

---

InstructivistOnTeachingPercent 26 Oct 2005 - 14:46 CatherineJohnson



Math Disaster



Maybe the Instructivist will come to Irvington to teach Christopher & me:

I teach math to eighth graders and know that teaching math successfully need not be rocket science. Most of my students can now convert fractions to decimals and percents (and vice-versa) in their sleep. They can also solve the three different types of percent word problems (unkown rate, whole and part) in their sleep.

I'm actually not familiar with percent problems called 'rate' problems.

?  ?  ?


I think I'm reasonably adept at converting fractions to decimals to percents & back, and at solving percent problems....so I can't tell if this is a problem I haven't encountered, or if this is a problem I have encountered, but called something else.

I like the chart

Instructivist's percent-fraction-decimal chart is a terrific idea, IMO.

It's the same principle as Saxon always printing the equivalent expressions on his fraction manipulatives, which Doug did, as well:

metacognitive moment

Converting percents to fractions generally poses no problems when the percent is a whole number, e.g. 47% --> .47 --> 47/100. A special problem arises when the percent is a fraction like 5-1/4 %. This is where the students need to realize that an additional step is required. Many students want to enter 5.25 in the decimal column. The task of the teacher is to focus on this problem and to show that the students must first convert to 5.25%, then to the decimal .0525 and on to the fraction.

I love this!

Instructivist knows where his students are going to go off the rails.

This is ESSENTIAL.

I learned this lesson back when I was researching a book on happy marriages. (I may have 'blookied' this before...)

I was driving all over creation, interviewing folks in their homes.

Some people could give directions a person could actually follow; some people couldn't.

I call directions a person can actually follow 'good' directions.

I call directions that end up with a person driving 30 or 40 miles around in circles 'bad' directions.

The problem with the bad directions wasn't that they were wrong. They weren't wrong.

The problem with the bad directions was they made no allowances whatsoever for the fact that a human being was going to be attempting to get somewhere on the basis of those directions.

People who give good directions invariably say things like, "If you get to the Stop 'n Shop, you've gone too far."

Invariably.

People who give good directions know what mistakes a normal human being is guaranteed to make and they warn them off!

That's what Instructivist is doing here.

J. D. Fisher on teaching fractions

It's necessary, I think, to make it instinctive in students to understand percent as a "number over 100."

From there, I've always liked the idea of moving the decimal point backwards.

5 1/4 = 5.25

5 1/4% = 5.25%

5.25% = 5.25/100

Move the decimal point to the left twice (the power of ten you are dividing by), write in the necessary zeros, and remove the percent symbol:

5.25% = 0.0525

lots more math horror stories, too

One Commenter left this:

I am a high school chemistry teacher at Bowie High School in Bowie, MD. I have students in their junior and senior year who have received straight As in math for their entire middle and high school careers. They can't do simple arithmetic. They don't know the 'why' of a mathematical operation and so do not remember the 'how'. In fact, they have never been taught 'why' they had to learn anything in math other than counting for the use of money. I kid you not.

This part is incredible:

I have to teach math for 4 to 6 weeks every year. The students have been taught the wrong rounding rules by their math teachers.

The wrong rounding rules?????

The wrong rounding rules?

I'm going to have to pause.

[pause]

There.

Breathing normally again.

Where were we?

Oh, yes.

The students have been taught the wrong rounding rules by their math teachers.

And that's not all—

They also can't find a percentage or know what it means, understand significant figures (significant figures!), do scientific notation, know anything about the laws of exponents, find the equation of a line or graph an equation without their $90 graphic calculators (which they don't understand how to use), solve for a variable in an equation (density = mass / volume is an example), convert inside the metric system, covert in the English system, understand the concept of conversion factors, or do anything without extensive direct instruction with days of practice and activities in the mathematical concept.

[snip]

What in the ever loving heck is going on in the math classes in my country? This is insane. You ought to see when I have a parent conference of an honor student and point out that the kid they say is not good at math (a backdoor plea to lower the standards) had received As and Bs in all their math classes and I pretend to act incredulous that they would offer such an excuse for their obviously highly mathematically competent child. The parent and admin damn near chew a hole in their cheek. I just sit there and look all innocent. Admin is way on to me...but they never say anything. They do glare and act cold.

what do you make of this?

another Comment:

It goes all the way up the line. When I was a college professor (at an expensive, selective school) teaching an upper-level molecular genetics course, I observed juniors and seniors, who had somehow gotten As and Bs in freshman calculus, who were mystified by the simple Algebra I equation-solving involved in teaching DNA renaturation kinetics. It's a wonder we manage to produce any scientists and engineers at all in this country.

Do these students really not know algebra 1 equation-solving, or have they......forgotten(?)

chuckleheads, too!

Last, but not least, we hear from teacher Bill D.:

I use my blog to combat ignoramuses like "instructivist" who are destroying education. Dumbing down education...please. Its the test nazis and the traditionalis who refuse to allow education achieve higher potential "Destructivist' is more like it. They destroy student's souls. As yo can see., I often use the blog to argue I also see great potetial for student/teacher interaction through blogging.

What is it with these people and their Nazi talk?

test nazis?

Where does this stuff come from?

And why is this person (presumably) teaching in our public schools?

---

SusanOnParentsGettingKidsThroughMath 22 Nov 2005 - 13:32 CatherineJohnson



By way of background, Susan's mathematically gifted son, who is in 5th grade, is taking 8th grade algebra. Susan's description of his class jibes with my own experience and with those of other parents:

Even with bright kids it is apparent to me that the math parent can seriously make or break the deal.

The other day math kid came home with homework (Algebra 1) where the chapter took a distinctly intense leap in difficulty (distance, rate, and time word problems.) Even Dad (who made A's in Calculus in high school) was surprised at how difficult they were. Dad looked in other Algebra texts that we have collected (Saxon, Dolciani, that other one that we talk always talk about...)to find similar problems, but had some difficulty finding the right level of intensity. I happened to have just bought a book called How to Solve Word Problems in Algebra by Mildred and Tim Johnson, which happened to have a chapter on time, rate and distance problems with several types of examples and then practice (with the answers and explanations nearby.)

Of course Dad was coming home late so I was alone with this stuff. I had him take a shot at the practice ones in which he whined, "There's not enough information! You can't do these!" Because if he can't do them at 11, then they can't be done, or so he believes. He looked for examples beforehand to see if he could figure it out and lo, and behold, the lightbulb started to come on (without me, thank God.) He had to go back to one or more of the examples a few times and one time he just couldn't figure it out at all, but looked at the answer and explanation and immediatley saw how to do it. This took over an hour, but he was motivated because he was actually learning something new and getting it.

On the quiz the next day there was a very similar problem to the one he worked on out of the practice book and so he had no problem with it. Later, it was learned that he and one other child made A's (he missed one. A dumb mistake) while the rest made a variety of scores including some 30's and 40's. The teacher explained that some of the kids had never asked for help and would probably need to be taking it over next year.

We are lucky. If my husband didn't check every single homework problem for understanding, as well as accuracy, and we didn't have our own copy of the textbook to read, I'm sure he would have been included as one of ones failing to make the cut. I can't imagine how lousy he would feel and since he is in grade school still it would be very difficult explaining to him that he isn't stupid.

What is aggravating about this kind of stuff is that the math itself is probably not beyond most of these kids, but the maturity to know when or how much you need extra help is unlikely to be there before high school. So, I can't help but think that some kids will be shut down pretty quickly based on that alone.

Along with that, the fact that the textbook took this intimidating leap without thoroughly explaining the concept (as the supplemental book that I purchased did so well) probably knocked all but the kids with math parents at home right off their game.

I'm beginning to think that hovering parents are the key until some kind of self-motivation kicks in. By then, you can let them fly because you figure they've got a good base and they can always return to it.

This is exactly what we're up against, only our kids aren't particularly encouraged to ask for help. The teacher actually made a joke about this early on. "I don't like it when you ask me questions," she said. That was a joke.

Our accelerated course, which is the only course taught at roughly the same level as math courses in high-achieving countries, is defined, from the get-go, as a course for mathematically talented kids. Kids who just naturally have it.

Christopher does not naturally have it.

The only way he's going to get it is through teaching.

That's why I have to keep 2 steps ahead of him. I have to learn all this stuff (which, yes, I'm enjoying, but still) just to have a shot at pulling him through this course.

Interesting, though, what Susan says about high school.

I have a terrific article by Willingham about kids not knowing what they don't know (I've been planning to get it posted for awhile).

I wonder if, once Christopher reaches high school, he'll be able to tell what he knows & doesn't know better than he can now.

At the moment, it's hopeless. He has zero idea whether he knows something well enough to work a problem on a test. Zero. And he's over-confident, thinking he understands and/or knows something he doesn't. Plus his teacher does not seem to do much, if any, guided practice in class, so I don't get the sense that a whole lot of Probing for Understanding is happening there.

She covers the material in class; he's supposed to show up knowing it the next day. (This is the way it's always been done; I'm sure his teacher learned math the same way.)

Sunday night I let Christopher do his math homework by himself, because I wanted to take the dogs for a run and I needed to pick up Jimmy & Andrew at their Program and Christopher was going over to Daniel's house and I forget the rest. A thousand things.

So he did his homework on his own.

I checked it the next morning, and virtually everything was wrong.

I asked if he'd understood the teacher's explanation. He said 'no.'

I asked if she had them do any practice problems in class. He said 'no.'

I demand a refund.


And don't even get me started on the Return of Ms. Roth, the English teacher.


keywords: survival of the fittest Darwinian Darwin best students accelerated classes accelerated math acceleration

---

MiddleSchoolHell 27 Oct 2005 - 21:38 CatherineJohnson



I am in Middle School He**.

If I had the energy I'd write an homage to KDeRosa; I'd write T2.

Since I don't have the energy, I won't.

I'm taking the dog-ate-my-homework route.

Because I'm in Middle School He**, I have not, as yet:

• opened, read, j-pegged, & posted Dan's fraction multiplication chart
• posted the data I (finally) found on how our top math students measure up
• posted Barb Oakley's comments about her daughters' experiences in Kumon (though these you can find by searching Comments)
• read email in....um....3 days?
• opened, read, used, & figured out how to post Doug's Excel practice problem generator.....

And those are just the things I remember, off the top of my head.

Meanwhile, I'm supposed to be writing a book proposal.

question for Doug (and everyone else)

The only reason I'm taking 5 minutes to post something now is that I came across a Cal State Northridge professional development program (pdf file) for math teachers that looks pretty good. (David Klein is at Cal State, so it's possible he had something to do with it.)

I haven't read through yet myself, but skimming I found this sheet on the distributive property:





What do you think of this visual mode of teaching & representing the distributive property?

I'm thinking.....it's kind of cool.

otoh, I don't think this way of drawing it is quite 'sharp' enough, but I'm not immediately seeing how to alter it to make it work (or possibly work).

So....yoo-hoo, Doug!

If you feel like taking a crack at this, you could be doing the World of Pre-algebra a Major Service. And Lord knows, the World of Pre-algebra needs help.

homage to Russian Math, too

Also on my Neglected Duties list: a summary of teaching techniques from Russian Math.

Another thing that will have to wait.

However, since I've begun using one today, I'll mention it now.

RUSSIAN MATH uses 'Out loud' problems to teach concepts.

'Out loud' problems are problems the student solves without pencil and paper (no calculator, either); technically they are mental math.

However, they are quite different from the mental math problems I've seen.

I've seen mental math used in two ways:

• to develop number sense
• to overlearn math facts

RUSSIAN MATH's Out loud problems don't serve either of these purposes.

Instead, Out loud problems are a teaching tool in which the problem or concept to be mastered is presented in its simplest form so that the student is practicing the concept, not the calculation.

A simple example. In a lesson on multiplying fractions, the Out loud problems, which always appear at the beginning of a problem set, would be super-easy problems of the 1/2 x 1/2 variety. They are so easy you barely see the math; you 'see' the procedure or the concept instead.

Recently, I hit on the idea of using RUSSIAN MATH to supplement PRENTICE HALL PRE-ALGEBRA by using the Out loud problems. Christopher can't do any more problems than he's already doing (he could, but I'm not going to ask him to); he doesn't have much time to be studying a second math textbook, either.

Out loud problems solve part of that problem. For one thing, kids like Out loud problems. I don't know why, but they do.

For another, an Out loud problem takes all of the extra handwriting/copying/keeping columns of numbers lined up straight/remembering the numbers/etc. burden off of a student's frontal lobes. Out loud problems are incredibly 'clean' in that way.

I assume that's why Christopher, who fights me tooth and nail on extra work I ask him to do in any subject, is perfectly happy to do a set of Out loud problems.

So I'm going to see what I can do with Out loud problems for the distributive property.

what is the proper sequence of Out loud problems for the distributive property?

I've begun, this morning, creating my own set of Out loud sheets, incorporating a second technique both RUSSIAN MATH & KUMON MATH use, which is to create problem sets on just one tiny piece of what I'm trying to get Christopher to see.

For example. Christopher simply can't distribute a negative factor to a negative addend. It's impossible.

I've written an Out loud sheet with four columns:

First column: All problems are of the form: 6 (x – 3)
Second column: All problems are of the form -3(x + 2)
Third column: All problems are of the form -4 (3 - x)
Fourth column: All problem are of the form -3 (-x - 2)


This will probably help, but it's not enough. I think I also need a sheet of problems demonstrating the fact that -x can also be expressed as -1x.

I'm also thinking I need to back up even further and do a sheet of strictly numerical distributive property problems:
3 (2 + 4) = 3(2) + 3(4)

and a second sheet (or column of problems) reversing this formulation:
3(2) + 3(4) = 3(2 + 4)


I'm thinking I may also need sheets like this using negative numbers.

And at this point I'm starting to get addled.

What do I actually need in order to teach the distributive property to Christopher in a way that makes sense?

If any of you have ideas, let me know.

a Saxon failure

The distributive property is one subject on which I think Saxon did a poor job.

Saxon 6/5 teaches the distributive property, but Christopher never came close to getting it, either conceptually or procedurally. This was, I think, a case of incoherence. There would be a lesson on the distributive property, 6 problems of Lesson Practice, and then you wouldn't see it again for weeks. By the time a lesson formally touching on the distributive property came up again, Christopher would have forgotten the first lesson entirely. The small bits of distributed practice didn't help.

In this case, Saxon's mode of teaching the distributive property was akin to spiralling, only within the same book. Christopher kept getting 'exposed' to the distributive property, but he never learned or remembered it. For distributed practice to work, you have to achieved some preliminary level of mastery. (I don't know what that level is to write about here, but I probably 'know it when I see it.')

I remain a Saxon fan, by the way; I'm working my way through 8/7 now.

But the Saxon Homeschool Edition can be incoherent at times.

---

DougsDistributivePropertyGraphic 26 Oct 2005 - 23:04 CatherineJohnson




this is beautiful!





In my next life, I want to come back as a graphic designer.

distributive property manipulatives?

Any thoughts on whether distributive property manipulatives might be a good idea?

I'm thinking something extremely simple, maybe a large grid and those round plastic number 'counters' (they look a little like thin Poker chips). Or you could just use paper, or pennies or buttons. Anything.

You could ask the child to show you:

3 ( 2 + 4)

as an array like Doug's, or possibly as the two different arrays, which might be best. The child would see the equivalence because he or she had just made the equivalence with his own hands.

Temple on using your hands

I talked to Temple (Grandin) again last night. She had lots of horror stories of professional architects who can't make scale drawings. These are all young people who learned to do scale drawings on the computer.

She is adamant that there is a motor component to seeing. She thinks you can't get your visual processing right if you haven't....done things with your hands (can't be more specific than that).

The mistakes these people made were all perceptual mistakes, not cattle handling mistakes. (We're talking about the meatpacking industry.)

I really think there's something to this. (It's making me curious about that strange-looking Borenson fellow with his hands-on algebra, I must say....)

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JDFishersDistributivePropertyManips 27 Oct 2005 - 13:35 CatherineJohnson


Incredible!





I can't wait to try these with Christopher!


hmm

I wonder if this image is slightly to big for the front page....

I have to go get Christopher & his friend Joe; back later. (If I need to cut this image down slightly, I'll do it when I get back.)

Extremely cool!


J.D.'s full-size graphic is here.

J.D.'s model for distributive property with subtraction

I just noticed J.D. also included a model for the distributive property used with subtraction, also in the Comments section. (Will jpeg it & post up front ASAP.)

NAEP analysis

And...I just discovered J.D. has posted an analysis of the new NAEP scores.

---

AnotherDistributivePropertyQuestion 31 Oct 2005 - 04:21 CatherineJohnson



Quick question.

I mentioned Christopher has a wicked time trying to simplify this type of expression:

5 ( 6 - x )

Even worse is an expression like:

-5 ( 6 - x )

or:

-5 [ 6 - ( -x) ]

I've been trying to figure out how to teach and explain this. (I didn't get to show him either Doug's or J.D.'s graphics last night, because he had to study for his English test, and do math homework....which reminds me, I have a question about last night's homework, too.)

Back to the distributive property.

It's correct to say that we are distributing multiplication over addition, right?

We're distributing an operation?

That's what I had thought we were doing, but when I went Googling around about it, I found some dissenters.

                                  

Unfortunately, when I say we are distributing multiplication over addition, Christopher gets even more confused by the minus-minus aspect of 'addition' when what he's looking at is a subtraction.

I've written some 'Out loud' sheets on the concept of addition being subtraction of the opposite....but if anyone has other ideas, please let me know.

I'm having trouble breaking this problem down into its component parts.

Should I have him, at this point, rewrite the question as addition of the opposite?

That's what I'm thinking at the moment, but I'm not at all confident this won't introduce even more confusion and angst.

finding   x - 15 = 30

Here's my other question.

Christopher came home last night with a bunch of simple equations to solve.

He knows how to solve all of them using inverse operations, because he practiced that a lot in Saxon Math.

The teacher told them they couldn't do it that way. She wanted them to do it this way:


   x - 15 = 30
      +15  +15
____________
   x + 0  = 45

       x = 45

So naturally we had a whole battle royale about that. Christopher didn't understand the teacher's explanation, and forgot to bring his notebook home, so I had no idea what he was supposed to do. When I said he needed to call a friend and find out he exploded; when I called one of his friends to find out what he was supposed to do he triple-exploded.

His plan was to just find the answers the way he always does, write them in the blank, and take the half-credit.

Here's my question.

To me it seems like a good idea for Christopher to do a bunch of problems the way his teacher showed him.

But why is that?

How do I explain that using the inverse operation is different, sometimes, from isolating the variable?

And is that what we still call it?

Isolating the variable?

I just remembered

Last question:

a = b

b = a

Is this an official property?

Or is it just obvious?


I ask, because I have two Out loud sheets based on this principle.

The first one is full of problems like this:

5 + (-2 ) = _____

The answer is:

5 - 2


Then I have a second sheet filled with the opposite problem:

5 - 2 = _____

The answer is:

5 + (-2 )


I plan to ask Christopher why, if 5 + ( -2 ) can be rewritten as 5 - 2, then 5 - 2 can be rewritten as 5 + ( -2 ).

And I intend for him to answer that if a = b, then b = a.

All a & b have done is switch sides.

But is that right?

Or is this an Official Property?

update from J.D.

You know, it strikes me that this is another Out loud sheet.

I probably better write up a lot of simple multiplication problems, and have Christopher tell me how & where the distributive property is used in the algorithm.

keeping track of graphics

I'm trying to get all these incredible graphics stored where people can find them, which I have taken to mean stored in multiple locations:

Book-style index
Math lessons
Our favorite supplements

I also have a page devoted to Carolyn's math explanations (seriously behind, unfortunately, but I'm working on it).

I do need a Kitchen Table Math intern.

I bet I could rustle one up.

I'm not quite as behind on this project as I am on others (I realized today, I should just go ahead and post Dan's fraction-multiplication graphic now, before I've had time to sit down & study it...).

In any case, these contributions should all be findable.

---

VisualizingDoesNotEqualUnderstanding 29 Oct 2005 - 13:26 CatherineJohnson





Visualizing isn't the same as understanding.

update, from Barry

If something can be visualized using an example,then go for it. Some things cannot. This is why I think learning proofs in geometry is so important. Sure, you can teach proofs in algebra and other math classes, but the concept of proof is difficult for beginning math students. Geometry allows the proposition being proved to be visualized in a picture (at least 2-D and 3-D does). Once students get a grasp of how proofs work in geometry, they are better equipped to tackle them in math classes where concepts are not so easily visualized.

I found proofs in real analysis to be difficult for this reason, but my understanding of proofs from geometry gave me a good foundation for proceeding.


keywords: proof integers negative times a negative Math Forum

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LinkingHighSchoolScoresToElementarySchool 31 Oct 2005 - 02:57 CatherineJohnson



I think this may be the first press release and/or news article (often one and the same thing, a little-known fact) to connect poor high school performance with what goes on in elementary school. Otoh, this article was published in 1998, so it's possible that the 'fourth-grade slump' meme has simply faded from view in the years since.

