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SaxonResearch 01 Sep 2005 - 04:20 CarolynJohnston

---+++ Update

I am happy to say that I was wrong when I wrote that there was no evidence supporting Saxon. There was a large study done in California, in which some pilot schools adopted Saxon math and saw their scores take off relative to those from other schools, which stuck by their existing curricular choice (Everyday Math). Apparently this study was not covered in the What Works Clearinghouse Middle School Math study, probably because it addressed not middle school but elementary school math.

The results are summarized here. -- Carolyn, October 3, 2005.

Original post

Apropos of the analysis of the research on Connected Math I did yesterday...

in the interest of fairness in reporting, it doesn't appear the evidence is overwhelmingly in favor of Saxon Math either. Saxon Math is a favorite 'traditional' curriculum of mine and Catherine's, sort of an 'anti-Connected Math' -- and it's served us very well in teaching our own boys -- but here is a roundup of what the (scarce) research says about it.

First, there is one study of Saxon Math that fully meets WWC's (the What Works Clearinghouse's evidence standards for a quality research study. Here is what WWC has to say about the study.

Peters, K. G. (1992). Skill performance comparability of two algebra programs on an eighth-grade population. Dissertation Abstracts International, 54 (1), 77A. (UMI No. 9314428).

WWC: Peters (1992) reports that students in the intervention and control groups showed gains on the Orleans-Hanna test during the course of the school year (that is, from pretest to posttest). However, the test score gains of the two groups did not differ significantly. There was no evidence that the Saxon Algebra curriculum (intervention) was more or less effective than the University of Chicago Mathematics Project curriculum (control).

The WWC warns that the number of kids involved in the study (only 36 kids total) was so small that it was very difficult to tell whether there had been a significant effect.

A second study of Saxon math met the WWC's evidence standards with reservations (meaning there was some not-quite-fatal flaw in the study's design).

Crawford, J., & Raia, F. (1986, February). Analyses of eighth grade math texts and achievement (evaluation report). Oklahoma City: Planning, Research, and Evaluation Department, Oklahoma City Public Schools.

WWC: Crawford and Raia (1986) found that students in the intervention group scored significantly higher than students in the comparison group on math computation, but not on total math or math concepts.

Here's what they did: they had one class working from Saxon Algebra, and one from Scott-Foresman Math (is this another non-fuzzy program? I wish someone would compare Saxon to a fuzzy curriculum!). They used a test (the California Achievement Test -- CAT) that breaks up the math scores into a math computation and a math concept subscore; they gave both a pretest and a posttest.

When they were ready to do their analysis, they matched students from each group one-for-one according to their total CAT score. That means that Fred may have been matched to Annie, because they both got X as a total score on their tests; but Fred may have far outscored Annie on the concepts subtest (with Annie stronger on computation).

They then looked at the mean posttest subscores of the matched children as a whole. They found that the mean scores were improved significantly in math computation, but not in math concepts.

The problem with this analysis is that, because the kids were matched by their total scores, one class may have had more conceptual skills to begin with as a whole. So interpret these results with care. However, here's a

Non-statistical side comment: I have read some parent reviews of Saxon that agree that it is great for developing computational skill, and not so great for developing problem-solving skills. These results are consistent with those comments.

To Summarize the Research: Of the two studies the WWC has reviewed on this topic, the second study has (to my mind) a flawed design, and the first shows an insignificant effect from the Saxon Math curriculum over the University of Chicago curriculum.

I'd love to be able to say that science proves Saxon is clearly superior; so far, it doesn't. However, Catherine and I have both said in the past that we would definitely recommend Saxon for kids who are struggling in math, and need to build their confidence by experiencing success; and I'll stand by that.

With Saxon, your kids won't miss out on any critical skill, either.

comments...

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DecisionMakingTime 01 Sep 2005 - 04:24 CarolynJohnston

I'm riffing on the research results in support of various curricula these days for two reasons:

1. I want to be able to counter claims that the research favors Connected Math, which I think is a lousy curriculum, and which has unfortunately been semi-adopted by my son's school;

2. I need to tutor my own son in math, and if there is evidence out there to support a particular curriculum, I'd like to know about it.

It doesn't seem that there is much evidence to support one curriculum over another. For one thing, quality research into the validity of math curricula is sparse.

There is one curriculum, however, that's been well supported by a very big study; the Trends in International Mathematics and Science Study (TIMSS). Singapore was the strongest performer in the 2003 study, and the Singapore curriculum (as I pointed out half-jokingly the other day) is, in fact, marketed in the United States, where wary parents like myself can eye it nervously when they're considering a home schooling or tutorial curriculum for their kids.

But I think I'm ready to give it some very serious thought and investigation.

comments...

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LetterFromJCobasko 02 Sep 2005 - 04:26 CarolynJohnston

I received an email today from Joanne Cobasko of Save Our Children from Mediocre Math (SOCMM). She drew my attention to a couple of articles, describing the improvement in California test scores after the new California standards were adopted.

I looked at the attachment and skimmed the second article. It's not a research study (i.e., it would not meet the WWC's standards of evidence for a well-designed study); but it is definitely one situation where Saxon went head-to-head with fuzzy math, and won.

Here's the letter (thanks, Joanne!):

Hi Carolyn:

Both these studies show fantastic classroom results achieved in CA classrooms which are attributed to Saxon Math. I believe Bishop & Hook down play the Saxon Math connection in favor of the "CA Key standards" so as not to promote any particular curriculum over another, they choose to promote the math standards employed.

