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MathInSalinaKansas 23 Jun 2006 - 13:28 CarolynJohnston

From a forum I sometimes visit, I followed a link today to an urban legends website with a page on an internet claim about an 8th grade final exam supposedly given in Salina, Kansas, in 1895. Here are a few of the test questions in the arithmetic section:

Arithmetic (Time, 1.25 hours) 1. Name and define the Fundamental Rules of Arithmetic. 2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How many bushels of wheat will it hold? 3. If a load of wheat weighs 3942 lbs., what is it worth at 50 cts. per bu., deducting 1050 lbs. for tare? 4. District No. 33 has a valuation of $35,000. What is the necessary levy to carry on a school seven months at $50 per month, and have $104 for incidentals? 5. Find cost of 6720 lbs. coal at $6.00 per ton. 6. Find the interest of $512.60 for 8 months and 18 days at 7 percent. 7. What is the cost of 40 boards 12 inches wide and 16 ft. long at $20.00 per in? 8. Find bank discount on $300 for 90 days (no grace) at 10 percent. 9. What is the cost of a square farm at $15 per acre, the distance around which is 640 rods? 10. Write a Bank Check, a Promissory Note, and a Receipt.

When I looked at the Urban Legends page about this 1895 test I found that, contrary to my expectation, they weren't debunking the claim that it was a genuine final test from 1895. They were taking issue with the claim that it showed that educational standards had fallen since 1895:

What nearly all these pundits fail to grasp is "I can't answer these questions" is not the same thing as "These questions demonstrate that students in earlier days were better educated than today's students." Just about any test looks difficult to those who haven't recently been steeped in the material it covers. If a 40-year-old can't score as well on a geography test as a high school student who just spent several weeks memorizing the names of all the rivers in South America in preparation for an exam, that doesn't mean the 40-year-old's education was woefully deficient -- it means he simply didn't retain information for which he had no use, no matter how thoroughly it was drilled into his brain through rote memory some twenty-odd years earlier.

Lame, lame, lame. If you can't prove that this is not an authentic graduate exam from 1895, then complaining about it just makes you sound like a whiner (and notice the dig about 'rote memory' -- memorization is in very bad odor these days).

Besides, it's not about us (and what we retained) anymore: it's about our kids. And I am afraid it does imply that we've dumbed down the junior high curriculum. Only a tiny minority of kids graduating 8th grade these days could handle sophisticated word problems like these, even if we gave them the bushel-conversion formulas for free. Apart from the emphasis on farming applications, which is kind of funny and endearing, the application area of problems 6 and 8 (just for an example) is as alive, or more so, in 2005 as it was in 1895, and we simply do not teach it. In the late 1980s, I taught an elective course at LSU on the material covered in these problems. The entering students were completely ignorant of that material, mastery of which I claim is necessary to living adult life competently (and they were very glad to finally learn it, too). Many students who were stronger mathematically, and didn't take that elective math course, are no doubt still ignorant of it, because it is not taught in public schools anymore.

The second thing that leaps out at me is that these are mostly application problems -- word problems -- not problems testing either basic computation or deep understanding of the beauty of mathematics (with the exception of problem 1). It was just assumed that these kids could do the computations necessary to solve these problems, without calculators. What they needed to do was to solve those problems, and get the right answer, and that hasn't changed a bit. And I'll bet there was no partial credit given for having the right idea, either.

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MathInSalinaKansasPart2 23 Jun 2006 - 13:28 CatherineJohnson

re: MathInSalinaKansas

Wow.

I spoke yesterday to a mathematics professor at a university here in New York state.

When I asked him what level of mathematical knowledge entering freshmen bring to their course work, he said, "We can't assume that a student knows anything we would want him to know."

Specifically, his students can't do algebra.

They can't set up a two-variable word problem and solve it.

These are college freshmen.

Posted on May 07, 2005 @ 11:21

MathInSalinaKansasPart3 23 Jun 2006 - 13:28 CatherineJohnson

re: MathInSalinaKansas

Three sample problems from the PRAXIS 1 Content Assessment college students entering the field of education are frequently required to take:

1. Which of the following is equal to a quarter of a million? a) 40,000 b) 250,000 c) 2,500,000 d) 1/4,000,000 e) 4/1,000,000 2. Which of the following fractions is least? a) 11/10 b) 99/100 c) 25/24 d) 3/2 e) 501/500 3. Which of the sales commissions shown below is greatest? a) 1% of $1,000 b) 10% of $200 c) 12.5% of $100 d) 15% of $100 e) 25% of $40 The Educational Testing Service (ETS) describes these problems thus:

The Pre-Professional Skills Test in Mathematics measures those mathematical skills and concepts that an educated adult might need. It focuses on the key concepts of mathematics and on the ability to solve problems and to reason in a quantitative context. Many of the problems require the integration of multiple skills to achieve a solution. [snip] Computation is held to a minimum, and few technical words are used. Terms such as area, perimeter, ratio, integer, factor, and prime number are used, because it is assumed that these are commonly encountered in the mathematics all examinees have studied. Figures are drawn as accurately as possible and lie in a plane unless otherwise noted.

TERC (Grade 5, “Suitable for Grade 6”, too)

Number of students in your class ____________

Suppose you get 6 cents for each bottle you return for recycling. For each problem show how you found your solution.

1. You have collected 149 bottles. How much will you earn?
2. If you share what you earn with one friend, how much will each person get?
3. If you share what you earn with two friends, how much will each person get?
4. Find the fairest way to share what you have earned with everyone in our class, so there is no money left over. How much will each person get?

Singapore (Workbook Grade 5B)

24. Adam bought 8 note pads at $1.45 each and 10 towels. He gave the cashier $100 and received $46 change. Find the cost of a towel.
25. A group of children went swimming. 3/8 of them were girls. If there were 40 boys, how many children were there altogether?
26. Three boys, Juan, Seth and Jared shared a number of stamps in the ratio 3:5:7. If Seth received 45 stamps, how many more stamps did Jared receive than Juan?

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CompareAndContrastPart6 10 Oct 2006 - 01:53 CatherineJohnson

math facts in Singapore, grade 3:

Studying Exhibit 3 in the big Singapore Math Report (pdf file), we learn that:

Singapore students master multiplication tables up to 10 x 10 in grade 3

math facts in Math Trailblazers, grade 5:

To be honest, it's difficult to say what, precisely, the MATH TRAILBLAZERS schedule actually is. It seems to vary from one document to another.

I did find this TRAILBLAZERS playlet on page 260 of the 5th grade TIMS Tutor: Math Facts (pdf file).

Suzanne: But the facts with nines are harder. I have to think about them, but I use the tens to make them easier.
Teacher: How, Suzanne?
Suzanne: Well, when I see 15 – 9, I think, “What do I need to get from 9 to 15?” I use counting up: from 9 to 10 is 1 and from 10 to 15 is five more. So, I get 6.

That's 5th grade, folks.

update 11-2005

I talked to a friend whose son is in second grade. He's a brainy kid who loves math, but he can't use the addition algorithm. Apparently, the algorithm hasn't been taught. If he's adding numbers smaller than 20, he counts on his fingers and toes. If the numbers are larger than 20, say 12 + 19, he draws 12 circles, then 19 circles, and finally counts them. Same process for subtraction, only in reverse. 63 - 19 means drawing 63 circles, then crossing out 19 of them.

The kids have the triangular flash cards that portray number families, and her son is working on flashcards with numbers 1 - 10. A friend of hers whose child is in 3rd grade told her the children in her child's class are working on the exact same cards.

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HayBalerProblemFromIMP 25 Jul 2005 - 19:13 CatherineJohnson

I've just this moment noticed the 'hay baler problem' Barry posted on his page.

Here's a problem that appears in IMP for 9th grade It is known as the "Haybaler Problem"
“You have five bales of hay. For some reason, instead of being weighed individually, they were weighed in all possible combinations of two: bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, bales 2 and 3, bales 2 and 4 and so on. The weights of each of these combinations were written down and arranged in numerical order, without keeping track of which weight matched which pair of bales. The weights in kilograms were 80, 82, 83, 84, 85, 86, 87, 88, 90 and 91. Find out how much each bale weighs. In particular, you should determine if there is more than one possible set of weights, and explain how you know.”
David Klein, a mathematics professor at California State University at Northridge comments on the problem. “The process of solving this problem made me resentful of the stupidity and pointlessness of it. There is nothing ‘real world’ about it. It is completely inappropriate for kids who likely have not been taught how to solve simultaneous linear equations, or exposed at most to two equations in two unknowns. If I had been given such problems at that age, I think that I would have hated math.”
Consistent with much of the philosophy of “real life math”, the goal of the exercise is to explore strategies and to be able to write about it. This is made apparent by the “student guide” that accompanies the problem. It is essentially a scoring sheet, containing categories, with points awarded for each, such as “Restate the problem in your own words” (4 points); describe all the methods you tried before reaching your solution(s) (4 points); describe the process that lead to your solution(s) (4 points); describe all assistance provided and how it helped you (2 points); state the solution (2 points); describe why your solution(s) is correct, include all supporting data (6 points). Out of a total of 50 points, only 2 are given for the solution. In fact more points are given for describing why the solution is correct.

It's unbelievable.

You really do have to see this stuff in the flesh to know what our kids are up against.

On the other hand, I'd bet money there are no more than 5 teachers on the planet willing to use the IMP grading rubric, (pdf file) if that.

I've been a teacher myself; I've used grading rubrics (teaching freshman rhetoric at the University of Iowa).

The IMP rubric asks the teacher to use 18 separate categories for a total of 50 points to score one problem.

Unless the NCTM is now allowed to send federal auditors into the classroom (which is pretty much what we've got in Manhattan at this point) that's not going to happen.

Students can earn a grand total of 2 points, out of 50, for the right answer.

No teacher's going to go along with that.

update

Check out the IMP web site.

"IMP™ Receives Award from the U.S. Department of Education"

Here's the Mathematically Correct review. (pdf file)

CompareAndContrastPart7 09 Jul 2005 - 13:29 CatherineJohnson

caveat

There are lies, damned lies, and statistics....so perhaps it's impossible to say, precisely, what international comparisons on mathematics examinations mean. I don't know.

Nevertheless, care & thought have gone into testing equivalent populations, & everyone takes the same test.

Take one look at the problems 6th grade Singaporean or Russian kids are doing, and you don't need advanced statistical theory to tell you who's ahead.

US world ranking

From this morning's NYTimes Book Review:

China, India, Japan and Europe all churn out more science and engineering degrees than we do. Worse -- and downright embarrassing -- is the state of American education. Globally, our 12th-graders rank only in the 10th percentile in math (that's 10th percentile, not 10th). Our students also rank first in their assessment of their own performance: we're not only poorly prepared, we have delusions of grandeur.

item from SAT math test

There are 20 packages of bagels on a shelf in a store and each package contains the same number of bagels. If 3 of these packages contain a total of 18 bagels, how many bagels are there in 7 of these packages?
(A) 21 (B) 36 (C) 40 (D) 42 (E) 49

I just asked Christopher (age 10) to do this problem. He did it in his head, while simultaneously plotting out his eBay bid for an Extreme Worldwide Wrestling cage that normally costs $35, and he muffed it the first time. ('Is it 6/7?' 'NO!')

When I told him, Christopher, look at the problem, he got it in a couple of seconds.

He's 10.

This is ridiculous.

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FirstPerson 13 Jul 2005 - 22:05 CatherineJohnson

I mentioned earlier that I talked to my cousin last night, discovering in the middle of our conversation that her daughter's school adopted Chicago Math 10 years ago.

Here's the first part of my impromptu interview with her, which she said I could post:

how Everyday Math came to my cousin’s town
The 2nd grade teachers had a grant and were very excited. I think the teachers were turned on by the program. So they started introducing it in the 1st grade.
Nobody else liked it. I hated it, and many parents complained.
Teachers in the upper grades didn’t like it, either. The district was always having these huge teacher-board meetings to convince the other teachers that they had to adopt it, too.
Eventually, when the grade school kids got to high school, the high school teachers were in horror because the kids coming in couldn’t calculate. They complained that the Chicago Math students had to spend all this time guesstimating and figuring out what the answer was to one small step inside a complex problem. [Everyday Math was developed by the University of Chicago. Everyone in my cousin’s town in MA called it ‘Chicago Math.’] The students were too slow; they were hung up on the basics.
This war went on for a decade. I don’t know how it came out. I do know that for at least the first couple of years after Chicago Math came in they were not getting lots of kids proficient on the state tests. I’ll ask my friend who teaches at the high school whether they’re still using the books. She had 3 kids who went through the system, and she hated Chicago Math.

part 2: easier for mathematically talented kids?
One of my daughter’s friends had a very easy time with it, and was successful at it. She really soaked it up. Someone told me that kids who are chronologically older and have math talent, maybe they respond to it better. My daughter was the youngest in the class.
My older daughter, though, had a babysitter who had Chicago Math at New Trier when we were living on the North Shore. She said it was a failure. The New Trier students were the first guinea pigs, because it was Chicago Math. She said Chicago Math came from a bunch of ivory tower people figuring the whole thing out and then trying to disseminate it to all these little children.

part 3: developmentally inappropriate

I once told the assistant principal that in the Saxon book, when you’ve done something wrong you go back. You can’t advance until you get it right. I said that’s what I like about the Saxon program.
He said, “Well children can do that with Chicago Math, too.’ He was suggesting that my daughter had the ability to assess herself in Chicago Math, and that’s what she should have done. She was a little adult who could self-assess.
But she couldn’t. She was too young, and she didn’t know enough about math to be able to assess how much she knew about math.
It’s like driving. When you know how to drive, driving is built into your thinking process.
If you don’t know how to drive, you’re not going to have the confidence to figure out what your problem is. If you can’t get from one corner to the next, you’re not in a position to assess why not.

part 4: spiralling
Chicago Math gives you advanced math problems sprinkled in with the elementary math your child is learning. They slip it in.
They would have you guess at the answers for the advanced problems, but then they never gave you the answers so you didn’t know if you guessed right or not. You’re always a work in progress with Chicago Math. So you never get a definite answer. And you never had a sense of completion or success on a day-to-day basis.
But my pet peeve was that it sped you along at a rapid pace and you never mastered the material that you left the page before. When my daughter was in the 2nd grade one work page would be coins; the next day you’d be dealing with weather; the next day you’d be dealing with problem solving. My daughter had no sense of what a quarter or a dime was.
When I was taught math, each day you built on what you knew. When you did the coins you learned a penny, a nickel, a quarter. You kept going. Telling time, same thing. You work on time until you get it. You don’t just have a flash of it one day.
In Chicago Math you had one page on one topic, then you went on to something completely different on the next page. There was no repetition. It was irresponsible, very ungrounded.

part 5: frustrating
They would want my daughter to guesstimate whether something was 50 or not, or 100 or not. And they wanted her to do that before she knew 25 and 25 was 50, before she knew what the building blocks that made a number were. It’s hard to estimate something before you know that numbers are created.
To guesstimate is so frustrating. Math has a yes or no answer. And with math, when you go 5 x 7, it’s 35. That’s the answer. Children at a young age want to have something concrete. They learn from ‘This is wrong’ and ‘This is right.’ They like getting the right answer.
In Chicago Math, children don’t get that reward.

demoralizing
First they give you an intuitive flash that of material that is above your level, that you aren’t successful at. It’s like a prelude.
The thinking is that when you get to the material for real, you’ve had a prelude. But on a day-to-day basis if you’re always getting preludes, the child never has a sense of completion or success.
There was never a sense of mastery; there was never a sense of completing a task successfully before moving on to the new material that you were supposed to pick up intuitively.
Chicago Math was like trying to learn a foreign language by hearing tapes every day and intuiting what the words mean. Then 3 months later you’re supposed to know what the tapes are saying.

boring
It was too abstract and theoretical and boring. It’s boring when you don’t have the light bulb go off in your mind because, ‘Oh! I got it right!’
The best you could think was, ‘Well, maybe I got it right.
I think it’s crippling.

Saxon Math
I moved my daughter to private school after 4th grade. She’s worked with the Saxon Math books ever since.
It took her awhile to get to a stable place in math because she had gaps in her knowledge, and because she didn’t have confidence in the basics. She learned new concepts; she could understand them. But under testing she would crumble, because she didn’t have confidence.
In Chicago Math, computation doesn’t become second nature. I guess in new math they teach you all these steps you have to take. They make multiplication into 5 steps. Chicago Math makes learning to multiply real slow, and so damn confusing.
So she was bogged down in trying to do it in the new math way. It took her several years to overcome that, to get solid in the basics.
She improved greatly with the Saxon book. She’s doing fine at the high school level. She just finished 9th grade, and she does well in math now.

why do kids like math?

JapaneseMiddleSchoolEntranceExam 13 Nov 2005 - 14:47 CatherineJohnson

Anne just asked about a bliki post or an article comparing a Japanese to an American assessment test showing a 3-year gap between there & here.

I don't think we've had a post on this exact topic, but I do have the URL for a set of sample problems on the Japanese middle school entrance exam.

You can also download or purchase a CD of these problems:

The story problems provided in the software "World Math Challenge Volume 1" are translated from Japan's Junior High School math placement test. This test is given to 12 year olds and each section of the full test consists of 225 story problems. Students are given a time limit for each problem ranging from 1 to 5 minutes. If completed within the time provided, the 225 story problems require over 8 hours to complete.
The problems are logic-based and consist of about 20 different types of story problems. The point of this site is to begin providing quality math content based on Japanese (maybe a world) standards. The Japanese continue to place among the top 3 countries world-wide in terms of their students' math abilities. The US was recently ranked #14 in international math placement among the industrial nations. We think that US students should be exposed to international level math content and this site may represents the first step.

Constructivists have claimed that TIMSS video studies of Japanese math classes show them using constructivist pedagogy.

This claim has been rebutted by Alan Siegel of the Courant Institute of Mathematical Science at NYU in Telling Lessons from the TIMSS Videotape: remarkable teaching practices as recorded from eighth-grade mathematics classes in Japan, Germany and the US (pdf file)

The fact that Japanese 12-year olds are given timed math tests tells me that Japanese schools do not subscribe to constructivist doctrine.

Japanese-online
Free registration required to view assessment problems.

sample problems from Japanese middle school assessment test

Q1 How many 'C' balls does it take to balance one 'A' ball? (2 minutes)

Q2 Jenny wanted to purchase 2 dozen pencils and a pen. Those items cost $8.45 and she did not have enough money. So she decided to purchase 8 fewer pencils and paid $6.05. How much was a pen? (2 minutes)

Q3 Hose A takes 45 minutes to fill the bucket with water. Hose B can do the same in 30 minutes. If you use both hoses, how long will it take to fill the bucket? (1 minute)

Q4 A job takes 30 days to complete by 8 people. How long will the job take when it is done by 20 people? 2 minutes

Look at these time limits.

A 1-minute limit doesn't give you a lot of time to guess and check.

International Red Cross Symbol for Guess and Check

NAEP's "hard" 8th grade problems are Singapore's 5th grade problems

....my own school district – Montgomery County, Maryland – is one of the most affluent, highly educated counties in America, yet our gifted students scored at the level of Singapore’s average student. NAEP classifies its problems as “easy,” “medium,” or “hard.” I benchmarked the “hard” 8th grade problems, examining NAEP’s highest level of expectation for 8th grade math. Most of these “hard” 8th grade problems are at the level of Singapore’s grade 5 – or lower.
[snip]

8th grade problem, NAEP
Consider: In one problem, for example, the student is shown a “Lunch Menu” with items like Onion Soup for $.80 and Ice Cream for $1.10. The question asks: “What is the total cost of Soup of the Day, Beefburger with Fries, and Cola?”
This is considered a “hard” eighth grade problem.

3rd grade problems, Singapore
But Singapore has harder problems than this in grade 3....

1 ) 5 oranges cost $2.25. What is the cost of 12 oranges? ________
2 ) I want to buy a calculator for $29.70 and a watch for $32.00. I have $28.50. How much more money do I need?

(1) $26.20
(2) $30.80
(3) $33.20
(4) $32.70

Both of these are two-step math problems. They illustrate Singapore’s expectation that all children should acquire mastery of the math skills needed for algebra and beyond. NAEP’s expectation is that children need to be able to order take-out from McDonald’s.

Testimony of John Hoven On Behalf of The Center for Education Reform At the National Public Forum on the Draft 2004 Mathematics Framework
(pdf file)

TeacherTrainingInChina 25 Jul 2005 - 00:06 CarolynJohnston

SusanS wrote the following post about teacher training and education on the Martin Gross thread, and it's got me so intensely curious now about the Chinese school system that I've decided to break it off and give it its own thread.
The Chinese system of teacher training and development has garnered a lot of interest because of Liping Ma's incredible book, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. The Chinese teachers whup us in understanding and pedagogy, of course, but it's the details of how they whup us, and what they do differently, that are fascinating.
I've long thought that what lies at the base of the difference in "teacher culture" is the difference in our cultures themselves. It appears to me that Chinese elementary math teachers are respected specialists, for one thing. Compare that with teaching in the United States, where teachers are anything but respected (as the Martin Gross column proves).

Here' s Susan's post:

Okay, back from the web... I found an interesting straightforward article concerning China.