Penn State researchers think they know what is behind Johnny's and Janey's inability to do science and math, but Americans may not wish to make the changes that could improve performance.

"U.S. students, in general, show a drop in international rankings in math and science between the fourth and eight grades, which many educators and members of the press have called a slump," says Dr. Gerald K LeTendre, assistant professor of education. "Our studies indicate that this is not really a slump, but simply a continuation of low gains from year to year."

[snip]

"The initial reaction to our drop in ranking is to assume that our middle schools are at fault," says LeTendre. "But no one has looked at the overall trends," he told attendees today (Aug. 22) at the annual meeting of the American Sociological Association.

"Most countries do not move up or down in ranking from fourth to eighth to 12th grade," says Baker. "The U.S. is one of the few that does."

The United States starts above the mean in fourth grade science and is at the mean in eighth grade. In math, we are again above the mean in fourth grade but below the mean by eighth grade. The researchers agree that on the surface this has all the indications of a slump. However, the survey sampled third and fourth grades and a grade comparison shows that the U.S. is already losing ground in third grade.

"Low gains between third and fourth, indicate this is not a middle school problem and it is not a slump, but indicative of a system-wide low level of achievement," says LeTendre.

The researchers note that it is not high performance in other countries that pushes U.S. scores down, but something the United States is doing, or not doing, in our education systems to create this mediocrity.

Sociologists of education have observed that known since the early 1900s educational systems in countries have become extremely similar over time, but little is known about how this might influence achievement cross-nationally. Our performances in math and science should all be similar, however, they are not.

do other countries have ed schools?

Apparently not.

The American system....employs teachers trained at universities in a wide variety of subjects besides teaching and their specialties. Other countries, however, have much tighter control over schools and teachers.

The American public is unlikely to accept a system like Singapore's, the number one country in the math and science rankings. There, teachers all receive exactly the same rigid training, school curriculums are uniform and the training institutes assign teachers to schools. Local and parental input to schools are nonexistent.

Agreed.

The American public is unlikely to accept a system like Singapore's.

The American public is likely, however, to accept a set of textbooks like Singapore's.

I'd bet the ranch.

headline: spiralling is bad

One issue looked at by the researchers is the opportunity to learn—the students' access to material in the curriculum. In the U.S., subjects covered in one grade are often again covered in another grade, taking away time from new concepts. Other countries have much tighter upward spirals in learning, only repeating the minimum.

so far, so good

Unfortunately, at this point the article goes off the rails:

Fixing what is wrong with the U.S. school system, however, could be problematic, say the researchers. The American system allows....a close parent teacher partnership....

I disagree.

good news, bad news

The outlook is not totally grim. While U.S. 12th grade students were near the bottom in science, Minnesota fourth graders were the best in science worldwide.

Is this a joke?

source:U.S. Math And Science Scores Indicate Mediocrity

middle schools are still worse

I'm not going to take the time to look it up right now, but I'm certain I've read, many times, that TIMSS data show no gain at all—zero—in math skills for U.S. students between the 7th and 8th grades.

I would be surprised to find that middle schools are simply as bad as elementary schools, but no worse.

Very surprised.

I changed my mind

I decided to go look it up after all.

from The Principal's Guide to Raising Math Achievement:

One of the most disappointing aspects of the TIMSS report as it described the United States was what a small amount of new learning actually occured during the eighth grade. Since both seventh- and eighth-graders took the same tests, researchers had the unique opportunity of creating a quasi-longitudinal study. Sadly, there was no significant difference between the scores of U.S. students at the end of seventh and eighth grades.

And see William Schmidt on U.S. middle schools.

update

Here's Ken on Minnesota fourth graders holding the number one spot in science:

Most likely because hardly any science is taught anywhere at these early grade. I think Singapore doesn't even start teaching science until the third grade.


Summer Supplement Time
linking decline in high school scores to elementary school
research on summer regression
the time costs of not teaching to mastery
U.S. fourth graders not doing as well as thought
Phase 4 topic list, grade 6 class
comments thread on pre-algebra as algebra

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WickelgrenOnAlgebraIn8thGrade 31 Oct 2005 - 15:34 CatherineJohnson



“The Third International Mathematics and Science Study, conducted in 1996, found that the material taught in U.S. eighth-grade math classes was taught in the seventh grade in many other developed countries and even earlier in Japan and Germany.”
—Wayne Wickelgren, Math Coach


“Researchers blame this pattern on the heavy repetition of basic skills that begins in 5th grade and persists through grade 8. Students fall so far behind in those years, Schmidt [U.S. research coordinator for The Third International Mathematics and Science Study, or TIMSS] explains, that they never have a chance to catch up....
—Elizabeth Duffrin, Math teaching in U.S. ‘inch deep, mile wide’


"The current middle school curriculum as described in the TIMSS data lacks intellectual rigor. In fact, the topics covered in the United States' seventh- and eighth-grade classrooms are much like those covered in third and fourth grades—lots of arithmetic (Schmidt et al., 1999, p. 49). In Japan and Korea, arithmetic is taught for mastery in those early grades and students then move on to a more algebra- and geometry-centered curriculum. One of the most disappointing aspects of the TIMSS report as it described the United States was what a small amount of new learning actually occurred during the eighth grade. Since both seventh- and eighth-graders took the same test, researchers had the unique opportunity of creating a quasi-longitudinal study. Sadly, there was no significant difference between the scores of U.S. students at the end of seventh and eighth grades."
— Elaine McEwan, Principal's Guide to Raising Mathematics Achievement


"...if I put in front of you a fifth, sixth, seventh, and eighth grade textbook in math and opened up to page 200 and I jumbled them up, and said, “order them from fifth through eighth grade in order,” you'd have a very tough time because they all look the same. That's because, unfortunately, we have this national strategy of “we're not really going to teach to master, we're going to teach to exposure and over lots and lots of years of kids seeing page 200 in the math book, eventually somehow they're going to learn it. We're going to teach them how to reduce fractions in fifth grade, in sixth grade, in seventh grade, in eighth grade, in ninth grade and continue until finally somehow magically they're going to get it.” Instead of thinking, “let's teach the kids how to reduce fractions at a mastery level in fifth grade, maybe spend a little time reviewing it in sixth grade but let's move on to pre-algebra and let's move on to algebra then.” And that's been our take and so it's not that we have a different math curriculum as much as we have a different math strategy and a different math philosophy."
—interview with Mike Feinberg, co-founder Knowledge Is Power Program (KIPP)

---

LearningCurvesMathBrain 02 Nov 2005 - 00:55 CatherineJohnson

Each year I come to realize more and more that very few of my students are like me. This even goes for the good students, and I need to stop teaching the type of course where I excelled.

The main differences, I think, stem from my experiences in math classes in sixth through twelfth grades. Don't think that this is shaping up to be an anti-calculator rant. It's not....

Middle School Math
I didn't take middle school math. My parents were absolutely furious when I was in sixth grade. The math teacher had a system by which before the beginning of each unit, we could take the unit test, and if we scored at least 90%, we didn't need to sit through the class. Instead we were given packets to work through (independently) while sitting in the back of the classroom. I learned all sorts of things: the difference between accuracy and precision, all manner of tests for divisibility, combinations and permutations, vectors. Most importantly I learned how to ignore someone yapping in front of a chalkboard and how to learn math by reading a textbook and doing problems until I understood the material. As an added bonus, sixth grade math was the time when most students were indoctrinated that "taking notes in math class" equalled "copying every glyph on the chalkboard onto a sheet of paper." This set the stage for years and years of listening in class instead of taking notes. About halfway through sixth grade the school district was sick of my mom's complaining, so they put a bunch of us in an enrichment class where we flew kites to learn about right triangle trig; in seventh grade they enrolled us in algebra.

Math Homework
From eighth grade through twelfth grade I took seven different math classes, and in none of them did anyone ever check my homework. Homework was assigned, and we were supposed to do it, but no one ever collected it or even walked around the room to verify its existence. (One class also had occasional "problem sets" that were turned in for a grade.) If the problems were interesting, I did the homework. If the material was too difficult to learn just by sitting and listening in class (like max-min problems), I did the homework. If I failed a test (integration by trig subs), I would go back afterwards and do the homework. Sure I made some stupid choices (like doing close to ZERO math homework in all of tenth grade), but in the end I knew what I needed to, and I had learned what I needed to in order to learn math.

My students, on the other hand, seem to prefer being told what to do. Do all these problems by this day. Write this down. Memorize this. Show up in this room at 8am on MWF. And I can't get through to them that they wouldn't need to wake up early and trek across campus in the cold and dark to come to my class if they would just read the textbook and do the problems. That's all it takes: read the book, do the problems. Aside from setting the pace and verifying achievement, I'm inessential. The two things that my students are most reluctant to do (read the book and do the problems) are the keys to learning the material in my class.

Of course I read this and I'm identifying with the mom.


It Seemed Like a Bad Idea at the Time

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MathematicalPrimalScreamTherapy 03 Nov 2005 - 11:22 CarolynJohnston


Reading Rudbeckia's post here reminded me of my own self-teaching experience in 8th grade.

My 8th grade math teacher took a few of us "math brains" aside and gave us a 9th grade textbook to work through on our own. We sat in the back of the class all year and worked on these books by ourselves, at a table. Like Rudbeckia's class, noone checked our homework and noone gave us tests. Every quarter, we got an automatic "A" on our report cards.

I, being the space-cadet wonder child that I was (I honestly believed, somewhere deep down, that all this work was for the other kids but not for me), didn't do a thing all year. I thought my thoughts and dreamed my dreams.

The kid who sat across from me at the table used to nag me to do something and tell me that I'd get in trouble if I didn't, but I didn't see that I was going to get into trouble at all. What trouble? I was getting As without lifting a finger, and noone was checking. Kim Osborn was her name, and she was a very earnest worker (Kim, wherever you are, you tried; it wasn't your fault).

And then, of course, I got into trouble. I took the Regents 9th grade math exam, and by the skin of my teeth and the dint of some generous grading, I got a 67. My Dad hit the roof when he found out what had been going on; he had assumed I was really earning those As, and he had never been to a parent-teacher conference and talked to the math teacher.


the moral of the story

Don't assume that your kid can work on his or her own, even if he or she is bright. Actually, the notion that a kid will do his homework, much less teach himself first-year algebra, without being nagged and ridden is probably wrong in a lot of cases.


a related thought about teaching

Much later, after I got interested in the subject, I became quite a good student. I got straight As in college math, without even realizing that not everyone in my class was in the same boat. I was quite shocked when I started teaching and found that students such as I had been were rare. My office hours were filled with students who just didn't get it. I was bewildered; it hadn't been hard for me; why was it so hard for them? Obviously some of them weren't trying, but many were. Most of them couldn't make it without a lot of extra help.

I was quite patient with them, but I lacked sympathy. And I wasn't the only one who lacked sympathy; everywhere I looked, the other student teachers and even professors were just as bewildered as I am by the difficulty their kids were having learning math, and by the resentment they felt toward the subject and us. In each case, you might say, we were haunted by the memory of the students that we had been. But each of us had been some teacher's dream student.

I think it's the hallmark of a mature teacher that she can learn to put aside her own experiences as a learner and give the kids what they really need, whether it's more or less challenging work, or a bit more support than they themselves needed -- just as it's the hallmark of a good parent that they don't let their own experiences as children get in the way of rearing their own kids.

And this works the other way too. I think a lot of what fuels the constructivist engine is the loathing that so many people in the ed business remember feeling for mathematics when they were kids. They might think that they hated it because it was plug-and-chug, drill-and-kill, sage-on-the-stage, and so forth; I suspect they really hated it because, at some point, they got left in the dust and every experience after that was one of failure. People who get through math successfully, but just don't like it well enough to pursue it further, don't have the same feelings of bitterness I so often see expressed by constructivists. Might I suggest that they, too, need to let their own childhoods go?

---

HowToWriteAlgebraEquations 05 Nov 2005 - 03:08 CatherineJohnson



Christopher's friend Marc just asked me for help writing equations for word problems.

Here's the question.

Is it the case that you can't write something like:

3 + 5 = x


Russian Math says the convention is to have the variable on the lefthand side of the equation.

However, Prentice-Hall seems to want not only the variable on the left-hand side, but also one of the numbers.

To pass muster you'd have to write:

x - 3 = 5


That seems wrong to me, and in fact, Pre-Algebra: An Accelerated Course by Mary Dolciani has one equation in the answer key in which the variable is isolated on the left side of the equation.

What is the convention?

Meanwhile Marc's dad told him, 'Just write the equation in the most complicated way you can think how.'

Marc is good at math, but even he was a little befuddled by that.

I came up with: Write it whatever way makes sense, then flip it.

That worked for Marc, so he is now writing the equation the way it makes sense, then inversing it.

"I can inverse it," were his exact words.

I have a sneaking suspicion this is the kind of homework scene that led people to think Reform Math might be a good idea.....

---

EmailToMathTeacher 08 Oct 2006 - 22:14 CatherineJohnson

Hi—

I think Christopher probably did poorly on yesterday’s test, which is distressing. When the test comes home I’ll have him re-do all the problems he missed, and I’ll write worksheets containing similar problems for him to do as well.

We are very committed to Christopher learning to mastery every topic you teach.

Christopher says the test included a number of very long equations to simplify.

That’s great; the kids should be able to simplify long equations. But he hasn’t had any long equations to simplify in his homework, and unfortunately it didn’t occur to me to write such problems myself until Sunday night, when it was already too late. (I’ve written several sheets of practice problems for this chapter.)

I’m really hoping you can send homework at the difficulty level of the items that will be on the test. Kids only learn through practice, and a test isn’t practice!

Thanks—

Catherine

P.S. This is funny. I just pulled up my Chapter Two worksheets, and on the very first page I have written:

Distributive property to do list:

Write some long, complicated equations incorporating all the properties

Also—
I’m attaching my Chapter Two worksheets. Feel free to use them if you like, but be sure to check the answer sheets yourself—

Christopher was having a lot of trouble distributing a factor over subtraction, so I focused on the various permutations of distribution over subtraction.

I also used the technique used in MATHEMATICS 6 & in KUMON, which is to create problem sets in which a student does the same thing over and over again before doing any mixed practice:

The first column of problems distributes a positive factor over subtraction.
The second column distributes a negative factor over addition.
The third column distributes a negative factor over subtraction.
The fourth column distributes a negative factor over an expression with two opposites.

Last but not least, I'm sending my ‘Out loud’ subtraction sheets. Those were very helpful, so you might want to give them to the other kids. I’ve started doing ‘Out loud’ sheets, because it’s a technique used by Mathematics 6, the award-winning Russian textbook.

Enjoy!

to send or not to send, that is the question

Ed read this and said, 'Don't you want to wait 'til you see the test, and find out if Christopher is right about the long problems?'

I think normally that would be good advice.

But in this case I'm going to email first & ask questions later.

I've mentioned that there was a lot of parent furor over this course last year. A major part of the problem—perhaps the problem—was that the tests contained material far more difficult than anything the kids had seen or done in or out of class.

That may be fine in college. (I don't see why it's good there, either, but ktm readers will have informed opinions on this, and I don't.)

It's not good teaching in 6th grade.

Christopher is taking a class in pre-algebra, and the school's job is clear.

The school's job is to teach pre-algebra and make sure the kids learn it.

So my thinking is:

• Christopher is most likely to be right, which means the sooner Ms. Kahl hears from me the better.
• If he's wrong, that's important in and of itself, and is information Ms. Kahl should have. Why is a committed student who's clearly working hard perceiving the test incorrectly?
• Christopher's situation aside, the words 'teach to mastery' probably cannot be spoken often enough. Spoken, written, emailed, tattooed to one's forehead: Teach to mastery.
  This is The Message.

I'm hitting SEND.

question

Does it make sense to have the kids simplifying very long equations at this stage?

To me, it seems as if maybe we're getting ahead of the game, but I don't know. (I'm thinking the kids need more practice on the component parts of equations....but, as I say, I'm just not sure.)

I'm serious about having Christopher learn to mastery every topic the teacher covers. I don't question her authority to decide content—especially since the course content has been excellent so far, apart from the Extended Problems, that is, and even those are probably coming under control. They did their last extended problem in class, and the kids were able to manage it on their own. That's as it should be.

I'm curious what math-savvy readers & teachers think.

---

TheDivisionsOfMathematics 15 Nov 2005 - 13:03 CatherineJohnson



A ktm guest left a link to a terrific web site called The Divisions of Mathematics, and says that "You can follow the links there to find out what some of the fields in statistics are."

I'm posting the link in the 'book-style index.'


This is incredibly helpful for me. When I first started teaching Christopher I was constantly trying to figure out the various genres & subgenres of the field.

NSF map of math

Here's the NSF's breakdown of the field:

• Algebra and Number Theory
• Topology and Foundations
• Geometric Analysis
• Analysis
• Statistics and Probability
• Computational Mathematics
• Applied Mathematics

hmm

I have to say, for me these categories raise as many questions as they answer, which I suppose was inevitable.

Good starting place, though.

ah-hah

The perils of scanning.

If I'd read this first, I would have understood:

Another way to divide the portions of mathematics is by level of complexity. Elementary topics include arithmetic and measurement; intermediate topics include simple algebra and plane geometry. From there we may pass to somewhat more complex topics built upon these: trigonometry, "advanced" algebra, analytic geometry, and calculus.

This website is limited to topics more advanced than these; little mention will be made of topics which are typically not considered (except in their most elementary aspects) until a student has progressed through some University studies. Our intended audience at the site is the person who has already studied some mathematics courses beyond these at the university level, although in this tour we try to be more inclusive.

---

ChapterTwoTest 15 Nov 2005 - 11:45 CatherineJohnson



So Christopher got a 74 on his Chapter Two test, and there weren't any extra-long, brand-new, never-before-seen-on-Planet Earth expressions to simplify.

He insists there were.

There weren't.

He missed virtually every problem involving an expression with a negative number; this after endless practice on his part & endless worksheet writing on my part. [update: Make that endless worksheet writing on my part and modest practice on his part.]

Plus he missed all the various definitions & true-false questions, which I hadn't managed to realize would be ON THE TEST.

I am now a middle-aged person whose most burning life question is: will it be on the test?

So, now, I get to make up vast quantities of extra practice worksheets, PLUS definition lists....

No, that's not right.

Christopher can make up his own definition lists as he goes along. This is what index cards are for; this is why he has index cards, and an index box to put them in.

He's gonna make up his own cards.

Under my goading & supervision, of course.

I may get Forgotten Algebra just for the problems.


does this problem make sense?

A string orchestra has 55 members. If 23 members play the cello, and 21 members play the violin, but 16 members play neither of those instruments, how many members play both the violin and the cello?

Amazingly, Christopher got this one right.

But I don't quite follow it.

I don't know what instruments are played in a string orchestra....and now that I've looked it up this is seeming like a 'not enough information' problem to me.

What am I missing?


He also got 5 out of 6 points for this one, which I thought was pretty good:

The variables x, y, and z each represent a different whole number. Given the three equations, find the value of each variable.

x + y + z = 12             x + y = z             y + z = 8

He lost a point for not writing:

x = 4
y = 6
z = 2

sigh

---

JamesMilgramOnLongDivisionAndTimeLagInMath 15 Nov 2005 - 21:42 CatherineJohnson



from James Milgram's talk:

In mathematics many skills must be developed for many years before they can be used effectively or before applications become available.

First of all, I claim that taking—even asking to take [long division] out of the curriculum—shows a profound ignorance of the subject of mathematics. The point is, in mathematics, many, many skills develop over an extended period of time and are not really fully exploited until perhaps 10, 12, or even 15 years after they've been introduced. Some skills begin to develop in the first or second grade and they do not come to fruition or see their major applications until maybe the second year of college. This happens a lot in mathematics and long division is one of the key examples.

• Students cannot understand why rational numbers are either terminating or (ultimately) repeating decimals without understanding long division.

• Long division is essential in learning to manipulate and factor polynomials.

• Polynomial manipulation and factoring are skills critical in calculus and linear algebra: partial fractions and canonical forms.
  

I regard the repeating decimal standard as relatively minor, but some people seem to think it is important. The next topic is critical and almost everyone thinks it's minor (Laughter). Long division is essential to learning to manipulate polynomials. Without it, you simply cannot factor polynomials.

So what, you ask? Again, this is a question that doesn't come up until the third year in college. At this point the skills that have come from long division through handling polynomials become essential to things like partial fraction decomposition which is important in calculus but finds its main applications in the study of systems of linear differential equations, particularly in using Laplace transforms, which is the critical construction in control theory. It is also essential in linear algebra for understanding eigenvalues, eigenvectors, and ultimately, all of canonical form theory -- the chief underpinning of optimization and design in engineering, economics, and other areas.