You will find references to the curriculum in their write ups though.

http://www.nychold.com/talk-hook-040404.pdf
http://www.nychold.com/report-wbwh-040619.pdf

There is also a great district comparison of standardized test results from Manhattan Beach, CA and Palos Verdes, both well to do communities (the comparison was provided to me by Martha Swartz from Mathematically Correct). [Note: Joanne points out that Manhattan Beach uses Saxon Math, and Palos Verdes uses Everyday Math. -- Carolyn]

Palos Verdes has the edge with a 26% Asian population, and one Kumon or other type tutoring facility for every 429 grade 2 - 6 elementary age student (the tutoring info was my informal review of the school population per the state testing info and a print out from the Kumon & other centers indicating their locations within a 5.22 mi radius).

Manhattan Beach, with a 7% Asian population and only 1 KUMON facility in town for 2,1113 grade 2-6 students, outscores Palos Verdes on the 2004 test scores.

Jo Anne Cobasko
Save Our Children from Mediocre Math (SOCMM).

comments...

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NewMathByTomLehrer 03 Sep 2005 - 02:17 CarolynJohnston

In case there's anyone here that still thinks that what's going on now with constructivist math is any different from what's been going on for decades, here's the lyrics to Tom Lehrer's song "New Math", written in... um... the 1960s.

{Spoken} You can't take three from two Two is less than three So you look at the four in the tens place Now that's really four tens So you make it three tens Regroup, and you change a ten to ten ones And you add them to the two and get twelve And you take away three, that's nine Is that clear?

Now instead of four in the tens place You've got three 'Cause you added one That is to say, ten, to the two But you can't take seven from three So you look in the hundreds place

From the three you then use one To make ten tens And you know why four plus minus one Plus ten is fourteen minus one 'Cause addition is commutative, right? And so you've got thirteen tens And you take away seven And that leaves five

Well, six actually But the idea is the important thing

Now go back to the hundreds place And you're left with two And you take away one from two And that leaves

Everybody get one? Not bad for the first day

{Refrain} Hooray for new math New-hoo-hoo-math It won't do you a bit of good to review math It's so simple So very simple That only a child can do it

Now actually, that is not the answer that I had in mind because the book that I got this problem out of wants you to do it in base eight. But don't panic. Base eight is just like base ten really, if you're missing two fingers. Shall we have a go at it? Hang on...

{Spoken} You can't take three from two Two is less than three So you look at the four in the eights place Now that's really four eights So you make it three eights Regroup, and you change an eight to eight ones And you add them to the two And you get one-two base eight Which is ten base ten And you take away three, that's seven OK?

Now instead of four in the eights place You've got three 'Cause you added one That is to say, eight, to the two But you can't take seven from three So you look at the sixty-fours

"Sixty-four? How did sixty-four get into it?" I hear you cry. Well, sixty-four is eight squared, don't you see? Well, you ask a silly question, and you get a silly answer.

From the three you then use one To make eight eights And you add those eights to the three And you get one-three base eight Or, in other words In base ten you have eleven And you take away seven And seven from eleven is four Now go back to the sixty-fours And you're left with two And you take away one from two And that leaves

Now, let's not always see the same hands. One, that's right. Whoever got that one can stay after class and clean the erasers.

Hooray for new math {Refrain}

Come back tomorrow night, we're gonna do fractions.

Go here to hear the song. It's a riot.

comments...

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ArtOfGettingBy 03 Sep 2005 - 17:59 CarolynJohnston

I liked this entry (from a teacher's blog called The Art of Getting By) in last week's Carnival of Education.

I totally sympathize with the blogger about the problem of having to get up in the morning, except that I think I have it far worse than she does. I struggle out of bed at the last possible minute every day, and wander around in pain until mid-morning, which is about when the coffee finally kicks in.

Anybody else have this problem? Probably not. People like me (and the rest of my family is even worse) don't seem to be the norm. I can't believe how many people seem to be completely chipper in the morning, meeting their friends in coffee shops apparently for conversation instead of for medicinal purposes.

comments...

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SingaporeMathPlacementExam 04 Sep 2005 - 04:05 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).

comments...

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SingaporeAndSaxonRoundup 05 Sep 2005 - 04:17 CarolynJohnston

We've been talking on this thread about doing a parent guide to Singapore and Saxon, which are the two most readily available "classic math" curricula available to homeschoolers and parent tutors (I want to avoid the use of the phrase "traditional math", since progressive experiments in education were the norm for most of the last century).

We have used both curricula, and will continue to talk about both of them frequently in these pages.

However, different kids need different curricula, and we wanted to help parents make a choice that benefits their child best (and also matches best their own ability and willingness to support their kids' math learning; Saxon is probably a lighter-maintenance curriculum than Singapore).

Along those lines, I've been planning to post these links to Saxon and Singapore word problem comparisons at Paula's Archives for a while. Have a look. Although it's not really an accurate comparison to pull word problems out of each book and compare them at random, I think it's generally true that Singapore has exceptionally good word problems. Any kid reared on these problems is going to be mathematically in darn good shape.

Here, too, are Paula's Archives on Saxon Math and on Singapore Math individually.

When assessing your kids for their placement in Singapore Math, you'll almost certainly find that their placement level doesn't agree with their grade level. Somewhere on this site, though, someone posted that the Singapore math levels through 6B are actually completed when Singapore kids are in the 8th grade (or the age-equivalent grade in Singapore, whatever it is) -- something to tell your kids if they refuse to back up and do something they think is meant for younger kids (I sure wish I could find the post where that comment was).

Here's a post Catherine did on a price comparison between the Saxon and Singapore product lines.

And let me say, once again (repetition is key!), that if you have a kid who is getting lost or has gotten lost in math, and needs to make up lost ground and rebuild their confidence, I still don't believe anything beats Saxon math's approach.

comments...