"There are three main educational aims for elementary schools in China today. The first is to develop the students moral character by teaching them to love the motherland, the Chinese people, manual labor, socialism and the Chinese Communist Party, and public property. The second goal is to enable students to obtain a fundamental education, develop skills in reading, writing and science, possess social knowledge and cultivate good study habits. The third goal is to enable students to develop physically. At least one hour a day students are required to perform some type of physical exercise."
"Originally, the duration of general middle schools was five years, but now in many places this has been changed to six years. The six years are divided into two levels: junior middle school and senior middle school. There are over 162,000 middle schools in China with over 65,400,000 students, more than sixty times higher than the number in 1949."
(This is kind of interesting....)
"Professional middle schools train middle level personnel for various vocations. Students entering these schools are required to have graduated from junior middle school and have some professional knowledge in a special area. The duration of these schools is from three to four years. Because all professional schools were closed during the Cultural Revolution some students entering these schools now have already graduated from senior middle schools and are completing the professional program in two years."
"There are seven types of professional middle schools: technical, agricultural, forestry, medical, financial and economic, physical education, and art. There are more than 1700 professional schools in China with more than 500,000 students enrolled."
"Teacher training schools are included in these schools. Students are drawn from senior middle school graduates and complete their training in three years. Tuition is free. Elementary school tuition is five yuan a year, middle school is 10 yuan a year. There are over 1,046 teacher training schools in China with an enrollment of more than 360,000 students (29% women)."

http://www.yale.edu/ynhti/curriculum/units/1982/4/82.04.02.x.html
I'm not certain of the validity of the source, but it's a place to start. I do believe that we can learn a lot from the Chinese and the Liping Ma book is absolutely a great book for any parent or teacher. But there are obviously some things that we probably can't do on any official level.

For me, this view into what's going on behind the scenes in the Liping Ma book (and I always had the feeling it was something very different from what goes on here) raises more questions than it answers.

I have no clue what 'middle school' would be the equivalent of in the US or Europe. It sounds like it might be a technical college, or what would once have been called 'Normal School'? (My grandmother, who like many intellectual women of her generation taught school, was educated at a Normal School, and it was a good education).

And are public schools for children called 'elementary schools', all the way through what we would call high school?

And why is there tuition for elementary school and not professional training schools?

And now I wonder whether people are tracked into professions by the government, or are free to choose what they want to do?

Susan raises an excellent point here. What exactly can we do -- what would we really be willing to do -- to have a teaching culture that is more like China's?

Susan S on teacher training in China
how Chinese teachers learn math
teacher release time & Liping Ma & Elaine McEwan's Princepal's Guide

ChineseTeachersPart2 19 Jul 2005 - 22:55 CatherineJohnson

From Liping Ma, on the education of Chinese teachers:

…the U.S. teachers behaved more like laypeople, while the Chinese teachers behaved more like mathematicians…
Obviously, these teachers are not mathematicians. Most of them have not even been exposed to any branch of mathematics other than elementary algebra and elementary geometry. However, they tend to think rigorously, tend to use mathematical terms to discuss a topic, and tend to justify their opinions with mathematical arguments. All these features contributed to the mathematical eloquence of the Chinese teachers.

We're talking pedagogical content knowledge, folks.

Chinese teachers acquire pedagogical content knowledge on the job:

they engage in intensive study of their students' textbooks

they study the textbooks together in teaching research groups, or jiaoyanzu

Susan S on teacher training in China
how Chinese teachers learn math
teacher release time & Liping Ma & Elaine McEwan's Princepal's Guide

MathsInEngland 26 Jul 2005 - 17:10 CatherineJohnson

I have no idea how I got to this link, so can't give credit....

Maths in England sounds even worse than here, if that's possible, which I suppose it isn't:

Lost count of gloomy reports about the state of maths in schools and universities? For more than a decade mathematicians have been moaning and the government has responded with inquiries, changes in the curriculum, numeracy hours in primary schools, golden hellos for maths teachers and a plethora of other initiatives in England.

Golden hellos, you say. Sounds good to me. Think I'll knock off here and go learn some more Russian Math. Which is an especially good idea given the paragraphs that follow:

Where will the next generation of UK mathematicians come from, asks the group, drawn from university maths departments around the country, learned societies and the government's curriculum watchdog.
At the moment the answer seems to be "from Russia and Hungary". In many university maths departments nine out of 10 of appointments go to candidates from abroad, while the shortage of maths teachers in schools has got so bad that the Department for Education and Skills has stopped collecting the figures.

Oh, boy. This next part jibes unpleasantly with Loveless's report on the importance of ability tracking for the most talented students:

There is also agreement on the need - outlined by Adrian Smith's report Making Mathematics Count - to boost the numbers of pupils taking A-level maths, the pool from which science graduates (and future maths teachers) will come. Maths has gone from the largest A-level entry to third place as numbers have dropped by nearly half from 80,000 in 1989 to 49,000 in 2002.
A curriculum for the most able 25% of pupils is needed to encourage them to progress to A-level, says the report, which also suggests awarding more university admissions points for a maths A-level than other subjects.
Dr Gardiner wants a national debate. He argues that in the last 15 years or so, "much of our mathematics teaching, and most of our assessment at all levels, have become fragmented - with multistep tasks being routinely reduced to (and assessed as) a collection of unrelated 'one-step routines'".
The upshot, he says, is that maths undergraduates cannot solve the kind of problems that 13-year-olds used to be expected to do.
He adds: "Students in general are no longer required to combine simple techniques in the most basic ways - so they no longer understand that the power of elementary mathematics lies in the integration of simple techniques into larger wholes.

This is an interesting assessment of the problem, in terms of Saxon Math versus Singapore Math.

From the get-go--and I mean from the 1st or 2nd grade--the Singapore curriculum (the old one, at any rate) asks children to do multi-step problems. That strikes me as the right way to go, but of course I can't base such judgments on anything more than what I think I see in Christopher & me as we learn math.

Nevertheless, the one aspect of Saxon Math that makes me feel chronically nervous is the one-stepness of the word problems. Christopher and I are now working through Saxon 8/7, which is in theory a 7th grade book, and the word problems are either one-step, or they're two-step problems that we're told upfront are two steps. That can't be right.

otoh, I had a fun moment the other day when Christopher, who is, after all, still only 10 years old, solved a problem (probably in the Primary Mathematics 3A Workbook) and then tossed off the comment, 'It's a two-parter,' like some guy in a bar casually mentioning he just wrestled a bear. He thought he was hot stuff, doing a two-parter.

I loved it. Macho in a 10 year old boy--especially macho about a story problem--is awfully sweet. (OK, maybe that's a mother's perspective.)

Still, if he gets manly I-wrestled-a-bear-feelings from doing maths, I say that's a good thing.

update

I just realized: I am supplementing the Saxon 7th grade book with a first semester 3rd grade book for Singapore.

I should say that the 3A problems are now far too easy for Christopher, thank heavens (although the bar model solutions are not too easy. He still can't fully do them. He'll get the bar model wrong for a problem he can do in a second just setting up the problem and doing the computation.)

However, I've worked all the problems in the Challenging Word Problems Grade 3 book, and I know there are problems in there he's not going to be able to do.

maths in England
maths in England, part 2
more maths in England, part 2
top students in England, US, & Singapore
why do kids like math?
another brilliant person who liked getting right answers (scroll down)
Catherine's cousin talks about Everyday Math

Call for national debate on maths teaching GUARDIAN
Where will the next generation of UK mathematicians come from? (GOVT REPORT: pdf file)

MathsInEnglandPart2 27 Jul 2005 - 13:45 CatherineJohnson

I just glanced at the British maths report, Where will the next generation of UK mathematicians come from?, (pdf file) and I think I'm going to read the whole document. It reminds me very much of observations both Carolyn and Bernie have made to me, as well as Carolyn's post, Whither American Talent?.

Still, I'd never quite thought of the issue as a 'failure to reproduce,' as the report sees it. I'm not surprised Britain would be thinking of it this way, because of Europe's declining, or soon-to-decline population, which seems to me to have been covered fairly extensively in the European press.

They're right in framing matters this way. For countries and civilizations to grow and thrive, they must reproduce themselves biologically and culturally--which means, I think, that it's not a great idea to allow math talent to dwindle away, as it seems to be doing.

(fyi, I'm having a metacognitive moment here: I'm asking myself, Do I know, for a fact, that any of these statements are true? Answer: no.)

So I'm assuming these things are true, until I learn otherwise. Excerpts from the report:

The UK mathematics community now falls far short of “reproducing itself” – as evidenced by the dramatic fall in the number of students taking A level Mathematics and Further Mathematics; the declining number and quality of students entering highly numerate university courses; the lack of qualified mathematics teachers; the shortage of high quality IT specialists; the narrowness of the UK mathematics PhD; and the apparent need to import large numbers of research mathematicians.

The most urgent short-term action was identified in the Smith report – namely to increase markedly the number of students taking, and enjoying, a serious A level in mathematics.

However, this goal cannot be achieved by simply easing the apparent demands of A level mathematics. In any effective strategy for recovery two key elements must be

(i) to strengthen the foundations laid at KS3 and KS4 in a way that better nurtures the interest, and raises the aspirations, of more able students;

(ii) to devise a concerted programme of professional development to ensure that current mathematics teachers appreciate why these stronger foundations matter.

The present situation is far more serious than is generally admitted and needs to be addressed as a whole – since many of the most serious weaknesses arise from a failure to recognise, and to deal with, the interplay between the actions of different agencies.

update

Still reading....

The domestic UK supply of mathematically competent manpower is in such decline that in many areas (including teaching, commercial specialist requirements, post-doctoral fellows and appointments to academic positions) we are now dependent on trawling recruits from other countries for “bread-and-butter” appointments (not just for “key” personnel).

I love it!

Nobody can write like the Brits, nobody. They're unbelievable. (I have GOT to go TRAWLING on the UK ed web sites to find out exactly how they do what they do.)

Have you ever in your life seen a government report in the U.S. produce language like this?

The answer is no.

ok, problem spotted

There are serious shortcomings at the level of individual government departments and agencies. But our failure to nurture the home-grown talent we need has been exacerbated by a consistent failure to coordinate policy between different agencies.

They may write better than we do, but thus far the content is just as stupid.

Sorry.

That was harsh.

it gets worse

(i) We have failed to recognise that the effectiveness of curriculum and assessment change (which is the responsibility of QCA) depends on providing appropriate training and support (CPD) for teachers (whichis the responsibility of the DfES, the TTA and the Strategies).

(ii) We have not faced up to the conflicts between

(a) the official goal of improving the career structure for home-grown post-doctoral fellows (which was the apparent reason for increasing research funding as part of the Treasury’s response to the Roberts review);
(b) the effect of EU law (or its current interpretation) on the way the consequent substantial increase in EPSRC funding is being used;
(c) the local pressures on university departments which arise from this more generous EPSRC funding; and
(d) the effective pressures imposed by the HEFCE controlled research assessment exercise and EU employment law on university administrations and on academic appointment practices.

I take it back.

This is much dumber than the stuff we put out.

let me see if I've got this straight

Apparently, the problem with maths education in England is that there've been a number of government inquiries, followed by a number of government reforms, followed by no discernible improvement whatsoever.

How could that be?

These reports and the published government responses, have subsequently led to significant initiatives by government and its agencies. It would be comforting to conclude that “the nature of the problem has been understood and is being robustly tackled”.

And, apparently the reason nothing got better, was that the government inquiries didn't take the whole thing seriously enough:

....the rest of the introduction [of the DfES response to the Smith report] includes a succession of statements (such as that “achievement in mathematics at . . . KS3 is the highest it has ever been”), which indicate that the nature and seriousness of the problem have simply not been grasped (we give clear evidence of this relating to KS3 below). This negative impression is strengthened by such facts as that the flagship policy of establishing a “National Centre for Excellence in Mathematics Teaching” is being “implemented” with an emasculated budget.

OK, so here we have a close reading of the introduction to a response to a report. This thing is a report about the reports.

OK, why don't I just read ahead until I find some actual content.

I do like the scare quotes around the word 'implemented,' though.

this is interesting

....some of Smith’s recommendations (such as the need for a serious reduction in the proportion of mathematics time devoted to “data-handling”, and the urgent need to consider the introduction of “incentives” to increase numbers taking A level mathematics) have not been pursued in the way the mathematics and mathematics education communities had expected.

If I'm understandng this correctly, what we have here is an anti-Trailblazers moment.

Less data-handling.

The whole entire point of Trailblazers is all data-handling all the time; the curriculum was originally titled TIMS, for Teaching Integrated Mathematics and Science. It's just pure data, every step of the way.

Data and investigations.

this is good

The mathematical community constitutes an increasingly important “micro-culture” within modern society. Hence the different parts of this community need to be structured and sustained so that this micro-culture can “reproduce itself” in a routine and orderly way, passing on to the next generation that which is known to be of value, while at the same time facilitating the development and application of new methods and techniques to serve business, management and society in general. Instead the routine reproduction of mathematical culture in the UK has been allowed to decay.
[snip]
In the whole of the UK there were around 85 000 A level mathematics entries in 1989; 66 000 in 2001; and just 54 000 in 2002. This has led to a concomitant decline in the number of competent undergraduates and graduates in highly numerate disciplines, and hence to a shrinking of the basic “pool” from which competent workers in areas that increasingly require serious mathematical skills (including mathematics teachers) can subsequently be drawn.

This is so long I'm going to put the rest on a separate page.

More Maths In England Part 2

maths in England
maths in England, part 2
more maths in England, part 2
top students in England, US, & Singapore
why do kids like math?
another brilliant person who liked getting right answers (scroll down)
Catherine's cousin talks about Everyday Math

Call for national debate on maths teaching GUARDIAN
Where will the next generation of UK mathematicians come from? (GOVT REPORT: pdf file)

EnglandVsAmericaVsSingapore 13 Nov 2005 - 18:29 CatherineJohnson

The British report, Where will the next generation of UK mathematicians come from?, (pdf file) includes this passage about the TIMSS study (Trends in International Mathematics and Science Study):

[a score of] 625 was fixed as the “Advanced benchmark”. In the “Comparison group” of countries [essentially, all countries with advanced economies], 13% of 14 year olds scored at this higher level – which might be taken as a rough indication of those who are well-positioned to subsequently study mathematics and other highly numerate subjects with some prospect of success post-16, or at university.
Naturally some countries in the “Comparison group” had a larger percentage performing at or above this level, while some fared worse. A mere 7% of the USA sample scored at or above this ”Advanced benchmark” level. And the International average was just 6%. But the results for England should have struck Ministers and officials as far more disturbing: the percentage of English 14 year olds scoring above the “Advanced benchmark” was just 5%!

I found this confusing, because the report tosses around a number of figures:

5 to 10% of any population are 'GATE' (gifted and talented) in maths

the top 25% 'most able' of any population 'is likely to include most of those who have the potential ultimately to become competent workers in those areas that increasingly require serious mathematical skills – including mathematics teaching'

and, finally, students who score 625 or above on TIMSS and are deemed to be 'well-positioned' to study math &/or 'other highly numerate subjects' (e.g., economics) in college

My question was: if the U.S. had 7% of its students in this above-625 level, and the developed world's average was 13%, how bad is our 7%?

And what was Singapore's number?

Well, I just found it, or something close to. It's high.

Forty-six percent of Singapore’s students were among the top 10 percent of all test takers, five times the 9 percent of U.S. students. Even a Singaporean student in the bottom quartile of Singaporean students outperformed more than two-thirds of U.S. students (Mullis, et al., 2000). In 2003, Singapore’s eighth-grade students retained the top average score among student from 46 countries (Mullis, et al., 2004).

I still don't know how a score above 625 relates to the various percentiles being bandied about. I'm assuming students in the top 10% on TIMSS received scores above 625, but I don't know. If that's true, it looks like almost half of Singapore's students could succeed in college-level mathematics or 'other highly numerate subjects.'

Only 7 to 9% of U.S. students are in a position to major in math, science, economics, or even the 'soft' sciences like experimental psychology & political science (which is pure math these days). I don't know anything about accounting, but these figures don't sound great for how many high school students are prepared to pursue accounting careers, either. And since calculus is still an entry requirement for business schools, we've got a pretty thin slice of the population on-track for B-school entry.

So I'm guessing we'll be seeing an upswing in applications to law school in 2011.

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 takes you to recommended reading page, which includes a comment & an attached pdf file of the full report)

update

OK, I'm losing patience with online pdf files, so I'll post these links and go clean up my desk (and my floor).

The 'big' report on the 2003 TIMSS seems to be this one:
TIMSS 2003 Technical Report (pdf files for all chapters)
Martin, M.O., Mullis, I.V.S., & Chrostowski, S.J. (Eds.)(2004)

I haven't been able to track down the percentile that corresponds to a score of 625, although it strikes me that I may have 'sufficient information,' as the story problems put it, to figure it out myself. (If we know how many Singapore students scored in the top 10%, and we know the average score of Singapore students--does that do it? I don't know! I will have to investigate!)

I did find this table showing average scores for each country (England was ommitted for some unspecified reason, & I don't see France on here, either....we may be lousy at math in this country, but we also have a glaring deficiency in Information Architecture....).

Singapore's average score is 605; ours is 504.

update, update

OK, now I need some math help. (Apparently I am not in the 10% or 25% or heaven-only-knows-what percent who is in position to major in economics in college any time soon.)

If the average score of Singapore kids is 505, and 625 is a reasonable cut-off for students in position to major in 'highly numerate' subjects in college...that means that the 46% of Singapore kids who scored in the top 10% could not possibly all have scored above 625, right? (Unless the distribution were extremely odd, of course.)

Am I missing a step?

update 3

Good grief.

I used the wrong average for Singapore.

Their average is 605, not 505.

I realize an average is not a median, but setting that aside, and making the mean stand in for the median just this once.....they've got half of their kids scoring 605 or better, just 15 points shy of the 625 cut-off.

Incredible.

Here's Carolyn's comment:

I think you're confusing two different populations here -- one is the population of all kids who took the test, and the other is the population of kids in Singapore who took the test.
The information you're missing is the standard deviation for all these populations -- the 'spread' of the bell curve. You can't figure it out without that bit of info.
Assuming that the distribution for the Singaporeans is a bell curve centered at 605, with a spread-out standard deviation (i.e. a 'fat' rather than 'narrow' bell curve, it is possible that 46% of the Singapore population earned a score above 625.
And it's likely (even without knowing the standard deviations!) that 46% of the Singapore kids were in the top 10% of the population of all kids who took the test, simply because the Singapore average was so high.

a word problem only the top 10% of 9 year olds can do

maths in England
maths in England, part 2
more maths in England, part 2
top students in England, US, & Singapore
why do kids like math?
Catherine's cousin talks about Everyday Math

Call for national debate on maths teaching GUARDIAN
Where will the next generation of UK mathematicians come from? (GOVT REPORT: pdf file)

HowAsiansAndWesternersThinkDifferently 29 Jul 2005 - 16:54 CatherineJohnson

I've mentioned Richard E. Nisbett's book The Geography of Thought a couple of times.

I can't possibly get into a whole long Thoughtfest about whether Asians actually do or do not think differently in some overarching way than Westerners....at least, not until I figure out reciprocals. (news flash: I've made progress on that front, thanks to Dan K!)

So here's what looks like a decent summary of the book (which I haven't read myself) in Education Review, and here's what looks like an interesting critique of the book at a blog I keep meaning to spend some time reading, Gene Expression.

warning: I've glanced at these 2 sites, & that's it. Both look interesting. End of message.

Nisbett is a psychologist who teaches at the University of Michigan. He's a serious guy, the recipient of a Guggenheim and a blurb from Howard Gardner, no less.

THE GEOGRAPHY OF THOUGHT is interesting to me, because of what Nisbett has to say about Asian superiority in math.

Most Americans (I'm willing to bet) think Asians are genetically superior in math. I've had 4th graders tell me Asians are genetically in math.

Nisbett says that not only are Asians not genetically superior at math, the only reason they're functionally superior at math is that, in essence, they're outworking us. Asian culture, in his view, does not particularly support mathematical thought, by which he means logical thought, or the logic of noncontradiction.

Most advances in mathematics were made by Westerners, few by Asians, and older generations in Asia in fact aren't particularly talented in math. (This is certainly something I heard from the Chinese mom I met at tennis lessons. Her husband, a Ph.D. mathematician, is to this day in awe of American mathematicians. I was shocked when I heard this, because I had the same Asian-math-awe everyone else does.)

excerpts from THE GEOGRAPHY OF THOUGHT:

The Greek faith in categories had scientific payoffs, immediately as well as later, for their intellectual heirs. Only the Greeks made classifications of the natural world sufficiently rigorous to permit a move from the sorts of folk-biological schemes that other peoples constructed to a single classification system that ultimately could result in theories with real explanatory power.
A group of mathematicians associated with Pythagoras is said to have thrown a man overboard because it was discovered that he had revealed the scandal of irrational numbers, such as the square root of 2, which just goes on and on without a predictable pattern: 1.4142135 ..... [yup, that bugs me, too] Whether this story is apocryphal or not, it is certainly the case that most Greek mathematicians did not regard irrational numbers as real numbers at all. The Greeks lived in a world of discrete particles and the continuous and unending nature of irrational numbers was so implausible that mathematicians could not take them seriously.
On the other hand, the Greeks were probably pleased by how it was they came to know that the square root of 2 is irrational, namely via a proof from contradiction....
The Greeks were focused on, you might even say obsessed by, the concept of contradiction. If one proposition was seen to be in a contradictory relation with another, then one of the propositions had to be rejected. The principle of noncontradiction lies at the base of propositional logic. ....The basic rules of logic, including syllogisms, were worked out by Aristotle. He is said to have invented logic because he was annoyed at hearing bad arguments in the political assembly and in the agora! Notice that logical analysis is a kind of continuation of the Greek tendency to decontextualize. Logic is applied by stripping away the meaning of statements and leaving only their formal structure intact. This makes it easier to see whether an argument is valid or not. Of course as modern East ASians are fond of pointing out, that sort of decontextualization is not without its dangers. Like the ancient Chinese, they strive to be reasonable, not rational.
Chinese philosopher Mo-tzu made serious strides in the direction of logical thought in the fifth century B.C., but he never formalized his system and logic died an early death in China. Except for that brief interlude, the Chinese lacked not only logic, but even a principle of contradiction. India did have a strong logical tradition, but the Chiense translations of Indian texts were full of errors and misunderstandings. Although the Chinese made substantial advances in algebra and arithmetic, they made little progress in geometry because proofs rely on formal logic, especially the notion of contradiction. (Algebra did not become deductive until Descartes. Our educational system retains the memory trace of their separation by teaching algebra and geometry as separate subjects.)
The Greeks were deeply concerned with foundational arguments in mathematics. Other peoples had recipes; only the Greeks had derivations. On the other hand, Greek logic and foundational concern may have presented as many obstacles as opportunities. The Greeks never developed the concept of zero, which is required both for algebra and for an Arabic-style place number system. Zero was considered by the Greeks, but rejected on the grounds that it represented a contradiction. Zero equals nonbeing and nonbeing cannot be! An understanding of zero, as well as of infinity and infinitesimals, ultimately had to be imported from the East.

pages 24-27

how Asians and Westerners think differently
describe this picture
how Asians and Westerners think differently, part 2
Harold Stevens, RIP
how Asians and Westerners think differently, part 3
creativity gap, part 2
don't know what we don't know

DescribeThisPicture 28 Jul 2005 - 16:28 CatherineJohnson

Then go to the University of Michigan press release for The Geography of Thought to see what Nisbett found.

how Asians and Westerners think differently
how Asians and Westerners think differently, part 2
How Asians & westerners think differently, part 3
Harold Stevens, RIP
describe this picture
creativity gap, part 2

OnlineTIMSSTest 27 Jul 2005 - 23:40 CatherineJohnson

This is a terrific resource. You can give your child 10, 15, or 20 questions from the 1995 & 1999 TIMSS tests. The web site scores them for you.