[snip]

What happens when you take long division out of the curriculum? Unfortunately, from personal and recent experience at Stanford, I can tell you exactly what happens. What I'm referring to here is the experience of my students in a differential equations class in the fall of 1998. The students in that course were the last students at Stanford taught using the Harvard calculus. And I had a very difficult time teaching them the usual content of the differential equations course because they could not handle basic polynomial manipulations. Consequently, it was impossible for us to get to the depth needed in both the subjects of Laplace transforms and eigenvalue methods required and expected by the engineering school.

But what made things worse was that the students knew full well what had happened to them and why, and in a sense they were desperate. They were off schedule in 4th and 3rd years, taking differential equations because they were having severe difficulties in their engineering courses. It was a disaster. Moreover, it was very difficult for them to fill in the gaps in their knowledge. It seems to take a considerable amount of time for the requisite skills to develop.

key words: gapology
James Milgram on long division & time
can you cram math: learning a year of math in 2 months
NYU math major
overlearning
remediating Los Angeles algebra students
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
formative assessment and Richard Nixon
Terminator

---

AdolescentBrainAndAlgebra 21 Nov 2005 - 11:57 CatherineJohnson



whoa—

New fMRI evidence suggests that adolescents could be at an advantage for learning algebra compared with adults. Qin and colleagues present findings indicating that after several days of practice adolescents rely on prefrontal regions to support the retrieval of algebraic rules to solve equations, as do adults. Unlike adults, however, after practice adolescents decrease their reliance on parietal regions, which assist in the transformation of the equations, suggesting an enhanced ability for learning algebra. These findings are discussed with regard to adolescent brain maturation.

is there a critical period for learning algebra?

In the framework of the proposed ACT-R model, the fMRI results indicate that adolescents decrease their reliance on the imaginal/parietal module after they have practised (‘learned’) algebraic equations, whereas adults are still dependent on this module even after practice. These results are very intriguing because they seem to suggest that, as adults, we might be limited in our ability to ‘learn’ the mental operations underlying this level of problemsolving. Could it be that our teenagers are actually ‘smarter’ than we are? [ed: the answer is no] It is premature at this point to say that adolescence is the ‘critical period’ for learning higher-order problem-solving, especially because actual performance for the two age groupswas equivalent, indicating no advantage to using one circuitry over another.

is there a different critical period for girls & boys?

Gender differences would also be of interest given the discrepancy in math scores between males and females. fMRI could potentially indicate brain differences that might limit females in their ability to learn such problem solving at the same age as males. [ed: I assume that if there is a difference, girls would need to take algebra at a younger age than boys]

This is highly preliminary work, but it's interesting, because Carolyn and I have talked about a possible critical period for learning math. I wonder about this because there's something of a critical period for learning accent-free spoken language, and because kids who are put radically off-track in math as children usually never get back on track. The standard explanation for this is that it's simply too hard to make up for lost time once you have the demands of teen or adult life to deal with as well. But I'm not so sure. I have an insanely demanding life, and I'm not finding it hard to go back and re-learn math; as a matter of fact, I'm finding it fairly easy (knock on wood).

It always seems to me that the reason I find it fairly easy is that I already learned this material once. I didn't learn it profoundly or conceptually....but I learned it in some way that worked.

Another thing.

There are plenty of times, dealing with the little math-brains in my Singapore Math class, when I think: uh-oh. These kids are way smarter than I am, when it comes to math. I know more; I can (still) do more. But when they get a problem, they get it fast.

The fact that Christopher easily solved the string orchestra problem is a perfect example. Ed and I both thought that was a 'not enough information' problem. Christopher is SERIOUSLY not a math whiz (if yesterday's test is any guide, and I fear that it is) and he solved a SET THEORY problem with ease.


calculus in middle age

This is something that gives me pause....can a person learn calculus for the first time in middle-age?

I guess I'll find out. It's not like there's a lot of people I can ask. I've never heard of anyone who's done it, or, more to the point, wanted to do it.

I hope a sudden urge to study calculus isn't symptomatic of some rare syndrome only Oliver Sacks has ever heard of. Carolyn said the other day, 'Well, you'll never get Alzheimer's.' That's probably true, unless suddenly wanting to study calculus is a sign I already have it.


btw, given what (little) I know of the brain (and given the fact that I've only skimmed this article), it's possible these findings tell us only that adolescents learn faster than adults....


source:
Algebra and the adolescent brain, Beatriz Luna, TRENDS in Cognitive Sciences Vol.8 No.10 October 2004, pages 437-439

---

MathPracticeSimplified 17 Nov 2005 - 17:17 CatherineJohnson



Searching for pre-algebra workbooks this morning, I found the Math Practice Simplified series at the Rainbow Resource Center. The books start in pre-school & run through 8th grade.

It's hard to get a look at any of the pages inside workbooks, but you can see one of the pages from the Pre-algebra book here.

And here's a list of all the Math Practice Simplified books.

For some reason, after staring at the computer screen for half an hour, it came to me that Math Practice Simplified is potentially better than all the other series whose covers I stared at this morning. I have no idea why. (Actually, I do. It's the clean graphic design.)

Rainbow Resource carries a number of workbook series, and their prices are terrific.


gold strike

Today's major find, though, was a website including the entire Glencoe Pre-Algebra Parent and Study Guide in pdf form.

Susan has mentioned before that Glencoe has a terrifically helpful web site, and this is fantastic. Every textbook series should have a Parent and Student Guide just like this one:

The Glencoe Parent and Student Study Guide is designed to help you support, monitor, and improve your child's math performance. These worksheets are written so that you do not have to be a mathematician to help your child.

I'm contemplating springing for this in print form; that's how good it is. Any concept Christopher is struggling with is instantly findable and directly expressed in the text. If he were using the Glencoe book in his class, I wouldn't hesitate.

I love the structural principal of these books.

Like KUMON, each page includes a brief explanation & illustration of the principal the student is practicing.

Beautiful!


Which reminds me. It's time for me to do my KUMON sheets.

Pre-Algebra, Parent and Student Study Guide Workbook (Paperback) by McGraw-Hill
(this is the print copy of the Guide, I believe)

Pre-Algebra, Skills Practice Workbook (no answer key?)
Glencoe Practice Workbook (no answer key?)


update

Illinois LOOP likes the Kelley Wingate workbook series.

from Teacher's Outlet:

Kelley Wingate: Math Practice
This curriculum-based series builds both math and test-taking skills. Practical problem-solving demonstrations and drill pages feature new skills and review. These reproducible resources are the perfect supplement to students' regular course of study. 96 flash cards and answer keys are included in every book.

Kelley Wingate Essential Skills

She has an extensive series of workbooks covering phonics, math, 'math fun,' science, test-taking, study skills, and even writing. There may be more; these are the workbooks carried by Teacher's Outlet. Search the site, and you'll get the list.

I'm contemplating ordering the study skills book. Yet another topic I'm apparently going to be afterschooling.

Did I mention that Christopher's 'study skills' class is doing character education?

I think I did.

---

StevesSchoolDistrictSkillsGap 19 Nov 2005 - 19:32 CatherineJohnson



comment left by Steve—

I emailed the chair of the math department at our public high school and asked her for details about their top math track. It consists of Geometry in 9th grade (requiring a rigorous course of algebra in 8th grade), Algebra II in 10th grade, Pre-Calc in 11th grade, and AP Calc in 12th grade. This is fine. I asked her about the math curriculum gap and how prepared the kids are entering high school. She said that they have meetings with middle school math teachers, but they have no control over K-8 curricula. She said that some students take summer courses to improve their readiness. Obviously, there is a problem. However, enough students make the jump to cloud the issue. It could be the curriculum or it could be the students. Nobody asks the question of how many top track kids got outside help.

She seemed hesitant to criticize. She said that the biggest transition problems are the study skills, amount of homework, and attention to mathematical details. She said that they emphasize precision rather than "close enough". That is telling. I told her that I can also see a gap in content and skills and I wanted to get a list of textbooks/syllabi of the high school math courses so I could judge for myself.


I find that shocking.

Incredible.

This is the school district where 25% of the parents have pulled their kids out & sent them to private schools.

When I told Ed about it he said, 'The entire administration should be fired.'

No kidding.

---

FearAndLoathingInSaltLakeCity 30 Nov 2005 - 16:18 CatherineJohnson



from Amazon's reader reviews of Algebra Survival Guide: a Conversational Guide for the Thoroughly Befuddled by Josh Rappaport, Sally Blakemore:

I purchased this book last spring in order to prepare myself to take college algebra this fall. In high school I failed algebra and I was beyond confused or befuddled. I put off going to college for 10 YEARS simply because I didn't want to do the math. I was dreading the idea of having to spend the summer studying it. I've always had a fear of math and algebra, and over time I began to hate it. Now when I say I hate it, the term hate may not be enough; my loathing was beyond measure; but from working through this book something amazing happened; I don't hate or fear algebra anymore! Seriously!!! And I understand it! And not only do I understand it; I enjoy it! If the idea of enjoying algebra makes little or no sense to you, if you have spent your time and your money struggling through books or classes that are boring, uninformative, over your head, and/or just plain stupid, then really, this book is for you! Please don't pass this book up; it will change your life. And if you could understand how much I hated algebra, you would understand how good this book really is.

Josh, you changed my life! Thanks!!!

I dunno.

On page 4 he's citing Jean Piaget, 'a famous Frenchman.'

Children can't learn algebra because it's abstract. Only teenagers can learn algebra. Because it's abstract.

Wrong!

I wonder if he's more accurate on the subject of algebra.

---

HowCanCollegeFreshmenFillGaps 30 Nov 2005 - 18:34 CatherineJohnson



from Anne Dwyer:

Going back to the question of what to do with students who have large gaps in their background:

We (someone, I forget who) once asked this question on this site: once you have these large gaps in your knowledge, can you ever catch up and close all the gaps?

I think this is especially relevant at the college level. There is a basic math course at our community college, but it goes incredibly slowly. The prealgebra class gives basic lip service to large number problems, then goes straight into algebra. Towards the end of the course, the curriculum goes back to decimals and percentages and conversion factors. But, by then, many of the students are completely and totally lost.

Then, they break basic algebra into two classes: elementary algebra and intermediate algebra.

Even with a tutor, there isn't enough time to determine where the weaknesses are and to go back and correct while the student is taking the class. This would require them to work on parellel tracks: making up gaps and keeping up in class. Everything is geared towards students keeping up in class not preparing the student with the basics for the class.

This was a conundrum for me.

I don't know the structure of mathematics well enough to be able to tell where I have significant gaps and where I don't; if I did, I (probably) wouldn't have gaps.

This is why I decided to go back and re-learn everything from the beginning. That way, I figured, whatever gaps I didn't know I had would get taken care of.

I didn't end up being able to do that, mainly because I had to keep up with Christopher. So I started in 5th grade, where he was.

I'm wondering whether KUMON would be a good idea for students in this position.

I started in Level D—roughly 4th grade—and moved to Level E after two weeks.

Algebra begins in Level H.

Each level has 200 worksheets, and you do 5 worksheets a day, 6 days a week. (I think you're supposed to do 5 worksheets a day, 7 days a week, but Mr. Liu only gives me enough for 6 days.)

If you figure roughly 7 weeks per level, I'll move from Level E to Level H in 21 weeks. I can do that and easily do everything else; my KUMON worksheets are the least demanding part of my day. So I think an ill-prepared college student swamped with remedial work could do KUMON sheets and keep up with his classwork.

I gather there are some adults taking KUMON; I wonder if any of them have written about it.

---

CommentsFromKtmGuest 19 May 2006 - 16:26 CatherineJohnson

I was discussing this bliki last night with a friend, who is a former teacher with experience in elementary, middle, and high school, and with both IEP and non-IEP classes, and she says she also preferred teaching the IEP adaptive behavior students. Not only was there a well-defined plan with exactly specified goals for each student, but also she was dealing with the same classroom management problems as the regular ed teachers, except with only five students and an emergency button on the wall!

Absolutely. Christopher's brilliant 5th grade teacher told me she was asked to teach the Phase 4 class and she opted, instead, to teach Phase 2, which was children one year below grade level. Many (perhaps all) of them had IEPs, which meant the school was required, by law, to teach them to mastery.

She said a lot of them were terrified of math. Some would even start crying. Every single child in her class scored above 80% on her first big chapter test, using the same book the rest of the school was using.

Steve said one day that all students should have IEPs. I've often felt this way myself. Now that I've read Engelmann I formulate this slightly differently. I'd like to see the law changed to state that all children are entitled to be taught to mastery (leaving it to the Engelmann's of this world to figure out what that would mean as a matter of public law and policy).

As things stand, the entitlement to a public education does not mean an entitlement to learn the content being taught.

It means an entitlement to be exposed to that content.




I need an emergency button on my wall.


did your parents afterschool you?

Another comment:

I don't recall either of my parents (1 Ph.D. in chemical engineering, 1 math major) helping me with my homework, ever. Well, okay, there was the one time in 10th grade where my mom helped me set up the electric typewriter so I could type up a 10-15 page term paper, but other than that, they had no idea what I was studying, what was assigned, or when it was due.

I did every single one of my shadow boxes and other projects by myself. (And the teachers could tell, I'm sure.)

This bliki has made me think about the elementary math education that I experienced in school, and I have come to realize that I don't remember a thing of the instruction -- because I wasn't paying attention at all. I don't think I ever had to do math homework at home until high school, because I was doing it in class while the teacher was instructing, or I did it the previous week by working ahead in class while the teacher was talking, or whatever.

I do, however, remember how to do fractions, decimals, long division, algebra, and calculus. I can even take square roots with a paper and pencil, something I taught myself out of an 1899 math book my mom found at a church yard sale. I am a little rusty at geometry proofs, but I can do geometry puzzles like the ones in the Singapore 6B entrance exam.

(Okay, okay, they encouraged and indulged my math mania by buying me math books and letting me read ahead in their high school and college texts. So sue me... that's not really helping with my homework. :) )

This comes up all the time.

Nobody I know had parents spending hours hauling them bodily through math and English language arts.

And yet most of us learned as much if not more than our own kids seem to be learning. I talked to Temple (Grandin) about this yesterday; she learned all fraction operations to mastery in the 6th grade, and she's used math all her life in her stock yard and meatpacking plant designs. This was a developmentally disabled child learning fractions to mastery in 6th grade. (I'll have to ask her how much time her mother spent filling in the gaps. I'll bet not much.)

What happened?

---

MyContractToImproveChristophersGrades 19 May 2006 - 16:27 CatherineJohnson



OK, I need help.

Christopher came home with this "Report Card Evaluation Contract to Improve My Grades," which he has filled out and signed.

I'm going to write a contract for his teachers to sign.

If I get really ambitious, I'm going to write a contract for the principal and superintendent to sign, too. (The superintendent, by the way, has created a 'Wellness Committee' open to parents and members of the community. I guess we're branching out from character education.)

I could crib the whole thing from War Against the Schools' Academic Child Abuse, but that wouldn't be as much fun.

What items should be on a teacher/principal/administrator contract to improve student grades?

I'll definitely have a line about formative assessment and teaching to mastery.

I also need a line about giving clear assignments and making sure students understand assignments, about not telling an entire class their short stories are 'horrible' and 'don't deserve to be published in a book,' and about not saying 'Stop making all that noise, you're not retarded.'

What else?


UPDATE 11-29-2006: Rejecting this "contract" turns out to have been a good call. We learned this fall that Christopher's grade 6 math teacher was instructed to hold down the number of As in her class, which she did. This directive runs counter to standard practice in New York state, which is to grade students in Honors and Accelerated courses up slightly so as not to punish them for taking more difficult classes. Parents were not informed of this policy, yet we were asked to sign a "contract" stating that our child was "responsible" for his grades.


my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day
KIPP Academy contract

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DougAndKenAtEdWonk 19 May 2006 - 22:10 CatherineJohnson



Ken and Doug have been been over at Ed Wonk, arguing about whether schools should be held accountable for student achievement.

Ed Wonk says students and parents have responsibilities, too. What can he do if a student refuses to do a simple 5-minute assignment?

This is a tough one for me, because while I'm foursquare on the side of school accountability, 'Ed Wonk' is a teacher, and teachers are getting mulched. (Doug and Ken both say this themselves several times in their comments.)

I'm at a loss as to what one individual teacher can do.

On the other hand, Temple made an enormous difference for animal welfare working inside the meatpacking industry. The odds were against her. She was a woman in a macho industry when women weren't welcome, she was a free-lance designer with no management experience or power, and she was autistic.

Her autism was her strength. Half the time she didn't even know people were mad at her, or laughing in her face. One time she gave a talk to a cattleman's gathering and thought it went well. Afterwards a member of the audience came up to her and said he felt really bad about the way everyone had treated her. She didn't know what he was talking about.

She just kept trying to make things better for animals. Today, 30 years after her career began, she's done it.

What can one teacher hemmed in by bad policy, lazy and/or damaged students, and dysfunctional and/or demoralized parents do?

I don't know.

My feeling is that the solitary individual has a responsibility to try to make a difference, and then, after he fails, to keep on trying.

Which I imagine is what Ed Wonk is doing.




speaking of which

Ed is good at academic politics. (Synchronicity moment. I typed the word 'Ed' and the phone rang; it was Ed. He's in Paris.)

Background: our Superintendent and Assistant Superintendent are drafting a policy, to be voted on by the school board, to make it impossible for me to teach Singapore Math in the after-school program. Under new policy no parent will be allowed to teach any academic course that might conceivably overlap or conflict with content being taught in school; hence no Spanish class in the after-school program, either, though a class in Chinese may be allowed.

Apparently, this is the way it's done in Ardsley. [ed.: Ardsley?]

Ed says there's a fundamental principle at stake, which is that the administration should not regulate parent activities. He told me to call the PTSA president and ask for an invitation to speak to the executive board. I did, and I'll be talking to the board next week. Meanwhile the President says she wants to show the Singapore Math material to her husband, who has a Ph.D. in computer science, proving the Jayne Mansfield dictum that all publicity is good publicity. (It was Jayne Mansfield who said that, wasn't it?)

My points:

• the administration should not oversee parent activities

• the administration should support any and all academic enrichment programs parents are willing to supply

• the after-school program should be expanded to the middle school (the PTSA isn't allowed to set foot inside the middle school)

• the administration should write and submit to the school board a formal declaration of gratitude to the PTSA for offering innovative and cutting edge academic enrichment courses in its world-class after-school program
  

I probably won't press that last point.

On the other hand, maybe I will.


what can one person do?

Which brings me back to the question of what one person can do.

When it comes to complaining about a lousy math curriculum, one person can be a gadfly.

A gadfly, or a thorn in the side, or both.

I've done a bang-up job on that front, it seems.

What one teacher can do inside a classroom is a tougher question.

I wonder what Siegfried Engelmann would say. Could you create your own formative assessment/Kumon-like series of tiny little in-class lessons that work with undereducated, burned-out 12-year olds?






what is the student's responsibility, anyway?

After allowing Christopher to sign a document acknowledging full responsibility for his grades (I'll be recanting via email tonight, now that I've given myself a day to cool off) my question is: what is his responsibility?

What is mine?

By which I mean.....what does the school have a right to expect from us?

It's crystal clear to me that Mrs. Roth is out of line. I've now talked to other parents in the class, and on the subject of Mrs. Roth they could be my long-lost twins. She's mean, parents say, and she doesn't teach. Moms are spending hours on the internet, pulling grammar lessons, pulling information on how to teach persuasive writing, pulling this, pulling that.

Worse yet, more than one of the children in her class believes that Mrs. Roth specifically hates him or her. These children don't perceive her as uniformly disliking everyone (she probably doesn't dislike anyone; she's just enjoying her caustic performance humor, which was on display Back to School night. She's an entertainer, and her jokes are all at the children's expense.)

So, no, the children don't think Mrs. Roth is just a mean person who dislikes all the children.

They think she dislikes them personally. They spend two class hours a day with this woman.

There's something new and bad practically every week. Actually that's not true; it's not every week. It just feels like every week.

This week's debacle was the 'Feature Story.'

Apparently, the Feature Story was supposed to be a persuasive essay.

Christopher didn't know that, and I didn't know it, either. Another parent told me Mrs. Roth did give the kids an assignment sheet, which I didn't see. I don't know what happened to it.

Is this a breach of responsibility on Christopher's part?

I'm going to say no. At this stage of the game, it's Mrs. Roth's responsibility to find out if her students know what the assignment is.

The fact that she handed out a piece of paper isn't good enough. I want formative assessment on the question of: Do these kids know what I've asked them to do?

So Christopher didn't do the assignment correctly. He wrote a very nice explanatory paper on school violence (what could have prompted him to develop an interest in school violence, I wonder), laying out one or two reasons for school violence, and two possible solutions. Then he told which solution he preferred, and why.