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HorseLaughsHeardInSingapore 05 Sep 2005 - 18:01 CarolynJohnston

This morning, I've been looking at the American Institutes for Research study that was made for the U.S. Department of Education Policy and Program Studies Service after Singapore aced the 2003 TIMSS study.

The study is titled: What the United States Can Learn From Singapore's World-Class Mathematics System (and what Singapore can learn from the United States): An Exploratory Study. (Link to the pdf here).

Their main recommendation is that we adopt, in the U.S., the practices that have made Singapore a success. I completely agree with that, and I only wish that U.S. educational institutions would adopt this study's recommendations.

My purpose here, though, is to fuss about the hypocritical subtext of this study -- that the U.S. is clearly superior to Singapore in some carefully selected respects. Perhaps it was necessary to throw this in for political reasons, but finding this kind of spin in a supposed scientific study really troubles me nonetheless.

Since Singapore got the highest scores on this large-scale international study of mathematics achievement in 8th grade, and the U.S. at 16th place is trailing the other industrialized nation in mathematics performance, it's difficult to imagine what Singapore could learn from United States education, except maybe how to posture arrogantly in the face of abject failure.

Here, from a summary (also by AIR), is what AIR thinks Singapore has to learn from the United States:

U.S. Strengths: Although the U.S. mathematics program is weaker than Singapore s in most respects, the U.S. system is stronger than Singapore s in some areas. The U.S. frameworks give greater emphasis than Singapore's to developing important 21st century mathematical skills such as representation, reasoning, making connections, and communication. The frameworks and textbooks also place greater emphasis on applied mathematics, including statistics and probability.

What chutzpah. The U.S. is better than Singapore at teaching reasoning? Are they crazy? The evidence is clear. Singapore students were demonstrably better than U.S. students at the TIMSS problems, which presumably involved reasoning. If the Singapore students are better at reasoning than the U.S. students, than one has to presume that Singapore teachers are better at teaching reasoning than U.S. teachers.

And who is to say that a greater emphasis on statistics and probability is desirable? That seems to be a given in discussions of mathematics education these days, to the point where U.S. math textbooks teach the same small set of tired topics -- mean, median, mode, and range -- every year throughout a child's education.

Here's another given in today's educational environment: that communication skills are important components of early mathematics education. Here's a quote from the AIR study, in which several U.S. study sites temporarily adopted the Singapore math curricuum:

Unfamiliar with the pedagogy laid out in Singaporean Teachers Guides, several sites were also concerned that the Singapore textbooks did not stress written communication skills by requiring students to explain their answers.

Again, who is to say that verbal or written explanations of one's answers are a critical component in the early development of mathematical skills, rather than an unnecessary distraction? If mathematical exposition is such a critical skill, perhaps English teachers ought to take it up as a topic for study.

Most bleakly humorous, to my mind, are the suggestions that our ill-formed '21st century mathematical skills' are going to be necessary for competition in the international marketplace. Our kids competed internationally in the TIMSS test and lost, folks, so whatever it is we're doing here, it's not benefiting our ability to compete internationally.

comments...

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FromAroundTheEdusphere 06 Sep 2005 - 04:35 CarolynJohnston

Here and there in the "edusphere" I've seen mention of Professor Plum. He's a fellow educational radical (as I've grown to think of people who favor actual instruction in the classroom), and today I checked out his website.

I learned, among other things, that Direct Instruction actually refers to a very specific method of instruction, and to a commercially available set of curricula. It's not just what happens when I Directly Instruct Ben on how to do a math problem, as I had thought. Professor Plum has a lot of material on it here, if you're curious.

But on a quick perusal, I wasn't attracted to Direct Instruction. I couldn't find what I thought was a sufficiently clear description of what Direct Instruction is about. I learned that it is scripted interaction between teachers and children, and that a great deal of teacher training is needed to implement it properly -- all of which statements I've also seen recently in the Connected Math context. I'd like to see more beef, up front and center.

One of Professor Plum's links also took me here, to a site for parents on how to develop contracts for children that help them achieve academic success. I really like this guy's ideas, which are built around a principle I've been using to good effect around here since Ben was a little toddler, namely bribery. It's not really bribery, of course; it's merely setting up a system of targeted incentives intentionally, rather than accidentally setting up the wrong ones haphazardly. There are lots of good suggestions and examples on this website; a lot of detail of the sort that makes you braver about actually implementing his suggestions.

I also did very much like a recent post of Professor Plum's, entitled Basic Features of Effective Instruction. This post is a gem; it summarizes the features of effective teaching very well, I think (I'd love to know whether KTM teachers agree with me on that!). While reading it, it struck me that I hadn't seen teaching methods of any sort described with such clarity since Ben was very young, and I was working with Applied Behavioral Analysts to implement the Lovaas curriculum, which is designed to treat young autism-spectrum children. There is no tougher customer to teach than a very young autistic child; they are extremely disinclined to pay the teacher any attention at all, and they are often not motivated by the things that motivate typical children (like praise and attention). A teacher can't mess around; her message has to be crystal clear, and her incentives have to be right on. Many of the principles he outlines here are typical-kid versions of those one uses in Applied Behavioral Analysis, to decrease confusion and ineffectiveness (and no surprise either, since he has worked with autism spectrum kids in his career). A terrific post.

comments...

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ParentsInfoNight 07 Sep 2005 - 04:21 CarolynJohnston

I attended a '6th grade parent's info night' at Ben's middle school tonight, in which the principal and the school counselor tried to fill us in on life in middle school, and answer our questions.

I learned a lot of interesting things in the course of the meeting. Here are a few:

• Instant Messaging is the bane of everyone's existence but mine ("No parent has ever come up to me and said, 'IM has done wonderful things for my family'", the principal said). Also, cell-phone-based text and photo messaging are totally new and very effective technologies for cheating.