Explore Your Knowledge

SampleEighthGradeTIMSSProblems 27 Jul 2005 - 23:50 CatherineJohnson

10 items

OK, I'm going to take this test.

I assume everyone can link to the same sample test, but I don't know for sure. The first question is about Penny & her bag of marbles.

oh, yay

I got all ten right, and my results around the world are just peachy. Penny and her marbles stumped 59% of U.S. students, 56% of international students (this is all intl students, I believe, including kids from very poor countries who've just started taking the TIMSS' test). Obviously, fractions are impossible. Although the Singapore Challenging Word Problems Grade 3 book made all the difference. That and Russian Math.

HighSchoolAlgebraTexts 02 Aug 2005 - 15:49 CatherineJohnson

Temple and I are writing an op-ed about American high schools, and I just came cross a treasure trove of PowerPoint slides filled with Horror Statistics, so naturally I had to stop dead in my tracks and get one posted on ktm......

This is a case where PowerPoint has a distinct advantage when it comes to conveying the Bad News.

The whole entire key to conveying bad news on PowerPoint is:

one piece of bad news per slide

or, alternatively,

don't bury the bad news inside a bunch of other junk

source: PowerPoint presentation on U.S. high schools at U.S. Department of Education

EasyMathIsHarder 02 Aug 2005 - 22:22 CatherineJohnson

Another slide from the Department of Ed.

Unfortunately, they don't have the lecture notes up along with the slides, but I think this is self-explanatory. Assuming I'm reading the slide correctly, it tells us that for all but the lowest quarter of students, 'hard' math is easier than 'easy' math.

In other words, the top 75% of students get better grades in college prep math than they do in 'low-level' math.

This is one of those cool findings that inspires me to search for terrific, high-level material for Christopher.....but I'm afraid the reasons for this phenomena may be that the college prep kids have better teachers. The report includes numerous slides showing that the poorest teachers are assigned to the lowest level classes, and that the quality of teacher makes a huge difference in children's achievement. (I'll drop those slides in soon.)

Still, I wouldn't rule out the possibility that 'real' math is more learnable than stripped-down, pretend math.

update

This slide, and a number of others in the presentation, is based on a study of 3000 high schools done by the Southern Regional Education Board, Middle Grades to High School: Mending a Weak Link.

This research brief is based on an SREB study of nearly 3,100 students from 44 middle grades schools and 38 high schools. It shows that ninth-graders in higher-level courses have a lower failure rate than students with similar characteristics in lower-level courses. The report offers specific actions that schools can take to improve student achievement.

The finding that the same level of student will do better in college prep courses than in non-college prep courses wasn't limited to math. It was true across the board.

from the SREB report (pdf file):

Take 100 ninth-graders with similar characteristics and test scores in the eighth grade. Place 50 in higher-level ninth-grade courses. Place 50 in lower-level courses. What happens? If you said fewer students fail in the higher- level courses, you are correct. Please read on.
The Southern Regional Education Board conducted a follow-up study of nearly 3,100 students from 44 middle schools and 38 high schools and found:
Ninth-graders who are placed in higher-level courses have a lower failure rate than students with similar characteristics who are placed in lower-level courses.
This fact begs the question:
Why do we continue to place large numbers of students in lower-level courses where they have little or no chance of gaining the skills and knowledge they need to succeed?
Here is what we know …
Our studies suggest that students who are assigned to higher-level, more challenging work are more successful in high school.
We also know that about one in five students in SREB's network of middle grades schools fails at least one course in the ninth grade, and about 10 percent do not earn enough credits to stay on track for graduation with their classmates.
Clearly, raising the achievement of high school students requires three actions:
1. Students must be challenged to perform at high levels.
2. Students must be prepared before they enter ninth grade to meet these challenges.
3. Students must be given the extra help and extra time they need to succeed.

Key Findings

Many students who expect to go to college are not taking the necessary courses in high school.

Some schools enroll many more students in college-preparatory courses than others. The difference is not explained by differences in students or demographics.

Enrollment in more demanding courses does not result in more failures. In fact, the evidence suggests that challenging content results in lower failure rates. It appears that many students in all kinds of schools can handle more challenging intellectual assignments than schools are willing to give them.

Taking algebra or pre-algebra in the middle grades leads to enrollment in higher-level mathematics courses in high school and does not increase failure rates.

Middle grades schools that successfully prepare students for college-preparatory courses in ninth grade provide extra help and link students with an adult mentor. Successful schools come in many sizes, and their students vary by ethnicity and socioeconomic status.

Teachers matter enormously; middle grades students who have teachers as advisers are more likely to have educational goals and plans for high school.

There are simple steps that middle grades and high schools can take to make sure almost all students will be successful in college-preparatory courses.

Now that I've had a chance to look at the report, I think we're seeing confirmation that people rise to expectations.

I notice, too, that this report does not find that differences in college-prep placement can be explained by 'differences in students or demographics.' I'm inclined to believe this, given my own experience here in Irvington. Last year we had, I believe, 40% of 6th graders enrolled in pre-algebra; next year this figure will be subtantially lower.

Reducing the number of students in accelerated math was a plainly stated objective of the middle school administration and math faculty.

We're talking about a super-affluent suburban district spending $18,000 per pupil.

Meanwhile 80% of 8th graders at the KIPP Academy, in the Bronx, pass Regents A. Compared to 40% of kids here.

I continue to find this utterly shocking.

SamuelsonOnScienceGap 11 Aug 2005 - 22:58 CatherineJohnson

Hi all--I'm back and Carolyn's off--then I'm off again!

I wish summer would last forever. Or at least another couple years.

Robert Samuelson has a column out today on the science gap, which he says isn't a science gap, yet. I find his conclusion a bit hard to follow, but his set-up is clear enough:

As late as 1975, the United States graduated more engineering and scientific PhDs than Europe and more than three times as many as all of Asia, reports Harvard University economist Richard Freeman in a recent paper. No more. The European Union now graduates about 50 percent more, and Asia is slightly ahead of us. By Freeman's estimates, China has reached almost half the U.S. total and will easily overtake us by 2010. Among engineers with bachelor's degrees, the gaps are already huge. In 2001 China graduated 220,000 engineers, against about 60,000 for the United States, the National Science Foundation reports.
Freeman also documents a second worrisome reality: U.S. scientists and engineers aren't well paid, considering their skills and -- especially for PhDs -- the required time for a degree. This means, Freeman says, that "the job market . . . is too weak to attract increasing numbers of U.S. students." Consider some pay comparisons. From 1990 to 2000, average incomes for engineering PhDs increased from $65,000 to $91,000, up 41 percent; PhDs in natural sciences (physics, chemistry) rose from $56,000 to $73,000, up 30 percent. Meanwhile, average doctors' incomes increased from $99,000 to $156,000, up 58 percent; and lawyers went from $77,000 to $115,000, up 49 percent.
The true situation may be worse. Next to other elites, scientific and engineering PhDs fare poorly. Look at the 891 MBA recipients of the Harvard Business School's class of 2005. At an average age of 27, they command a median starting salary of $100,000. It's true that the two-year cost of a Harvard MBA is steep ($120,000 and up), and four-fifths of the students are left with debts averaging $81,000. But these new Harvard MBAs also got huge one-time bonuses; the median was $43,000. As for scientific and engineering PhDs, they typically require seven to eight years to finish their degrees, notes Freeman.

Normally these statistics are presented as catastrophic at best; Samuelson says they're not. At least, not necessarily.

I'm inclined to agree, since I have yet to see catastrophic predictions pan out, which is not to say bad things don't happen, but that when bad things do happen they're usually different from the bad things everyone was braced for.

This brings up two of my favorite sayings, the first one being:

It doesn't pay to worry, because the worries you have are never the worries you get.

People always tell me Mark Twain said that; I have no idea if they're right. Regardless, this observation precisely captures the nature of Bad Events in my own life. I figured this out early enough that back when I had just turned 30 I used to tell friends that what I really wanted was to get done with my current set of problems (endless dating in L.A.) so I could move on to the next set (marriage & kids).

Hmm. That reminds me of yet another saying:

History is just one damn thing after another.

Wasn't that Edna St. Vincent Millay?

[pause]

OK, no it wasn't.

It was Arnold Toynbee.

I'm happy to know that.

My other favorite saying on the subject of catastrophic predictions isn't a saying at all, but something I heard on NPR. They were talking about Hurricane Andrew. The interviewer was asking some official about hurricane preparation, and the guy said,

We prepared for a hurricane. We just didn't prepare for this hurricane.

When I heard that, I thought: yup. That pretty much sums it up.

Not this hurricane.

That other hurricane.

OK, back to Samuelson on why 3 paragraphs of stats demonstrating radical decline in math & engineering graduates isn't the problem it seems to everyone else:

The grim prognosis wrongly presumes that another country's gain must be our loss. Hardly. ... If Microsoft's research center in Beijing (to take one oft-cited example) develops stunning new software, the advances will soon be incorporated in Microsoft products worldwide.

In 1981 American companies and laboratories accounted for 45 percent of research and development among the members of the Organization for Economic Cooperation and Development, which are generally the world's richest nations. In 2000 the U.S. share was still 44 percent -- despite the increase in other countries' scientists and engineers and a decline in U.S. defense research and development.

Finally we get to the dangers, as Samuelson sees them:

The U.S. share of the world's technology workforce has declined for decades and will continue to do so. By itself, this is not dangerous.
The dangers arise when other countries use new technologies to erode America's advantage in weaponry; that obviously is an issue with China. We are also threatened if other countries skew their economic policies to attract an unnatural share of strategic industries -- electronics, biotechnology and aerospace, among others. That is an issue with China, some other Asian countries and Europe (Airbus).

OK, that sounds bad! So here's the part I have trouble with, Samuelson's conclusion:

What's crucial is sustaining our technological vitality.

And that's pretty much it.

The answer is to sustain our technological vitality.

Well, maybe it is. I suspect he ran out of space here. I think what he means, generally, is that American business vitality, which depends upon technological vitality, is the factor to watch and to support. As long as we maintain this factor we can import foreign talent & foreign research and run with them. I've had similar thoughts myself, if only because, as he says, it's not the engineers themselves who are making the big bucks. It's the corporations that hire them.

That's not an anti-business sentiment, by the way. Bringing a good idea to market is hard, and most (or many) good ideas fail as far as I can tell.

In any case, assuming I'm interpreting his final paragraphs correctly, I don't disagree out of hand. I simply don't know enough about economics to have an opinion.

Nevertheless, I think it's nuts to create an entire generation of kids who don't have the option of majoring in math and math-related subjects when they reach college, because we stopped teaching them how to do long division in 5th grade.

My guiding principle with Christopher is to close no doors in grade school.

Maybe fewer and fewer American students will go into science and engineering because the pay is low relative to what they could earn if they went to law school.

However, I don't want to determine that outcome now because an entire generation of children spent 5th grade doing lattice multiplication.

At a bare minimum I want the next generation of managers & entrepreneurs to be able to understand the technology & engineers they're importing from India.

Whither American talent?
Congressional incentives for study of math

InvisibleBoys 15 Aug 2005 - 13:43 CatherineJohnson

Reading through the Carnival entries, I found further evidence of the invisibling of boys at A Passion for Teaching and Opinions. The blogger, a male high school teacher, is taking a required course in Multiculturalism (with a capital M) this summer.

Here are 4 of the 7 questions on an assignment asking him to rate his Cultural Responsiveness (also capitalized):

Are roles of minorities and women presented in a separate manner from other content-isolated or treated as a distinct topic?

Are minorities and women treated in a positive, diversified manner or stereotyped into traditional or rigid roles?

Are problems faced by minorities presented in a realistic fashion, with a problem-solving orientation?

Is the language used in the materials inclusive or are biased terms used such as masculine forms (mankind, mailman)?

The word 'boy' appears nowhere in the assignment.

The word 'man' appears twice, as a negative to be avoided. In the Culturally Responsive classroom, the word 'man,' including compound words ending in 'man,' is not to be spoken.

I feel a bout of protest letter-writing coming on.

USA Today report on 135:100 boys:girls ratio in college
sexism in Everyday Math
invisible boys
boy trouble (New Republic on boys)
slacker boys, middle school, & forbidden positive images of boys in textbooks
throw rocks at them
please remain seated at all times
Ann Althouse thread sums up classroom change
cooperative vs. competitive learning
the girl show (8th grade graduation awards)
the boy show (character ed)
the other boy show
Where the Boys Aren't

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

HowGoodAreOurBest 18 Sep 2006 - 18:14 CatherineJohnson

Now I'm confused.

Jenny D. has a post up saying that our schools 'serve rich white kids well.'

Best example is TIMMS data. The highest scoring kids in the U.S. score as well as the highest scoring kids anywhere in the world. Our best and brightest are as good as the best and brightest anywhere. We are indeed producing scholars. They tend to be white and affluent, according to the statistics. They go to public and private schools.

I distinctly recall reading, in more than one place, that in fact our best and brightest are not as best & bright as the best and brightest in, say, Singapore. However, since I can't recall my source, I'm going to take Jenny D's word for it.

It does strike me that the various scare stories we read about drastic declines in science & math majors frequently don't spell out what is meant by 'decline.'

Do we have an absolute decline in numbers, or a relative decline?

Are there fewer American students in graduate programs because there are fewer American students in grad school math & science period, or are there the same number of American students as always, but lots more foreign students?

I would like someone to nail this down.

Assuming that our best and brightest are just as best and bright as everyone else's (and just as numerous) I wouldn't take this to mean that our schools serve rich white kids well. Not unless we're talking about the big rich, and even then I'd have to see data.

(Back when we were moving to NY, I read an article saying New Yorkers had begun distinguishing between the big rich and the little rich. When I told my friend Debra, she said, 'What does that make us, the big poor?)

Having spent my day cruising Dept of Ed data on high school graduates, I'm pretty sure we can't conclude that the schools are doing a bang-up job with the little rich, the big poor, the little poor, or any other slice of the pie you care to name.

UPDATE 9-17-2006

I now definitively disagree that our public schools serve rich white kids well. Our best schools have parents who are reteaching content and spending a fortune on tutors. Even then rich suburban schools are letting kids down.

From the AFT, here is the story on our rich white kids compared to rich white kids in other advanced nations:

ADVANCED MATH
TIMSS also tested students who are classified as “advanced.” (A different test was used from that given to the General Knowledge population.) Only 16 countries took part in this portion of the test. The TIMSS rule was that countries had to include between 10 and 20% of students in their last year of school.
The U.S. included 14% of its students who were identified as those who had taken four years of high school mathematics. 34% of this group had taken AP calculus, 15% had taken non-AP calculus, and 51% had taken pre-calculus. In other countries the advanced students amounted to an average of 19% of the population and all those students had taken calculus.
When scores were broken out for all the calculus-taking students, U.S. performance rose to 11tth among the 16 countries with 6 nations significantly outscoring the U.S. The U.S. average score for calculus students was 492 compared to a mean of 505 for all TIMSS Advanced Math students.
When scores for only AP Calculus students were extrapolated, the U.S. scored similarly to most other countries (tied for 8th out of 16) with only France scoring significantly better. The average for AP Calculus students rose above the mean of 505 to 513.
The advanced math test consisted of 17 items in the numbers (functions) and equations category, 23 in geometry, and 13 calculus-related items.
source:
The American Federation of Teachers Looks at TIMSS (PowerPoint)
SOURCE: NCES,1998. Pursuing Excellence

other data points:

Twelve percent of high school students take calculus; 6.7 percent take AP calculus.

A large number of these students haven't learned calculus well enough to be prepared for college math courses:

Only about 14 percent earn math or science credit in Advanced Placement (AP) or International Baccalaureate (IB) programs. And while the level of AP coursetaking is rising, many AP students still aren't fully prepared—only about 60 percent of students who take AP tests in Biology, Chemistry, and AB Calculus get a score of "3" or better, generally the minimum score needed for college credit.

Families earning more than $84,000 per year are 20% of the population.

John Saxon estimates that we should have the top 30% of our students taking calculus in high school.

The only U.S. math students who are fully competitive with their peers in other developed nations are the 6.7% of our students who take advanced calculus in high school (or, possibly, the 4% who take AP calculus and pass the AP test).

Seeing as how rich white kids — kids whose families earn more than $84,000 a year — make up 20% of the population it's a fair bet that there are a significant number of rich white kids whose schools have failed them.

UPDATE 9-17-2006

Survey of U.S. Manufacturers

80% report 'Moderate to Serious' shortage of qualified job candidates (20% 'Serious')

For Hourly Workers
- 59% report 'Poor Basic Employment Skills'
- 26% report 'Inadequate Math Skills'
- 32% report 'Poor Reading/Writing Scores'

Then, there's this:

Small Businesses Seek 20th Century Skills for 21st Century Workforce

1,000 respondents place high value on
- Verbal & written communications
- Math
- Computer expertise
- Interpersonal skills

Only one-third satisfied with pool of available applicants

source: Preparing America's Future: High School Initiative Hans K. Meeder, Deputy Assistant Secretary Office of Vocational and Adult Education United States Department of Education February 29, 2004 PowerPoint presentation

There's plenty more where that came from (and eventually I'll get to it....)

Given what we know about the demographics of people who do and do not go to college--i.e., there are more than a few rich kids who don't go to college, and more than a few poor kids who do--I think it's safe to say we need improvements all around, no matter how much money a student's folks make.

But I seriously want to see the nitty-gritty on the high-end TIMSS scores.....

statistics question
how can you tell whether A caused B?
low birth weight paradox
best performing students, part 2
a word problem only the top 10% of 9 year olds solve
England vs America vs Singapore

keywords: beststudents

PrincipalsGuide 27 Sep 2006 - 16:45 CatherineJohnson

I can't believe I haven't written about The Principal's Guide to Raising Math Achievement by Elaine K. McEwan, but it seems I haven't. (It is listed on the Recommended Reading page.)

This is one of the very best books I've read on math education. Wonderful. Well worth the price.

Here she is on middle school math:

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 occured 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.

'no significant difference between the scores of U.S. students at the end of seventh and eighth grades'

school starts soon
a gift for your principal

HowAsiansAndWesternersThinkDifferentlyPartTwo 15 Aug 2005 - 19:22 CatherineJohnson

I've been meaning to follow-up on my original post about differences between Asian & Western cultures with this second passage from Richard Nisbett's The Geography of Thought: How Asians and Westerners Think Differently...and Why:

I am sometimes accused of a contradiction myself. Why do nonlogical Asians tend to do so much better in math and science than Americans? How can this be if East Asians have trouble with logic? There are several answers to this question.
First, it should be noted that we don't actually find East Asians to have trouble with formal logic, we just find them to be less likely to use it in everyday situations where experience or desire conflicts with it. Second, Eastern lack of concern about contradiction and emphasis on the Middle Way undoubtedly does result in logical errors, but Western contradiction phobia can also produce logical errors.
The Eastern reputation for math skills is really quite recent. Traditional Chinese and Japanese culture emphasized literature, the arts, and music as the proper pursuits of the educated person. In research with young and elderly Chinese and Americans, we and others find that only the Comparably schooled older Chinese and Americans perform similarly in math.
Asian math education is better and Asian students work harder. Teacher training in the East continues throughout the teacher's career; teachers have to spend much less time teaching than their American counterparts; and the techniques in common use are superior to those found in America. (Asian math-education superioity to Europe in these respects is less marked.) Both in America and in Asia, children of East Asian background work much harder on math and science than European Americans. The difference in how hard children work at math is likely due at least in part to the greater Western tendency to believe that behavior is the result of fixed traits. Americans are inclined to believe that skills are qualities you do or don't have, so there's not much point in trying to make a silk purse out of a sow's ear. Asians tend to believe that everyone, under the right circumstances and with enough hard work, can learn to do math.
In short, Asian superiority in math and science is paradixical, but scarcely contradictory!

pp. 188-189

girls and boys and math in Asia??

I'm curious whether there is the same gap in math performance between the sexes in Asian cultures that we see here. Ed's & my autism gurus, Bob and Lynn Koegel of UCSB, once gave talks saying that there wasn't. They had read Stevenson's & Stigler's data on East Asian attitudes toward ability versus hard work many years ago, before they had their two daughters.