The paper was short, well-organized, and well-written.

Mrs. Roth thought it was terrible, and told him so, loudly, in front of the class.

Then she accused him of 'not trying' and 'not working.'

He was humiliated.

I've had it.

Number one, no child needs to be humiliated in front of the class.

Number two, where is the instruction?

Christopher has no idea what a persuasive essay is, yet he was asked to write one. Meanwhile I, the parent, do not hear the words 'feature story' and think 'persuasive essay.' I have yet to see a single constructive or informative comment written on a paper Christopher has turned in to Mrs. Roth; I have yet to see any comment written on any paper at all. When Mrs. Roth came back from 6 weeks out with pneumonia, she told the class, "Your stories are horrible. They don't deserve to go in a book."

And that was that. My story is horrible; next time I'll try to write something not horrible.

I have yet to see any sequence of writing instruction: rough drafts, revisions, 2nd revisions, anything at all. [correction: Christopher says they wrote a rough draft in class and handed it in. And that was that. Mrs. Roth provided no feedback..]

So....I guess I'm going to have to take back my question.

In theory I'm interested in what Christopher's & my responsibilities to the school may be. In reality, I'm far more riveted by the question of what the school's responsibility is to us.

But I am interested in any thoughts all of you have on the subject of student and parent responsibility in middle school.

---

AleksIndividualizedLearningAssistant 03 Dec 2005 - 21:25 CatherineJohnson



Nick's Mama sent an email asking about ALEKS.

Does anyone know anything about it?

All I know about it is that a blogger named Parent Pundit used it with her daughter with good results.


slipped my mind

hmm

I see that back in May I was planning to 'check out' ALEKS right away.

Obviously that didn't happen.

Time for me to read Getting Things Done again.

If I can find it.


David Allen has a blog

This could be interesting.

update 6-30-2006: David Allen doesn't have a blog.


good grief

Now here is a photo I would not publish on my blog if I were David Allen.

David Allen needs a blog consultant.

I think by now most of us here at ktm could set up shop as blog consultants.


if you're killing time?

Why is David Allen providing me with suggestions on how to kill time this weekend?

Wouldn't I be killing time reading David Allen's blog because I have a problem with killing time?

Think and discuss.


a parent's experience with ALEKS
ALEKS Graphic
formative assessment on wheels
ParentPundit uses ALEKS to fix Everyday Math
ALEKS question
ALEKS assessment coming right up

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AleksAndIndividualizedProblemSets 04 Dec 2005 - 01:01 CatherineJohnson



This is the aspect of ALEKS that intrigues me:

• Adaptive, dynamically chosen small set of questions

• Details precisely what the student knows

• Constantly updated as work is completed

The idea of 'dynamically chosen' worksheets sounds good, but I wonder whether you gain anything you don't with a program like KUMON, where the worksheets aren't dynamically chosen. Saxon Math has students do the same worksheet many times during a school year, and I know from experience it works fine. You don't need a new mix of problems every time you practice.

On the other hand, even small gains in efficiency would add up over time.


formative assessment on wheels

Interesting.

Here's a link to the research/marketing paper ALEKS has posted on their web site:

ABSTRACT

This paper is adapted from a book and many scholarly articles. It reviews the main ideas of a novel theory for the assessment of a student’s knowledge in a topic and gives details on a practical implementation in the form of a software system available on the Internet. The basic concept of the theory is the ‘knowledge state,’ which is the complete set of problems that an individual is capable of solving in a particular topic, such as Arithmetic or Elementary Algebra. The task of the assessor—which is always a computer—consists in uncovering the particular state of the student being assessed, among all the feasible states. Even though the number of knowledge states for a topic may exceed several hundred thousand, these large numbers are well within the capacity of current home or school computers. The result of an assessment consists in two short lists of problems which may be labelled: ‘What the student can do’ and ‘What the student is ready to learn.’ In the most important applications of the theory, these two lists specify the exact knowledge state of the individual being assessed. This work is presented against the contrasting background of common methods of assessing human competence through standardized tests providing numerical scores. The philosophy of these methods, and their scientific origin in nineteenth century physics, are briefly examined.

Of course now I'm super-intrigued.....

This is all I need, right now. One more high-concept math-learning scheme.

Curiosity doesn't seem to kill cats, but it's going to be the end of me.


a parent's experience with ALEKS
ALEKS Graphic
formative assessment on wheels
ParentPundit uses ALEKS to fix Everyday Math
ALEKS question
ALEKS assessment coming right up

---

EndOfParentalInfluence 06 Dec 2005 - 01:44 CarolynJohnston


Catherine and I were just talking a little while ago about having boys in middle school. It's really amazing. Three months ago we had boys who weren't substantially different from the boys we'd had for several years. But they've really changed since entering middle school.

One thing that's caused a lot of domestic trouble around here lately is Ben's long-term reaction to our decision to take him out of his regular Connected Math class, and have him work with an aide from Saxon Math instead. Last year, I'm quite sure, it wouldn't have distressed him to be taken out of math class every day for different work; but this year it's a different story. He's obsessing about his forcible removal from the bosom of Ms. Fredson's math class morning and night.

Sometimes he's angry about it, as when he yelled the other night, "Connected Math is JUST FINE for me, MOM!", and "Ms. Fredson is a perfectly good teacher, MOM!" Sometimes he's imploring, as when, just a few minutes ago, he asserted that Ms. Fredson had never been unkind to him and so he should be able to go back into her class. When I made this decision, I honestly wouldn't ever have thought he'd have such a negative reaction -- though I would make it again.

I've explained to him any number of times that we liked Ms. Fredson and thought she was a good teacher; that what we don't like is the curriculum she has to work with. A curriculum, if you think about it, is a pretty abstract notion compared to that of a teacher.

I tried to give him a concrete example. I pulled a worksheet that Ben had done in his first week in Ms. Fredson's class: it was a quiz they'd taken on odd and even numbers. A number would be read off, and the kids would write 'odd' or 'even'. This was in a 6th grade accelerated math class. I don't even know for certain that that was a Connected Math activity (since the school actually uses a hybrid math curriculum - Connected Math and Prentice Hall); but I do know that he could do that easily in 2nd grade.

"That's pretty easy," Ben had to admit. I seized the advantage. "They just aren't learning as much as you are, Ben!" I said. And it's true.

It's hard to explain the notion of a gross institutional mistake to a kid, especially one on the autism spectrum.

Moral of the story

Try to get your accelerating and/or afterschooling done while your kids are in grade school. They become suddenly and definitively less pliable in middle school.

It's too late for me and Catherine, so save yourselves!

---

MoreMiddleSchoolTrauma 19 May 2006 - 21:48 CatherineJohnson



So I'm going to ask Carolyn (hi, Carolyn!) to add a homeschooling category. That and a how-to-teach-writing category. (Smartest Tractor has left some books & advice, so I'll get those pulled up front tomorrow. Thank you. Please tell us more when you have time.)

I should have homeschooled Christopher.

Period.

We're watching him fall apart before our eyes. Tonight we had crying. Twice. He came home from school with two Ds on two English papers, another one on his chapter test in math. He's very close to failing his two main courses.

This was the Distinguished Student last spring, a child who has never earned less than a 4 on the state tests (and the English test is serious); now his father is talking about therapy. We're seeing his behavior deteriorate; we're seeing his handwriting deteriorate. Ed, tonight, was shocked by the regression in the look of his written work. He's writing like a child in first grade, and not a happy child, either.

I have now told them both that homeschooling is on the table.

Christopher and Ed say no, homeschooling is not on the table.

That's pretty much my position on therapy, come to think of it; we're not paying for therapy unless Ed gets another career. A much bigger, fatter career. And even then, forget it. I'm not paying a fortune in property taxes and therapy bills so Christopher can attend Irvington Middle School.

The one good thing is that Ed has written a letter to Mrs. Roth, copied to both principals and to the guidance counselor, that is destined to become a classic in the annals of IMS history. I don't know if he'll let me post it, but we can all hope.

Tomorrow he's writing the letter I didn't manage to write about the Grade Contract. I didn't manage to write it myself because I spent the week exhibiting impulse control.

Which, under the circumstances, was best for all concerned.


synchronicity

I've just this moment opened an email from my neighbor:

Michael Viscardi, a senior from San Diego, won a $100,000 college scholarship, the top individual prize in the Siemens Westinghouse Competition in Math, Science and Technology.

Viscardi said he's been homeschooled since fifth grade, although he does take math classes at the University of California at San Diego three days a week. His father is a software engineer and his mother, who stays at home, has a Ph.D. in neuroscience, he said.

Sounds like those folks hit the same wall I've hit. I'm printing it out for Ed.


oh—and tomorrow I get to talk to the PTSA Executive Committee about my sins as a Singapore Math instructor.

Pray for snow.

---

MeetingWithThePrincipal 19 May 2006 - 21:39 CatherineJohnson



We're meeting with the principal tomorrow morning.

The Mrs. Roth issue is simple at this point. We know what needs to happen for Christopher, and we'll stay on the case until it does happen.

The larger issues are tough.

I've just had a call from the Study Skills teacher.

Her voice was cold and critical from the get-go; mine was friendly.

That changed fast.

She was calling, she said, to tell me that Christopher is suddenly coming to class unprepared.

I asked what he hadn't done.

But here's a question: does one 'prepare' for a class called 'Study Skills'? Wouldn't Study Skills mean that the child is being taught how to prepare?

At first I assumed she was calling to say, 'He's close to failing English and math; I'd like to talk about what's happening.'

But that wasn't it.

She was calling to say Christopher is unprepared for Study Skills.

I didn't learn all the facts of the situation, because the teacher hung up on me not too long into the conversation.

This is what you pay the big bucks for.

$18,000 per pupil spending, and the Study Skills teacher calls you at 10 am, interrupts your work day to tell you your child is unprepared, then hangs up on you.

I did learn that Christopher failed to hand in his Grade Contract.

Good. Here I was, set to write a formal email rescinding my signature, and Christopher didn't hand the thing in.

Given that opening, I told her that we aren't signing the contract; nor will we allow Christopher to sign.

Things took a turn for the worse.

I said the school's contract puts the onus for learning on the child; she said Christopher "shares" the onus for learning; I said Christopher is a child who loves school so much he sits down at night, every night, to do his homework happily and willingly, who was the Distinguished Student at Main Street School, who has 4s on all state tests—and that if Christopher is suddenly coming to class unprepared that is due to the school causing him emotional damage.

I said, too, that after two months of Study Skills Christopher does not have the slightest idea how to study for a test. I can't have him sign a contract saying he will study more effectively when he doesn't know how to study at all.

That observation also failed to ignite even a spark of interest in the person responsible for teaching Study Skills.

The only thing Christopher has learned about study skills, as far as I can tell, is 'Find a quiet place to work.' (Good luck finding a quiet place to work when you have two autistic brothers.)

Again: no interest in this information from the Study Skills teacher.

I'll add that my own voice became sharp and cold as the conversation progressed, or, rather, failed to progress.

But I remained 'professional' (can parents be professional?); I used appropriate language; I said that I felt we are confronting a school-level problem and that I did not specifically blame her for the difficulties we're having.

She hung up.

When I say the Irvington School District does not seek a partnership with parents, what I mean is: the Irvington School District does not seek a partnership with parents.


so here's the question

At the moment, I'm at a loss as to how to frame our problem.

We are asking for a paradigm shift.

Our school, like most or perhaps all American schools, blames the student when the student fails.

That was the tone and attitude of the Study Skills teacher; it hadn't crossed her mind to wonder whether Christopher's behavior has anything to do with her.

Here's a terrific passage from Engelmann:

Galen Alessi wrote an article in 1988 in which he diagnosed diagnosis. He asked 50 school psychologists to indicate how many cases they referred during the year. The average was about 100 per psychologist; so the group provided information on about 5000 kids. Alessi next tried to determine the different causes of the kid's learning problems. How many of the kids had the learning problem because of inappropriate curriculum? How many had learning problems because of poor teaching, or because of school administration problems? How many kids had problems because of home problems, or because there was some defect in the kid?

The percentages came out something like this:

• The curriculum caused 0% of the referred problems:

• The teaching practices caused 0% of the referred problems;

• The school administration caused 0% of the referred problems;

• The home environment caused 10-20% of the referred problems;

• The child caused 100% of the referred problems.

This is where we are.

There isn't going to be any public acknowledgment that the school is associated in any way with the deterioration in Christopher's learning.

Behind the scenes the principal will, I assume, take some steps.

We won't be there for that.

What is it we need to be saying tomorrow?

What documents should we take with us?


and what about math?

The question of Christopher's math class is probably thorniest of all.

Ed seconded Steve and Anne this morning; I think he may have said he was told explicitly not to do cross multiplication.

He had terrific math teachers in high school. He learned math well enough to pass the advanced calculus class for engineering students at Princeton freshman year, and to teach high school math successfully to G.E.D. students later on.

His teacher never taught them 'tricks.'

The students set up all problems as equations, and solved the equations according to general rules. Much later, after these foundational principles had become second nature, he learned the shortcuts that are derived from foundational principles.

I'll set up a separate meeting with Ms. Kahl, obviously.

But I need to be able to tell the principal, tomorrow morning, what Christopher needs to succeed in pre-algebra.

And I need to be able to do this clearly and succinctly.

So if you have ideas, let me know.


what I'm thinking . . .

I'll broach the issue of teaching procedures and 'tricks' simply and behaviorally.

I'll say that the teacher should tell Christopher to write out all problems as equations, and solve them—and that he needs enough paper on tests to do this.

I've already requested that Christopher be allowed to use scratch paper in tomorrow's test (this may be something the kids are always allowed to do, I don't know).

All I know is that the teacher gives very long tests in very small fonts with insufficient space for 'side calculations,' and with minimal space for showing one's work. His handwriting doesn't fit the space given.

I will also say that he needs to do 30 practice problems per concept or procedure taught.

That's as far as I've gotten.


update: scratch all that

Ed has much better ideas.


documents

I'm taking with me:

• the grade contract Ken found

• the study cited by Engelmann

• probably a printout of Steve's and Anne's Comments about teaching general principles and practicing those general principles to mastery

What else?

One or two articles from Willingham?

Something else I've forgotten for the moment?

Is there a particular passage from Engelmann I should have? (I'm sure there is.)


my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day

---

StudySkillsTeacherClimbDown 19 May 2006 - 22:08 CatherineJohnson



So where did we leave things?

• Superintendents bigfooting Singapore Math class

• Mrs. Roth distributing Ds and public shamings

• Study skills teacher calling to berate hapless parent

• Study skills teacher hanging up on hapless parent

• Big Meeting with principal cancelled due to snow

I think that's where we were.


further developments

The Study Skills teacher has come to her senses. (Come to her senses or been told to come to her senses, more likely.)

Christopher came home from school and reported that the Study Skills teacher had said to the class that she 'could tell' which children have to be reminded to do their homework.

Then she named four children, all of them boys. Christopher was one.

Next she said she could tell which children did not have to be reminded to do their homework.

She named a girl (who promptly said, 'Yes, I do have to be reminded to do my homework.')

So then it was back to the Email Factory. Writing emails to the school is becoming a full-time job. I don't like writing emails to the school. I certainly don't like writing emails to the school on an hourly basis. But I'll do it if they keep this up. (My friend M. tells me she knows moms who send hostile emails to the school every day. I believe it.)

Christopher never has to be reminded to do his homework. He always does his homework; he likes to do his homework. He's done his homework without being reminded since he was a tiny boy.

He has to be reminded to do my homework.

He has to be bludgeoned to do my homework.

He is, however, devoted to doing the school's homework.

So I sent an email, the tone and content of which I would characterize as terse, to the Study Skills teacher, copying it to the principal, to Ed, etc., etc.

I closed with the line, "Another item to add to tomorrow’s expanding agenda."

I heard back promptly.

Chris has always been a wonderful student. She was 'half teasing' when she said he has to be reminded to do his homework. She is 'puzzled' and 'surprised' by his recent lack of preparation. She 'meant no harm,' and she is 'concerned.'

Fine.

This isn't what I would call an apology, as in I'm sorry I hung up on you, it was rude and unprofessional, it won't happen again; and it's simply a softer version of the your defective child theme, but fine.

She can be taken off the agenda, because there's already too much stuff on there.

Of course, we are going to be talking about the Grade Contract. We are going to be talking about the punitive, child-blaming nature of the school's educational philosophy. I know I said we'd be concrete and specific, but it turns out we're going to be abstract and theoretical. Then we'll be concrete and specific.

The highly abstract and theoretical point we'll be making from now on is:

If Christopher is getting Ds on essays, it's the school's fault.

If Christopher is getting Ds on math tests, it's the school's fault.

If Christopher is coming to class without his freaking Contract To Improve My Grades, it's the school's fault.


I know J D has debriefed many an ex-teacher who thinks parents are crazy. I know, because I've debriefed them myself.

I know our school administrators are going to attempt to think we're crazy.

But we're both writers, and we're both educators, or have been. Educators treat educators and writers differently. They just do. We've gone into situations like this before, and we've made our point.

One last thing.

We've been at this for 15 years. You have to think longterm, not short-term. (I realize I say this as a person who stinks at strategy.)

We won't Change Things tomorrow.

We don't have to.

We'll get what we need for Christopher, or, at a minimum, we'll be one step down the path toward getting what we need for Christopher. (Pupil personnel is the next stop; then an Advocate, etc.)

Meanwhile the school will know they have two highly educated parents demanding that the school perform systematic formative assessment and teach students to mastery.

This concept is not unknown to American educators, no matter how much edu-blah-blah they've been forced to regurgitate for their Ed.D.'s. We're tapping into thoughts and ideas they already have, and we're talking about techniques some of their teachers are already using. There are teachers at the Irvington Middle School who are using formative assessment. The administrators know this.

I've learned over the years that taking a radical stance 'works.' At least, it works for us. Being 'unreasonable' on purpose shakes things up. It refuses to play the game of I-have-to-be-realistic, when what I-have-to-be-realistic means is I don't have to teach your child.

What we're confronting now is the regular-ed version of I-have-to-be-realistic.

The regular ed version is Your child is responsible for his grades.

or, alternatively, 'I am concerned.' (See email from Study Skills teacher, above.)

When I taught writing, I had the students go through each and every sentence in an essay and answer the question, 'What is the underlying assumption?'

What is unspoken because it goes without saying?

The underlying assumptions, in each and every conversation parents hold with Irvington Middle School personnel, are:

1) My child is responsible for his grades.

2) My child's character is not what it should be. ('Your child will be a better person.')

We reject both assumptions, and we'll say so.

Then we'll keep right on on saying it.


the bell curve

This is rich.

My friend M. just told me that someone actually came into her son's math class, drew them a bell curve on the board, and explained to them that a grade of 'C' is average and normal, so they shouldn't expect to get As. Just a few children can get As. Not everyone.

Christopher says this didn't happen in his class, but that all the teachers tell them 'C' is average. They're supposed to be happy to be average; that's the message.

That explains a lot. Christopher has been constantly telling us that 'C' is average and good. We've been very unhappy with his recent Cs and Ds, and his answer is 'C is average, it's a good grade.' Obviously there's a systematic effort underway at the school to convince the 6th graders that their Cs are OK.

M. said, 'How can they tell these kids C is average and then have them sign a contract promising not to be average?'

Good question.

She also told her son, who just got a C on his math test, 'You're not average.'

Meanwhile I'm learning that the high school won't let kids into various courses if they do have Cs, which means the middle school is handing out Cs left and right, Cs that will track them into lower level courses in high school, without informing the parents that this is the case.

That's another agenda item for the Big Meeting. We want a precise list of all high school courses and tracks, the requirements for being admitted to AP courses and tracks, and the school's plan for making sure Christopher is prepared to enter these courses and tracks and succeed.

"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."

I'm certain the new superintendent didn't contemplate the possible consequences of creating this mission statement.

Too bad.

That's the mission and we're holding them to it.


my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day

---

PlugAndChugInSixthGrade 19 May 2006 - 21:57 CatherineJohnson



Quick question.

My thoughts about Christopher's math class are starting to cohere.

Here's what I'm wondering.

The chapter tests are plug and chug: they're 4-pages long, small fonts; at least 25 questions to finish in 45 minutes (with work shown, so no super shortcuts or 'just knowing' the answer allowed).

Is that a good idea?

As things stand, the chapter tests have the glaring problem of offering virtually no space on the test itself for kids with large, immature handwriting to do side calculations—and so far the teacher hasn't told anyone it's OK to use scratch paper. I've sent an email asking if Christopher can use scratch paper; no response as yet.

I don't know if the teacher doesn't allow scratch paper, or if it's just that no child has asked.