• There is something kids do called 'Slam Books', an online phenomenon in which kids write awful things about each other and spread them via the internet (in fact, using Instant Messaging).

• My town has the highest per capita rate of alcohol use by minors, among towns in a state with the highest per capita rate of alcohol use by minors. "By the eightth grade," the principal said, "if they're at a party, there's almost surely alcohol there somewhere. Either it's in the bushes, or out in the open."

• 'Cutting' is a fad among teenaged girls these days (that means they are cutting themselves with sharp implements). I recall that some friends of mine did some cutting when I was in high school, before it was popular; I thought they were crazy.

And of course I had my own questions: about things like the line in the lunchroom, whether there would be a biking club, and when the gym clothes we ordered at registration would arrive.

It all reminded me of the time, maybe ten years ago, when my Dad called me and told me that some kids had been busted for running a drug ring in my old high school.

"You're kidding!" I said. "I don't think anyone was doing that when I was there! Or perhaps I was just out of it."

"Carolyn," he said, "you were out of it."

warning: drastic topic change

I really have enjoyed practically everything I've read by E.D. Hirsch (except, actually, for Cultural Literacy; I think he's right about its importance, but I didn't like the book). I came across this article, "Classroom Research and Cargo Cults", in which he teases out what is wrong with education research, and recommends using cognitive science instead as a more reliable guide to educational practice. It looks interesting.


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

comments...

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MiddleSchool 07 Sep 2005 - 17:36 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





comments...

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MiddleSchoolPart2 07 Sep 2005 - 18:41 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

comments...

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MiddleSchoolPart3 07 Sep 2005 - 20:03 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

comments...

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FactoringNumbers 08 Sep 2005 - 03:13 CarolynJohnston

A factoid: When you're trying to determine whether a number is composite (i.e., not prime), it's sufficient to check whether all the primes less than the square root of the next greatest square number divide it. If nothing less than the next-larger whole number square root divides the number, then you know the number is a prime.

For example, to check whether 221 is prime, all you have to do is test all the prime numbers less than 15. To check whether 133 is prime, check the prime numbers less than 12.

My question: how do you teach the reasoning behind this rule? I was tackling this tonight with Ben, and I wasn't getting it across very effectively. I tried saying that whenever a number factors into two numbers, one must be less than and one must be greater than the nearest square root. This didn't really click for him.

Next I tried drawing rectangles to demonstrate the idea. I did 36, and showed the special square rectangle that you can make with that area. I asked him what other rectangles you could draw with that area; we drew 4 by 9, 12 by 3, 18 by 2, and so forth.

I then pointed out that all the rectangles we'd drawn that weren't square had one number less than 6 (the square root) and one greater than 6. I claimed that this is always true. He then said "Oh, I get it!" but I think he's learned that I like it when he says aha, and that it wasn't a genuine aha. It's hard to fake these things.

Anybody have any ideas on how to teach this? I think one problem is that square roots are still a pretty vague concept at this age, and I wonder if this is a trick that 6th grade kids are generally taught. But if they're not taught this trick, then where are they taught to stop checking for divisibility?

comments...

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VacationReport 08 Sep 2005 - 14:37 CatherineJohnson


We have emerged from the first day of school unscathed.

Christopher does have the math teacher who scandalized the entire Phase 4 Parent Body last year, so I'm expecting to see a massive packet of Math Olympiad problems later on today. Ed says every time they send home Math Olympiads I should send back my own Math Olympiads. Don't think I won't do it.

otoh, Christopher was utterly charmed by Ms. Kahl (I think that's her name). He reported every single one of her rules to me in detail, a serious look on his face. 'I like Ms. Kahl,' he said. 'She's nice.'

This reminds me of the goofy feminism of my youth. For a while there, everyone was talking about RAISING BOYS WHO LIKE STRONG WOMEN. Even though I was still childless & quite possibly husbandless at the time, I thought the whole thing was ridiculous. The implicit antagonism to boys got on my nerves.

Then I turned out to be the kind of mother who raises boys who like strong women.

When Christopher was 4 he came home from nursery school one day and said, 'Mommy, I like a girl. Jean.'

I wasn't sure who Jean was, so I asked another mom. 'That Jean,' she said. 'She's a bossy one.'





teach your son math and set him up for a happy marriage, too!

It's probably just as well. A few years ago John Gottman came out with one of his Key Factors determining whether a marriage succeeds or fails, and it turns out the Key Factor is how much the husband is willing to be 'influenced' by his wife.

85% of the variance in whether a marriage succeeds or fails is based on the husband's actions and attitude. John Gottman, PhD, discovered that successful marriages involve husbands who resist immediate negative reactions to their wives' concerns. These men increase the odds of having a happy marriage by allowing themselves to accept the influence of their spouse....

Clarke, a 30-year veteran of marriage, demonstrates these principles in a contribution to SecretsofMarriedMen.com. "When my wife asks me to do something, almost anything, my initial reaction used to be annoyance because I have lots of work to do, lots of things to do around the house, and lots of other bullsh-t reasons why not. However, most of what she asks me to do is actually quite reasonable, usually my responsibility, and I probably will end up doing it anyway. So, now I've trained myself to say 'yes' or 'no problem' as my initial response. This has contributed to less arguing and a better relationship."

By the time Ms. Kahl and I get done with him, Christopher will not only be Good At Math, he'll be excellent Future Husband Material to boot.





Here is Gottman's The Mathematics of Marriage: Dynamic Nonlinear Models





I'm afraid one of my Life Goals has become learning enough math to be able to read, understand, and form an educated opinion about the contents.





my vacation wow

Two days into the school year and I'm already so re-absorbed by Math-Math-Math I almost forgot the whole point of this post. My Vacation.