(interruption ... Looking for material on Asians & math, I've come across sad news, which I'm going to post now. Lynn's story continues in how Asians and Westerners think differently, part 3)

how Asians and Westerners think differently
how Asians and Westerners think differently, part 2
How Asians & westerners think differently, part 3
Harold Stevens, RIP
describe this picture
creativity gap, part 2

HaroldStevensonRIP 15 Aug 2005 - 20:07 CatherineJohnson

I've just had one of those strange synchronicity moments.

Last night, after talking to Caroline about E.D. Hirsch's The Schools We Need and Why We Don't Have Them (which Caroline was raving about), I went to my bookshelves & pulled out Hirsch's book, determined to read it at last.

But then I pulled out Harold Stevenson & James Stigler's The Learning Gap: Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education, which I've been reading off and on today. This morning, too, I returned to Nisbett's Geography of Thought....and was in the midst of writing my follow-up post on Asians and math when I discovered that Harold Stevenson has died, 3 weeks ago, at the age of 80.

from his obituary in the GLOBE:

The book punctured stereotypes of Asian elementary schools as high-pressured learning factories and illuminated what many specialists came to agree were grave deficiencies in the US education system, including weak academic standards, overburdened teachers, and misguided cultural beliefs about parental roles and the importance of individual student effort....
Although educators had known as early as the 1960s that Japanese and other Asian students ranked higher than Americans on international assessments of academic achievement, the explanations were ''too often cloaked in speculation," said Jack Schwille, assistant dean for international studies in education at Michigan State University. ''Stevenson collected data on classroom teaching and learning [that] could help explain the differences," Schwille said, ''and he got educators and laypersons to pay attention to them."
Dr. Stevenson's work was often cited during the national debate over education standards in the late 1980s and early 1990s, particularly in discussions of US students' poor mastery of math. He argued that US educators would do well to emulate the systems in Japan and Taiwan, where learning goals are carefully plotted and clearly defined, and creative hands-on exercises are considered crucial.
At the core of the Asian schools' success in math, Dr. Stevenson believed, were thoroughly trained teachers who were given ample support during the school day to craft lessons and share ideas with colleagues.
''Stevenson's work made clear the kind of education that was really going on in Asia . . . and helped pave the way for some improvements we see now, especially in California," said David Klein, a mathematics professor at California State University, Northridge, who has been active in the movement to strengthen math teaching in the United States....
The researchers eventually focused their inquiries on math achievement because the gap between American and Asian students in that subject was so wide. By fifth grade, Dr. Stevenson and Stigler found, the lowest-scoring Japanese classroom still outperformed the highest-scoring US classroom.....
In contrast to the Japanese, American teachers were loathe to submit their students to public scrutiny out of fear it would damage the youngsters' self-esteem, Dr. Stevenson and his colleagues found. Moreover, US teachers often segregated students into low- and high-ability groups, a practice that Stevenson said reflected a deeply held belief that not all students could succeed.
Another important difference he found was that Japanese and Chinese teachers received considerably more time during the school day to prepare lessons, discuss goals with other teachers and work with individual students. On average, they spent only three to five hours a day in front of a classroom.
In the United States, however, ''we keep teachers busy in front of the classroom all day long," Dr. Stevenson told The Dallas Morning News in 1993. ''We deprive teachers of opportunities for . . . extending their knowledge, both in the subject area they're teaching and also in methods, so that it's very difficult for American teachers to do a good job."

Ed and I knew James Stigler a little at UCLA, and we saw his videos of Japanese math classes there. He was a terrific guy.

how Asians and Westerners think differently
how Asians and Westerners think differently, part 2
How Asians & westerners think differently, part 3
Harold Stevens, RIP
describe this picture
creativity gap, part 2

HowAsiansAndWesternersThinkDifferentlyPartThree 15 Aug 2005 - 20:10 CatherineJohnson

I had just started writing about Bob and Lynn Koegel when I found Harold Stevenson's obituary, and interrupted myself to write a post on his life and death.

Getting back to the Kogels, when Lynn had her daughters she decided to see whether she could raise American daughters with Asian-style math skills. She put together a little neighborhood group of girls, and they did all kinds of embedded math activities involving cooking and anything else the girls liked to do.....and it worked. (Bob and Lynn created a form of behavioral treatment that's like John Dewey for autism, which in their case is a Good Thing. They're brilliant.)

I'll have to ask her for the details, which I've forgotten, but IIRC, every girl in the group grew up to be very advanced in math skills & performance--way past typical American girls, and way past brainy American girls, too. (I'll track this down!)

In any case, I do have a memory of reading that there is a sex difference on math in Asian countries, too, but only at the very highest levels of performance. Apart from that the sex distribution is exactly as Lynn described it; everyone assumes that math achievement is hugely a function of hard work, and everyone equally assumes that girls can perform hard work, too.

More Googling ahead, I can see that.

how Asians and Westerners think differently
how Asians and Westerners think differently, part 2
How Asians & westerners think differently, part 3
Harold Stevens, RIP
describe this picture
creativity gap, part 2

BestPerformingStudents 15 Aug 2005 - 21:22 CatherineJohnson

I think I'm going to force myself to give up on the Quest to discover what TIMSS has to tell us about the presence or absence of a gender gap in math achievement in Asia.....

But naturally, I've happened across all kinds of interesting factoids en route to not finding what I was looking for, most of it relating to the question of whether our schools do a good job with rich white kids.

From the 1998 TIMSS:

Nine percent of U.S. fourth-graders would be included in a talent pool made up of the top 10 percent ofall students who took TIMSS. Not bad.

But only 5 percent of U.S. eighth-graders would be included in this pool instead of the expected 10 percent. Not good.

And, the most advanced mathematics students in the United States (only about 5 percent of the 12th grade cohort), performed similarly to 10 percent to 20 percent of that same cohort in most other countries. Terrible.

Lessons from the World: What TIMSS Tells Us about Mathematics Achievement, Curriculum and Instruction (pdf file)

My sense is that these numbers haven't changed appreciably since 1998. So my feeling is that it's not correct to say that our schools do well by rich kids, unless every single child in that 5% is rich, and unless you define 'rich' as meaning 'the top 5 percent in income.' And if those two conditions happen to be true, then we can definitelysay that while our schools are doing a bang-up job with the big rich, they're seriously shafting the little rich. Not to mention the big & little poor.(I'm gonna have Carolyn take a walk through that logic before I COMMIT....)

statistics question
how can you tell whether A caused B?
low birth weight paradox
best performing students, part 2
a word problem only the top 10% of 9 year olds solve
England vs America vs Singapore

BestPerformingStudentsPartThree 14 Nov 2005 - 02:32 CatherineJohnson

The question of how our top students compare to everyone else's top students has made me realize I need to be paying attention to this. My goal as a homeschooler-on-the-side is for Christopher to be able to major in a math-related subject in college if he chooses, which apparently means he should be able to score a 625 or higher on TIMSS.

So I'm going to start scouting information on all ranges of student achievement, and posting it here.

Here's my first:

Researchers determined which items students who achieved at the various levels on the total test were likely to get right. Then they placed the items on a scale from 200 to 750. So we have a pretty good idea of what the best students know that others have difficulty with.

Only the top 10 percent of 9-year-olds were likely to get this math item right. Students had to explain their answers verbally, symbolically or pictorially.

In the first part they had to indicate that 20 is twice as large as 10 or that 10 is half of 20. 10 percent of third graders and 21percent of fourth graders did this. A small number of students (less than 1 percent in any country ) received credit for satisfactory explanations even though they did not give a yes or no response to whether Julia was right.

U.S. percentages were 13 percent at third grade and 25 percent at fourth grade.

For the second part, only 6 percent of third graders and 15 percent of fourth graders responded correctly. 6 percent of U.S. third graders and 17 percent of U.S. 4th graders got credit. However, 30 percent or more got credit in Japan, Korea and Singapore.

I'm going to spring this one on Christopher tomorrow. I really can't tell whether he could have gotten this item right at age 9. If you showed him 10 girls and 20 boys he would have known instantly that boys and girls weren't half and half.

But I tend to think he would have been thrown by the sight of the numbers '10' and '20.'

As well, I'd say this problem imposes a high cognitive load. You have to keep Juanita and Amanda straight in your mind, unless you've developed seriously good informal chart-making skills, which Christopher has not done now and certainly had not done in 4th grade.

update: Christopher's answer

Christopher turned 11 yesterday (boo hoo).

His first impulse, as I feared, was to say 'yes,' Amanda is right.

He obviously had the 'environmental dependency' effect of seeing the numbers '10' and '20' and thinking: 1/2.

But then he corrected himself, and said, confidently, that Juanita is right and Amanda is wrong. (Nice to see that the Designated Stupid Person concept has spread to TIMSS, too.)

His explanation was a bit strangled, but it was right. He said, 'Well, if there's 1 girl for every 2 boys, then there's 1 girl and 2 boys, then 2 girls and 4 boys, then 3 girls and 6 boys...'

This is pretty interesting, because I think he had a 'number sense' or 'pattern' way of getting this answer. In other words, I think he got the answer without really knowing why or how he got it. He just knew it. Juanita's correct statement of the problem instantly became his statement of the problem; he didn't have to do any adding or subtracting or logical reasoning to test Juanita's statement.

Then, when I asked him to explain why Juanita was right, he explained how her answer would work as a kind of Fancy Skip Counting Mechanism. If you kept counting up by 2-to-1 ratios, eventually you'd hit 30 kids, and your ratio would be 10 girls, 20 boys.

After he gave this illustration I asked him, 'how many girls and how many boys would there be in the class' (forgetting that in fact THE PROBLEM TELLS YOU THIS UP FRONT) and Christopher said, instantly, '10 girls and 20 boys.'

When I asked him how he knew (TIMSS should just have 'Catherine' be the Designated Stupid Person) he said, 'I just knew it.'

Apparently he had forgotten the fact that we'd been given this information, too. Like mother like son.

In any case.....this is something I was talking to Carolyn about the other night: what is the relationship of implicit knowledge to expertise when you're talking about math?

Certainly in every other field (I think) implicit knowledge is a sign that you're getting good at what you do, because you don't have to think about it. You 'just know it.'

But math has been confusing for me in this realm.....our friend Fred was here a few weekends ago, and I asked him to take a look at a RUSSIAN MATH problem that was stumping me. Fred is a Big Brain; he went to Yale undergrad, then got a Ph.D. in experimental psychology at Stanford, I think it was; then got a law degree at Yale; then clerked for the Supreme Court.

So I hope you're impressed.

Anyway, Fred was keenly interested in math when he went to college, but pretty quickly found out that pure mathematics wasn't going to be for him.

anti-constructivist digression

"I always loved finding the right answer," he said.

This is SO important; it's one of the core pleasures of math. Finding the right answer. Radical constructivists gleefully snatch this pleasure this pleasure away, the drips.

back on topic

Anyway, once he realized that pure mathematics was beyond him, Fred moved to statistics. Looking at the Russian Math problem, he instantly knew how to do it. But he didn't know why He knew.

This was yet another Problem Involving Reciprocals, and Fred said, 'I don't know why I knew to use the reciprocal there.'

So......

This is where I get confused.

Fred is a super-smart person with, I would say, high expertise in elementary math & in applied math. On the other hand, he isn't doing a math-related job as a career, so maybe he's no longer in the 'expert' category after all these years. I don't know where to put him.

So I don't know what to think about the fact that he could instantly solve the RUSSIAN MATH problem, but didn't know why his solution worked. Is that a sign that he has advanced knowledge (because people with advanced knowledge often 'just know' things they can't explain), or a sign that he doesn't?

This brings me back to Christopher.

Watching and listening, I felt like the fact that he instantly knew Juanita was right was a sign he's developing expertise. It was as if math is starting to be 'in his bones.'

On the other hand, I don't think he could show me how to do the problem, if the problem were too advanced to do just by eyeballing it. (If the numbers weren't 'friendly.')

Actually, that's a good question. In the next day or two I'll find out what he would do with a more complicated version of this question.

How good are our best?
BestPerformingStudentsPartTwo
a word problem only the top 10% of 9 year olds solve
England vs America vs Singapore

SummerReruns 16 Aug 2005 - 17:28 CatherineJohnson

Carolyn left a comment that reminded me about the translations Ed and I did of books criticizing French schools back when Carolyn & I first started Kitchen Table Math. Hirsch (like Ed) is under the impression that progressive education hasn't got very far in France.

These books claim otherwise, though I have no idea how representative they are.

I wouldn't have an opinion if it weren't for the teacher I talked to at the French Embassy who told me:

math is a language
math is a dead language, like Latin
math is not the future

He also told me, directly, don't study math.

This man was married to a major figure in French education, and is himself, I believe reasonably important in the field. Still, I have no idea how representative his ideas are, either.

It's a metacognitive moment!

I know nothing!

Cue Don Rumsfeld!

He did sound so like an American constructivist, with his ad hominen explanation of people who reject his views. I wish I could remember exactly what he said about the foot-draggers who were refusing to get on board for progress. I think he said they were all conservatives longing for the return of Napoleanic times!

(In fact, I'm darn sure. 99% sure.)

I need to start taking notes.

that reminds me

If I had a penny for every time I've read the phrase, 'Math classrooms today don't look like the classrooms parents remember' or 'Parents don't understand when they see math classrooms that are very different from the classrooms they remember' I'D BE RICH.

Someone needs to Explain The Rules to these folks.

The rule is: when you're having a disagreement with a person, and perhaps especially when you're having a disagreement with many persons, no psychologizing.

wrong: Math classrooms today don't look like what parents experienced

right: Parents believe it's important for children to master their math facts by 3rd grade.

also wrong:They are conservatives who want to return to the age of Napolean.

France & Mexico

AchievementGapWhitesAsians 18 Aug 2005 - 23:34 CatherineJohnson

It's between whites & Asians:

Results from the California standardized tests (STAR) from 2005 were published August 15. One note: the Achievement Gap in Algebra II proficiency was 27 percentage points....58% vs. 31%
Snooze, right? But that's not the black/Hispanic to white gap. That's the Asian to white comparison! The black/Hispanic to white comparison is actually SMALLER, where Algebra II proficiency is 9% black, 15% Hispanic, 31% white.

(from eduwonk)

Vivian Shuh Ming Louie's research on the other gap

Race, class still matter: Undermining the myth of the model minority

She has a book out as well. Looks interesting.

AlanGreenspanOnRisingInequality 21 Aug 2005 - 02:25 CatherineJohnson

I'm going to start posting this email from NYC Math Forum at NYC HOLD once a month:

In the matter of preaching to the choir, C-Span has a video of Alan Greenspan's testimony to the House Joint Economic Committee. There is a fascinating exchange between Greenspan and Senator Reed about the divergence in income between skilled/supervisory workers and unskilled workers. They agree this is a very serious problem. At one point, Reed asks what short term policies can be implemented to "enhance the incomes of most of the workers of America.
I transcribed about two minutes of testimony which you can hear for yourselves, starting around minute 34:00 of the video clip.
Greenspan:
Well, Senator, I don't think there are short term policies, other than the ones we typically use to assuage those who fall into unemployment or policies in the tax area in which we endeavor to redistribute income.
The basic problem, as we have discussed previously, as best I can judge, goes back to the education system. We do not seem to be pushing through our schools our student body at a sufficiently quick rate to create a sufficient supply of skilled workers to meet the ever-rising demand for skilled workers which means that wage rates are accelerating. But the very people who have not been able to move up into the education categories where they become skilled overload the lesser skills market and cause wages to be moving up well below average.
The consequence, of course, is an increased concentration of income. And, as I have often said, this is not the type of thing which a capitalist democratic society can really accept without addressing. And as far as I am concerned, the cause is very largely education.
It is not the children because at the 4th grade they are above the world average. Whatever it is we do between the 4th grade and the 12th grade is obviously not as good as what our competitors abroad do because our children fall below, well below, the median in the world, which suggests that we have to do something to prevent that from happening and I suspect, were we able to do that, we will indeed move children through high school, into college, and beyond in adequate numbers. As indeed we did in the early post WW II period, such that we do not get the divergeance in income which is so pronounced in the data we currently looked at.

Rising inequality has been Topic A for months now (make it years) with the WALL STREET JOURNAL & the NEW YORK TIMES both running major several-part series on the subject. Rising inequality alond with declining social mobility.

Well, what is the reason for rising inequality and declining social mobility?

Is it just that the rich get richer? (Which seems to be the thesis of everything I read, but don't go by me.)

I'm with Alan Greenspan. It's basic supply and demand. If you don't have enough highly educated people to fill jobs requiring highly educated people, those wages go up.

If you have too many highly uneducated people to fill jobs where advanced education isn't a requirement, those wages go down.

Now I'm going to indulge in some psychologizing, which generally speaking I don't approve of.

I think the reason journalists don't bring up this possibility is that journalists, being highly educated, and NOT being highly educated when it comes to math & economics (I speak from experience), just naturally tend to assume that of course the wage gap between them and the custodial staff is widening; what journalists do is lots more valuable. (I'm only dinging journalists here because I'm talking about journalism. I'll hazard a guess that just about every highly educated person other than Alan Greenspan thinks the same thing.)

Alan Greenspan on rising inequality
rising inequality, part 2
rising inequality, part 3
median income families UCSC students
another statistics question
channeling the Wall Street Journal
Financial Times on US college costs
Economist on US higher ed
The Economist on rising inequality in universities

RisingInequalityPart2 20 Aug 2005 - 01:28 CatherineJohnson

from The Economist (probably subscription only):

This is not the first time that America has looked as if it was about to succumb to what might be termed the British temptation. America witnessed a similar widening of the income gap in the Gilded Age. It also witnessed the formation of a British-style ruling class. The robber barons of the late 19th century sent their children to private boarding schools and made sure that they married the daughters of the old elite, preferably from across the Atlantic. Politics fell into the hands of the members of a limited circle—so much so that the Senate was known as the millionaires' club.
Yet the late 19th and early 20th centuries saw a concerted attempt to prevent America from degenerating into a class-based society. Progressive politicians improved state education. Philanthropists—many of them the robber barons reborn in new guise—tried to provide ladders to help the lads-o'-parts (Andrew Carnegie poured millions into free libraries). Such reforms were motivated partly out of a desire to do good works and partly out of a real fear of the implications of class-based society. Teddy Roosevelt advocated an inheritance tax because he thought that huge inherited fortunes would ruin the character of the republic. James Conant, the president of Harvard in 1933-53, advocated radical educational reform—particularly the transformation of his own university into a meritocracy—in order to prevent America from producing an aristocracy....
The evils that Roosevelt and Conant worried about are clearly beginning to reappear. But so far there are few signs of a reform movement [today]. Why not?
The main reason may be a paradoxical one: because the meritocratic revolution of the first half of the 20th century has been at least half successful. Members of the American elite live in an intensely competitive universe. As children, they are ferried from piano lessons to ballet lessons to early-reading classes. As adolescents, they cram in as much after-school coaching as possible. As students, they compete to get into the best graduate schools. As young professionals, they burn the midnight oil for their employers. And, as parents, they agonise about getting their children into the best universities. It is hard for such people to imagine that America is anything but a meritocracy: their lives are a perpetual competition. Yet it is a competition among people very much like themselves—the offspring of a tiny slither of society—rather than among the full range of talents that the country has to offer.
The second reason is that America's engines of upward mobility are no longer working as effectively as they once were. The most obvious example lies in the education system. Upward mobility is increasingly determined by education. The income of people with just a high-school diploma was flat in 1975-99, whereas that of people with a bachelor's degree rose substantially, and that of people with advanced degrees rocketed.
The education system is increasingly stratified by social class, and poor children have a double disadvantage. They attend schools with fewer resources than those of their richer contemporaries (school finances are largely determined by local property taxes). And they have to deal with the legacy of what Michael Barone, a conservative commentator, has labelled “soft America”. Soft America is allergic to introducing accountability and measurement in education, particularly if it takes the form of merit pay for successful teachers or rewards for outstanding pupils. Dumbed-down schools are particularly harmful to poor children, who are unlikely to be able to compensate for them at home.
America's great universities are increasingly reinforcing rather than reducing these educational inequalities. Poorer students are at a huge disadvantage, both when they try to get in and, if they are successful, in their ability to make the most of what is on offer. This disadvantage is most marked in the elite colleges that hold the keys to the best jobs. Three-quarters of the students at the country's top 146 colleges come from the richest socio-economic fourth, compared with just 3% who come from the poorest fourth (the median family income at Harvard, for example, is $150,000). This means that, at an elite university, you are 25 times as likely to run into a rich student as a poor one.