Ed and I are asking. ('Asking' as in formally-requesting-slash-demanding.) The kids need scratch paper and plenty of it, especially given the fact that the elementary school did not see fit to teach handwriting. (The BRILLIANT Ms. Duque was ferocious on this point: MAYBE if you'd taught them HANDWRITING IN THE SECOND GRADE, she would fume, THEY COULD LINE UP COLUMNS OF FIGURES IN THE FIFTH.)

Good point.

We're prepared to go to war on the subject of scratch paper if we have to, so I figure scratch paper will soon be part of the test-taking scene in Phase 4 math.

We'll see.

(If we don't get scratch paper we'll demand testing for occupational therapy & we'll bring in Christopher's vision therapy records to prove he has a visual processing disorder & make everyone read them and hold meetings about them—and that's just what I come up with off the top of my head. Have I mentioned that once, back in Los Angeles, when the special ed people were playing hardball about a placement we wanted for Jimmy, we told them, laughingly, that we were thinking if we couldn't get the placement we'd ask for full inclusion? I think I was the one who said it; then I chuckled. Our attorney, who was present, probably chuckled, too. The special ed people smiled wanly. I'd read about people smiling wanly in novels, but until that moment I'd never seen a person actually do it. We got the placement.)

Back to Christopher's math class. Apart from the mechanics of having 11 year olds with terrible handwriting take a plug and chug test, the course itself has problems, namely little or no formative assessment and no practicing to mastery ever.

But suppose all of those things were in place. Suppose systematic formative assessment were happening every week or every day, all students were practicing all skills to mastery, and the kids had all the scratch paper they needed to do a plug and chug math test in their lopsided, too-big handwriting.

Would a plug-and-chug test be a good idea?

Does plug-and-chug testing tell you the students not only have mastery, but have mastery to the point they can get through a 4-page test without folding?

Is that important as you head towards algebra? (I'm not asking whether mastery is essential; it is. What I'm asking about, I think, is stamina.....or is it?)

I have no idea.


observation from Tracy W

Tracy just left a comment that made me realize my question isn't clear.

At the moment, I'm not concerned about the heavily procedural nature of the course. There's probably too much teaching of 'math tricks' like cross-multiplication without reference to the general rules that make shortcuts possible, which of course means you're going to be giving the kids plug and chug tests, since plug and chug is mostly what you're teaching.

But at the moment I'm wondering only about the question of giving a 'killer test' to 11 year olds. (I don't use the word 'killer' to prejudice the answer, believe it or not.)

I assume that the reason the teacher does give killer tests is that she's whipping through a vast amount of material in a very short space of time, so there's a huge amount of material to cover in each chapter test.

However, if that's the only reason she's giving massively long tests (massively long for kids this age who are new to the material) she could just as well test all of the material through frequent administration of shorter quizzes and tests.

I'm wondering if there's a specific gain from giving a long, hard test in pre-algebra. It strikes me that there may be, but on the other hand I can't say what it would be.

---

NewPlanForPractice 19 May 2006 - 16:31 CatherineJohnson



I've got some great Comments to pull up front, and will get to those ASAP.

But first, I wanted to put this out there in case any of you have ideas.

Christopher's math course is now officially a disaster.

For Christopher, it's pure memorization of fragmented procedures that have nothing to do with each other. That's how he's experiencing it.

We'll talk to the teacher and the principal, and they'll do what they can. But it won't be enough. We need a do-over.

So we've moved into the minimize-the-damage phase. We have to get Christopher through the course in one piece, so I can reteach the material next summer. We have to make sure he doesn't get a C, D, or F, and we have to prevent him from deciding he hates math, if possible. (Actually, he could take a C and stay in the track, I think. I'll find out.)

This weekend, trying to think what we need to do just to get through 'til spring, I decided to start giving Christopher timed practice. The tests are 'plug and chug'; they're about speed and accuracy and the ability to memorize huge quantities of (seemingly) unrelated material.

Here's what I came up with; I'd appreciate any feedback you might have.

I went through the sections of the chapter that would be on the quiz and pulled out each component task that was either assumed or taught by the book.

There were 21 separate skills in 4 Lessons.

Then I wrote out 5 or 6 problems in each of the 21 categories, and had Christopher do them while I timed him on my running watch.

Side note: on top of everything else, he's now developing test anxiety. Just what we need.

We pointed out he doesn't have test anxiety for KUMON, and he didn't have test anxiety with Saxon......so he won't have test anxiety for pre-algebra, either, if he knows the material cold.

So.

He did his 6-problem timed sets, and I checked them.

If he could do them top-speed and get everything right, we moved on. I'll have to figure out some way to fit in distributed practice, since this stuff is going to be out of his head the minute he finishes the test. But he looked like he was OK for the quiz.

If he made a lot of mistakes, we did another set.

We also talked strategy.

We told him he's very fast, much faster than he needs to be. He did one set of 6 calculations—reducing fractions to lowest terms—in 21 seconds. In fact he has close to two minutes per problem, and if he's doing 6 calculations in 21 seconds he's going to make mistakes he can't afford.

I did that with KUMON at first. I pounded through the worksheets as fast as I possibly could, and I made lots more mistakes than I needed to. Then I read somewhere, possibly in one of the TIMSS studies, that this is yet another difference between U.S. & Japanese students. U.S. students sprint through their tests and finish every problem, getting lots of things wrong; Japanese students apparently follow a systematic, and more deliberate strategy of doing problems they know how to do, and getting those right. I guess it's a quality over quantity thing...In any case, it's definitely a useful skill to learn how to pace yourself. I had no idea about this until I started doing KUMON worksheets. Sometimes, now, I deliberately slow myself down.

So we started coaching him on slowing down.

We also told him to look at the quiz when he gets it, find the questions he can do, and do them. Skip anything that stumps you; just go past it. Come back if you have time. Etc.

He's due home from school any minute, so I'll ask him how the quiz went. Then we'll see how he did when his teacher grades it.

But if any of you have thoughts on teaching a child to take timed tests on material he doesn't understand and learned only a few days before, I'm all ears.

Thanks.


existential question

Ed is champing at the bit to ask the principal exactly how he sees kids going from TRAILBLAZERS to this course.

I'm so horrified by the whole thing, I don't even want to watch a school administrator try to handle that question.


good news

Christopher just came in saying the quiz was "extremely easy."

'Extremely easy' means he knew the material and did well. At least, so far 'extremely easy' has always meant that he did well. His ability to judge his performance breaks down in the middling realm, but at the extremes, he seems to know.

We'll see.

The teacher gave him scratch paper.

um.....I mean scrap paper.

---

ExtendedProblem6 19 May 2006 - 21:59 CatherineJohnson



What is the digit in the hundreds places of the sum of the following addition problem:

7 + 77 + 777 + 7777 + ... + 77777777777777777777

(The final number has 20 7s)

Thanks—





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

---

ScienceWithoutCalculus 15 Dec 2005 - 20:37 CatherineJohnson



Samantha just left this comment:

Incidentally, from what I've read about science, it's near impossible to teach real science without calculus already - most of what they doing in school before students do calculus is just junk science.

Is this true?

Offhand, it sounds true to me.

But I have no idea.

---

HappyEndingMostLikely 08 Oct 2006 - 22:15 CatherineJohnson



The meeting with the principal went great.

Great, great, great.

All my predictions were wrong; I have no ability to judge social situations or Other People's Intentions; in the future I will limit my contributions to Kitchen Table Math to comic relief.

Our school is great, Irvington is great, our property taxes are great and I'd like to pay more next year!

OK, I don't mean that last part. But we're thrilled.






Just in case you're experiencing Emotional Whiplash, I'm going to quote something Carolyn said a couple of weeks ago.

She was up in arms about a situation, and naturally I was egging her on (Scots-Irish alert).

So then a few days later we were talking, and I asked her how the situation was going.

She said, 'Oh, we had lunch & it was fine. I can't hold a grudge.'

I can hold a grudge if I decide to.

But it doesn't come naturally.






so what happened?

It was interesting.

First of all—and this is why we're so happy—we have a much better impression of the principal.

We didn't know him at all going in, and so far he doesn't 'show' terribly well in large public gatherings.....and we weren't able to interpret what this meant. The Middle School is difficult for us to read, partly because we're new there, and partly because the people are so young. The principal is very young; many of the teachers are super-young.

This is an important part of the reason why the math class has been tough for me to cess out and deal with. I don't want to hammer young people who are at the beginning of their careers and are obviously trying.

Plus I don't want to tell people how to do their jobs.....

And then (psychoanalysis alert) there's the issue of Mama Bear Emotion, which trips me up.

I'm ferocious about my young, as all parents are.

My own mother, who may be the single most naturally cheerful person on earth, told me a story once.

"I used to think I could never harm anyone," she said.

"But when you were born, and I was holding you in my arms, I looked down at you and I knew I could kill anyone who tried to hurt you."

That's a strong story coming from anyone, but if you knew my mom, you'd be sitting there thinking, right now, 'What can I do to not tick this woman off?'

I feel exactly the same way about my own children, and those emotions get triggered when I see Christopher sinking in math & crying over homework.

These emotions get in my way, because it's obvious no one in the math department is remotely trying to make my child cry over his homework. Quite the opposite.

I may be sounding like a nut right about now, but I'll just go ahead and sound like a nut, because I think parents often feel like nuts when they're dealing with the schools.

So my Mama-Bear emotions will get triggered, I'll perceive at once that there's no mountain lion trying to eat my cub, and then I'll try to figure out which emotional register I should be in, if any, and after a few days of this have passed I can end up just deciding to stifle myself.



Math

So back to the principal. He's great.

We had zero talk about moving Christopher down to Phase 2. Zero. There was NONE of that.

We showed him the latest test, with a grade of D, and the principal, who strongly supports his staff and clearly likes Ms. Kahl, expressed surprise that she hadn't been in touch. Ed said all the obvious things. He said that when you have a child who's started the year with a B, moved to a C, and is now finishing out the semester with a D, you've got a problem that needs immediate attention.

The principal completely agreed, and said he was surprised and sorry to hear that hadn't happened.

He asked us to talk to Ms. Kahl, and possibly to the Math Chair as well—which is good.

He also has complete awareness that it's not OK in math (or any other subject, but especially not math) to take your 'C' or your 'D' and move on. He said, 'Math is foundational' and he knew what he was talking about. This wasn't remotely a novel concept to him.

Unforunately, I don't think the math situation can be fixed this year. They're going to have to spend some time seriously thinking about how to do this course.

And I suspect the plan is simply to dump the course altogether. "I'm not a fan of tracking," the principal said. They all feel this way, universally.

There's the crux of the larger issue; that's where the paradigm shift needs to happen.

That's fine; we can push for a paradigm shift and we will. When it comes to Christopher, they'll jump in, work to make sure he's getting the concepts, & work with Ed & me.

One last thing. I took in the write-up of Carol Gambill's class, and I would say that the principal was actively interested in it, and wanted the math teachers to see it as well.

That's good.



whose job is it?

Ed opened the meeting by saying that we are having a problem with the school's philosophy, which is to place full responsibility on the child for learning and succeeding—and to use assessment as punishment, instead of information.

I gave him a copy of the Grade Contract, along with the DI contract and the Smartest Tractor contract.

I was wrong about this prediction; I thought he'd essentially disavow the Grade Contract.

But he didn't.

He felt I hadn't been nice to the Study Skills teacher, and it wasn't good for Christopher to be telling the Study Skills teacher that his mom wouldn't sign the contract, etc.

We worked through that one OK. He told me that I had taken her by surprise, that I had been angry (true), and that the Study Skills teacher felt I had been blaming her for.....something. I didn't follow that part of it. Of course, I had been blaming her; I had been blaming her for not teaching him any study skills and then making him sign a contract promising to improve his study skills.

I said it's not appropriate for a teacher to hang up on a parent regardless of whether the parent is angry. He agreed, and said he'd told the teacher as much. (That was clear from the email she'd sent later that day.)

This part of the meeting was fine, because Ed and I don't particularly have a beef with the study skills teacher, and said so. I said, too, that the study skills teacher had walked into an Already Existing bad situation, which was obvious to all. We were already upset about the math class; then two Ds & the public humilliation of our child & the subsequent taunting at school and crying at night hit; and at that precise moment the study skills teacher picked up the phone to call me on the carpet about the Grade Contract.

It was obvious that's what had happened, and we moved on. The principal would like me to make a conciliatory gesture towards the teacher, and I probably will.



quality going up, I think

Here's another great thing: the principal cleary thinks the Study Skills course is pointless.

As I say, he's strongly supportive of his staff.

But he clearly believes that study skills should be taught in the context of academic content, not abstracted out as Study Skills. He also thinks Study Hall is for the birds, and explained why.

This was terrific, too, because we could agree on what had occurred. Basically, Ed and I see Study Skills as a wash, and we weren't squawking about it, because we don't spend huge amounts of time squawking. We wouldn't have started squawking if we hadn't gotten 3 Ds home in one week along with a Contract to Improve My Grades from Study Skills.

This is his second year as principal; the Study Skills class was in place long before he got here.

It's probably going to be phased out. (In fact, I think he may actually have said, 'Would you rather have your child in Study Skills or in an extra hour of math?'—nirvana.)

hmm

The comparison may have been to Study Hall versus Extra Hour Of Math.

In any case, he raised the question of wasted time during the school day.

Good.



Ken's DI contract & Smartest Tractor's self-assessment contract

These documents were tremendously helpful.

thank you, Ken & Smartest Tractor

The principal looked closely at both (as closely as he could in a meeting), and saw exactly what we were talking about.

He wanted to give me an argument, and he did give me an argument. The student needs to take responsibility.

But I said, "I don't think a clinical psychologist would tell you this is a good thing to do to a child. You're forcing him to check off Bad Things About Me, and you're forcing him to assume a vague, general responsibility for something wrong that he did and doesn't even understand.

Most of the conversation was highly constructive and collaborative; this part was a clear 'win' for us. He wanted to argue the case, and he stopped because he didn't have a case. Christopher received two Ds on two papers with no feedback as to what's so terrible about his work; in the same week he has to sign a Contract saying he'll bring those Ds up to As by doing......what?

What could he do to earn an A from Mrs. Roth?

He doesn't know, and neither do we.

Ken will like this part.

Offhand, the principal didn't really like the Direct Instruction contract so much.

He liked the Smartest Tractor contract.

Serious direct instruction is a tough sell.

In this context, it didn't matter.

The point was made.



is the school harsh?

As I say, Ed opened by taking issue with the overriding philosophy of the school as we see it.

The principal said—and this was astounding—"Do you see the school as harsh?"

Ed said, "Yes."

He took it in.

He took it in, because it's obvious he does not want to be heading a school with a harsh culture. That isn't the plan, at all.

If he has parents telling him "Your school is so harsh that our son is being emotionally harmed" that's a problem.



Mrs. Roth

I will be shocked if, tomorrow, we don't hear that Christopher is changing classes.

Ed's not as sure.

The school's policy is No changing classes.

Interestingly, the principal doesn't seem to have been hearing lots of complaints about Mrs. Roth. If he has, he gave no hint of it, which is probably good.

He was clearly 'taking in information'; he was in debriefing mode.

I told him that if he hadn't heard from other parents yet, he was going to be hearing; that registered.

I told him, too, that my sense of the situation is that Mrs. Roth's caustic sense of humor bounces off the rough-and-tumble boys, but upsets the girls and sensitive boys like Christopher.

He heard that, too. (I'll add that I asked a teacher I know about Mrs. Roth's reputation this week. Her reputation is, "Not a lot of warmth." The principal can't possibly not know that.)

Ed says the principal will want to run this by his vice principal; he thinks she'll object to moving a child on principle, which could be an obstacle.

So we'll see.

(Given that none of my earlier predictions was remotely on the money, I don't know why I'm even bothering to make one.)



the unbearable brilliance of Ed

He is a master at these things.

I'm serious.

It's like being in the presence of genius.

Actually, it's not like being in the presence of genius; it's the real thing. (Jeez. Genius at dealing with school administrators......you don't usually hear about that category.)

The principal wanted to argue the Mrs. Roth situation with us.

First off, he wanted to critique the email Ed wrote. He said it was 'over the top.'

We said the email accurately describes our position.

The principal pulled up the email on his computer, and read the first line, which was:

Dear Ms. Roth,

My wife and I have serious concerns about the writing curriculum in your class and about your grading methods and lack of constructive assessment of our son's work.  Catherine and I know something about writing, having published six books between us, with two more in the works.  (Catherine's most recent book, Animals in Translation, was a NY Times bestseller.) 

The principal thought this was outrageous, though he put it more diplomatically.

He said, 'Six books between us—that's telling her she doesn't know anything about teaching writing.'

We said, 'She doesn't know anything about teaching writing.'

He said, 'This email was written in anger.'

Ed said, 'We are angry.'

I said, 'We are going to stay angry.'

We went on like this for awhile. Ed was in full command of his tone; I was a tad......not in control of my tone.

sigh

(Although, a line like 'We are going to stay angry' is effective whether you're in control of your tone or not.)

The principal gave it one last shot at some point, saying, 'This email sounds as if you wrote it to hurt Mrs. Roth.'

We said, 'We wrote it to hurt Mrs. Roth.'

(These are almost verbatim quotes.)

At some point, it became clear to the principal that we weren't going to be reasonable.

I'd say he did a good job absorbing this information, which was obviously not what he expected.

He made another stab at saying we should have talked to the teacher first; we should meet with her; etc.....

We said there was no reason for us to meet with or speak to this teacher under any circumstances.

At some point he saw that reality clearly, and said, 'So there's no reason to have you sit down at a table with Mrs. Roth.'

Here's where Ed is so amazing, and where I would have folded.

The principal wanted to shift things to emotion. We are angry because our child is upset.

This is true. We are angry because our child upset.

This wasn't a 'dishonest' strategy on the principal's part; it was the way he understood things. He didn't know about the 'You're not retarded' comment, and was visibly upset when he heard it. He didn't know that Christopher has been teased and taunted on a daily basis since Mrs. Roth handed him his public Ds and said 'Are you doing the work at all?' in front of the entire class.

sidebar: Rudbeckia's FERPA link was also helpful.

Mrs. Roth announces grades every day. It's constant. I can cite half the grades of half the kids in that class from memory, and Christopher could tell you all of them.

This was a killer, because the principal several times told us that since we hadn't been present in the class, we couldn't know what was really happening there.

The fact that I can recite the other students' grades instantly neutralizes that argument. I shouldn't be able to recite the other students' grades.

I said that this was a possible FERPA problem. He said it didn't violate FERPA, but it was certainly unprofessional and shouldn't be happening. I said that if it didn't violate FERPA, it was getting close.

This was all to the good. I don't want to make a FERPA case, hire lawyers, etc.

What I needed was simply to know about FERPA, so I could raise the issue.

I'll say that I didn't necessarily have to raise FERPA, since the principal was taking the situation seriously.

Still, what he wanted to do was tell us we'd written an over-the-top email in anger, and ask us to sit down with Mrs. Roth and work things out now that we'd had some time to cool off.

Raising FERPA helped impress upon him the point that we weren't going to be meeting with Mrs. Roth under any circumstances, and we weren't going to be cooling off.

Rudbeckia, thank you



I know. This is long. But I figure.....this is My Personal Record of Events, so....it's long. (Sorry.)


staying on message

Back to Ed.

Once the principal heard the 'You're not retarded' line, things changed. He was visibly distressed to hear that a student in his school was being teased and taunted at lunchtime because of something a teacher had done. That was geniune

It also allowed him to move things to the emotional register, where he felt more comfortable.

I've mentioned several times that in the Middle School there is a chronic your-kids-aren't-as-smart-as-you-think culture, which the people there may not even be aware of.

Our position on Christopher's paper is that it deserves a grade of A.

Mrs. Roth's position is that it deserves a D.

The principal wanted to maneuver us to the point of agreeing that it was a bad paper—or, failing that, simply to drop the issue of the grade altogether, and 'admit' that the 'real' problem was the 'You're not retarded' remark.

I would have gone for that. (Sorry.)

Ed was like a dog with a bone.

He just kept coming back to the grade.

He said, "I would never give a student a grade of D on a paper he wrote and handed in. A grade of D is a failing grade. If I had to give a grade of D, I would provide a full page of constructive feedback explaining why the paper fails the assignment, and I would discuss the paper in private with the student, not in front of the class."

Then he hammered away at the idea that this wasn't a 'D' paper in any case.

Once Ed led the way, I was OK here, too.

I pointed out, a couple of times, that I write feature stories for a living.

Mrs. Roth's biggest beef is that Christopher's paper is short ("awfully short for a major research product" is the way she put it).

I pointed out that a 'feature story' isn't the same thing as a 'persuasive essay' which isn't the same thing as a 'major research product.' [update: A mom told me tonight that one of the girls in the class raised her hand and asked if the feature story and the persuasive essay were the same assignment. Mrs. Roth said, "That's a stupid question."]