It was great!

It was the first fun family vacation we've had since Andrew was born!

One word: Abilify

If it doesn't work for your kid, it'll probably work for you.





update update: this man is a genius

comments...

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MiddleSchoolPart4 08 Sep 2005 - 21:54 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

comments...

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ExtendedResponse 08 Sep 2005 - 23:41 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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BookRecommendationAboutReading 09 Sep 2005 - 04:28 CarolynJohnston

Ben has an independent reading project for school. He is in a class called "Reading Clinic", which is supposed to be for weak readers, and in fact he is a weak reader of sorts. However, he can read at speed, and he'll actually get most of the story; it's the subtleties he misses -- the inferences, the innuendoes, and sometimes the main idea of the story. You'd be amazed how much of readng requires you to make inferences.

The kids went to the library the other day and picked out books to read. Ben has been enjoying Goosebumps, so one of his buddies helped him find an R. L. Stine book. Unfortunately, the Stine book wasn't the usual Goosebumps sort of book -- i.e., it wasn't about vampires or ghosts or zombies -- it was about some guy who was stalking babysitters. I don't really want to explain about stalking babysitters to Ben.

So I want to find something else for him to read, something in the horror genre that's maybe a little bit of a departure from the Goosebumps thing -- something by a different author, perhaps. So tonight I went digging around the house looking for one of my favorite parent books on kids' reading -- Parents Who Love Reading, Kids Who Don't, by Mary Leonhardt.

Ms. Leonhardt is a teacher who developed a simple approach for getting kids to become avid readers. It's actually more of a philosophy than a teaching approach. Her attitude is that you let them read whatever appeals to them, whether you personally think it's trashy or not. So comics are in, celebrity tabloids are in, Danielle Steele is in. Reading all the books by a single author that they love is fine. You try to hook them into reading, and then you count on their branching out on their own.

I've been using this philosophy for years with Ben, who is an especially tough case because of the autism spectrum disorder; he has a much greater tolerance for repetition than most of us do, and won't necessarily branch out on his own. He has to be gentled along. All through elementary school, though he hated reading, he was at least reading comics; particularly Calvin and Hobbes (which I love) and Garfield (which I don't -- and you'd be amazed how many Garfield comic collections there are in print). Last year he branched out a bit and started enjoying the Foxtrot comic; I tried him on Bloom County, but he didn't like it. This year he's loving his first chapter books, the Goosebumps series.

There is more to love about Ms. Leonhardt's book than her attitude toward kids' reading. I like her advice to parents about dealing with big problems their kids are having at school. Some teachers, she says, do enjoy emotionally battering children; if your kid gets one of these, move heaven and earth to get the kid out of their classroom. She has extensive advice on how to help your child if he is doing poorly in school (based partly on some insight a friend gave her into how to deal with panic attacks --often, simply knowing there's a way out will calm a person enough to allow them to carry on!).

It's got 5 stars from 4 reader reviews at Amazon.

comments...

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BrainEvolution 09 Sep 2005 - 18:12 CatherineJohnson

I added a section on the ISAT rubric to the post on 'extended response' test items below, so if you're interested scroll down.

Also, a comment Carolyn made about wasting mental energy on a way-too-busy test item reminded me of a terrific Scientific American article from a few years back: Food for Thought: Dietary change was a driving force in human evolution

Here's the salient passage:

From a nutritional perspective, what is extraordinary about our large brain is how much energy it consumes-- roughly 16 times as much as muscle tissue per unit weight. Yet although humans have much bigger brains relative to body weight than do other primates (three times larger than expected), the total resting energy requirements of the human body are no greater than those of any other mammal of the same size. We therefore use a much greater share of our daily energy budget to feed our voracious brains. In fact, at rest brain metabolism accounts for a whopping 20 to 25 percent of an adult human's energy needs-- far more than the 8 to 10 percent observed in nonhuman primates, and more still than the 3 to 5 percent allotted to the brain by other mammals.

Since reading this I've been very aware of which kinds of activities waste children's mental energy (and my own) and which do not. Susan H has written about this, in a comment I'm going to send to Education Wonks (just reminded myself!)

Children don't have energy to squander on fruitless undertakings.




comments...

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ConstructivistMathInWashingtonState 10 Sep 2005 - 00:52 CatherineJohnson

JoanneJacobs links to an article on constructivist math in Washington state:

Erin Bennett doesn't really care that her students can solve 12 x 3 = 36.

When the Columbia Elementary School teacher conducts a math lesson, she's more interested in how her students solve the equation, and if they can explain themselves well. And the right answer doesn't hurt.

"You did it in a really cool way," she told student Jarred Brutscher. "Tell us how you did it."

Brutscher wrinkled his nose and launched into a quiet explanation of his thought process: the fourth-grader knew that 10 x 3 = 30, and 2 x 3 = 6. So using those two equations, he deduced the answer....

Hey!

Isn't that the DISTRIBUTIVE PROPERTY??????

I think it IS!!!!

WAY cool, Jarred!!!!!


Reading on we learn that--

Teachers hope as they, their students and parents adjust to new approaches to mathematics, students' affinity for the subject will grow.

Right. Good luck with that!

Then there's this:

"We're asking students to communicate their understanding," said Jim Carlson, a math teacher at Kamiakin High School in Kennewick. "That's what you need to do to be successful. You have to be able to communicate and to make connections."

I swear, these people are like Stepford wives.

Communicating!

Making Connections!

Robotically Intoning Various Assorted Gerunds that have nothing whatsoever to do with math!


So I'm thinking. If Success in the 21st Century is going to mean a whole lot of people running around Communicating and Making Connections, my best move is to head for the hills now.