Alan Greenspan on rising inequality
rising inequality, part 2
rising inequality, part 3
median income families UCSC students
another statistics question
channeling the Wall Street Journal
Financial Times on US college costs
Economist on US higher ed
The Economist on rising inequality in universities

FinancialTimesOnCollegeCosts 25 Aug 2005 - 16:28 CatherineJohnson

source: Soaring costs leave poor students struggling to make grade By Scott Heiser, page 4, Published: August 22 2005 20:44 (subscription only)

While US inflation has been contained for the past decade, the higher education sector has proved a glaring exception. The College Board, a US educational testing and surveying group, says tuition and fees rose 10.5 per cent in the 2004 academic term at four-year public (government-funded) universities, and 6 per cent at four-year private universities.
Adjusted for inflation, students at four-year public institutions paid 51 per cent more in 2004 than in 1994, while those at four-year private universities paid 36 per cent more.
Over the same period, total student aid has risen 122 per cent to $122bn in 2004; grant aid has increased 84 per cent; and the number of student loans has risen 137 per cent, according to the College Board.
The rising cost of higher education in the US is raising new questions about whether universities will still be able to serve as ladders of social mobility. While overall enrolment has been surprisingly unaffected by the growing expense, there are signs poorer students are being frozen out of the best schools, in spite of generous aid programmes....
US higher education is already the most expensive among advanced industrialised countries. According to US education department data, the US spends $20,358 per student each year, equivalent to 2.7 per cent of gross domestic product. Canada spends $14,983 per capita on post-secondary education, or 2.6 per cent of GDP. In the UK, higher education spending is just $9,657, or 1 per cent of GDP. Yet enrolment at US universities continues to surge, rising from 14m in 1995 to 16m last year.

editorial aside: U.S. higher education is the best

U.S. universities are the best in the world, bar none, a fact that seems to come as news to most Americans. This year Ed had lunch with an NYU economist from France, and asked him why he came to an American university. The guy basically just laughed at the question. If you're the best in your field, you want to be at an American university, period.

back to the FT

Indeed, the benefits [of a college education] have proved well worth the costs, in spite of the growing debt burdens for students. US Census Bureau data show that average lifetime earnings of college graduates are $2.1m, compared with $1.2m for high school graduates.....
Thomas Mortenson, a scholar with the Pell Institute, has found that poor students receiving Pell Grants the government's biggest educational grant programme decreased by nearly 17 per cent over the past decade at the top 20 schools, as ranked by US News & World Report magazine. Mr Mortenson's data, which correlates family income and degree attainment, shows that the number of bachelor degrees awarded to students from the poorest quarter of US families has stayed nearly level over the past decade, and has improved only slightly since 1970.
In contrast, degrees given to students from the richest quarter of US families have risen steadily from about 40 per cent in 1970 to nearly 75 per cent today. In 2003, 74.9 per cent of the top income class attained degrees, compared with just 8.6 per cent of the bottom income class.

the top 146 universities

Inequity at top schools is a particular problem, says Richard Kahlenberg of the Century Foundation, be-cause students attending these top schools are the ones who will join the “leadership class”.
At the top 146 colleges and universities, 74 per cent of students come from the wealthiest quarter of society, compared with 3 per cent from the poorest quarter, Mr Kahlenberg says.

They don't give comparable figures for community colleges, but we don't really need them, since we know that only 8.6% of kids in the lowest income group earn Bachelor's degrees.

what about the middle?

So if the top 146 universities and colleges enroll 74% of their students from the top quartile & 3 percent of their students from the bottom quartile, that leaves 23% of the slots for students from the 2 middle quartiles, something nobody seems to be worried about in the slightest.

This is the kind of thing that gets my goat.

Alan Greenspan on rising inequality
rising inequality, part 2
rising inequality, part 3
median income families UCSC students
another statistics question
channeling the Wall Street Journal
Financial Times on US college costs
Economist on US higher ed
Economist on rising inequality in universities

TomFriedmanSingaporeMath 13 Nov 2005 - 14:59 CatherineJohnson

Apparently I have been channelling Tom Friedman.

No sooner do I coin the term page splatter than I discover that Friedman has, today, published an op-ed calling for the complete and total destruction of Singapore's mathematics curriculum as we know it.

Singaporean math textbooks are very good. My daughter's school already uses them in Maryland. But they are static and not illustrated or animated. "Our lessons [at HeyMath] contain animated visuals that remove the abstraction underlying the concept, provide interactivity for students to understand concepts in a 'hands on' manner and make connections to real-life contexts so that learning becomes relevant," Mrs. Sankaran said.
[snip]
With a team of Indian, British and Chinese math and education specialists, the HeyMath group basically said to itself: If you were a parent anywhere in the world and you noticed that Singapore kids, or Indian kids or Chinese kids, were doing really well in math, wouldn't you like to see the best textbooks, teaching and assessment tools, or the lesson plans that they were using to teach fractions to fourth graders or quadratic equations to 10th graders? And wouldn't it be nice if one company then put all these best practices together with animation tools, and delivered them through the Internet so any teacher in the world could adopt or adapt them to his or her classroom?

answer: no

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

CreativityGapInAsia 16 Sep 2005 - 21:20 CatherineJohnson

Barry Garelick says Singapore may not be engaged in the wholesale destruction of its curriculum, so I'm going to hold that thought. HeyMath is apparently going to be more of an online tutoring site than a replacement curriculum.

This is the time to mention that Asian countries are apparently highly focused on U.S. creativity. From The Learning Gap, by Stevenson & Stigler:

Wherever one goes in Asia, one hears the complaint that although Chinese and Japanese students show high levels of academic achievement, they lack creativity, a characteristic Asians believe is more prevalent in American students than in their own. Committees appointed by Asian ministries of education are frequently charged with finding ways to foster greater creativity among their students.

DanDreznerThreadOnMathEd 20 Sep 2005 - 12:54 CatherineJohnson

Joanne Jacobs also links to a post about U.S. math ed on Daniel Drezner's blog. One comment caught my eye:

I don't think the US has anything to worry about. East Asian education is always going to be good at the rote fundamentals, but that's a far cry from producing strong students.
I went to a well-known Ivy league school and my profs. admitted to me privately that the Koreans and Mainland Chinese were by far the weakest students. Why? Because of their inability to think analytically. They admitted this to me since I've spent a lot of my life living in East Asia (and live there now). None of these East Asian societies have been good at reforming their education systems and they have nothing like the US's system of higher education which is superb.
Even working in a research laboratory in the US is better than working in an Asian lab. They may be better at their multiplication tables, but education is about a lot more than that.

He's right about American universities. They're the best.

However, the idea that we have nothing to worry about because we're so darn creative is, I think, overstated.

I do believe Americans are more creative, broadly speaking, than Asians living in Asia. I'm halfway through a post on that subject (a post that involves tracking down studies & URLs, so it will take awhile to finish).

I've also come up with some solid information on how our very best students (which I think is about 5% of the total student population) stack up against Asian students (I'll get to that, too, but it looks like the kids at the very top of the American heap do well).

However, that doesn't address the question of the gazillion Americans who can't solve a simple percent problem. I'm going to follow along in Alan Greenspan's wake & assume that productivity gains happen because lots of people are good at what they do, not because a thin slice of the population majored in math & lived to tell the tale.

math horror stories

This summer two guys came out to fix the air conditioning. One of them was in his 20s, and when Ed told him he'd already paid 25% of the bill, the guy didn't know what to do. 'I'm not good at math,' he said.

If he hadn't had an older co-worker with him, he wouldn't have been able to collect the fee.

You hear stories like this everywhere; I've got a small collection of them myself.

Here's another.

My mom went to Home Depot to get some dowels and the young employee could not measure the length she wanted cut. Period. Finally my mom had to show him how to measure 25 inches or whatever it was she needed.

That kind of thing can't possibly be good for productivity, I don't care how creative you are.

Being creative won't get your dowels measured & cut.

I'll have to see if I can find the article on this subject that ran in EDUCATION WEEK. The author directly addressed the 'Does it matter if Americans stink at math?' question, and cited work by an economist, I believe, who had calculated how much GDP we've lost due to Zero Math Skills.

one more thing

This observation is flat wrong:

East Asian education is always going to be good at the rote fundamentals

Anyone who's spent five seconds looking through the PRIMARY MATHEMATICS series or Liping Ma's book can tell you there's nothing rote about Asian math teaching.

update: I found it

This is the article looking at the question of 'Does it matter if Americans stink at math?' The Seeds of Growth by Eric A. Hanushek, in Education Next.

From the abstract:

For more than three decades, the United States has been scoring below the international average among participating nations on tests of math and science achievement. Again and again, civic leaders have pointed to this fact when warning that a crisis in American education may imperil continued growth in economic productivity. Yet after two decades of nearly uninterrupted boom times, the United States remains the most prosperous nation in the world.
What’s the relationship between education and economic growth? ....
After looking at international evidence on the impact of educational quality on economic productivity, Eric A. Hanushek finds a tight, if delayed connection. Unless the United States does a mid-course correction, a price will eventually have to be paid.

Hanushek's study found that quality of math & science education 'account for' variations in productivity:

Significantly, the quality of the labor force as measured by math and science scores proved to be extremely important.
Worldwide, we found that a difference in test performance of one standard deviation was related to a 1 percent difference in the annual growth rate of per-capita GDP. The impact of such a difference in growth rates is very large. As we saw earlier, 1 percent higher growth—say, growth of 2 percent versus 1 percent per year—over a 50-year period yields incomes that are 64 percent higher. Moreover, adjusting the data for other factors that are potentially related to growth, including aspects of international trade, private and public investment, and political instability, leaves the effect of having a quality labor force unchanged.

Another excerpt:

During the past century, the United States led the world in the expansion of its education system, contributing to the dominant position of the United States in the world economy. Nonetheless, there is reason to be concerned about the future. The evidence suggests that the American K–12 education system is falling behind those of other developed nations. As a result, it is unclear whether we will be able to count on the education system to fuel future U.S. economic growth. As economic growth is crucial to our well-being, this is a matter we should take very seriously.

I haven't re-read the piece in detail, but he seems to think that we've been 'getting away with' poor schooling by substituting quantity for quality. We were the first to try to educate everyone, and we've benefited.

But as other countries catch up to us on this score, that advantage will be lost.

hmm. Now I'm remembering an EDUCATION WEEK article on this subject.....

spaced repetition

...a difference in test performance of one standard deviation was related to a 1 percent difference in the annual growth rate of per-capita GDP...

Education Week weighs in

This 1998 article is useful: Weak Scores, Strong Economy: How Can This Be?:

As Newsweek columnist Robert J. Samuelson put it: "If our students are so bad, why is the economy so good?"
[snip]
Most economists and education experts say they continue to believe that the quality of precollegiate education affects the economy. But, by and large, they're no longer talking about competitiveness as the driving force for school reform, as A Nation at Risk did in 1983.
Income Gap
That influential national commission report put forth what became the prevailing view: The United States was in danger of losing its "slim competitive edge" in world markets unless it reformed its schools through such measures as tougher graduation requirements.
"Workforce 2000," a 1987 report by the Hudson Institute in Indianapolis, reinforced that view by asserting that "from an economic standpoint, higher standards in the schools are the equivalent of competitiveness internationally." The report warned that the poor state of K-12 education would lead to a national shortage of workers to fill high-skills jobs.
Where much of the argument has now shifted is to a belief that schools must be improved to help close a troubling income gap between people with high and low skills.
"The widespread agreement that the economy is doing well, thank you, is largely an agreement in the top two-fifths [of the population]," said Marc S. Tucker, the president of the Washington-based National Center on Education and the Economy. "People with high skills find their incomes rising. People with low skills find their incomes falling."
Mr. Tucker and others make a distinction between the strong performance of the economy and whether Americans are benefiting equally from the good times.

Until someone seriously persuades me otherwise, I believe this; I believe we've got a major 'education gap' directly causing an income gap. And I do mean 'causing,' though I acknowledge that other factors, such as fatherless families, also play a role. Nevertheless, this is one of those questions where I'm going to believe what I see until someone proves me wrong. And I see majorly lousy schools in poor areas. (I see majorly mediocre schools in rich areas, too, but that's a subject for another post.)

The funny thing is, experts routinely note that wages are rising for high-skill jobs and falling for low-skill jobs, as if that were just the inherent nature of Your Big-time Fancy Information Age.

It wasn't until I read Alan Greenspan's 2004 testimony to the House of Representatives testimony to the House that it occurred to me that 'skilled' labor isn't intrinsically more valuable than unskilled labor.....which any fool who spent 5 seconds contemplating the incomes of professional poets would know.

The laws of supply and demand apply to brainiac information age workers, too. As far as I can tell, our schools are turning out a huge supply of graduates who don't know what 25% means.

Greenspan on education

The point at issue here is that we are ending up with an inadequate ability to move skills up sufficiently quickly. And this, as you point out, has created a problem of excess supply versus demand amongst our lowest skills and the reverse in the top. And that is something we have to address. And I happen to agree with Congressman Frank, that it is very important in this country not only to have an equitable society, but to have it perceived as being equitable because no democratic system can function unless the people believe it is equitable. And I think that it is crucially important for us to reduce the income inequality in this country and I think the way that one has to do that is through education. And I must say to you the community colleges in this country have been in the forefront of a major change in the quality of what we are doing with respect to reestablishing skills.

I've only recently become aware of community colleges as a 'movement,' and of how important they've been....

Here's more:

I find discouraging the fact that the recent evaluations of the ranking of our students internationally in math and science, find the American students sort of average, maybe slightly better than average in the fourth grade and by the time they get to the eighth and the 12th grade we have deteriorated significantly. And what this suggests to me is that we are falling short in getting an adequate number of people through our elementary and secondary schools into colleges, and thereby increasing the supply of skilled workers and effectively bringing down the so-called skill premium, which would be a major factor in reducing income inequality in this country. Not only is the issue one of moving students much more rapidly from fourth grade through high school and into colleges, and its impact obviously on higher skills, but in doing that, you also reduce the supply in a number of the lower skills which will raise their wages and have an effect of rebalancing the structure of wage changes in the United States, so that the skill differentials are significantly different from where they are at this particular stage. And that, to me, says that we have to find ways to create a curriculum which enables us to compete with a significant part of the rest of the world, and a lot of the rest of the world to which I am referring to is the so-called developing world. And I don't know enough about the specifics of curricula and how one would improve that, but I do know what the effect is. And I do know that it is obviously possible, because they are doing it everywhere else in the world and we are not. And if we want to maintain an economy and a society which has been at the cutting edge of technology, with the highest real incomes of any major country, we have to enhance the capability and the skills of people coming out of our schools. You cannot have a highly complex capital structure without skilled people to essentially staff it. I think immigration is obviously one thing that is helping in part. It is filling in a lot of the slots where skills are required. But we shouldn't be needing to do that. We should be doing it with our own students and enhancing their capabilities in a manner which would enable our increasingly complex capital stock to function and maintain these very long term improvements in productivity, which even though I expect them to slow down from the recent pace, nonetheless, even at half of where they have recently been, it would be a major advance over what we experienced in the period of say the 1970s and the 1980s.

Of course, now I'm thinking: gee.

Am I really on the side of bringing down the so-called skill premium?

I mean, it's not just math people can't do.

Nobody can write, either. Or spell.

Sigh. And here I thought my big fat advance for Animals in Translation was a simple sign of how great the proposal was.

Never crossed my mind that decent nonfiction writers might be in short supply.

SeniorSlump 19 Sep 2005 - 01:54 CatherineJohnson

Another great chart from Education Next. I love these things.

I don't know why.

source:
The Seeds of Growth by Eric Hanushek
Education Next
Fall 2002

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.....

DanDreznerThreadOnMathEdPart2 20 Sep 2005 - 10:07 CatherineJohnson

mission accomplished

I have submitted Kitchen Table Math to Google. Believe it or not. Now I just have to do Alta Vista, Yahoo, .... and whatever else I'm supposed to do. (Suggestions?)

question: are there 'specialty' search engines I should know about?

thank you, Independent George

As usual, one thing led to another: first I Googled Kitchen Table Math to see if, by some chance, the folks at Open Directory had sent ktm to Google so I wouldn't have to. (answer: no)

Then up popped a reference to Kitchen Table Math on Daniel Drezner's blog, the very same thread I linked to last night.....

I'm going to have to do more reading & less skimming.

speaking of which.....no dumping on special ed, please!

Here's the post I wrote last night & then took down, because I'd stepped on Carolyn's post:

This is annoying.

One of Drezner's commenters has raised the Special Ed Is Soaking Up All Our Resources issue. (i.e. we're really NOT spending gobs more money on education than anyone else, because we assign $25,000-a-year personal aides to autistic kids and other countries don't)

So here's Jay Greene, whose research has been cited in Supreme Court cases, writing on that very issue:

...the most pernicious thing about blaming special education is not that it is politically correct, it is that it's not true. Special education can be held responsible neither for soaring education costs nor for stagnant student achievement. Yes, more money is spent on special education than on regular-education students. And yes, more students are being enrolled in special-education programs. But the shell game in education is that there has only been an increase in the students labeled as needing special education and not an actual increase in students with those learning difficulties.
There is nothing in the water that has created more children with learning problems. Better survival rates for babies born prematurely or mothers using drugs during pregnancy have also not led to a spike in students with learning problems, or, if they have, other improvements in public health, such as the reduction in lead-based paints and better child car seats, have countered any increase in children with learning problems.

Greene's book is out. It's in my cart.

DanDreznerPart3 19 Sep 2005 - 19:10 CatherineJohnson

Working my way through the Drezner thread, I found this:

I was able to bluff my way through two college degrees and a CPA certificate, but I could not help my seventh grader do long division.
We have innovated the math curriculum into a bizarre shambles which makes absolutely no sense to anyone who acutally knows arithmetic.
My daughter got a "D" on a paper with all correct answers because she did long division the way I was taught, rather than using the "process," whatever the hell that is.
In the sixties my small, poor school produced a 100% reading literacy rate and a 100% literacy rate in basic mathematics, including the student who took "shop." How far we have fallen.
Teach arithmetic in grade school, teach real math after that.

DanDreznerPart4 19 Sep 2005 - 20:48 CatherineJohnson

One last comment from the Drezner thread:

Want an outsider view ? I went to live in the US when my children were 12, 10 and 5 , the middle child made the Iowa test of skills and rated into the best 8 percent in the country...I will never forget the face of the teacher that interview me afterwards , when I told her my daughter , did not speak any english a year before, pretty amazing for a family coming from a third world country, ah ?
You americans must stop looking only to your navel, brag about your good schools , sorry for the bad news they are pretty bad indeed, at many levels (even though I believe they are a few exceptions but the average cultural level of an us student in Atlanta´s good neighborhood, golfcouse condo kind of neighborhood is lousy in my experience) , and learn from others in Europe and elsewere ...we have found a few things:
-Yes , respect for the teacher is important, respect, no fear , is different you know.
-Respect is teached by parents,in their daily interactions, fear too I am afraid
-Respect in high school is earned
-The kid uniqueness and personal gifts , we all have some ,you know, are important to acknowledge
-american teachers ,I am a witness to some of them loving ability, do they have time for that ?

Here are the paragraphs that mean most to me:

those in contact with my southamerican educated children were amazed at them ...My oldest one got an achievement certificate from the US President in high school, it took me only an afternoon to teach them how to go through those impressively shallow text books ...and get the right answers for the minimal test they got , does that rings any bell ?
-Something that got my attention , no recess , how do you expect a child 10 or older, full of energy to behave at lunch time if he does not have 10 , 20 min of rest in between ...do you know anything about how the brain works ?it needs a rest after 45 mins , or don´t you adults , do ? That is only in Georgia schools , I hope, for the sake of children.

This is your core narrative, that's for sure. When you've got folks moving here from aboad & discovering their kids are suddenly in the top point-o-o-o-5 percent of the country, common sense dictates that this has to mean something.

And RECESS IN SOUTH AMERICA.

In Japan, kids have a 15 minute recess after each and every class.

We've probably got the most hyperactive population of school-age kids on the planet (I think that's where our creativity comes from) and we're asking them to make it through the day on ONE recess?

Which reminds me: I'm adding a tae kwan do 'aerobic counting exerercise' to my after-school Singapore Math class this fall. We're gonna spend 10 minutes JUMPING. (Or something. The chair of the program is going to teach me the routine.) We're gonna jump so high and so fast they're gonna be grateful to sit down and do math.

CreativityGapPart2 13 Nov 2005 - 18:45 CatherineJohnson

Susan has a funny comment on the creativity gap:

"However, the idea that we have nothing to worry about because we're so darn creative is, I think, overstated."
I think it's bordering on myth. I almost posted over there because it was apparent to me that most of the posters, smart as many of them are, do not have children in the system. They seemed to be all over the map with what it all meant(children aren't valued, teachers aren't valued, unions are the problem, etc.) finally arriving at the ole' "we're so creative because we don't do as much rote." Give me a break. None of them has any idea how much rote Asian students actually do, it just has to be a whole lot because there can be no other explanation.
It's also fascinating how critics of Singapore and Saxon mention that they're okay curriculums if you just want to do good on SAT's and standardized tests. No, I want to to perform poorly, yet take solace in the knowledge that I'm just too creative for a standardized test.
It also seems apparent that some people are mixing up spontaneity with creativity. As someone whose career has been in the fine arts, I assure you that the two traits do not really mean the same thing, much as many people wish they did.

I'm LOL-ing over that one, because I always have the exact same reaction whenever people start carrying on about teaching that 'only' allows a child to do well on standardized tests.

My reaction is always: Oh, yeah. I want my child is to know nothing that might appear on an SAT. I want him to score a 10. Or, better yet, a zero.

And I want to live in a town where my property taxes go up each and every year so we can afford to purchase a curriculum that will make sure he retains nothing in long-term memory.

I'm gonna go out on a limb here and say this is a Geography of Thought moment. We Americans--apparently We Westerners in general--are Logic of Noncontradiction folks.

So if we start thinking there's a contradiction between doing well on a standardized test and being creative, we are going to Polarize Like Crazy. We're gonna choose sides.

I've done plenty of logic-of-noncontradiction thinking in my time, but never on the subject of standardized tests. My feeling, from the get-go, has always been: Yes, I agree, you're right, strict memorization of formulas and nothing else, so a child can score high on a standardized test, is a Bad Thing.

All the same, I would like my child to score high on a standardized test, thank you very much.

I refuse to Pick One.

on not living in a consensus culture

Here's the line I like from Geography of Thought:

In another experiment described in the book, Nisbett and colleagues found that Americans respond to contradiction by polarizing their beliefs whereas Chinese respond by moderating their beliefs.

When I read this to Ed, he said it's a commonplace in the field of history to call Asian cultures consensus cultures.

We do not live in a consensus culture.

how Asians and Westerners think differently
how Asians and Westerners think differently, part 2
How Asians & westerners think differently, part 3
Harold Stevens, RIP
describe this picture
creativity gap, part 2

keywords: polarize polarizing Western thought Western thinking

GeneFlow 22 Sep 2005 - 15:15 CatherineJohnson

One of these days I'm going to finish my post on creativity in Asian societies & in America, but for the time being, here's a link to a page on gene flow, an expression I'd never heard before.