Mrs. Roth gave all three labels to the kids when she made the assignment.

I pointed out that, in writing a feature story, the writer constantly has to cut. Constantly.

You have to learn to write short.

(That's the problem with this post; it's too long. Too short is never an issue for a professional.)

This was our only moment of Fractured Logic. The principal said, 'But these are 6th grade kids, we can't compare them to professionals.'

It was apples and oranges again!

A professional has to write short & sweet; a 6th grader should write long & boring, because he's a sixth grader.

If he writes short and sweet, HE FLUNKS!

We went back and forth on this.

The principal said he'd shown the paper to other members of the English department, and they agreed it was bad.

Ed said, 'Did you show it to them with the grade on it?'

The principal said, 'OK, I'll take the grade and the comments off and I won't tell anyone who wrote it or who the teacher is.'

We weren't interested. The paper is good, we said; it deserves an A.

Ultimately, we abandoned this question. It was clear we weren't going to budge; nor would we countenance a Floating, School-wide Assessment Scheme.

At some point the principal as much as said, 'This paper isn't a D.' He didn't say it was an 'A'; he doesn't think it's an A.

What he probably thinks is that it's a 'C,' but that a reasonable teacher, operating under the same grade inflation every other student is given the benefit of, would have given it a B.

I told him—this was my role—that Christopher had worked hard on his paper. That's true. He worked hard on it, and he was proud of what he'd written.

I said, 'This is his work. He tried hard to write a good paper for Mrs. Roth. He's been crying for two weeks.'

Hearing this, the principal looked pained. It was obvious that he perceived the 'D' as a terrible thing to do to a brand-new middle-schooler.

Suppose his paper really was a D?

Suppose it really was awful?

A child who really couldn't write well would never have been treated so harshly.



almost done.....(must pick Christopher up)




the high point

I think the best part of the meeting had to do with Ed's over the top email.

The principal's central goal was to get us to climb down.

We weren't having it, but he kept trying different tacks.

Finally he said to Ed, 'How would you feel if you got an email like that from a parent?'

Ed said, 'I wouldn't get an email like that.'

I almost fell out of my own chair.

The principal looked like he was experiencing the same loss of balance, but—and I admire this—he recovered fast enough to persist.

That was something else I liked. He was thinking on his feet. We weren't doing what he thought we'd do, and we were throwing him curves. He had no idea there was a You're not retarded problem.

He has chops. He was outgunned, seeing as how Ed has a good 20 years on him. But he was game. I like that.

So he tried again. He said, 'What would you do if you got an email like that?'

Ed said, 'I would never get an email like that.'

The principal took the point.

That was a great moment for me. It was another moment where I saw clearly why other people are administrators & I'm not.

Being a good administrator means taking responsibility for things I wouldn't want to take responsibility for, and probably couldn't take responsibility for.

Being a good administrator it means taking responsibility for not getting enraged emails from parents.

It means running a school so smoothly and so competently that things don't reach that point. The staff is doing what they're supposed to do, and the parents trust you to the point that when the are furious, their first move is to pick up the phone and talk.

Not send an email bomb.


'it's on the table'

I can't remember how we finally came to the end of the conversation.

Basically, after we'd gone through the Mrs.-Roth-inspired taunting and teasing Christopher was going through, the nightly crying, the 'I'm stupid, I don't want to go to school,' the 'Stop banging around and making all that noise, you're not retarded.....' all of that.....the principal said something exactly right.

He said, 'Alright. I have to talk to Mrs. Roth. I can't make this decision without hearing her out.'

His tone was direct and simple; this was administrator-to-administrator.

Then he said, without pausing, 'Ordinarily we don't allow students to switch classes, but I can see that's on the table. I'll talk to her today, and I'll call you tomorrow.'

To me, that was amazing.

I was radically not expecting to hear this. I was expecting to get the run-around; I was expecting to go to Pupil Personnel; I was expecting to bring in an Advocate (and in fact had already talked to the Advocate who helped us with Jimmy).

It was a good moment, and it was exactly what he should have said.

We'll see what tomorrow brings.



how to write

So I'm a fan of the principal's, and, barring something unhappy-making tomorrow, I'll remain a fan.

But there were two problems, one of which I understand fairly well, the other of which everyone is already talking about in the Comments thread, concerning gifted kids, and which I don't understand well.

The problem that's making sense to me is the writing problem we have in Irvington schools.

The principal thought Christopher's paper was bad.

Mrs. Roth thought it was awful.

That's a problem, because not only was it not awful, it was good for his age and for what he understood the assignment to be.

Here's an example.

The assignment said that a persuasive essay should Begin with a grabber or hook to get the reader's attention.

Christopher's opening line was: School should be a safe place, right?

One line.

The body of the paper began in the next paragraph.

That's good writing. Number one, it's a 'grabber.' It pulls the reader—especially a kid reader—the 'right' at the end of the sentence makes the essay interactive; it almost commands the reader to start thinking.

The brevity makes it work.

The principal pulled out Christopher's essay and said, 'To be honest with you, I don't like this first sentence. It's not grammatical.'

I didn't remember the first sentence, and I was thinking Christopher had reversed the words 'school' and 'should.'

But he hadn't. The sentence is not only grammatically correct as it stands; it fulfills the assignment. It's a hook.

So......we're in trouble on the Writing Instruction front. Which we already knew. (hey. was that a sentence fragment? i think it was!)

I already know this is a school-wide problem, because it's been happening to the son of a friend of mine. Writing is his particular talent, and he writes well. 'Writes well' means he doesn't write like a 16 year old producing a 5-paragraph essay for the SAT. He's getting clobbered. My friend has been terribly upset about this, because she doesn't have the confidence to know that the teacher is wrong and she's right.

One time she sat in her car and cried after a teacher told her how bad her son's writing was. (I've read his writing. He's good. Trust me.)

The lesson here is simple, of course; Christopher is going to have to do boring, bad writing his teachers will perceive as good.

We can handle that.



Reader's Digest Condensed Version

Here's what an over the top email sounds like:

I've been a teacher and educator for 25 years, and one of the things I learned early on was that you must always highlight the positive aspects of a student's work, even if you have to look hard to find a narrow ray of light.  According to you, there's not even scintilla of quality in Chris's recent piece.  

We beg to differ.  Take the opening sentence: "School should be a safe place, right?"  This seems an excellent way to start.  With just these few words, Chris has nicely set up this essay.  He establishes the reader's expectations, suggesting that the reality of schools may leave those expectations unfulfilled.   Chris goes on to say that there have been shootings in certain schools and then to explain why those shootings might have occurred (bullying, parental abuse, violent video games).  Next, he suggests how the shootings might be stopped and then tersely sums up what he's said.  All this in 175 words!  Not bad for a novice writer with no real instruction under his belt.

The paper deserves an A; your having given it a D would be laughable, except that you have made Chris cry.  You should know, by the way, that Chris wrote this paper entirely on his own; we gave him not an ounce of help.  We're well aware that other parents are writing their kids' papers, but if Chris is to learn to write, he needs to do it himself.  

That's about as obnoxious as it gets.

Scratch that.

What I meant to say is, That's about as obnoxious as it gets, right?



how to write, part 2

The other Writing Instruction issue is that the principal didn't recognize the rhetorical strategy in Ed's email.

That strategy was simple. Write an email so over the top that the only possible option would be to remove Christopher from the class, because if he stayed there would be no way to guarantee his emotional safety.

The point was, specifically, to prevent the school from 'opening a dialogue,' 'meeting with Mrs. Roth to discuss Christopher's work,' etc., etc.

I don't know that a person reading the email for the first time should see this, necessarily. But I do think that the principal should have picked this up quickly from the meeting—and should have recognized that, regardless of how he felt about the email, it had achieved its purpose.

How many angry emails from a parent unhappy about his kid's grade on a Feature Story get you as far as we got in the space of one meeting?

None.

boy

We're going to be doing a whole lot of Genre Writing around here for the next 3 years. Put on your SAT Face and go go go!


Department of Irony

On the way home, Ed said, 'The point of the email was to declare war.'

Then he said, 'It was firing on Fort Sumter.'

We drove along for awhile, and finally he said, 'It was preemptive war.'

You can probably all guess just how big a fan Ed was of preemptive war back when George Bush came up with the idea.






This is it.

This is the sum total of the instruction and feedback Christopher received on his papers.

That and Are you actually trying to do the work? asked in front of the class.

One last thing: Christopher says he turned in a 'work cited page.'

We have no idea what's going on in that class.

---

TheMathPage 21 Dec 2005 - 19:55 CatherineJohnson



I like The Math Page

What do you think?

---

AnneDwyerIsObsessed 19 Dec 2005 - 17:20 CatherineJohnson



from Anne Dwyer:

How do you know you're obsessed with mathematics education?

When you walk into a used book store and have to buy a Grammar School Arithmetic book published in 1892 because you want to see what math education was like before the progressive movement got involved.

Here are some cool things that I hadn't seen before:

The book teaches how to divide by a fraction (flip and multiply) but it also teaches this method for simplifying a fraction: Reduce 3/4/5/6 to a simple fraction (of course it was written as three fourths over five sixths) The answer: divide the top and bottom by 12 which is the lowest common multiple of 4 and 6 and it reduces to 9/10. I like this method because it works just like getting an equivalent fraction.

A number is divisible by 2 if the last or right hand digit is even.

A number is divisible by 4 if the number denoted by the last two digits is divisible by 4.

A number is divisible by 8 if the number denoted by the last three digits is divisible by 8.

A number is divisible by 3 if the sum of its digits is divisible by 3.

A number is divisble by 9 if the sum of its digits is divisible by 9.

A number is divisible by 5 if its last digit is a 0 or 5.

A number is divisible by 25 if the number denoted by the last two digits is divisible by 25.

A number is divisible by 125 if the number denoted by the last three digits is divisible by 125.

A number is divisible by 6 if its last digit is even and the sum of its digits are divisible by 3.

A number is divisible by 11 if the difference between the sum of the digits in the odd places is either 0 or a multiple of 11.






Well, I have a roped-off pew in the church of my heart for the obsessed.

Edie: An American Biography by Jean Stein


key words: divisibility

---

IfTheStudentHasntLearned 23 Dec 2005 - 22:16 CatherineJohnson









revision

From Catherine:

Our new pretend-shirt specifically says "If the student hasn't learned, the school hasn't taught," not 'the teacher hasn't taught'.

No more thoughtless (and unintended) teacher-bashing.

Seriously. I'm the last person to want to make teachers feel blamed and bashed, seeing as how half my relatives have been or are currently teachers. I'm sure I'll be one again at some point, too.

The problem is that, when you talk about schools, it's the teachers who are visible. They're in the trenches, so they get the blame. (I realize I'm not telling teachers anything they don't know.) I know better than that, but I've been sounding like I don't.

Time for a course correction.

From Carolyn:

Hey, my entire family on my mother's side were also teachers, every man and woman Jack of them. I've been a teacher too; so has Catherine.

My observation is that policy flows downhill in a school, and the buck stops with the teachers. They get the responsibility, but not the authority; policy changes really have to start with upper management.

We're here to put the pressure on upper management, and support the teachers in doing what they know how to do.

---

DeathMarchToAlgebra 19 May 2006 - 16:30 CatherineJohnson



Christopher's class took the Chapter Three test on November 30.

They will take the Chapter Five (Rational Numbers and Expressions, aka fractions & decimals) test on Tuesday, December 20.


Chapter 5 content:

5-1 equivalent fractions and lowest terms
5-2 fractions and decimals
5-3 rational numbers
5-4 comparing and ordering rational numbers
5-5 adding and subtracting rational numbers
5-6 working backwards
5-7 multiplying and dividing rational numbers
5-8 rational numbers with exponents
5-9 addition and subtraction equations
5-10 multiplication equations
5-11 the stock market


After tomorrow, the kids will have had thirteen school days to study Chapter 5.

Of these, one was a snow day, and they had a substitute teacher on Friday.

So, 11 days of instruction to cover....11 huge topics. Fractions. Decimals. Equations with fractions and decimals. In 11 days.

Judging by the homework Christopher has brought home, and by what Christopher himself says, they've only gotten as far as 5-7.

That leaves three units, 5-8: rational numbers with exponents, 5-9: addition and subtraction equations, and 5-10: multiplication equations, to get through tomorrow, one day before the test.

They've had some coverage of addition and subtraction of fractions. I know this because Christopher told me yesterday that Ms. Kahl had showed them how to borrow, but it was confusing everyone, so she said they should just convert the mixed number(s) to improper fraction(s) and do the subtraction that way. That's what he was planning to do for the rest of his life.

I told Ed to tell Christopher he was going to have to learn to borrow no matter what Ms. Kahl said. Ed did, and Christopher cheerfully agreed. Boys love their dads.

We are in rote-land. Tonight Ed gave Christopher a problem like this one:

2/3 x 5/6 x 3/10

Christopher knew that he could cross out the 2 and the 10, and write a 5 next to the 10. Ed was thrilled.

Then he asked Christopher why he could do this, and Christopher said, "Ms. Kahl told us we could." They studied the properties in Chapter One, but Ms. Kahl does not seem to have pointed out in class that the commutative property and the multiplicative identity property make it possible to 'cancel' numerators and denominators. If she did tell them this, and she may have, she did no formative assessment to discover whether Christopher either heard or understood.

Apparently she keeps early office hours every day so kids can come in for extra help. I didn't know this. You'd think this information might be pointed out, stressed, and underlined for the parents, but no. The kids are, as their Grade Contract states, 'fully responsible' for their grades.....so nobody told me about it. At least, I don't remember it if they did.

I'm not that interested in 'extra help' in any case. We're way past 'extra help.'

It's obvious that the only way to get him through this is to begin serious study for the Chapter Test the minute the previous chapter test is done. We started doing fairly serious extra problems 5 days ago, but that wasn't nearly enough. I suggested to Christopher that he stay home tomorrow to study for the test. He doesn't want to.

But things may yet come to that.


pre-algebra is bunk
death march to algebra
NYU ed textbooks; NY math test

---

BrendaMOnMathTexts 23 Dec 2005 - 17:07 CatherineJohnson



I hated textbooks like this when I was in school.

"Read, Plan, Solve, Look Back." I'm busy learning algorithms, and the stupid book wants me to memorize this sequence logo thing? Gee, let's make everything easier by adding the number of things you need to remember.

"Read." Well, DUH!

"Plan." It's just like Solve, but you use words instead of symbols, and you don't actually do anything. Did they really need this? They could have made a triangle logo thingy instead of a circle.

"Solve." Double DUH!

"Look Back." In the real world, we call this Check Your Work, Doofus.




My thoughts exactly.



International Red Cross Symbol for Guess and Check

---

EmailToTheSuperintendent 19 May 2006 - 21:16 CatherineJohnson



I know I said I wasn't going to post this until after the holidays.

I lied!

Seeing as how the District saw fit to barge into my Christmas Eve with its Interim Report, I decided Christmas day would be a fine time to send this:




Dear Dr. Matusiak:

We received our son Christopher’s ‘Interim Report’ yesterday, Christmas Eve.

It was cold, clinical, anonymous, and gender-stereotyped. Using the canned comments with which our school district labels and pigeonholes children, Christopher’s teachers, who work together as a ‘team,’ spoke with one voice:

Capable of better work

Capable of better work

Effort is inconsistent

Needs to be more attentive

Unprepared


In short, Christopher is a generic boy not working up to capacity.

Dismissed.


We don’t live with a generic boy.

We live with an individual child who has a name. Christopher.

Christopher loves school. He wants to please his teachers. Every night he tells me what they said in class. He reads his school notes out loud to me. (But he ‘needs to be more attentive.’)

He thinks he’s doing a good job, although he senses that his teachers do not agree. He’s trying very hard, and he is chronically anxious now because he perceives that his teachers aren’t impressed. He doesn’t understand what he’s doing wrong, or why they are unhappy with him.

Every day now he says to me, ‘Mommy, I’m going to get bad grades.’

He still calls me ‘Mommy.’


Christopher was the Distinguished Student at Main Street School. His state test and TONYSs scores are 4s. He was a happy child who was thriving in school.

Now he’s frightened, and his grades are in free-fall. He’s learned little this semester. Only one of his teachers contacted us about the decline in his performance, and that teacher called to complain that Christopher had failed to hand in his ‘Grade Contract,’ another pre-fab list of failings Christopher was to confess to, sign, and hand in.

When I told this teacher that he would not be handing in a Grade Contract stating that, at age 11, he is fully responsible for his grades, she hung up the telephone.


We requested a team meeting some weeks ago. Nothing has happened.

We requested a parent conference with the math teacher. Nothing has happened.


And now, on Christmas eve, the school has sent us a computer generated form telling us that the problems our son is having at school are his fault.

He is Capable of better work.


We have a problem.

Catherine Johnson, Ph.D.

---

ExtendedProblemsSevenEightNine 21 Feb 2006 - 00:57 CatherineJohnson



I am back.

I am back, but my luggage is not. My Kenzo top, my on-sale Ralph Lauren Black Label blouse and woolen vest, my French jeans (which I will be needing, given the number of Meetings With The District we'll be attending), my camera charger, my cel phone charger, my handheld charger—none of it is here.

Which means I am now fresh out of Sunday go to meeting clothes.

Also missing: the book I spent my entire week reading, underlining, and annotating: The Organized Student, by Donna Goldberg. And: the zippered binder Donna Goldberg says is The Answer to All Our Problems. [UPDATE: It's not.] I picked it up in the Studio City STAPLES so I'd be able to get Christopher pulled together before he went back to school tomorrow.

Today was to be Get Christopher Organized day. Set up the Zippered Binder & order the Desktop Filing System. A fresh start in the New Year!

But no.

I can't do that, because I don't have the book, so I don't have the list of Lifesaving Organizational Paraphernalia I was going to order and/or purchase today.

Which may be just as well, since we had three Extended Response problems to do. Two of them fall into the category Carolyn calls FWOT.





This one's fine:







Extended problems #8 and #9 are ludicrous.

Actually, Extended Response #8 is ludicrous; Extended Response #9 should be illegal. There is nothing to be learned from Extended Problem #9. It is simply 3 division problems written in the most confusing manner possible.

So we spent hours doing 3 division problems in the most confusing manner possible instead of doing KUMON or reteaching the decimal chapter Christopher got his D on or previewing the Lesson on isolating the variable Christopher will be tested on five seconds after the teacher throws a couple of isolate the variable problems up on the blackboard.

FWOT, indeed.

We spent hours on these today. Hours and hours.





maybe I should be running an airline

After reading The Organized Student, (chapter excerpt) I returned vowing to improve my organizational skills.

Now I'm thinking: compared to American Airlines, I'm a freaking organizational genius. We landed at 9:00; didn't get out of the airport - sans luggage - til 11. There were at least 40 people in line who also didn't have luggage, and the lady at the desk said, 'This has been happening all day.'

All day?

You started losing luggage first thing in the morning and then you kept on losing luggage? For the rest of the day?

There wasn't a point where you said to yourselves, 'Hey. We're losing luggage. Let's get on top of this'?





update

6:23 pm

Ed just called the airline again, and now we're Describing Unique Items in each of our 2 suitcases, just in case the identifying tags come off. The lady taking notes had no idea what's become of anything; she's working with 15 other people on the L.A. flight alone.

I wonder who's dealing with the people who'd just flown in from Aruba. They were all luggage-free but nicely tanned.



just deserts

There is justice in this world.

After I spent all that time ribbing Carolyn about microshift wind shear and the like, we experienced the worst turbulence I've ever flown through on the way out to L.A. I was sitting between Christopher and Andrew, who are both too young to think they could die in a plane crash, while I'm too old to think I couldn't. The plane was doing sudden 3-foot drops when Andrew, who thought this was tremendous fun, started jumping up and down in his seat, hard. It's probably time for me to learn some physics or aerodynamics or something, because every time he came down for a landing on his bottom, I felt like I was in a canoe, not a jetliner.

That's IT!!!!! WE'RE GOING DOWN!!!!!!

So I was clutching his arms, trying to keep him stationary, when Christopher decided to read me some endlessly long narrative joke from The Greatest Joke Book Ever that I was supposed to a) follow and b) laugh at when he got to the punchline.

I was frantic.

Frantic, as in, Are you out of your mind!? Can't you see I'm trying to keep the plane in the sky?! I have no idea what you just read to me about the little boy saying his prayers and the next day the milkman dropped dead of a heart attack!



I will be back later with a better attitude

First I have to take the dogs for a walk in the pitch dark. That ought to improve my outlook.



check your answers

If anyone feels like working these problems, we've got our answers...





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

---

BestResourcesForLearningToMastery 06 Jan 2006 - 00:32 CatherineJohnson



Our Team Meeting is set for Thursday, and I'm wondering what to take.