Before I go, however, I'm going to take a moment to drop Ms. Bennett a note making a connection between Jarred's cool solution and the standard paper-and-pencil algorithm for multiplication. Seeing as how neither Ms. Bennet nor Jarred seem to have noticed.





Teachers trying to change the image of mathematics

update

aack!

It occurs to me that the reason Ms. Bennett did not make the connection between Jarred's cool solution and the paper-and-pencil algorithm is that Jarred may not know the paper-and-pencil algorithm, because Ms. Bennett may not have taught it.

I wonder.
keywords: making connections communicating 21st century future




comments...

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MathFluency 10 Sep 2005 - 01:30 CatherineJohnson

I spoke too soon, and I shouldn't be picking on teachers anyway, even when I've never met them and they're featured in news stories that make them sound dumb. (OK, probably especially not when they're quoted in news stories that make them sound dumb.)

Fourth-graders at Columbia Elementary School in Burbank increased their math scores by nearly 20 percentage points.

Fourth-grade teacher Erin Bennett said much of the growth is because of a new strategy called math fluency. Teachers give a short math assignment every night, and then go over it in class the next day. The assignments revisit the same concepts over and over again, to help children really get it.

I was wondering whether 'math fluency' could possibly mean actual math fluency, and it appears that it does. Here's what looks like a terrific short summary of math fluency and the 4 stages of learning over at Illinois Loop:

The second stage of learning is the fluency stage where the learner acquires the information at an automatic level.

[snip]

Research shows that to be fluent children should be able to accurately solve math facts at a rate of one per every 2 seconds. Naturally, if the child has poor fine motor skills or is younger, that has to be taken into account on any written timed test. One of the biggest teaching mistakes in math is when teachers don't stick with this part of instruction with children who have more difficulty. I'll give my son as an example. Not only was Justin one of the slowest learners of addition math facts I had ever worked with, but once he finally knew them he had absolutely no fluency. It could take him hours to complete 50 addition math fact problems. (I waited him out once.) Fortunately, his teacher wouldn't let him move on until he was fluent with them and I started to work with him on fluency every evening for ten minutes. Now many an educator would have said, "He has an attention deficit disorder and just doesn't have the attention span to do a timed math test." I was not willing to put this limitation on my son in second/third grade. To work on fluency, every night I set aside a time and gave him a sheet with all his addition math facts. I then set the timer and his goal was to complete one more problem than he had answered the night before. I think when he started he could answer 4 or 5 problems in the ten minutes. He literally progressed problem by problem. If he didn't beat his goal, we would practice saying the answers and then set the timer again. Fortunately once he could do the addition, the other facts came much easier. By fifth grade Justin was the fastest student to complete the once-a-year check-up math timed tests, and not only will he be studying algebra in eighth grade, but he can take any timed math achievement test and score around the 90th percentile. If we hadn't focused on the fluency, none of this would have been possible.

This directly contradicts the stated policy of TRAILBLAZERS, which is that math facts 'aren't gatekeepers.'

Good.


And notice: this mother brought her son to fluency in 10 minutes a night.

This is something I've been thinking about. So far, it seems to me that you don't have to put vast hours of time into homework, classwork, Saturday work, summer vacation work, and on and on and on in order to learn math.

It seems, based in what I've seen, that shorter bursts of effort repeated every day are incredibly effective. It's the consistency and the repetition that are the magic, at least some of the time (I've seen this with math facts specifically).

I'm hoping to find some research on this, but I'm not optimistic that 'efficiency' of learning has been an important focus of investigation. Most of us think of studying as work, and of work as good. I certainly do. The question of 'how little you can get away with' is uncomfortably close to the question of 'Will it be on the test?'

So I'm guessing we don't know too much about this. But we'll see.

update

Another very nice statement of the cognitive science supporting math fluency:

Grover Whitehurst, the Director of the Institute for Educational Sciences (IES), noted this research during the launch of the federal Math Summit in 2003: “Cognitive psychologists have discovered that humans have fixed limits on the attention and memory that can be used to solve problems. One way around these limits is to have certain components of a task become so routine and over-learned that they become automatic.” Whitehurst, 2003)

update

The Grover Whitehurst quote comes from a 'promotional white paper,' the kind of marketing document publishers and vendors are producing in response to NCLB's requirement (if that's the correct word) for research-based textbooks & teaching methods (and possibly before). In this case, the product being sold is a software program designed to help students achieve fluency with math facts.

I find these promotional materials incredibly helpful, so long as you bear in mind that they are not literature reviews; i.e., you're not going to hear the contravening evidence.

Just wanted you to know--

Here is the whole paper, which is almost certianly worth skimming. Research Foundation & Evidence of Effectiveness for FASTT Math (pdf file)


fuzzy math in WA state

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ClocksWithoutHands 10 Sep 2005 - 02:56 CarolynJohnston

This just in from Lamprey River, New Hampshire: kids will be learning a new way to tell time this year! This is a news article that parodies itself. From the article:

RAYMOND - Students at Lamprey River Elementary School will learn a new way to tell time this year, thanks to a math program called Everyday Math.

They will be learning to tell time from clocks that have no hands. At least the first time they spiral through telling time.

The research-based and classroom-tested program (which is also recommended by No Child Left Behind) will break with the traditional worksheet-centered approach and embrace a more hands-on strategy.

Except that the hands will actually be off. The clocks. At least to start.

Principal Jane Lacasse says that rather than teaching children basic computation facts, Everyday Math emphasizes concepts and making sure children understand why. The program is centered on a "spiraling curriculum," which means that instead of moving on to a new topic after the old topic has been completed, classroom teachers will keep coming back to topics that had already been studied and expanding on them.