And here is an abstract from SCIENCE:

Separate Ways
Built to keep out marauding tribes, the Great Wall of China, completed during the Ming dynasty (A.D. 1368-1644), has affected the course of plant as well as human history.
"The Great Wall has served as a physical barrier to gene flow between [floral] subpopulations separated for more than 600 years," according to plant geneticist Hongya Gu of Beijing University. Gu and colleagues studied one population from each of the four species of insect-pollinated plants and two species of wind-pollinated plants that grow on both sides of the Great Wall. They report in the March issue of Heredity that, compared with control plants from two sides of a road, there was "significant genetic differentiation" between plants and their counterparts on the other side of the 2400-kilometer wall, whose height ranges up to 7.1 meters. Wind-pollinated species showed less differentiation than insect-pollinated species. "This is a fine example [of] how easy it is for populations to diverge," especially because of the absolute dating, says Peter Raven, director of the Missouri Botanical Garden.
Science, Vol 300, Issue 5625, 1501 , 6 June 2003 , p. 1501.

Gene flow happens to people as well as plants, and I take it as a given that Americans have experienced far more gene flow than many or most Asian societies. Since I believe creativity is sparked by difference, I assume that, when it comes to creativity, gene flow is a good thing.

You probably have to study history (which I haven't) to get a sense of how closed societies like Asian & Japan were and are still today. When you think about the fact that, as a country, we are so pro-immigration that we don't police our borders.....and then contrast that to the Great Wall of China.....the difference is vast.

(In the spirit of nonpartisanship, I'd like to add that I'm not making a critical statement about immigration policy here. Personally, I think 'something needs to be done' about the illegal immigration situation...and, at the same time, I'm pro-immigration & pro-immigrants. I'm probably exactly in the middle of mainstream American opinion on the subject, which is why I feel qualified to say that America is a distinctly open society.)

BarbaraOakleyAndSteveHOnCreativityGap 22 Sep 2005 - 17:03 CatherineJohnson

I wanted to make sure these comments made it 'up front.'

from Barbara Oakley:

Having taught engineering in China as well as the US, I think the 'fear' that you alluded to regarding Asians refers to loss of face, which is a devastating experience for Asians. I was told it was very difficult to get Chinese to volunteer to respond to questions in class because they feared looking bad if they got the wrong answer. Also, I wonder if there is some residual fear from Mao's Cultural Revolution. During that horrific ten year period from rough 1966 to 1976, creativity could get you killed. For example, even in the manufacturing of something as prosaic as Yixing teapots, all of the craftsman just regurgitated old styles of pots. They were afraid if they did something new and creative, other potters would get jealous of them and denounce them for something or other, which could result in their internment in brutal work camps, or even in their execution.

and from Steve H

I see all levels of creativity. Perhaps one would call it innovation in the technical world. And, I don't think it is limited to finding a solution that comes from out in left field. It could be a small improvement applied to someone else's work. I see that all of the time in the technical literature. It may be small, but it is new. Let me add that the technical literature is full of papers from East Asian authors.
Most all innovations in the technical world are small improvements. I would say that trying to develop the sort of creativity (luck or hard work) needed for major leaps is quite unrealistic. (Although, one of the three goals I have for my son is to know the value of hard work.)
When educationalists talk about creativity they say that learning knowledge and skills first ruins creativity. In the technical world, you can't be creative without basic skills and knowledge. Was Edison creative? Most would say so, but Thomas Edison called genius "one percent inspiration, 99 percent perspiration." Modern reform math seems to think it has found a way to teach (learn?) math without hard work.

creativity in math
keywords: creativity gap

OK, I am going to take a break, have some lunch, get some exercise, and fill out my Irvington PTSA gift wrap paper order form. Assuming it's not already too late.

SchmidtCoherentCurriculum 26 Sep 2005 - 20:03 CatherineJohnson

It had been awhile since I'd last read William Schmidt's American Educator article, Coherent Curriculum.

I'd forgotten this section:

Some people might ask, “What difference does it make if we can’t do fancy math problems?” It does make a difference. A typical item on the TIMSS 12th-grade math test shows a rectangular wrapped present, provides its height, width, and length, as well as the amount of ribbon needed to tie a bow, and asks how much total ribbon would be needed to wrap the present and include a bow. Students simply need to trace logically around the package, adding the separate lengths so as to go around in two directions and then add the length needed for the bow. Only one-third of U.S. graduating seniors can do this problem, however. This is serious.

Lately I've been seeing the claim that our seniors blow off the TIMSS test, while Asian kids spend weeks in grueling preparation.

Color me not impressed.

A 17 year old should be able to do this problem in his sleep.

RisingInequalityPart4 27 Sep 2005 - 16:05 CatherineJohnson

A few weeks back we were talking about 'rising inequality'--whether it's real, and, if so, whether bad schools are a major cause.

For the time being, I believe both propositions: I do believe we're seeing rising income inequality, and I also believe that poor schools are a major cause. (I believe this because I'm taking Alan Greenspan's word for it. I have zero Special Knowledge on this score. )

In one of our exchanges we talked about what it meant that elite universities have a huge percentage of students from the top income quartile. I think it may have been Steve who pointed out that parents with college age kids are in their high-earning years, so you would expect to see colleges mostly populated with kids from top-quartile families.

The Economist article on higher ed has some further statistics on this:

William Bowen of Princeton University and two colleagues, in a study of admissions to elite universities, found that in the 11 universities for which they had the best data, students from the top income quartile increased their share of places from 39% in 1976 to 50% in 1995. Students from the bottom income quartile also increased their share very slightly: the squeeze came in the middle.

Is rising inequality the correct interpretation?

Or do demographics explain this shift as well? Do the delayed childbearing of the baby boom generation, smaller families, and employed mothers account for college students at elite universities today having parents with higher income?

Or are we seeing a 'real' rise in inequality?

those durn Americans

The real threat to meritocracy, however, comes not from within the universities but from society at large. One consequence of the squeeze on funding for public universities, created by Americans' reluctance to pay taxes, has been an academic brain drain to the more socially exclusive private universities. In 1987, seven of the 26 top-rated universities in the US News & World Report rankings were public institutions; by 2002, the number had fallen to just four.

It's always fun reading THE ECONOMIST, because of the little asides they slip in about the shocking woe caused by Americans' reluctance to pay taxes & the like. Every time I see one of those I have to discount the claim being made, because they never offer the slightest evidence that the character foible being cited has anything to do with the subject at hand.

It's interesting to know that there's a brain drain from public universities to private (Ed is part of it, as a matter of fact).

But I wouldn't assume it has anything to with rising inequality in higher education one way or the other. When private universities recruit academic stars, typically they promise them they won't have to teach undergraduates. (Not the case for Ed. He teaches graduates and undergraduates.)

It should be obvious (and it is obvious to people like Ed who teach in elite institutions) that an expensive college filled with world-renowned professors who don't teach undergraduates isn't a good school for undergraduates.

Or isn't obviously a good school for undergraduates, at any rate.

rising costs of college

Between 1971-72 and 2002-03, annual tuition costs, in constant 2002 dollars, rose from $840 to $1,735 at public two-year colleges and from $7,966 to $18,273 at private four-year colleges. True, the federal government spends over $100 billion a year on student aid, and elite universities make every effort to subsidise poorer students. One study of admissions to selective colleges shows that, in 2001-02, students with a median family income paid only 34% of the “sticker” price.
Still, the sheer relentlessness of academic inflation is worrisome. Elite colleges have little incentive to compete on price; indeed, they tend to compete by adding expensive accoutrements, such as star professors or state-of-the-art gyms, thus pushing up the cost of education still further. And the public universities that played such a valiant role in providing opportunities to underprivileged students are being forced to raise their prices, thanks to the continual squeeze on public funding. The average cost of tuition at public universities rose by 10.5% last year, four times the rate of inflation.
The dramatic rise in the price of American higher education puts a heavy burden on middle-class families who are too rich to qualify for special treatment. It also sends negative signals to poorer parents who may be unaware of all the subsidies available. Deborah Wadsworth, an opinion pollster, points out that universities may be courting a popular backlash. Americans increasingly regard universities as the gatekeepers to good jobs, but they also see them as prohibitively expensive. The result is a steady erosion of public admiration for these formerly much-esteemed institutions.

I wonder if this is true. Are universities losing legitimacy because their prices are rising?

Sounds wrong to me.

I love reading THE ECONOMIST. It's like having a mom forever, A British mom. You're always getting little REMINDERS that your behavior is not passing muster, only the behavior in question is economic, not social. Message to America, as Tom Friedman might say, and so frequently does: Behave yourself. Pay your taxes, and stop charging exorbitant fees for services.

my favorite sayings about America

The Americans will always do the right thing...after they’ve exhausted all the alternatives.

- Winston Churchill

What was really amazing was the speed with which the Americans adapted themselves....They were assisted in this by their tremendous practical and material sense and by their lack of all understanding for tradition and useless theories.

- George Rommel

Animals studied by Americans rush about frantically, with an incredible display of hustle and pep, and at last achieve the desired result by chance.

- Bertrand Russell on American laboratory rats 1927

I don't quite know what that last one means, but I like it anyway.

update

Years ago, when I went to England for the first time, I could barely stand it. Everyone sounded like my mom. I love my mom; that wasn't the problem. Our mom is so great, we four kids practically hero-worship her to this day.

The problem was that everywhere I went some complete stranger would step forward to correct my manners. At one point Ed and I were actually scolded by the people seated behind us at a play about Elvis's last night of life. It was a very silly play, featuring a fat Elvis sitting around lecturing his entourage about the Third World in a bad southern accent.

At intermission, when the people behind us asked us how we liked the play so far, and we pointed out that Elvis was unlikely ever to have used the words 'Third World' in the lucid moments of his life, let alone on the night he was overdosing on drugs, they got huffy. Then they made comments about our manners, as I recall, though I no longer remember what they said.

Drove me nuts.

I went back to England a little while ago--just after the Madrid bombings, as a matter of fact--and this time I loved meeting my mom everywhere I went.

It was a lovely trip, and when a 22-year old waiter collecting my plate in a karaoke bar said to me, 'Aren't you going to eat your peas?' I could have kissed him.

No!

I am NOT going to eat my peas!

But THANK YOU FOR ASKING!

That's what ageing will do to you.

I don't know how many of you saw this blog reaction to the London bombings, but it expresses my feelings about England, and about any and all attacks on England. (LOTS of four-letter words, so not for kids.)

Alan Greenspan on rising inequality
rising inequality, part 2
rising inequality, part 3
median income families UCSC students
another statistics question
channeling the Wall Street Journal
Financial Times on US college costs
Economist on US higher ed
The Economist on rising inequality in universities

MathProfessorsVsComputerScienceProfessors 17 Sep 2006 - 01:14 CatherineJohnson

Very interesting comment from Lesley Stevens:

Tangential to the "math brain" discussion, my husband has made a very interesting observation.
A smidge of background here: He has always been one who has no fear of questioning or correcting his instructors, something that many of his primary school teachers didn't much care for, as you can imagine. He has a double major in mathematics and computer science and he'll graduate with his B.S. this spring. (He is 31, finishing his degree after a 10 year hiatus.)
What he has noticed is that while his CompSci and gen ed instructors often resent being corrected, his mathematics instructors do not.
His theory is that people who do math are accustomed to being wrong. They make mistakes all the time, and it's easy to do when working a complex problem on a blackboard. He thinks that you pretty much can't do math all the time and still maintain an infallibility complex, or superior attitude towards students. Especially since math is a young person's game, and most math professors are already past their "peak" in math ability, and know it.
In addition, in "soft" liberal arts areas, or conversely, extremely complex areas like programming, mistakes may not be obvious, or may be open to some debate. In math, an instructor can't wiggle around a mistake. If he has added 6 to 7 and gotten 14, that's just wrong, end of story.
What I think I'm getting at here is that making math easy for students through "no one answer", etc. is not helpful because it delays an understanding that math is hard for everybody including people like my husband, and that the best mathematicians in the world make mistakes all the time. This understanding actually makes me feel a lot better about my own anxieties about math.
Oh, and as for "math brains", my husband's major the first time around, before the 10 year break, was Philosophy.

This discussion has been a revelation to me. I'm going to keep all the URLs handy so I can print out these comments out and/or send the links to friends, teachers, & administrators as needed.

The vast majority of people simply assume, without even realizing they are assuming, that doing math comes naturally to the select few AND that those select few are the ones who ought to be doing math, and who deserved to be put in Phase 4.

I was just this afternoon talking to a mom whose son was moved from Phase 4 to Phase 3; according to figures I was given, 35% of Irvington's Phase 4 5th graders failed the Phase 4 placement test at the end of 5th grade, something most parents don't know. Most of these children switched to Phase 3, though some parents refused the move. I know of two; there may be others.

All of this gatekeeping activity is based on the explicitly stated judgment that 'he/she doesn't belong in Phase 4.'

It's an essentialist argument.

I was already off the boat for the whole 'He's a three' business, thanks to Wayne Wickelgren, and to Ed ("We want Christopher to be an overachiever.")

Now I'm seriously off the boat. And I'm armed.

Confessions of an engineering school wash-out
more confessions of an engineering school washout
the Terminator, or 'the magical number 7, plus or minus 2'
On Having a Math Brain (by Carolyn)
Wayne Wickelgren on mastery of math & on creativity & domain knowledge
late bloomers in math & Wickelgren on children's desire to learn math
math brain debunked (by Carolyn)
math professors versus computer science professors
Wayne Wickelgren on math talent

BlueCollarWhiteCollarUnionsSchools 01 Oct 2005 - 00:19 CatherineJohnson

from the Wall Street Journal today (subscription required)--

My father encouraged his children to study a profession. Why? "Because, no matter the job market, you'll always be able to hang up a shingle," he assured us.

[snip]

In my youth, future white-collar wearers took college-prep courses while other kids were lumped into vocational programs, where they welded and drilled. We learned how to solve those pesky word problems involving cars speeding away from Cleveland at 62 miles an hour with half-tanks of gas. They actually learned how to make those cars go.

Forget revenge of the nerds. These days it's revenge of the electrician, the mechanic and the plumber: Blue collars aren't what they used to be. General Motors may advertise Mr. Goodwrench, but a good mechanic must master computer diagnostics. Go over to the waiting room at the Mercedes dealer and you'll see white-collar America at the mercy of blue-collar. I might be able to forecast the future path of the euro-to-yen ratio, but you think I can replace the catalytic converter under the hood of my car? Say, where'd they hide the hood latch, anyway?

My point is not merely that the educated class is the bumbling class .... Rather the old-fashioned distinction between blue collar and white has been lost in an economy that demands ever-stronger skills and active brain cells. In the 1950s (and into the 1960s) a stumblebum in a gray flannel suit with a bachelor's degree had a good chance of receiving a high, stable income complete with suburban house and a manageable mortgage. Think Darrin on "Bewitched." But these days carrying around your college diploma doesn't entitle you to much. For one thing, a college degree is a cheapened currency. In 1950, only 6% of the population had one, compared with 28% today.

[snip]

The outsourcing threat from Asia no longer aims at just the blue collars. American architects, radiologists and tax accountants feel nervous about Indian competitors (hence the white-collar unions). A guy wearing a turban in Bangalore can push the TurboTax buttons just as fast as a guy in Teaneck.

In "Bait and Switch," Barbara Ehrenreich's latest plunge into working-world disguises, she impersonates a laid-off white-collar executive. She wastes her time attending self-help seminars and sneering at hapless people while rejecting job offers. What should she have done? Taken a job! Learned a new trick besides snobbery! A year of community-college schooling can raise an older female's income by 10%, according to a Chicago Federal Reserve Board study.

Blue-collar assembly workers started facing these threats a long time ago. Between 1940 and 2000, U.S. manufacturing output soared 11-fold. But while one-third of U.S. workers once walked through a factory gate, only 13% need to do so today -- a stunning productivity gain. Ross Perot's twangy warning of the "giant sucking sound" was aimed at blue-collar assemblers. But now the white collars are itching.

[snip]

We are in a global race for IQ points. Not useless Mensa meeting points but applied IQ points. Brains put to work. Those countries that best harness IQ will prosper most. The U.S. produces about half the annual patent filings in the world. That's an outstanding number. But new ideas are not enough if we do not have a motivated, educated work force to exploit them. Despite improved high-school graduation rates, our kids are the Jamaican bobsled team of education, to judge by international test scores. They lose to the Slovenians.

Mr. Buchholz, an economic adviser in the White House of George H.W. Bush, is the author of "Bringing the Jobs Home" (Penguin/Sentinel, 2004).

applied IQ points

Now there's something I wasn't thinking about back when I got a Ph.D. in Film Studies.

GuidanceCounselorInNewYorkCity 01 Oct 2005 - 12:32 CatherineJohnson

Mr. Fish, guidance counselor extraordinaire

SamFreemanOnAchievementGapTimes 03 Oct 2005 - 16:13 CatherineJohnson

eduwonk says The Achievement Gap in Elite Schools is must reading. Get there soon, because the TIMES keeps articles posted for 7 days & then they're gone.

update

OK, maybe it's not so hot after all.

SatRecenteredScores 04 Oct 2005 - 14:32 CatherineJohnson

SAT scores were 'recentered' in 1995. Anyone tested before 1996 can use the charts posted below to convert his or her scores.

The interesting thing, as KDeRosa has pointed out, is that it's mainly verbal scores that shot up after recentering. Not math scores.

That was a big disappointment for me back when I first tracked these down. I was psyched to have my 620 Math shoot up into the 700s.

No such luck. A 620 then is a 620 now.

Instead, my Verbal score went from 720 to 790.

I find this intriguing.

update

Of course, the good news is I could probably go get a job at Advantage Tutoring today.

College Board on recentering

"In April 1995, the College Board recentered the score scales for all tests in the SAT Program to reflect the contemporary test-taking population. Recentering reestablished the average score for a study group of 1990 seniors at about 500 — the midpoint of the 200-to-800 scale — allowing students, schools, and colleges to more easily interpret their scores in relation to those of a similar group of college-bound seniors."

source:
College Board Equivalence Tables
College Board conversion table, SAT 1

"For 1972-1986 a formula was applied to the original mean and standard deviation to convert the mean to the recentered scale. For 1987-1995 individual student scores were converted to the recentered scale and then the mean was recomputed. From 1996-1999, nearly all students received scores on the recentered scale. Any score on the original scale was converted to the recentered scale prior to computing the mean. From 2000-2003, all scores are reported on the recentered scale."
source:

2003 College Bound Seniors: A Profile of SAT Program Test Takers, page 3 (pdf file)

what does an SAT math score mean?

This chart is interesting to me in light of my own history with math.

I've mentioned before that I had always assumed I was "reasonably good at math."

I didn't think I was a math whiz; I didn't think I had any special talent. I thought I was 'pretty good' at math.

That's why it came as a shock to find I couldn't begin to teach a 4th grade math curriculum to Christopher - and that, in fact, I understood practically nothing about the subject.

That may be overstating it, which I don't want to do. Still, when I started trying to teach math to Christopher, I was constantly confronted by the discovery that I didn't-understand-fractions or didn't-understand-long-division or I didn't-understand-this or I didn't-understand-that.

I'm still having these discoveries over a year later.

Of course one can say that elementary math is deep; a person could continue making such discoveries forever.

That may be so, but it's not what I'm talking about. I'm talking about having done well in math as a child, and having minimal conceptual understanding as an adult.

..........

This 3rd chart shows you where I stacked up, percentile-wise at the end of high school. Bear in mind that SAT tests are taken only by kids going to college, and bear in mind that back when I was taking the SATs no one had ever heard of an SAT prep course. I walked into the SATs cold, not having looked at a math book in a year, sat down, and took the test.

Where did I end up among the college-bound population?

On math: top 10% of all girls, the top 13% of all boys. 11th percentile overall

At the age of 17, I concluded that this meant I was, yes, reasonably good at math.

Now I find out I don't know what a fraction is.

source:
2003 College Bound Seniors: A Profile of SAT Program Test Takers, page 13 (pdf file)

so what does an SAT score mean? (part 2)

The short answer is, I don't know.

What I think, based in my experience, is that it's entirely possible that SAT scores do tell us something about 'how good' a person is at math.

I think it's probably true that I'm "reasonably good" at math, or at least reasonably good at learning math. I've been able to teach Christopher and me, and I've been able to figure out how to do this under intense time pressure.

So...I don't think SAT scores 'lie.'

The SAT test was always supposed to be a test of aptitude, not knowledge. People have challenged that claim forever, but in my own experience, as an 'n of 1,' that's pretty much what the SAT tested. It tested my ability to learn math, not my ability to do math.

I think.

more SAT trends to come

KDeRosa has sent me some charts on long-term trends in SAT scores that I'll get posted as soon as I find them on my desktop!

Number 2 Pencil thread on SAT recentering

Grudge Match: SAT vs ACT

SAT tests: recentered scores
SAT scores & calculator use

SatScoresCalculatorUse 06 Oct 2005 - 17:51 CatherineJohnson

So now that Carolyn and I have gone on record as being Against Calculators, here's the scoop on calculator usage as it correlates with SAT scores (still working on this, bear with me):

SAT I Percent Verbal Math
Number Percent Male Female Mean SD Mean SD

source:
2003 College Bound Seniors: A Profile of SAT Program Test Takers, page 11 (pdf file)

update

I just re-read this chart and the Message popped: this is How do you get to Carnegie Hall.

Look at the wording:

Use (calculator) Almost Every Day

Use Once or Twice Weekly or Less

They're not measuring calculator use. They're measuring practice.

I now use my calculator each and every day, because I'm studying math each and every day.