Which reminds me: I used an 8-pocket folder for our meeting with the principal. I recommend it.





The one I took is much cooler than this one, seeing as how the one I have is all purple.

But this one would do nicely. The 8 pockets are the thing.

What 8 pockets mean is: you can whip out the Documentary Evidence without missing a beat:

Think we're kidding when we say the school culture is harsh and punitive?

Check out this Contract to Improve My Grades!


Want to see the kinder, gentler Direct Instruction alternative?

Got it!


And speaking of kinder & gentler, I have with me today a Self-Assessment form used in Canada.

IT'S RIGHT HERE, LOOK AT IT NOW.

8-pocket folders.

A Good Thing.



teaching to mastery, overlearning, formative assessment —

The 'Team Meeting,' btw, is a meeting of Christopher's "Team," i.e. his teachers and his guidance counselor, which the parents request & attend.

The parents are not part of the Team.

Our points are simple:

• Christopher was in great shape when he entered IMS, and his first Interim Report reflects that

• now he's a mess, and his second Interim Report is stark evidence of his decline

• IT'S YOUR FAULT

After which we segue to:

• WHAT YOU NEED TO DO TO FIX IT

part 1 is easy

The one fun part of this situation is the fact that the school uses computer-generated canned comments on its Interim Reports in order to avoid liability issues. Apparently the thinking is that a teacher could get in trouble writing her own, individual comments. Somebody could sue. The pre-fab comments have all been vetted by lawyers, I guess.

At least, that's what I gleaned from the Assistant Principal's remarks when the issue came up during our Coffee with Principal Fried. I could be wrong.

Needless to say, I object violently to the idea that avoiding liability is a more pressing goal than communicating with parents, not to mention the fact that I am funding the purchase of software packages that enable the school to avoid liability by strictly limiting the information divulged to parents.

So the fact that, in our case, the canned comments nail our case gives me great joy.

Think about it.

Christopher comes into the school in great shape, and every teacher picks the exact same pre-written one-liners to say so.

Six weeks later he's a wreck, and every teacher picks the exact same pre-written one-liners to peg him for the loser he so obviously is. They've dumped one set of cliches for the polar opposite cliches, and they're talking about the exact same kid. A kid who has had no changes in any area of his life except the school. Their school.

Have I mentioned Mrs. Roth was absent for most of the first quarter?

She was. She was out with pneumonia for 6 weeks.

So here's how things shape up:

Mrs. Roth absent 6 weeks during 1st quarter = positive canned comments and good grades

Mrs. Roth present for 2nd quarter               = negative canned comments and bad grades

One of our sub-goals, btw, is: the canned comments go away.

Another sub-goal: we are never, ever, to be sent an Interim Report on Christmas Eve again. Period, full-stop. If they can't get their reports out while school is in session, we don't want to hear from them — not unless they're going to be receiving Interim Reports from us. That might work.

So I will be perseveratively mentioning the Rank Cultural Insensitivity of the timing whenever the opportunity presents itself (and I can tell you going in that the opportunity will be presenting itself frequently). The teachers can't do anything about when reports are sent out, but so what? Perseveratively mentioning the Rank Cultural Insensitivity of the thing is what counts.

Speaking of which, anyone who hasn't read Radical Chic and Mau-Mauing the Flak Catchers should add it to the list.





Let's see. I'm pretty sure we have some other sub-goals.

Oh, yes. We do have another sub-goal, which will serve nicely as a bridge to Part 2.

Before we leave we'll schedule a follow-up Team Meeting for 4 weeks from Thursday. Ed will handle this one. (Actually, he'll handle the whole thing. I will be the hype man. I am a very good hype man.) He will point out that while the Team approach offers many educational benefits, we all know that it has its downside, which is groupthink, and that is what has happened here. He will say it is apparent that the Team should not meet without an Advocate for Christopher being present to represent his needs. That would be us. So we will be scheduling regular Team Meetings in the months and years to come.

Then we'll pull out our PDAs and make the next appointment.



Part 2

Part 2 is probably harder, though in intellectual terms it's simpler: we are going to tell Christopher's Team that they must teach Christopher to mastery.

We'll say they need to perform systematic & frequent formative assessment to find out whether he's learned the material they've covered, and we'll say we need to know the results, too, seeing as how we've joined the Team and all.

We'll ask the guidance counselor to give us a full report on any and all standardized testing they've done; we'll ask for evidence that Christopher has gained 3 months' skills and knowledge in the 3 months he's been in school.

If they have no idea whether he's gained 3 months' knowledge in 3 months' time, we'll ask what they plan to do to measure his gains from this point forward. Possibly, we'll raise the idea of giving him a Before-and-After ITBS ourselves. I don't know.

Part 2 is hard, because it's a Revolution. Ed says we'll be the first parents ever to tell the school to teach to mastery. I don't see how that could possibly be the case, but he could be right.

So....I'm thinking I need something short and sweet.

Something on teaching to mastery, another something on formative assessment.

I probably have what I need on formative assessment.

I need to figure out the single best thing on Teaching to Mastery.



Part 3

I know this sounds like too many parts, but I think we need them, and I think we can make it work.

Part 3 is the Boy Thing & the Frontal Lobe Thing.

We're going to tell them they are confusing Frontal Lobe development with Character.

The adults who work in the school hold the children responsible for the content they learn and the grades they receive (SEE: GRADE CONTRACT). It's sink or swim.

I'll bring up some Boy Stuff (slower frontal lobe development; no boys have been Student of the Month, only girls; teachers telling jokes about boys having to be reminded to do their homework while girls don't, and so on). I don't know that IMS is systematically harsher on boys than on girls. The school may be just as difficult for girls to manage; I don't know. But I don't like what I'm seeing thus far, and I've heard enough from the moms of other boys that a flag has been raised.

So I'm thinking......I'm thinking I need to know what the Official School Policy is on 'Girls rule' t-shirts.

Or on 'Boys are stupid, throw rocks at them' t-shirts.

Or on 'Girls go to college to get more knowledge, Boys go to Jupiter to get more stupider' t-shirts.

As the mother of a boy, I'd like to be assured that such sentiments aren't sported on girls' clothing in the halls of IMS.

Or not. I'll play it by ear.

The reason we need to get into this is that we are going to be the first parents to tell an Interdisciplinary Teaching Team that when they fill out a report card for our child, they are filling out a report card for themselves.

To make that stick, we're going to have to make a big-time Appeal to Authority (neuroscience) and we're going to have to mau-mau the flak catchers like he**.

We have to do both, because we're going to ask for things I assume they don't normally grant.

For instance, we're going to ask that they give Christopher a standing pass to come in early for extra help in math. He hasn't been in for extra help in math, because he has to remember to get a Pass the day before he comes in. To his mind this means he has to decide he's going to have trouble with his homework before he's even tried doing his homework.

That's a level of metacognitive awareness a lot of adults would have trouble with, including the adults who are teaching in his school.

He needs a standing pass. The school needs to make it easy for him to come into his own school early for extra help in math, not set up bureaucratic hurdles to keep him at bay.



suggestions?

I would immensely appreciate any ideas, thoughts, suggestions, and article tips you may have.

The Suggestion Box is open.



update: our luggage has arrived

I will be wearing my French jeans to meet the Team.

Heh.

---

TeamMeeting 30 Jun 2006 - 11:00 CatherineJohnson



Mission accomplished.

I'm exhausted.

My office is a wreck.

My child is a possibly-recovering wreck. Christopher was great on vacation, but fell apart when we got home. Crying at night; had to sleep on the sofa in our room; didn't go back to school on Tuesday when he was supposed to; crying again Tuesday night; had to sleep with the light on......have I mentioned how much I'm loving Middle School?

However, when he did go back to school yesterday, he had an 85 on his math test waiting for him, which was a huge boost (there is a God), and the kids all admired his groovy new zippered binder with the P-touch Home & Hobby labels on the divider tabs. One of the kids in his math class, a child actor on TV, asked Christopher how he got the labels. When Christopher said, 'My mom made them,' he said, 'Your mom is great.'

The funny thing is, a number of the kids have now copied the first system we set him up with: my personal favorite, the 8-pocket folder.

Boy, will they be sorry.

The whole thing explodes in about 6 weeks' time.

Only a grown-up can use an 8-pocket folder.



the end of childhood

Last night Christopher said, 'I want to thank you for all the effort you're putting into me learning.'

This is the end of childhood. He's still saying incredibly cute things — things that make me laugh — but now they're cute not because they're malapropisms, but because the language is too formal.

His English teacher is having him write a short biography in lieu of starting over again with the feature story. So he told me, as we were working on KUMON reading, 'I use big words when I write. I said, 'And then I had a gruesome surgery.'

The gruesome surgery in question was a tonsillectomy.



still loving the principal

We love this guy.

It's terrible.

It's like Carolyn not being able to hold a grudge.

We come into the school loaded for bear, we see the principal, we dissolve into shmoozing mode.

I would be a TERRIBLE litigator.



math mystery

The Team Meeting was interesting. The principal attended, no doubt to back his staff, manage the situation, etc. So he was there, along with the very young guidance counselor, the very young math teacher, the very young English teacher, the very young science teacher, and the middle-aged social studies teacher.

Sigh.

These people are all at the beginning of their careers.

Ed and I spoke our piece, and it registered.

We said:

• we suspect groupthink has occurred, with one member of the faculty causing other members of the faculty to think poorly of Christopher

• we actively dislike character assessment in an Interim Report; we want to know exactly what his level of learning is & we're not interested in what they think about his work habits at home

• we need to see formative assessment happening; we need to know what he's learned & what he hasn't

• we need review sheets for the tests

• METACOGNITIVE WOE: this one's big enough that I'll write a bit more...

metacognitive woe

Christopher has no idea how to study for tests. No idea at all. He's been in a study skills class since the beginning of the school year, and has learned nothing. The teacher may have told them how to study for tests; I don't know. If so, he didn't hear it or retain it. update 6-30-2006 The study skills teacher did not teach study skills. She taught "character."

But the problem is bigger than that.

The problem is that he doesn't know he needs to study.

The problem is: he thinks he knows the stuff.

He doesn't know what he doesn't know.

free advice: when the rest of you hit middle school, the words he doesn't know what he doesn't know will probably come in handy. This observation was very helpful today; Christopher's new English teacher actually repeated it back to me.

I said, to the math teacher: "Christopher understands what you teach in class, & he comes home thinking he knows it. But when he tries to do the homework, he can't."

I gave a version of this to the other teachers. "Christopher understands what you've covered in class, and he assumes that he remembers it. He actually does not know that he won't be able to reproduce this content on a test."

This was the right way to frame the issue, not just because it's true, but because it's somewhat less accusatory. They all visibly relaxed at the information that the initial presentation of the material isn't the problem.

My sense is that all of the teachers except for the math teacher are thinking about what the student has actually learned. There's probably not a school in Westchester operating under a 'teach to mastery' philosophy, but clearly everyone thought it was a bad thing for parents to be re-teaching content at night.

The issue isn't quite as simple as I'd been feeling. It's not precisely that his teachers 'blame' the student for failing.

They blame the student for not studying enough, which is a bit different.

Nevertheless, it was obviously helpful for them to hear the phrase 'doesn't know what he doesn't know.' Probably most teachers are inclined to moralize a child's study habits. If he's not studying, he's misbehaving.

These teachers had never heard the metacognitive formulation put so starkly.



spaced repetition

Christopher, in the 6th grade, is not studying for tests because:

a) he doesn't want to

BUT, even more importantly —

b) he thinks he knows the material



the boy issue, in brief

I raised the boy issue very briefly, because I wanted it in their thoughts.

I pointed out that only girls have been Student of the Month so far. This turned out to be wrong. Good. I don't care if I'm right or wrong; I want them saying to themselves, when it comes to Bestowing Honors upon 6th graders, Boy-Girl-Boy-Girl. Or, um, Girl-Boy-Girl-Boy.

I pointed out the fact that 60% of college students are female. It seemed possible some of the teachers didn't know this.

Now they do.

I pointed out the fact that boys are a full year behind girls in frontal lobe development and may never have the same degree of frontal lobe development females do. (I'll post some of that stuff later....)

When the principal objected strongly to this line of attack, as I expected he would, I suggested he check his database of Canned Teacher Comments and find out whether there's a gender difference.

Instantly he said, 'There's definitely a gender difference. Boys do much worse in middle school than girls. Everyone knows that.'

sigh

I guess we're not worried about equality of outcomes when it comes to boys!

Just try saying, 'Everyone knows blacks do worse than whites in middle school.'

See where that gets you.

Anyway, it was fine. My goal was to insert the words BOYS WILL BE BOYS into everyone's conscious mind, and to give this phrase a compelling, updated, NIH-endorsed neuroscientific definition.

BOYS WILL BE BOYS MEANS BOYS WILL NOT BE PICKING UP THE PROMINENTLY POSTED SCHOOL PASS FOR EXTRA HELP WITH MATH ON THE WAY OUT THE CLASSROOM DOOR.

PERHAPS A GIRL WILL PICK UP THE PROMINENTLY POSTED SCHOOL PASS FOR EXTRA HELP WITH MATH ON THE WAY OUT THE CLASSROOM DOOR.

YOUR BASIC BOY, HOWEVER, IS GOING TO NOT PICK UP THE PASS & THEN REMEMBER HE DIDN'T PICK UP THE PASS THAT NIGHT AT HOME, WHILE HE'S FIGHTING WITH HIS MOTHER ABOUT MATH.

IN CONCLUSION: BOYS WILL NEED THE GUIDANCE COUNSELOR TO SET UP A FORMALLY SCHEDULED EXTRA-HELP-WITH-MATH SESSION WITH THE PARENTS.

My point: 11 year old boys stink on executive functions.

fyi: neuroscientists are still figuring out what the executive functions are, but roughly they include:

• motivation

• persistence

• working memory

• organization & planning

• impulse control

• flexibility (being able to stop doing what you're doing if it's not working, and try something else; flexibility is the opposite of perseveration)

• sustaining motivation over time ('remembering' the future)

what the teachers said

The teachers' comments were encouraging.

It seems clear that Christopher fell apart at the end of the semester, as the situation with Mrs. Roth came to a head.

Apart from that, he talks too much in class, and the science teacher has now moved him to the front of the class where she can keep an eye on him. We thanked her for that, and asked her to move him any time she needed to. We know he talks too much in class (Ed and I were both in chronic trouble for TALKING TO OUR NEIGHBOR when we were kids), but it was good to have this fact underlined. We'll hammer him about it, which will help a little. They'll continue to move him some place where he won't have as many temptations.^*

At the end of the semester he was supposed to be doing a weather project in science, which required keeping a daily log of the weather reports. The teacher had him write this down every day in his assignment book, and showed him how to look up the weather on the internet.

He never did it.

That's an important sign of breakdown in the household. By that point we were all in crisis; plus I never read his assignment book, because a) I hate reading his assignment book & b) I don't want to read his assignment book & c) I forget to read his assignement book & d) I can't read his handwriting.....I could go on.

The point is: I haven't been reading his assignment book.

NEW YEAR'S RESOLUTION, 2006: READ THE FREAKING ASSIGNMENT BOOK

It's a further sign that Christopher had fallen apart, because he has always been able to do his homework on his own — on his own meaning he knew what he was supposed to do & did it without prompting from us. We've had no problem with Christopher doing homework; the problem has been with his knowing how to do the homework.

The social studies teacher said he's been fine in her class, but couldn't do the most recent text-reading exercise, which concerns me. She's teaching them how to identify main & subordinate ideas & evidence. He did the first assignment well, but couldn't do the second.

So I'm going to have to look at that closely. I'll also use the reading strategy described in How to Double Your Child's Grades in School, a Sputnik-era book that is going to change my life. (I'm not kidding.)

She's teaching them to take notes now, which is good.

That was pretty much it.



math mystery

The math situation is probably hopeless.

Apparently the teacher tells them, each and every day, that they should do the odd numbered problems in the book, then check their answers.

She doesn't assign these problems. She just tells them it's a good idea to do them.

She also tells them they can try some of the even-numbered problems.

Christopher has never mentioned this to either of us, and he's a talkative kid (as we've established).

Does he know she's been telling them all year to do extra problems?

I'll find out tonight.

She has the help-with-math school passes posted on the wall, and every day she tells the kids to pick one up if they need to. He never does.

We don't know why. I'll try to find out why, but I'm not confident he knows why himself. (My guess is that he's in such a rush to pack up all his stuff & get to the next class on time that he forgets.)

She says that every day they do one problem from the book, and Chris knows how to do them. Somehow, he's forgotten by the time he gets home.

Her description of the problem-doing was hazy, though.....they go over the homework in groups, and they're supposed to raise their hands with questions. Well, of course, Christopher has done his homework with me & I've gone over it & had him re-do all the problems he couldn't do, so he doesn't have any questions. He should have questions, but he knows he has the answers right, and he knows he was more-or-less doing the problems on his own the night before.....For Christopher, the going-over-homework-and-asking-questions portion of the class is a waste.

But I'm puzzled about the Final Problem Christopher Can Do.

I asked the teacher directly, 'Can he actually do those problems.'

She said, 'I think so.'

We left it that she would pay closer attention to whether Christopher can actually DO THE PROBLEM, not GET THROUGH IT WITH HER HELP.

I bet he can't.

But if he can do these problems, and he's losing his memory of how to do them between school & home,......I'm puzzled.



question for you math brains

What do you make of this?

Obviously his component skills are extremely shaky; we see that every night. He's now solving equations that contain negative numbers & fractions with different denominators & he's at sea. He can handle the components taken in isolation; he can find a common denominator; he can add & subtract integers; etc.

But these skills are shaky. When he tries to put them together, he falls apart. He has terrible handwriting problems, too. He simply can't see a negative sign that he's written. I'm now requiring him to put parens around negative numbers. I'm also going to start having him write the negative up at the top of the number, which I think might help. Like this: ^-2

But what do you think about the loss between school and home?

Is that typical?



The Organized Student

Over vacation, I discovered The Organized Student (chapter excerpt) in a Barnes & Noble.

More evidence that there is a God.

I think disorganization is probably the heart of the problem. (The situation with Mrs. Roth is in a category unto itself, and has had a wounding sequelae. But that situation has been dealt with, and the you-hurt-Mrs-Roth teasing is subsiding somewhat, and I think will continue to subside.)

While there have been problems with the school's performance, the fact is that some children are doing just fine. Perhaps many children.

The principal was very sweet about this. When I said in the meeting that I was asking myself why Christopher is doing so badly when other children are doing well, he said, 'Other children are having problems, too. A lot of children have problems coming into Middle School.' I found that dear. He was rushing to Christopher's defense, not caring that he was handing us more ammo if we were inclined to use it.

Nevertheless, the question remains.

Why is Christopher one of the kids who falls apart when he hits Middle School?

THE ORGANIZED STUDENT describes a category of kid just like Christopher.

They excel in K-5.

Then they hit middle school and collapse.

She argues, convincingly, that these children have poor organizational skills and don't pick these skills up on their own. They have to be taught how to manage a Middle School life.

(Probably most kids need to be explicitly taught organizational skills, but some kids need it more than others.)

The author was a librarian at the Dalton School for many years, and she says she came to the point where she could pick out the children who were going to fold when they hit Middle School: these were the kids who lost all their library books!

Christopher hasn't lost too many library books, but we've spent years of our lives frantically searching the house for GameBoys, tennis rackets, soccer shoes, tennis shoes, coats, TV remotes, and on and on and on.

I've already set up the zippered binder recommended by the book. I'm going to be setting up everything else the book recommends, too. (She tells exactly how to set up a child's desk, and recommends a desktop filing crate, which I'm ordering from THE CONTAINER STORE.)

I'll use HOW TO RAISE YOUR CHILD'S GRADES to teach study skills explicitly.

I think this will work.

Assuming I've got the problem diagnosed correctly.

We'll see.

^* Mrs. Roth kept moving Christopher next to a very shy little girl who never spoke in class. The girl hated that. Christopher would come home and say, 'S. hates when Mrs. Roth moves everyone, because Mrs. Roth treats her like an empty desk.'

Poor thing.

Of course, judging by the amount of info Christopher seemed to be pulling out of her, she was talking a whole lot more under the new seating arrangement.

---

OrganizedStudentWakeUpCall 18 Jan 2006 - 13:50 CatherineJohnson






This is what I don't get.

This child goes clear through 6th grade turning in no homework.

His mom gets the Call in......May?


source:
The Organized Student

---

NegativeExponents 11 Jan 2006 - 22:58 CatherineJohnson








Ed spent 3 hours, sum total, doing homework with Christopher tonight.

This is a nightmare.

Christopher was 'taught' negative exponents for the first time today. He's never seen them before.

Then he was given problems like this one. Lots of them.

These problems are so hard that 4 of the answers in the teacher's manual are wrong.