Hence, we'll start in first grade with handless clocks, then add the hour hand, then the minute hand, then the second hand, and in fifth grade we'll take up money, starting with pennies.

For example, Lacasse said, in first grade, children might learn to tell time to the hour, while in second grade, when time-telling is revisited, they will learn to unravel the mystery of the clock to the quarter hour or to the minute.

"The mystery of the clock" used to be taught outright in first grade, didn't it? Never to be spiraled back to again? Why not just ditch the clock completely, send it the way of the slide rule? Telling time is so 20th century.

The school purchased Everyday Math from the McGraw-Hill Publishing Company, investing in new textbooks and workbooks (although assistant principal Dan LeGallo is quick to point out that "this is not a textbook program").

I'll bet they spent real money on those non-textbooks.

The school also had to retrain its personnel.

I'll bet they did! They had to train them to tell time from the handless clocks. Perhaps they told them that there were hands on the clocks that only the most virtuous people could see.

What on earth does it mean to be "recommended by No Child Left Behind"?

comments...

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WallStreetJournalSingaporeMath 10 Sep 2005 - 18:44 CatherineJohnson

I'm teaching my little Singapore Math class again this fall, in the Main Street School after-school program. Last year I had one blinding success, a boy who took to the Singapore bar models like a fish to water and decided, apparently as a direct result, that he liked math and wanted to do well in it. He was a Phase 3 kid, now boosted to Phase 4!

So I'm looking foward to it.

(The other kids all did great, too; I don't mean to draw negative comparisons. They just didn't experience major life epiphanies as a result of drawing bar models.)

I was revising my course writeup today, and had to go hunting for the WALL STREET JOURNAL article on Singapore math, which I apparently had neglected to post anywhere on the site. So here's the link.


Excerpts:

Singapore's curriculum was developed over the past few decades by math experts hired by the Ministry of Education, who continually interviewed math teachers to find out what works and where kids need help. The elementary textbooks cover only one-third of the topics typically found in U.S. textbooks, but the material is taught far more thoroughly. While rote learning plays a part, kids in Singapore also learn to use visual tools to understand abstract concepts.

Singapore math texts, for example, ask kids to draw bars and other diagrams to visualize problems -- a technique called "bar modeling." When this strategy is applied consistently over a number of years, children tend to be better able to break down complex problems and do rapid calculations in their head.

[snip]

The National Council of Teachers of Mathematics in the U.S. suggests that it might not be possible to copy what Singapore's done simply by importing its books. The success of its math program may have roots in Singapore's highly disciplined culture, where the entire community -- particularly parents -- expects kids to buckle down and work hard, argues the NCTM.

There's little doubt, though, that math teaching in America needs to be overhauled. Tuesday, Boston College will release a four-year global study that is expected to show the math gap with Asia remains. The college's last study, the 1999 Trends in International Mathematics and Science Study (TIMSS), ranked eighth-graders in Singapore the best in math, while U.S. kids came in 19th, just behind Latvia. American kids also fall further behind the longer they're in school; as fourth-graders, American kids ranked 7th on the 1995 study.

That decline has already had an impact on U.S. universities.

today's horror factoids:

• Among U.S. freshmen who plan to major in science or engineering, one in

five requires remedial math courses

• Enrollment by U.S. citizens or permanent residents in graduate science and engineering programs, meantime,

dropped 10 percent between 1994 and 2001. Enrollment of foreign students grew 35 percent.


another link to the WSJ article: As math skills slip, U.S. schools seek answers from Asia


key words: decline in U.S. engineering math and science enrollment

comments...

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MiddleSchoolPart5 10 Sep 2005 - 19:13 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

comments...

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MiddleSchoolBlog 10 Sep 2005 - 19:32 CatherineJohnson

You stumble across the most amazing things on the internet.....I've just landed on the blog of a Middle School teacher in Michigan whose district is dumping Connected Math for Glencoe PreAlgebra.

June 24, 2005 Our new math program is on order! I am so excited. A bit intimidated as well... I have NEVER taught using a text book primarily and I am not so keen on doing it either. I do think these books will better suit our population. We are going to Glencoe from Connected Math. I love so much about Connected - the higher level thinking skills are great but I have always doubted the effectiveness of it really giving my students the down and dirty skills they need to succeed, in high school math, and in life. I just don't see kids developing NUMBER SENSE anymore. I am hoping the more parent and kid friendly layout of the Glencoe books will help our MEAP scores rise. Our new superintendent really layed it out - if he buys the books, the SCORES MUST IMPROVE.... I understand his point.. I really do.. but kids are unpredicatble.

August 29, 2005 Another reason I am excited is our new math program. After 10 years of usingConnected Math, we have gone to a more traditional series, using GlencoeMath 2, Math 3 and Pre-Algebra (eventually Algebra) in a hopes to get moreof our high schoolers ready to take Calculus as seniors. While there wasmuch I loved about Connected, it was difficult for many of our students,parents were unhappy, and it did not meet our Michigan standardseffectively. I feel intrepid [sic] about following a text since I have alwayspretty much winged my way through the year, with my classes workingprimarily on project based learning experiences. But with this newcurriculum/text, I will be expected to adhere more to the "norm".

The Middleweb has a list of several middle school blogs, including at least 3 from math teachers (one of them a 7/8 Math Teacher at the American Community School in the United Arab Emirates).

update

I was just looking at these entries again, and the language struck me: I have always doubted the effectiveness of [Connected Math] really giving my students thedown and dirty skills they need to succeed, in high school math, and in life.

I'm used to seeing math 'skills' equated with, say, handwriting skills: low level, but undeniably useful on occasion.

I haven't seen the ability to multiply, divide & remember one's math facts characterized as down & dirty.

The ed schools have a lot to answer for.


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





comments...