Before I embarked on my all-math-all-the-time regimen, I used my calculator once or twice weekly or less.

and, from TIMSS:

"Calculators. TIMSS found an almost linear relationship between the amount of calculator usage in school and high achievement at grade 8 and 12. The higher the grade level, the stronger the link. The more the calculator was used (gleaned from both students and teacher questionnaires) the higher the scores. This may mean that the tasks were of such complexity and required such a level of mathematical thinking that computation was a minor/simpler part of the problems.

More research should be done on the various uses to which calculators were put. Were they scientific, graphing or other types? The correlation did not hold, however, at fourth grade. Only two countries reported calculator use at grade four.

Computers. Computer use was a different story. It appeared that too much use could lower achievement. The probably key is knowing how and when to use computers. The Japanese geometry teacher in the TIMSS public use videotape illustrates a powerful use of the computer to quickly and concurrently show the construction of many variations of triangles between parallel lines in one image."

also:

"The problems on TIMSS (and on NAEP) are virtually all multi-step. This has implications for what should be going on in classrooms."
source:
The American Federation of Teachers Looks At TIMMS (PowerPoint presentation)
to find: Google "AFT" and "TIMSS" and "ppt"

SAT tests: recentered scores
SAT scores & calculator use

SATScoresDecline 28 Sep 2006 - 20:33 CatherineJohnson

Ticket to Nowhere
by Paul E. Peterson

NAEPDataFromKenDeRosa 05 Oct 2005 - 21:48 CatherineJohnson

KDeRosa sends 2 charts, & observations:

1. The NAEP data only goes back to the early 70s and misses most of the substantial decline in scores that took place in the 60s and early 70s. Of course, the SAT data does not include the entire student population, only the college bound one and it is normalized. Nonetheless, it shows a very serious degradation of skills.

2. The high-water mark in both verbal and math scores was in 1963. 42 years later and we still haven't recovered.

3. There was some debate on why the decline in the 60s took place. One side says changing demographics are to blame. The other side says most of the change in demographics took place by 1963 with almost no decline in scores. Moreover, the decline in scores after 1963 included substantial declines among the smartest students at the top of the curve which is not explainable by changing demographics. I haven't been able to locate a good analysis of this period online. Maybe a more knowledgeable reader can help.

4. The SAT people have monkeyed around with the test in 1974, 1995, 2005 and sometime in the 80s I believe. Not sure what effect all those changes had, but I do know that SAT scores post 1995 no longer correlate reliably with IQ scores.

5. Did I mention that the teachers' unions came to prominence in the 60s. Coincidence?

6. Math scores for the NAEP and SAT exams have been rising in the past few years. Never mind that both tests have been dumbed down (no more quantitative section in the SAT). The SAT people say it's a bona fide gain. The ACT people say it's a phony gain. I guess the college math professors would know best.

It would be nice if a knowledgeable psychometrician could provide some insight.

"When the SAT was renormed in April 1995, mean scores were set at or near the midpoint of 500 of the 200-800 score scale, a process called recentering. All scores in this table reflect that process. Means after 1996 are recentered, and those for 1996 are based on recentered scores plus scores converted from the original to the new scale. Means for 1987-1995 were recomputed after individual scores were converted from the original to the new scale; means for 1972-1986 were converted to the new scale after a formula was applied to the original mean and standard deviation; and means before 1972 are based on estimates."

Laurence Steinberg's 1996 Beyond the Classroom: Why School Reform Has Failed, which chronicles the results of a massive study he headed, has one of the best discussions I've seen of this data. (He sees slacker parents as a major if not the major source of the problem.)

the 60s

This reminds me that I have to ask my mother about my grandmother's experience teaching in Springfield, IL. There was a point at which, quite suddenly, my grandmother perceived teacher quality to have plunged. I think this happened in the 60s, but I'll have to make sure.

SampleNaepQuestions 05 Oct 2005 - 00:21 CatherineJohnson

from Our Nation's Report Card, the 8th grade test:

sample NAEP questions search tool

...and see Tom Loveless on the new, improved fraction-free NAEP here

StevensonAndStiglerOnGroupLearning 09 Oct 2005 - 16:21 CatherineJohnson

Carolyn and I have been reading emails from a friend who's just discovered that the math teacher at her son's private school is promising to make 'prolific' use of collaborative learning in his classroom this year.

Like Carolyn, I view the word prolific, used in this context, with suspicion. (Hmm. I wonder what Google will give me for 'red flag'?)

red%20flag.jpg

Just in case you were wondering.

You can also access lyrics & music to The Red Flag by James O'Connell.

And that's about it.

back on topic

I'm inclined towards the position that group learning, when not used prolifically, is fine and dandy.

I think so for a couple of reasons:

first of all, a California Department of Education study found that group learning was supported by quality research

second: group learning, I think, can set up healthy competition, both within a group and among groups

and third: people are natural born observational learners, and a group is, or could be, the place where a child can observe other children doing math. (No time to expound on the history of observational learning in the field of behavioral research on animals. But, if you're interested, see Alex the parrot. Alex didn't learn a thing until he had a rival learner getting the right answer & snapping up all the goodies.)

Oh, OK, I will say something about the history of observational learning in the field of animal behavior studies.

Even better, I will make this a Discovery Task!

Think and Discuss

For many years, behaviorists believed animals learned through classical conditioning, which many people call 'trial and error' learning.

What problems might an animal experience if he has to learn everything he needs to know through trial and error?

Do you think errorless learning might have some advantages for an animal living in the wild?

Bonus question

If you were a baby antelope, which way would you prefer to learn about lions?

Through trial and error, or through watching other baby antelopes turn into lunch?

Explain.

group learning in Japan

Here are Stigler & Stevenson on group learning in Asia versus America:

Perhaps the most profound difference in the way Asian and American children spend their time at school is in the degree to which they are alone versus being part of a group. American children have far fewer opportunities for group participation than do Chinese and Japanese children.
[snip]
Chicago children spend a great deal of time working on their own. The time spent at their desks filling in workbooks or handout sheets, reading, and doing other solitary activities occupied nearly 50 percent of their class time, but never more than 31 percent of the class time int he Asian cities. Conversely, Sendai, Beijing, and Taipei children spend most of their time in classrooms that were organized so that all of the children were working as a unit with the teacher as leader. Participation in lessons that involve the whole class, even in classes with many students, enhances students' feelings of group membership and reduces their sense of isolation. [ed.: notice that, in Asian countries, the entire class can be experienced as a group]
Several of the American mothers we interviewed expressed approval of the fact that their child's teacher allowed the children to work at their own pace. This practice may have benefits, but working at one's own pace means working alone, and the slower one's pace, the more time spent alone. Many times we observed a class where all but a few of the children had finished their assignment. The remaining few children struggled alone.
[snip]
When small groups are formed in Chinese and Japanesse classrooms, children are selected so that all levels of achievement as well as other characteristics will be represented in each group. In Japan, these groups are known as han.
[snip]
One Japanese teacher explained to us her method of grouping children: "I mix the groups so that each child has something to contribute. Each group should have a top student, but it would not be good to put all of the top students together. A group needs other talents as well: someone with artistic talents, someone who is good at sports, and so on."
[snip]
Witin each han, different children exercised leadership based on their particular skills.
[snip]
We understood why American children are more likely to seek other children for after-school play, why they spend so much time in their classrooms talking inappropriately to other children, and why they might not find school an especially pleasant place to be. Indeed, American children are less likely than Chinese or Japanese children to say they like school. For example, between 75 percent and 86 percent of the children in Taipei, compared to between 52 percent and 65 percent of the American children...indicated that they liked school.

NAEPScaleProblem 08 Oct 2005 - 00:29 CatherineJohnson

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

MissingBoys 28 Jan 2006 - 00:37 CatherineJohnson

Number 2 Pencil links to an article in USA Today about missing boys:

Currently, 135 women receive bachelor's degrees for every 100 men. That gender imbalance will widen in the coming years, according to a new report by the U.S. Department of Education.

And there's this:

Nearly as many men are behind bars or on probation and parole (5 million) as are in college (7.3 million).

is that what you'd call a 'hostile atmosphere'?

Here's Glenn Reynolds:

There seems little doubt that universities have become less male-friendly in recent decades, to the point of being downright unfriendly in many cases. The kind of statements that are routinely made about males and masculinity in classrooms and hallways would get professors fired if they were made about blacks, gays, or many other groups. Sexual-harassment policies start with the presumption that men are guilty, and inherently depraved. And colleges now come at the tail-end of an educational system that is (compared to previous decades) anti-male from kindergarten on, meaning many males probably just want to get out as soon as they can.

no good boys

Christopher has complained about this since he was quite young.

"Why are the boys always the dumb ones?"

"Why do the boys always lose?"

"Why do the girls always win?"

"Why can't I have a shirt that says Boys Rule?"

His friend, next door, who's a year older, asked his mother last school year, "Why does misogynist mean 'hates women' and that's bad, but feminist means 'hates men' and that's good?'

He was serious. His mother has been a feminist all her life; she certainly does not hate men; yet her son, living in the same culture she's living in, has absorbed the idea that hates-men is good.

you can't say that

I've already written about my own experience trying to publish an article on the mismatch between little boys and school culture 20 years ago.

no good boys, part 2

source:
Banned Words, Images, and Topics: A Glossary that Runs from the Offensive to the Trivial

Think about being a boy today, growing up in a world where it is against the rules for children's textbooks to portray boys as curious, strong, intelligent, brave, strong, or able to overcome obstacles.

key words: positive stereotypes positive stereotyping

USA Today report on 135:100 boys:girls ratio in college
sexism in Everyday Math
invisible boys
boy trouble (New Republic on boys)
slacker boys, middle school, & forbidden positive images of boys in textbooks
throw rocks at them
please remain seated at all times
Ann Althouse thread sums up classroom change
cooperative vs. competitive learning
the girl show (8th grade graduation awards)
the boy show (character ed)
the other boy show
Where the Boys Aren't

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

KumonDay1 17 Nov 2005 - 14:22 CatherineJohnson

They weren't kidding about Kumon homework being easy.

I did mine this morning:
Total number problems: 115
Total number correct: 112 (apparently, in the parallel universe that is my brain, 7 x 57 sometimes equals 64)
Total time: 6 minutes, 10 seconds

Christopher:

Total number problems: 210
Total number correct: 210
Total time: 13 minutes

total time spent fighting over Doing Math:

0 seconds

blessed spill-over effect:

approximately 2 minutes spent fighting over Doing Spelling and/or Grammar

Normally the way fighting over Doing Spelling and/or Grammar works is this.

Christopher demands a break 'first,' before getting down to work
I protest, then cave
I become distracted & lose track of time
Christopher does not see fit to remind me his 15 minutes are up

That's part 1.

Part 2 begins when I come to and remember:

SPELLING! GRAMMAR!
I shout up the stairs: GET DOWN HERE RIGHT NOW! YOU HAVE SPELLING! YOU HAVE GRAMMAR!
silence
I shout up the stairs again
silence again — or, sometimes, Christopher shouts WHAT???!!!
I climb the stairs to our bedroom (where the PlayStation lives) stalk into the room, bark at my son:COME DOWNSTAIRS RIGHT NOW AND DO YOUR SPELLING
Christopher, not taking eyes off screen: WAIT JUST 5 SECONDS!

etc.

It's too embarassing to go on.

Around here, 'break' means 'transition.' Christopher can't stand the idea of going directly from CHURCH to MOM'S HOMEWORK, or from SCHOOL to MOM's HOMEWORK, or from anything at all to MOM'S HOMEWORK. (He's conscientious about the school's homework, and seems often to enjoy doing it. He wants, and I think needs, 'a break' before doing his school homework, too. But he doesn't try to play out the clock.)

I sympathize with the transition business. But Christopher's Problem With Transitions long ago became a ploy, and I'm sick of it. Plus, it's rotten for my own frontal lobes not to mention my own productivity; as David Allen says, you need to get stuff OFF your mental list. David Allen is right. Constantly having to remember who's not doing what is eating up what little executive function I have left.

So on the way home from the KUMON Center yesterday I nipped the transition business in the bud. I said: I don't think you should take breaks before KUMON. You should just do your KUMON worksheets the instant you get home.

My timing was perfect. There's a little bit of Magic at the KUMON Center, and Christopher was still under its spell. 'OK,' he said, looking serious. Then, a little later, "I need to build up my speed on addition."

Today, after Christopher did his KUMON worksheets, I said, "You have spelling and grammar to do."

"NO!"

etc.

I did the Choose One routine ('you can choose which one you want to do'), which also elicited a big fat NO!

But within a couple of minutes, Christopher was calmly doing a page in Megawords.

Then he checked it himself.

This is gonna be good.

LoneRangerMichiganArticlePart2 25 Oct 2005 - 14:02 CatherineJohnson

A couple of lines caught my eye in the article Lone Ranger sent Carolyn:

The problem is clear in the enrollment for remedial math at Wayne State, which has soared 85% in the last four years. There are 1,200 students in 12 sections of the class, a computer-based course.
"These students are coming in at the level of ninth-grade math," said Patty Bonesteel, developmental math coordinator at Wayne State. "Without a doubt, the idea of being bad at math is perfectly fine in our culture, and that's unfortunate."

going into the 13th grade doing 9th grade work

Golden Ageism

This line's funny:

"It's a national survival issue," Geltner said. "The American standards of education are simply not world class anymore."

As far as I know, the U.S. has never had a world class curriculum K-12.

article from Lone Ranger on remedial ed in MI colleges
more from Lone Ranger's MI article

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

BeyondTheClassroom 09 Nov 2005 - 03:49 CatherineJohnson

Stop!

Drop whatever you're doing!

Go read this book right now!

♦ ♦ ♦ ♦ ♦

Believe it or not (you won't), I think this one book Explains It All.

I'm actually serious about that, and I'll be interested to see how other folks feel. The EconoLog has a long discussion thread here that's probably interesting. (Haven't read yet, but I will.)

from the Acknowledgments:

This book is based on an extensive program of research conducted over the past ten years. During that time period, we surveyed more than 20,000 teenagers from nine high schools and spoke with hundreds of their parents and dozens of their teachers....The project was a collaborative effort that involved three universities and research teams...An intensive longitudinal study involving nine research sites and thousands of participants comes with a large price tage. We gratefully acknowledge the financial generosity of the following organizations...the William T. Grant Foundation, the Spencer Foundation, the Office of Educational Research and Improvement of the U.S. Department of Education, the Lilly Endowment, the Carnegie Corporation of New York.

I think every word of this book is true. Basically.

And yet I disagree with his conclusion that school reform not only has failed, but must fail. (Have I mentioned I Am A Real American?)

That's the $60,000 question, but just in terms of my own life, this book, along with The Learning Gap by Harold Stevenson and James Stigler clear things up for me.

Carolyn and I were talking about the Russian constructivists a couple of nights ago—the Russian constructivists & de Saussure. De Saussure said 'meaning comes from difference'; the Russian constructivists believed that art was 'the familiar made strange.'

Both of those slogans are true for me, and these two books, for me, defamiliarize American schools just enough so that I feel, for the first time, that I see our situation with some clarity.

Looking forward to hearing what everyone else thinks.

update

The EconoLog thread isn't worth your time. No one has read the book, and nearly everyone is resting his case on a proposition that's flatly contradicted by all of Steinberg's data.

AsianWhiteIQDifference 06 Nov 2005 - 15:39 CatherineJohnson

OK, Ken thinks he's so smart with his fancy shmancy four color chart.

Well, hah!

I am gonna drop kick that chart right outta here, AND I am gonna CHEAT to do it.

Because I'm ruthless.

from Stevenson & Stigler:

The claim that Japanese students are more intelligent than American students has been made by the Irish psychologist Richard Lynn, whose work was publicized several years ago in the cover story of a national magazine. Using American norms, Lynn computed Japanese children’s scores on a commonly used test of intelligence. On this scale, Japanese children’s average IQ was significantly above the American average. Lynn’s claims, if correct, would add greatly to our understanding of cultural differences in achievement, but as another publication has pointed out, they are wrong. Asian children may learn more during their school years, but their capacity for learning—which is what intelligence tests attempt to measure—does not different from that of American children.
The fundamental flaw in Lynn’s report was his failure to consider two important variables: location of residence (urban versus rural) and socioeconomic status of the children’s families. One of the consistent findings since intelligence tests were devised nearly a century ago has been the large differences between IQ scores of city children and children living in remote villages, and between children from upper-income families and from disadvantaged homes. Lynn did not gather any of his information himself, but instead relied on the norms of the test that were published in the test manual. His choice was unfortunate. Because intelligence tests in Japan are used primarily in large cities, only urban children had been tested to established the norms. Moreover, no attention had been paid to the necessity of selecting a representative sample of children from each Japanese city. The norms for the American test, by contrast, were based on a truly representative sample of urban and rural children of all socioeconomic levels.
We can do more than criticize Lynn’s methodology. Data we obtained from an intelligence test given to the children in our 1980 study contradict his claims. The test, constructed especially for use in Japan, Taiwan, and the United States, included items tapping the children’s vocabulary, general information, memory, spatial, and perceptual skills, ability to use a code, and so on—all topics not explicitly taught in school. As with the mathematics tests, we developed these items with a team of researchers from each of the cultures.
Contrary to what would be expected if cross-cultural differences in general intelligence could explain the striking differences in achievement, we found little overall difference in the levels of cognitive functioning of children across the three cultures. American children did not display lower intellectual abilities than Chinese and Japanese children. Scores for the individual children from each culture on the different types of items were not identical, but by the fifth grade the scores for the total test did not different significantly from one culture to another. Children in each culture displayed slightly different cognitive strengths and weaknesses, but by the time they were enrolled in the fifth grade, the most notable feature was the similarity of their performance.

♦ ♦ ♦ ♦ ♦

from Count down: The Race for Beautiful Solutions at the International Mathematical Olympiad:

Questions about the academic achievements of Asian Americans are not limited to math competitions. The group has a reputation as a ‘model minority’ that excels academically. Asian Americans are overrepresented in gifted and talented classes from elementary school through high school. Compared with all other ethnic groups, including European Americans, Asian Americans have higher rates of graduation from high school, college matriculation, and graduation from college.
One possible explanation is that people with Asian ancestors are biologically smarter….
[snip]
Think about the three Asian Americans on the team representing the United States at the Forty-second Olympiad. All were born outside the United States. Tiankai came from China; Ian was born in Australia, though his parents had emigrated from Vietnam; and David had emigrated from Korea.
[snip]
By the third generation most Asian American kids are more American than Asian. First-generation immigrants from Asia tend to receive grades at school that are higher than the average, but over the generations he grades regress to the mean. On many measures of health, attitude, and well-being, recent immigrants score far higher than families that have been in the United States for longer periods.
The ethnic makeup of U.S. Olympiad teams clearly shows this effect. Most Japanese families in the United States, for example, have been in the country since before World War II. As third- or fourth-generation Americans, most of the young people no longer speak Japanese. They tend to be good students, but they do not necessarily excel in mathematics, and they do not gauge their self-esteem in those terms. Accordingly, they are not particularly numerous at math competitions, and no U.S. Olympiad team has included a member with a Japanese background.

♦ ♦ ♦ ♦ ♦

and from Beyond the Classroom: Why School Reform Has Failed and What Parents Need to Do by Laurence Steinberg:

The High Costs of Americanization

Most of us expect that individuals would have an especially tough time when they first arrive in a new country, and that, as a consequence, children who are recent immigrants would exhibit more distress and difficulty than their counterparts whose families have been living in the new country for some time…..We would hypothesize, therefore, that students born outside the United States would be doing worse in school than those who are native Americans, and that native Americans hose families have been in this country for several generations would be faring better than their counterparts who arrived more recently.
Surprisingly, just the opposite is true: the longer a student’s family has lived in this country, the worse the youngster’s school performance and mental health. Consider some of the following findings from our study. Foreign-born students—who, incidentally, report significantly more discrimination than American-born youngsters and significantly more difficulty with the English language—nevertheless earn higher grades in school than their American-born counterparts….The differences in school performance favoring immigrants over native Americans remain just as large even after we take family background into account.
It is not simply that immigrants are outperforming nonimmigrants on measures of school achievement. On virtually every factor we know to be correlated with school success students who were not born in this country outscore those who were born here. And, when we look only at American-born students, we find that youngsters whose parents are foreign-born outscore those whose parents are native Americans.
The more Americanized students—those whose families have been living here longer—are less committed to doing well in school than their immigrant counterparts.
The adverse effects of Americanization are seen among Asian and Latino youngsters alike….with achievement decreasing, and problems increasing, with each successive generation.