We think.



this is fun

Ed is now ranting and raving about Prentice-Hall, the Phase 4 math course, IT SUCKS! IT SUCKS! etc.

Ed never rants.

He sounds like me.

haha


(yes. i am evil.)


update

I forgot to mention.

Christopher has only spent about two days of his life practicing how to simplify complicated expressions with positive exponents.

Two.

At most.

OK, maybe three.

By the end of this year I'm going to be able to write a dissertation about what happens when you combine two or more skills that HAVEN'T REMOTELY been learned to mastery.

Two words.

Sink hole.

---

AccordionFileForTheOrganizedStudent 09 Jan 2006 - 20:28 CatherineJohnson






This is one of the systems Donna Goldberg recommends for middle school kids.

She says middle school is getting so much more complicated than it was just 10 years ago that a lot of kids are switching from her preferred system, the zippered binder, to the accordion file.

Christopher's zippered binder comes with a small accordion file of its very own.




(this isn't it. this is the zippered binder linked to on MrsKsPlace.)

UPDATE 7-23-2006: We've given up on zippered binders. They explode in two weeks. We're using the Globe-Weis Fabric Poly Files now and they work great. Christopher managed to get through 4 months of school with one file. His friend M. has one, too, and all is well.

---

OnceMoreWithFeeling 09 Jan 2006 - 17:47 CatherineJohnson



I should have homeschooled.

---

ThreeHolePunchForPacketWorld 10 Jan 2006 - 02:10 CatherineJohnson







Swingline® LightTouch™ Desktop Hole Punch
12-sheet capacity
Item 506360
Model A7074026



Middle school these days is all about PACKETS.

I don't know why.

If J.D., Charles, Greta, or Carolyn Morgan are around, maybe they can fill us in.

I didn't have a gazillion PACKETS to keep track of when I was a kid.

Of course, my school didn't have a Xerox machine, either. There's probably only so many mimeographs a teacher can stand to run off before she gives up and just teaches the stuff that's in the book.

Our new system around here, thanks to The Organized Student, is that each night Christopher or I will 3-hole punch that day's PACKETS, and put them in his zippered-binder where he can find them.



breach of copyright

Actually, I do know one reason why we have so many PACKETS.

Schools are Xeroxing old copies of 'consumables' (workbooks) instead of buying new copies as they're legally obligated to do.

Yet another reason why schools should get out of the character education business.



a fancy math packet cover





Don't say I never gave you anything.


compare and contrast

Interesting.

The reason this math packet cover was produced by a PTA is that the Renton Park Elementary PTA sponsors all kinds of educational activities, such as reading programs & summer math.

That's as opposed to the Irvington PTSA, which shuts down its Singapore Math course the moment the Superintendent levels anonymous charges against the parent-teacher, a long-time PTSA member and volunteer — and agrees, furthermore, that the PTSA will henceforth offer no after-school courses that cover the same subjects already covered by the school. ("For instance," the president said, "we might offer Chinese, because Main Street School doesn't offer Chinese. But we wouldn't offer Spanish.")

Perhaps our upcoming PTSA Forum should be apprised of Renton Park's involvement in math & reading.

I'm thinking.....why, yes!

I think this is something people need to know!

This is something parents need to know!

---

PreAlgebraIsBunk 30 Jun 2006 - 10:57 CatherineJohnson

Great minds think alike.




Ken left this comment about the negative exponent problems Christopher was trying (and failing) to do

Er, isn't this algebra and not "pre-algebra"?

I suppose pre-algebra now is pick an algebra lesson (and I use that term loosely) at random, teach it poorly or not at all, and ask the student to memorize the answer solve the problem.

Ken beat me to it.

Saturday night, after Ed had lived through his first Screaming Pre-teen Math Test Study Session, he said, "This is spiralling."

What he meant was, pre-algebra is not pre-algebra.

Pre-algebra is algebra.

Pre-algebra is called pre-algebra, we both think, because it's the beginning of the Second Spiral in an American child's life.

The Algebra Spiral.

In K-6 or K-7, kids experience the Arithmetic Spiral.

Then, starting somewhere in middle school, they move on to the Algebra Spiral.

They spend two years learning Algebra 1:

• 1 year of Pre-algebra

• 1 year of Algebra 1

Both courses are algebra, and both courses cover the same material.

This is the only explanation we can come up with for the torture that is Phase 4 math. (OK, there's the This was supposed to be a course for gifted children, but then the high achievers jumped on board and ruined everything meme, which could be true. That's a side issue I'm curious about: are the one or two gifted kids learning well in this course? I'd love to know.)

Leaving gifted children aside, Prentice Hall Mathematics: Explorations and Mathematics was not written for gifted children. As I understand it, it's intended for use in the regular 8th grade pre-algebra course. (Of course, if that's true, then the good news is: WE'VE BEEN TEACHING ALGEBRA TO 8TH GRADERS FOR QUITE SOME TIME NOW.)

Christopher is trying to learn one whole brand-new topic in algebra a day, every day.

He can't do it. Period. I'm assuming the gifted kids can, but I'd bet the ranch they're the only ones.

What we're doing now is the equivalent of forcing an 11-year old to cram for tests every single day of his school week. We're ramming rules, numbers, notations & mathematical conventions into his head so he can — yes — regurgitate them on a test, knowing all the while that he'll forget everything we're 'teaching' as soon as the test is over.

Why would a textbook present this much new material in one year's time?

J.D. will have an answer, I'm sure. Perhaps this book is intended to be used over two years' time?

However, I have the Teacher's Edition, and I don't get the sense that's the case.

I think the book is set up to 'cover' a vast amount of basic algebra in 1 year.



Glencoe's Table of Contents

The Glencoe pre-algebra text, which I believe is the other 'big,' widely used pre-algebra book, has a terrific Parent and Student Guide available online.

The book has 14 chapters:

Chapter 1 - Tools for Algebra and Geometry

Chapter 2 - Exploring Integers

Chapter 3 - Solving One-Step Equations and Inequalities

Chapter 4 - Exploring Factors and Fractions

Chapter 5 - Rationals: Patterns in Addition and Subtraction

Chapter 6 - Rationals: Patterns in Multiplication and Division

Chapter 7 - Solving Equations and Inequalities

Chapter 8 - Functions and Graphing

Chapter 9 - Ratio, Proportion, and Percent

Chapter 10 - More Statistics and Probability

Chapter 11 - Applying Algebra to Geometry

Chapter 12 - Measuring Area and Volume

Chapter 13 - Applying Algebra to Right Triangles

Chapter 14 - Polynomials

That's a lot.

Each chapter has 8 to 10 separate lessons, all of which cover new material.

Approximately 130 separate items of brand-new material for students to learn in a 180-day school year?

This weekend I pulled out all of the individual topics, so I could try to keep track of them — so I could try to figure out quickly what Christopher needs to practice today.

Here's the list.

What elements of Algebra 1 are missing here?

applications
applying equations and inequalities

arithmetic sequences
geometric sequence

coordinate plane
ordered pairs

data
circle graphs

estimation Estimating sums and differences

equations
solve using inverse operations
solve using addition & subtraction
solve using multiplication and division
one-step equations
two-step equations
one-step equations with whole numbers
two-step equations with integers
one-step equations with fractions
two-step equations with negative fractions
one-step equations with decimals
two-step equations with decimals
one step-equations complex (positive & negative fractions, distributive property, solve by addition, subtraction, multiplication, division)
solve equations with variables on both sides
writing two-step equations

expressions & variables
simplify expressions
write expressions

exponents
negative exponents

factors
factors
greatest common factor
least common multiple
monomials
negative exponents
powers & exponents
prime factors
multiplying & dividing monomials

formula
using formulas

fractions

functions and graphs
relations & functions
scatter plots
graphing linear relations
equations as functions
draw a graph
slope
intercept
systems of equations
graphing inequalities

geometry
circles & circumference
area and perimeter
geometry terms
angles & parallel lines
triangles
congruent triangles
similar triangles & indirect measurement
quadrilaterals
polygons
transformations
area: parallelograms, triangles, trapezoids
area: circles
geometric probability
surface area: prisms and cylinders
surface area: pyramids and cones
volume: prisms and cylinders
volume: pyramids & cones

inequalities
solving inequalities by adding or subtracting
solving inequalities by multiplying or dividing
writing inequalities
solving multi-step inequalities

integers
absolute value
comparing and ordering
adding integers
subtracting integers
multiplying integers
dividing integers

measurement
metric system

order of operations

polynomials
adding polynomials
subtracting polynomials
powers of monomials
multiplying a polynomial by monomial
multiplying binomials

problem solving
Draw a Diagram
Make a plan
Look for pattern
Eliminate the possibilities
Use logical reasoning
Work backwards
Make a table
Use a simulation
Make a model or drawing
Venn diagrams

Properties
Distributive
Commutative
Associative

Ratio & proportion
Ratios & rates
Simple probability
Using proportions
Using the percent proportion
Using statistics to predict
Fractions decimals & percents
Percent & estimation
Using percent equations
Percent of change

Rational numbers (decimals & fractions)
Adding & subtracting decimals
Multiplying and dividing decimals
Estimating sums and differences
Estimate products
Fraction to decimal
add subtract like fractions
add subtract unlike fractions
multiply fractions
divide fractions
solving equations with rational numbers
solving inequalities w/rational numbers

right triangles
squares & square roots
real number system
Pythagorean Theorem
Special right triangles
Sine, cosine, & tangent ratios
Using trigonometric ratios

statistics
scientific notation
measure central tendency
stem and leaf plots
measures of variation
displaying data
misleading data
misleading statistics
counting
permutations & combinations
odds
probability of compound events

how would a mathematically gifted child handle this course?

What do you think?

One more 'data point': the class does no word problems.

Just the extended response problems.

These concepts are taught as isolated procedures with no application to problem-solving.


Summer Supplement Time
linking decline in high school scores to elementary school
research on summer regression
the time costs of not teaching to mastery
U.S. fourth graders not doing as well as thought
Phase 4 topic list, grade 6 class
comments thread on pre-algebra as algebra
death march to algebra
NYU ed textbooks; NY math test

---

APDeathMarch 13 Jan 2006 - 15:12 CatherineJohnson



New York Times articles stay online for only a week, so be sure to read Sunday's article on AP courses in the next few days if you're interested.

This is a shot of a girl who's just won a car because she passed 5 AP exams.


Ed is appalled.

Professional historians, I gather, think A.P. courses are bunk. No college professor teaches a course 'covering' all of U.S. history, from pre-Columbian Societies through The United States in the Post-Cold War World, in two semesters.

[pause]

Just checked again: Ed's not sure about this. History departments do survey courses.....but Ed is highly skeptical that an A.P. history course can do what the College Board says it does, which is:

The AP program in United States History is designed to provide students with the analytical skills and factual knowledge necessary to deal critically with the problems and materials in United States history.

I repeat: actual college professors, teaching actual college courses (at least in history), think this is bunk. They don't like A.P. courses, and they aren't impressed that kids have taken them.

The NYU history department gives students one semester of credit for AP courses, period. A student could have taken all three AP courses offered in history; she'd still get one semester's credit. (NYU has 60% girls to 40% boys.)



gimme that old-time religion

from the article:

The Advanced Placement program, administered by the College Board, began 50 years ago as a way to give a select few high school students a jump-start on college work. But in recent decades, it has morphed into something quite different - a mass program that reaches more than a million students each year and is used almost as much to impress college admissions officers and raise a school's reputation as to get college credit.

[snip]

....many of the elite schools that pioneered A.P. are losing enthusiasm, looking for ways to cut their students loose from curriculums that can cram in too much material at the expense of conceptual understanding and from the pressure to amass as many A.P. grades on their transcripts as possible. A few have abolished A.P. programs altogether, and many have limited students to taking three a year, fearing burnout and bad scores.

It's not that a large number of private schools shun A.P. courses - to the contrary, the number offering them rose 15 percent last year - but teachers and college counselors at many top-notch schools, public and private, confess to discomfort with the way the program seems to hijack the curriculum.

"We've been put off for quite a while about the idea of teaching to the test, which is what a lot of A.P.'s are," says Lynn Krahling, guidance director of the Queen Anne's School in Upper Marlboro, Md. "We're convinced, as an educational institution, that they're not as valuable as what we could be offering on our own.

"But," she says, "I think we're going to stick with A.P.'s - purely out of fear. Parents are so terrified that if we drop our A.P.'s it would really affect college admissions that I think some of them would jump ship."

shoot the moon

Sixty percent of American high schools now participate in the program, which offers courses in 35 subjects, from macroeconomics to music theory. Last year, 1.2 million students took 2.1 million A.P. exams, and the number of students taking A.P. courses has increased tenfold since 1980. Newsweek magazine has gone so far as to rank the nation's best public high schools using the number of students who merely show up to take A.P. or International Baccalaureate tests as the sole criterion.

No wonder, then, that more than 3,000 students took seven or more A.P. exams last year. No wonder, either, that some students use the A.P. program tactically, knowing that their senior-year A.P. course listings will appear on their transcripts, and be counted in admissions decisions, long before they take the A.P. exam in May - if they ever do. (The A.P. brand is a curious one: students can take the exams, which run three hours, without taking the courses.) Part of the pressure to take A.P. classes also springs from the fact that most schools weigh A.P. grades more heavily than others - an A in A.P. is often worth five points, while a regular A is worth four - so savvy students know that A.P. courses can raise their G.P.A.'s, one of the most important elements in college admissions.

SO many more students are arriving at colleges with a slew of A.P. courses under their belts that some institutions have become more choosy about giving them credit. Harvard, for example, no longer gives credit for scores below 5.

[snip]

Despite its explosive growth, only 23 percent of last year's public high school graduates had taken at least one A.P. class, he says, adding: "Among those who take A.P. exams, 1 in 10 students in urban schools score 3 or higher, compared to 6 in 10 in suburban schools."

Research shows...

....that good scores on A.P. exams are strong predictors of college success. But last year, a study of University of California freshmen by two Berkeley professors found that the number of A.P. courses on students' transcripts bore little or no relationship to their college performance. So, the authors suggested, selective colleges should reconsider their use of A.P. enrollment as a make-or-break criterion in admissions. Another study, in Texas, found that A.P. classes had no advantage over other kinds of college-prep classes in raising a student's performance once in college.

In 2002, a committee of the National Research Council, part of the National Academy of Sciences, sharply criticized A.P. math and science courses for cramming in too much material at the expense of understanding and failing to keep up with developments in the subjects. The College Board is now revamping its science and history courses.

ONE striking oddity of the Advanced Placement program today is that while many less-than-distinguished public high schools have open-door policies about who can enroll in A.P. courses, many academically superior schools still act as gatekeepers, allowing only top students to enroll. At many suburban and private schools, students must have good grades or a teacher recommendation or both. [ed.: oh swell] And at Stuyvesant and Bronx Science, the two most competitive public high schools in New York, demand is so great that only students with the highest grades get into the popular A.P. classes.

Some of the most academically demanding private schools - among them, in New York, Brearley, Fieldston and Dalton - take a different approach: they do not offer Advanced Placement, although many of their students still take the exams.

"At Dalton, advanced classes aren't called A.P.'s, but I think most of my grade took A.P. exams last spring," says Nell Hawley, a senior who took three exams last spring and scored 5 on each. "But not having A.P. classes at Dalton means that you get to learn for the sake of learning, not taught to the test."

Ed said this afternoon, "So they have 8 years of constructivism; then they're thrown into courses where they're expected to succeed through brute memorization."

Makes sense.

Ed thinks the Phase 4 course is a preview of AP in high school.

I hope that's not the case.

I do know that in elite high schools kids work 24 hours a day. They're overrun with work; it's relentless.

I'd bet the ranch half that work is pointless.



death march through physics

....the pace can be overwhelming.

"In our physics A.P., we had a test where our whole class did badly, and we asked our teacher if we could slow down and review," Eden says. "We love our physics teacher, and he understood, but he said we had so much material to get through before the break that there was no time for review. I think he was as frustrated as we were."

[ed.: I wonder what Engelmann has to say on the subject of Advanced Placement courses? I'm guessing he'd make short work of the College Board.]

Lawrence Weschler, director of the New York Institute for the Humanities, became critical of A.P. courses based on the experience of his daughter, Sara, who decided on Brown but has deferred enrollment.

"When Sara would go on her college tours, everywhere she went, they said, 'We will be looking to see if you took every challenging course you could, and that's how you will be judged,' so of course she took as many as she could," he says, adding that it seemed misguided for high school students to try to place out of classes they should be looking forward to taking in college.

"Even where the A.P. courses got the kids excited," Mr. Weschler says, "the excitement would immediately be doused. In European history, the kids got very involved in the causes of World War I and wanted to talk about it, but the teacher said they couldn't because they had to move on and cover all the material for the test.

[snip]

"On one hand, many of the classes are ambitious and wonderful, and I'm glad we have them," says Scott White, a counselor at Montclair High School in New Jersey. "I also understand that colleges have no good way to consistently assess the highest level kids, and A.P.'s can provide an external paradigm for doing that. But from the student's point of view, there is a horrific rise in the expectations on the part of colleges, almost a sense that if a student isn't taking the highest level in every course, there's something wrong. So we have students taking five A.P.'s, grinding away at all that memorization in a way that's more appropriate to boot camp than to kids growing up."

Some schools say there is now a sense that Advanced Placement classes have become inevitable.

"Part of it is that the College Board has done a very good job in marketing their products, working to increase access and enrollment, and the more students take the A.P.'s, the more they perpetuate the idea that students should take A.P.'s," says Emmi Harward, director of college counseling at Hampton Roads Academy in Newport News, Va.

I love the way we have all these enterprising National Curriculum Creators.

In K-8 the NCTM & the NCTE decide what our national curriculum will be.

In 9-12 it's the College Board.

Who asked these people?



....how important are A.P. courses in college admissions?

That depends. Certainly, most schools count them in an applicant's favor. One common approach is used at the State University of New York at Geneseo, where admissions officers tally the number of foreign language, math and science courses an applicant has taken, along with the number of A.P. or other advanced courses. Community college courses, often taken by advanced students in districts that lack an A.P. program, count, too, says Kristine Shay, director of undergraduate admissions, but "not exactly on the same basis, since they don't have that known national curriculum."

SUNY Binghamton takes a different tack. Admissions officers look at the grade point average and SAT scores, circle the number of A.P. and honors courses, consider what coursework was available at the high school and make a nonnumeric judgment: "All things being equal, if we had a kid with an 88 average and three A.P.'s, versus a kid with a 90 average and no A.P.'s, we'd probably take the one with the A.P.'s - but make it an 85 average and three A.P.'s and I'm stumped," says Cheryl Brown, director of undergraduate admissions. She adds that almost 100 students arrived on campus this academic year with enough credits for sophomore standing.

Admissions officers at the most elite colleges say, in almost identical words, that they want students who have taken "the most rigorous program the school offers" (Marlyn McGrath Lewis, Harvard); "the most demanding program they can take at their high school" (Karl Furstenberg, Dartmouth); "courses that challenge them academically" (Jeffrey Brenzel, Yale); and "the most challenging program that's available and that they can handle" (Richard Nesbitt, Williams).

"We don't expect students to take every A.P. that's offered, but if their school has 15 A.P.'s and they've avoided them all, that would certainly say something," Mr. Nesbitt says.

While admissions officers acknowledge that taking the most difficult A.P. courses, like Calculus BC, indicates a strong academic background, they take pains to say that there is no magic, no numeric formula - and no penalty for students from schools that do not have an A.P. program.

"Sheer A.P. firepower, having 10 A.P.'s, doesn't impress us," says Mr. Brenzel. "It's just one factor in evaluating a student's background and preparation."

[ed.: I just bet]

[snip]

Marc Paulo Guzman, Hackensack's top-ranked senior, takes the literature class, along with A.P. biology and A.P. calculus.

"I wish there were more A.P.'s offered," he says. "They're fast-paced, and you learn a lot." Marc, whose family emigrated from the Philippines in 1993, is applying to Princeton, Yale and Duke. "I've done a lot of research about college on the Internet," he says, "and I know A.P.'s can help you get in."

how much does calculus count?

I've been getting the vibe that AP Calculus is the big kahuna.

So I'm thinking....maybe if Christopher just takes that (assuming he can stand the sight of a math book by the time he's a junior in high school) it will do.

He'll probably want to take A.P. history no matter how crazy it is.

So maybe those 3, and after that he can spend his time taking courses where he actually learns something he can remember two months later.

Of course, that's assuming he can 'get accepted' into the courses in the first place.

Another mysteriously-never-mentioned School Policy to look into.

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IsMiddleSchoolBadForKids 08 Oct 2006 - 22:41 CatherineJohnson







Carolyn's post yesterday made me realize I've been 'blaming the student' myself.

I've been thinking that the awful way Christopher and his friends treat each other is developmental, just part and parcel