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MiddleSchoolPart6 10 Sep 2005 - 23:04 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

comments...

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MiddleSchoolPart7 10 Sep 2005 - 23:25 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

comments...

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PaulosBooks 11 Sep 2005 - 03:31 CarolynJohnston

I went to the library today, among other things to look up a book I've been curious about reading -- Innumeracy, by John Allen Paulos. They didn't have it, and instead I ended up picking up another similar book by the same author, A Mathematician Reads the Newspaper.

I was wondering if anyone had read either of these books? There are 26 reader reviews of "A Mathematician Reads the Newspaper"; some love it, and some do not. I get the impression that a lot of it covers the same ground as books like "How to Lie With Statistics", and "Lies, Damned Lies and Statistics", not to mention "Innumeracy" by the same author.

By the way, if you enjoyed Richard Feynman's "Surely You're Joking" book, try Adventures of a Mathematician, by Stanislaw Ulam. Ulam's book was published well before Feynman's, and he was also in Los Alamos for the Manhattan Project; the first description I ever read of Feynman picking the locks at Los Alamos was from Ulam. I read it when I was young and impressionable, and it left me with the attitude that being a mathematician is Really Cool (thereby, no doubt, sealing my subsequent fate).

Coda

There is also a website called innumeracy.com (it's unrelated to John Allen Paulos). It bills itself as a collection of links to articles and sites pertaining to numeracy and critical thinking. I haven't checked it out (it's rather disorganized) but there were a couple of very interesting-sounding articles linked on it.


books by Paulos
book rec: What the Numbers Say
false positives & Bayesian statistics

comments...

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BookRecommendation 11 Sep 2005 - 14:45 CatherineJohnson

V doesn't think too much of John Allen Paulos's Innumeracy, which got me to thinking: I don't believe I've ever read, all the way through, an entire book devoted to debunking the misconceptions of the American Reading Public. (Or even the American Writing Public, for that matter; I can't get throuh entire books on the many grievous errors committed by the press.)

And now that I think about it a bit more, there's a reason for that. It's a waste of time.

I don't need a mathematician to tell me most people don't understand math. I'm aware most people don't understand math; I don't understand math myself.

I need a mathematician to help me join the tiny group of people who do understand math.

So it looks like I'll be reading every last page of a fantastic book published just last year: What the Numbers Say : A Field Guide to Mastering Our Numerical World by Derrick Niederman, David Boyum. Check out the reviews on Amazon. 6 5-star reviews (including one by Arnold Kling) and 1 4-star review.

It's wonderful.


I've been planning to put up some posts about the FIELD GUIDE. Here's a link to the one I wrote a few weeks ago on false positives.








books by Paulos
book rec: What the Numbers Say
false positives & Bayesian statistics

comments...

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ShangriLa 11 Sep 2005 - 15:39 CatherineJohnson

Go read about the Shangri-La diet right now!

I have reason to believe it probably works as described, but there's no time to say why, because we are off to the U.S. Open!


Christopher, Jimmy, & I are going to drink some olive oil before we leave.

update

The Open was grand. So fun.

However, and this is a NOTE OF CAUTION, a soup spoon of olive oil, an empty stomach, and a long stop-and-go car trip to the Queens are a mistake.

Fat Politics

The Freakonomics web site & blog have all kinds of fun supporting material for the Shangri-La Diet. It's worth taking a look no matter what your weight, because the diet was created by a Berkeley psychologist who has spent a lifetime conducting experiments on himself. Not only has he lost 40 pounds & kept them off, he cured his insomnia and his depression to boot. Here's his paper:

Surprises from self-experimentation: Sleep, mood, and weight
Seth Roberts, University of California, Berkeley.

I'm especially looking forward to Fat Politics: The Real Story behind America's Obesity Epidemic by J. Eric Oliver, also linked to by the site:

In Fat Politics, Eric Oliver unearths the real story behind America's "obesity epidemic." Oliver shows how a handful of doctors, government bureaucrats, and health researchers, with financial backing from the drug and weight-loss industry, have campaigned to misclassify more than sixty million Americans as "overweight," to inflate the health risks of being fat, and to promote the idea that obesity is a killer disease. In reviewing the scientific evidence, Oliver shows there is little proof either that obesity causes so many diseases and deaths or that losing weight makes people any healthier. Our concern with obesity is fueled more by social prejudice, bureaucratic politics, and industry profit than by scientific fact.

Such misinformation, Oliver argues, is the true problem with obesity in America. By telling us we need to be thin, the proponents of the "obesity epidemic" are pushing millions of Americans towards dangerous surgeries, crash diets, and harmful diet drugs. Oliver goes on to examine the surprising reasons why we hate fatness and why we are gaining weight, and also the real threats to our health that are being displaced by our fat obsession.

I'm not even going to bother reserving judgment about the Shangri-La diet; I'm just going to dive in and believe Roberts' findings without reservation. Not to go out on a limb here, but I've always thought the whole Fat Police thing was a crock. Whenever you see every feature writer in America fervently agreeing on the horrors of X, the horrors of X invariably turn out to be cr**. Of course, that's my Scots-Irish talking.

If it's not Scottish, it's cr**!.

update update

Speaking of the Scots Irish, I hooted when I read Why don't the Irish like us? What have we ever done to them? at Chase me ladies, I'm in the cavalry.

(btw, Chase me ladies is one of my favorite blogs, but I haven't posted a link to it because I hope Kitchen Table Math will have kids reading Math Help pages soon, and Cavalry has lots of bad words and stuff about sex. So consider yourself warned.)

The Shangri-La Diet at Amazon
Seth Roberts website

Shangri La diet in freakonomics
Shangri La diet part 2
early adopter
diet, evolution of the brain, & McDonalds