♦ ♦ ♦ ♦ ♦

last but not least (here's the cheating part), here's Richard Nisbett, in The Geography of Thought: How Asians and Westerners Think Differently...and Why:

The Greek faith in categories had scientific payoffs, immediately as well as later, for their intellectual heirs. Only the Greeks made classifications of the natural world sufficiently rigorous to permit a move from the sorts of folk-biological schemes that other peoples constructed to a single classification system that ultimately could result in theories with real explanatory power.
A group of mathematicians associated with Pythagoras is said to have thrown a man overboard because it was discovered that he had revealed the scandal of irrational numbers, such as the square root of 2, which just goes on and on without a predictable pattern: 1.4142135 ..... [yup, that bugs me, too] Whether this story is apocryphal or not, it is certainly the case that most Greek mathematicians did not regard irrational numbers as real numbers at all. The Greeks lived in a world of discrete particles and the continuous and unending nature of irrational numbers was so implausible that mathematicians could not take them seriously.
On the other hand, the Greeks were probably pleased by how it was they came to know that the square root of 2 is irrational, namely via a proof from contradiction....
The Greeks were focused on, you might even say obsessed by, the concept of contradiction. If one proposition was seen to be in a contradictory relation with another, then one of the propositions had to be rejected. The principle of noncontradiction lies at the base of propositional logic. ....The basic rules of logic, including syllogisms, were worked out by Aristotle. He is said to have invented logic because he was annoyed at hearing bad arguments in the political assembly and in the agora! Notice that logical analysis is a kind of continuation of the Greek tendency to decontextualize. Logic is applied by stripping away the meaning of statements and leaving only their formal structure intact. This makes it easier to see whether an argument is valid or not. Of course as modern East ASians are fond of pointing out, that sort of decontextualization is not without its dangers. Like the ancient Chinese, they strive to be reasonable, not rational.
Chinese philosopher Mo-tzu made serious strides in the direction of logical thought in the fifth century B.C., but he never formalized his system and logic died an early death in China. Except for that brief interlude, the Chinese lacked not only logic, but even a principle of contradiction. India did have a strong logical tradition, but the Chinese translations of Indian texts were full of errors and misunderstandings. Although the Chinese made substantial advances in algebra and arithmetic, they made little progress in geometry because proofs rely on formal logic, especially the notion of contradiction. (Algebra did not become deductive until Descartes. Our educational system retains the memory trace of their separation by teaching algebra and geometry as separate subjects.)
The Greeks were deeply concerned with foundational arguments in mathematics. Other peoples had recipes; only the Greeks had derivations. On the other hand, Greek logic and foundational concern may have presented as many obstacles as opportunities. The Greeks never developed the concept of zero, which is required both for algebra and for an Arabic-style place number system. Zero was considered by the Greeks, but rejected on the grounds that it represented a contradiction. Zero equals nonbeing and nonbeing cannot be! An understanding of zero, as well as of infinity and infinitesimals, ultimately had to be imported from the East.

♦ ♦ ♦ ♦ ♦

misdirection

OK, I changed the subject with that last one.

But I could have done that even without being ruthless, because I think the history of mathematics is important to a discussion of whether Asians Are Smarter.

As I understand the history of mathematics, Asians did not make (many) major contributions. Mathematics is largely a creation of Western Europeans and Indians.

On those grounds alone, I would be highly reluctant to give credence to any argument that Asians possess an innate, inborn IQ-advantage in the subject of mathematics. (Do they have higher 'g' overall? They might. For the moment, it's a question of choosing whom to believe, and I'm choosing Stevenson & Stigler, who actually went to Asian countries and tested Asian children's IQ directly. As well, I've mentioned that we know Jim Stigler&mdahs;we know him well enough to trust him. That's not a reason for anyone else to choose Stevenson & Stigler over the VDARE folks, but it's my reason, and I'm sticking to it.)

RUSSIAN MATH versus SINGAPORE

On the subject of Asian superiority in math achievement, Nisbett also has this to say:

I am sometimes accused of a contradiction myself. Why do nonlogical Asians tend to do so much better in math and science than Americans? How can this be if East Asians have trouble with logic? There are several answers to this question.
First, it should be noted that we don't actually find East Asians to have trouble with formal logic, we just find them to be less likely to use it in everyday situations where experience or desire conflicts with it. Second, Eastern lack of concern about contradiction and emphasis on the Middle Way undoubtedly does result in logical errors, but Western contradiction phobia can also produce logical errors.
The Eastern reputation for math skills is really quite recent. Traditional Chinese and Japanese culture emphasized literature, the arts, and music as the proper pursuits of the educated person. In research with young and elderly Chinese and Americans, we and others find that only the Comparably schooled older Chinese and Americans perform similarly in math.
Asian math education is better and Asian students work harder. Teacher training in the East continues throughout the teacher's career; teachers have to spend much less time teaching than their American counterparts; and the techniques in common use are superior to those found in America. (Asian math-education superioity to Europe in these respects is less marked.) Both in America and in Asia, children of East Asian background work much harder on math and science than European Americans. The difference in how hard children work at math is likely due at least in part to the greater Western tendency to believe that behavior is the result of fixed traits. Americans are inclined to believe that skills are qualities you do or don't have, so there's not much point in trying to make a silk purse out of a sow's ear. Asians tend to believe that everyone, under the right circumstances and with enough hard work, can learn to do math.
In short, Asian superiority in math and science is paradoxical, but scarcely contradictory!

I've mentioned many times that I've worked through every problem, and studied every page, of Mathematics 6 by Enn R. Nurk and Aksel E. Telgmaa.

That experience changed my perception of Singapore Math.

Carolyn says "Russian mathematicians have chops." You see that right away, working through RUSSIAN MATH.

The book is bloody brilliant. Studying RUSSIAN MATH, I saw the little SINGAPORE MATH 'student helpers' as an earnest, hard-working lot. Not naturally gifted, but willing, always, to put in the time.

RUSSIAN MATH is the real deal, SINGAPORE MATH the overachiever.

I like overachievers; I hope to be one myself when it comes to math.

But an overachiever is different from an Enn Nurk or an Aksel Telgmaa.

it's the culture, stupid Part 2

Basically, I'd have to see a great deal more solid data before I'd believe that Singapore kids, or Japanese kids, or Chinese kids, or any other kids are naturally better equipped to learn math than any other kids.

And now that I've read Steinberg, I'm looking at the culture even more than the schools.

That's the bad news.

JumpOnReadingVersusMath 06 Nov 2005 - 22:19 CatherineJohnson

A Comment from Ken got me thinking....

K-8 in most schools are an intellectual wasteland. The only kids in a position to achieve in high school are the high cognitive kids who can deal with challenging material they get, for the first time, in high school.
In math, you can do well in calculus as long as you learn algebra. That's a four year timespan.
In English, there is so much to learn—spelling, grammar, reasoning, writing, vocabulary—you just can't begin in 9th graded and get yourself up to AP level in four years. It takes more than being an avid reader to achieve. You need to be challenged from day one in kiundergarten to get your verbal ability to the same high level then you can get in math in four years.

I realize I've been framing this issue wrong.

I've been thinking it's worse to fall behind in math, because math is a hierarchical subject, whereas subjects like history aren't.

That's true as far as it goes.

What I've been missing is the core skills of English language arts. Spelling, grammar, reasoning, writing & vocabulary. I haven't asked myself the question, How hard is it to make up lost ground in reading and writing?

This is probably another case of my cognitive unconscious knowing more than I do. I've had Christopher on a formal spelling curriculum for more than a year now, and we started on SAT vocabulary last summer. Obviously, some part of my brain is telling me, "He's not gonna be able to cram spelling, vocabulary, grammar, reading, & writing in an SAT course."

meanwhile, back in the real world....

....I've noticed time and again that whenever there's a big push to bring disadvantaged kids up to speed, they always do much better making up lost ground in math than in reading. That's how things are at the KIPP Academy. KIPP works miracles taking kids who don't know their times tables & getting them ready to pass the Regents by the end of 8th grade. They don't do nearly so well closing the gap in English language arts. Same story with the achievement gap on SAT scores. It's the math gap that's been closing.

And here is JUMP:

learning disabilities
Children with learning disabilities or attention deficits find it easier to catch up in math than in other subjects. At one inner-city school where we have a significant presence, School Board psychologists were surprised by the number of children diagnosed as slow learners who were testing at grade level in math. The confidence gained from doing well in math has spilled over into their other subjects and had a positive effect on their overall behaviour.

english as a second language
Children who speak English as a second language often struggle with math because they can't read their texts. In practice however, we have found math to be one of the easiest subjects to teach newcomers to Canada. A number of JUMP students who were insecure about speaking in class (including two who had been diagnosed as selective mutes) raised their hands for the first time – during the math lesson.

more on 'getting math into the hand'

from JUMP (pdf file):

In our public education system, we now try to teach reading and literacy at the expense of mathematics by loading too much language into our elementary textbooks. By neglecting to ever teach elementary students math in a purer form, as a symbolic language in its own right, we neglect a tool that could help students become more literate. If we were to use less language in the early part of our math programs (and introduce it more carefully in the later part) and if we were to allow students to sometimes play math more as a game of manipulating symbols, generalizing rules and seeing patterns, I would predict that we could accelerate students’ development as readers. (And we would undoubtedly allow children in inner-city schools to be far more successful at school: students who have English as a second language, or who are delayed in their reading, often fall behind in mathematics unnecessarily because of the language in the textbooks.)
To teach the Fractions Unit effectively, you should think of the unit – in part – as an exercise in reading (or a preparation for reading) for your weaker students. Rather than having to grapple with the 26 letters of the alphabet and a vast number of ill-defined rules for combining those letters, your students can experience mastery in a more simple symbolic universe that contains only a handful of symbols (i.e. the numerals from zero to nine as well as a few operation signs) and a handful of rules for combining those symbols. You should not underestimate the degree to which manipulating these mathematical symbols mentally, and copying and lining the symbols up properly on the page, will affect your weaker students as readers and as writers.
I was invited to speak at the Hospital for Sick Children in Toronto in 2004, after teaching the Fractions Unit to a very challenged nine-year-old boy: his doctor invited me to talk to a group of specialists on childhood development because he had noticed remarkable changes in the boy, not only in ability and attitude, but also in handwriting skills. According to the boy’s doctor and mother, the boy could learn cursive letters much more quickly after completing the Fractions Unit. I have noticed similar changes in handwriting and motor skills in other students who have completed the unit. In the Fractions Unit, students are required to constantly organize sequences of symbols on the page, while having to look for patterns and to remember and generalize rules. At the same time, they are in a state of extreme excitement at being able to do advanced work and at being offered the opportunity to show off to a caring adult. I believe that the combination of these factors is what causes so many changes in weaker students: each factor on its own would not have the same effect.

I'm wondering whether we've got everything upside down.

Maybe it's math that should be the (relatively) easy subject in elementary school!

OhioPublicSchools 08 Nov 2005 - 16:21 CatherineJohnson

via joannejacobs:

[The Fordham Foundation report's] single most compelling finding is that "if money were not an issue," only 46 percent of white public school parents and 30 percent of black parents would prefer that their child continue to attend a district-operated public school. A staggering 48 percent of white public school parents and 68 percent of black parents would opt for private (or charter) schools.

HomeschooledPreTeens 10 Nov 2005 - 15:41 CatherineJohnson

What are homeschooled pre-teens like?

Are they as hostile to their parents as public school pre-teens?

Does anyone know?

MileWideInchDeep 13 Nov 2005 - 14:49 CatherineJohnson

Probably some of you remember this passage from Cathy Seeley's online chat on 10-25 (content is no longer on line):

...a dubious distinction for the United States. We are among the countries with the most topics addressed per grade level of any country in the world. These questions point out the most common, and most well-deserved criticism of the American mathematics curriculum, often characterized as 'a mile wide and an inch deep.' Depending on the state in which they live, some teachers face lists of 40 to 80 or 90 things for students to learn at a particular grade.
NCTM is initiating what we hope will be the next round of discussions in mathematics curriculum with a new effort around Curriculum Focal Points. Currently, a writing group is working on identifying and describing 3 to 4 major focal points at each grade level. This document will be available for review during the next year or so, providing a basis for discussions among teachers, curriculum developers, mathematicians, teacher educators and others. Watch the News Bulletin for updates as this effort advances.

some of you expressed doubt
here

here

and

here

you are not alone

A mile wide and an inch deep is a catchy slogan. This phrase is used to critique U.S. math education for having too many topics, as suggested by the TIMSS reports, with the implication that this factor results in poor achievement.
The prevalence of this interpretation gives the impression that the number of topics is a major cause of the poor showing of U.S. students, and therefore a reduction of the number of topics ought to be a high priority. Indeed, this idea may have become the main lesson learned from TIMSS.

How does the U.S. compare to "successful" countries? Inspect the number of topics per year for Japan, Singapore, and the U.S. in the middle- and high-school grades and the difference isn't all that clear. Singapore is actually closer to the U.S. than to Japan in grades 7, 9, 10, 11 and 12. Yet, in grade 8 where the U.S. did so poorly, Singapore seems to have done just fine. The number of topics in Singapore actually exceeds that of the U.S. for grades 11 and 12.

What is the relationship of topic count to mean scores? Compare the number of TIMSS topics in the 8th grade to scores on the 8th grade TIMSS statistically. The relationship is indeed negative, but only 3.1% of the variability of country mean scores can be accounted for by topic count. This is a rather small percentage to support inferences that will impact upon curriculum decisions.

A counter example Not much lip-service is given to equation-related algebra when people talk about TIMSS findings. The proportion of the 8th grade text devoted to equation-related algebra is positively related to achievement. It accounts for 7.4% of the variance of country mean scores.

The oft-ignored warning Pascal D. Forgione, Jr., Commissioner of Education Statistics, warns that "... we should avoid the temptation to zero in on any one finding or leap to a conclusion without carefully considering the broader context."
Indeed, making causal inferences from a cross-sectional study with so many uncontrolled confounding variables is risky business. The TIMSS remains a remarkable descriptive study, but it simply does not justify the topic-count fever that has resulted.

topic count fever
There's just one answer here: if you can't beat 'em, join 'em.

I nominate lattice multiplication as Excess Topic Number One.

It can go.

update
This is another Lost Source observation, but the Singapore kids have a HUGE amount of material to cover in school, because they all have to learn English and Chinese. I believe the slowest learners are put in a 'simple English' class, but even they are being asked to learn English and Chinese, and learn them fluently to boot. The PRIMARY MATHEMATICS books are written in English (I believe; I'm fairly certain they haven't been translated).

It boggles the mind.

Powder River Math

The Powder River has been described as a mile wide and an inch deep, too wet to plow and too thick to drink.

Doug found this:

I love it!

SingaporeStudentHelper 13 Nov 2005 - 14:51 CatherineJohnson

Parker & Baldridge on the student helpers:

The children pictured in the margins give the precise definitions and key ideas in very few words. These ‘student helpers’ often clearly convey an idea that might otherwise take an entire paragraph!

a 5th grader in TRAILBLAZERS

and remember N.S., also from TRAILBLAZERS, grade 5

Wow! That number is mind-boggling! Is it in the millions or in the billions? Reading and writing big numbers is not so easy. I've seen most of these words on the list before, but when I try to think about numbers in the millions, I get confused about what some of the words mean.
(Student Guide, grade 5)

A Student Helper in the Singapore series would never be shown saying something like this.

There are pictures of children all through PRIMARY MATHEMATICS.

Not one is confused, bewildered, befuddled, or wrong.

FourthGradeMathEnrichment 17 Nov 2005 - 01:15 CatherineJohnson

The fourth grade math enrichment program is meant to complement and enhance the distict's new mathematics program, Math Trailblazers. It is a flexible, "push in" model that allows small groups of children the opportunity to explore the previously learned concepts in greater depth.
Most recently, all of the fourth graders constructed runways for various types of airplanes. The focus of the activity was to find the perimeter of different sized runways built with square tiles, noting patterns found during the process. As an enrichment activity, students built runways with shapes other than squares, such as triangles, pentagons and hexagons. Then, we discussed patterns and "function rules" that were devised from shape. With the discovery of each shape's function rule, we could calculate the perimeter of any number of blocks arranged in a line, without having to build the runway.
The math enrichment program can also extend any topic being taught in class. As fourth graders continue to explore our Hindu-Arabic number system with base ten blocks, enrichment activities will focus on other number systems such as the Roman numeral system. By studying the rules and symbols of other number systems, the students can compare and contrast the similarities, differences, pros and cons of our current number system.
As with Math Trailblazers, all enrichment activities align with NCTM and New York state mathematical standards appropriate for grade four. In addition, the children are often encouraged to show their work and explain their thought processes in complete sentences as they will be expected to do on the upcoming state test in March.

think and discuss

Our Hindu-Arabic number system, pros and cons

Hindu-Arabic number system
pros cons

Roman numeral system
pros cons

meanwhile, back in Singapore

11.
David spent 2/5 of his money on a story book.
The storybook cost $20.
How much money did he have at first?

source:
Primary Mathematics 4A Textbook, p. 67

update
A lot of the Regulars (see Comments thread) think these activities are worthwhile.

This tells me I've done a poor job writing this post—and, in fact, thinking it through in the first place.

Thanks to all of you, I'm clearer now.

Here's where I am:

First of all, it pains me that, apparently, it's only the 'enrichment kids' who are learning about the Roman numeral system and about irregularly-shaped figures. Saxon Math teaches these subjects to all children, as does Singapore Math.

Second, having now spoken to the mother of a mathematically gifted child struggling with TRAILBLAZERS in 2nd grade, I'm finding myself drawn to the issue of what exactly my school district is doing for these kids. These are very brainy children; I know, because I have them in my Singapore Math class. I do not see or hear evidence of a commitment, in our district, to serve the needs of gifted children as we serve the needs of other children. The reason these children are having 'push-in' enrichment is that our district is philosophically opposed to allowing high-achieving and gifted children to move ahead in the curriculum. So now we're spending money on 'Math Differentiation' specialists to help teachers teach math to below-average, averge, high-achieving, and mathematically gifted and talented kids all in the same time and place. The decision to end tracking was made in a hierarchical, top-down fashion, and imposed upon protesting parents.

Third, I'm highly skeptical of the use of manipulatives at this age. First of all, we do have some reasonably good research on the subject of manipulatives, which shows—counterintuitively—that manipulatives work for middle school kids, but not for elementary school children. Manipulatives may impede learning in earlier years. (see posts here and here) But leaving aside the handful of studies we have, what bothers me is that all of these kids are bright. Their math skills are strong; they're good readers; they have smart, dedicated parents to help with homework. These children, I believe, can be using the abstract symbols of mathmatics to reason and learn.

Finally, I simply loathe the tone of this document. I know that's harsh, but that's the writer in me. The fourth grade math enrichment program is meant to complement and enhance the distict's new mathematics program, Math Trailblazers. This is spin, and, reading it, I feel my blood rise. When a document like this comes home in the backpack, I am not being treated with respect. I am being public relationed, in Carolyn's memorable phrase.

NewYorkStatestandards 17 Nov 2005 - 23:18 CatherineJohnson

We're going downhill.

WhiteFlightInCupertino 21 Nov 2005 - 04:11 CatherineJohnson

CUPERTINO, Calif. -- By most measures, Monta Vista High here and Lynbrook High, in nearby San Jose, are among the nation's top public high schools. Both boast stellar test scores, an array of advanced-placement classes and a track record of sending graduates from the affluent suburbs of Silicon Valley to prestigious colleges.

But locally, they're also known for something else: white flight. Over the past 10 years, the proportion of white students at Lynbrook has fallen by nearly half, to 25% of the student body. At Monta Vista, white students make up less than one-third of the population, down from 45%—this in a town that's half white. Some white Cupertino parents are instead sending their children to private schools or moving them to other, whiter public schools. More commonly, young white families in Silicon Valley say they are avoiding Cupertino altogether.

update—more on Cupertino

At Cupertino's top schools, administrators, parents and students say white students end up in the stereotyped role often applied to other minority groups: the underachievers. In one 9th-grade algebra class, Lynbrook's lowest-level math class, the students are an eclectic mix of whites, Asians and other racial and ethnic groups.
"Take a good look," whispered Steve Rowley, superintendent of the Fremont Union High School District, which covers the city of Cupertino as well as portions of other neighboring cities. "This doesn't look like the other classes we're going to."
On the second floor, in advanced-placement chemistry, only a couple of the 32 students are white and the rest are Asian. Some white parents, and even some students, say they suspect teachers don't take white kids as seriously as Asians.
"Many of my Asian friends were convinced that if you were Asian, you had to confirm you were smart. If you were white, you had to prove it," says Arar Han, a Monta Vista graduate who recently co-edited "Asian American X," a book of coming-of-age essays by young Asian-Americans.
Ms. Gatley, the Monta Vista PTA president, is more blunt: "White kids are thought of as the dumb kids," she says.
Cupertino's administrators and faculty, the majority of whom are white, adamantly say there's no discrimination against whites. The administrators say students of all races get along well. In fact, there's little evidence of any overt racial tension between students or between their parents.
Mr. Rowley, the school superintendent, however, concedes that a perception exists that's sometimes called "the white-boy syndrome." He describes it as: "Kids who are white feel themselves a distinct minority against a majority culture."
[snip]
Four years ago, Lynn Rosener, a software consultant, transferred her elder son from Monta Vista to Homestead High, a Cupertino school with slightly lower test scores. At the new school, the white student body is declining at a slower rate than at Monta Vista and currently stands at 52% of the total. Friday-night football is a tradition, with big half-time shows and usually 1,000 people packing the stands. The school offers boys' volleyball, a sport at which Ms. Rosener's son was particularly talented. Monta Vista doesn't.

jocks

Teachers everywhere will tell you that 'parents,' by which they mean white parents, put sports above homework.

They're right.

In Sacramento, where my sister lives, parents are spending small fortunes to send their kids to special soccer training camps; here in Irvington there's a whole soccer war blazing on that parents of kids who aren't soccer-star material don't even know about. Ed spent years coaching soccer just so Christopher, who is not-soccer-star-material, could play. And we were both sad when Christopher, who was a soccer star at age 5 (one of the dads used to shout, 'Here comes the money' every time Christopher got control of the ball) turned out not to be a natural athlete.

I wondered, when he was five, whether he was athletic or just smart.

What made him good back then was that the other kids didn't have a clue. Little-kid soccer is adorable because their entire concept of what to do when the ball is in play is TO CLUMP.

CLUMP!!!!

EVERYBODY CHASE THE BALL AND CCCCLLLLUUUUMMMMPPPPP!'

They're like little puppies. MOVING OBJECT! CHASE IT! RUN! RUN! RUN!

That's Kindergarten soccer.

Christopher could hold a position.

He may have been the only 6 year old in all of AYSO who could hold a position. That made him look like a genius on the field, and as a matter of fact, he was a genius on the field, come to think of it. Being able NOT to chase a moving ball when you're 5 is probably the definition of genius at that age.

It turned out he was playing smart.

So maybe White Men Can't Jump, but that doesn't stop us from spending a huge amount of time thinking about jumping, practicing how to jump, and watching other people jump on TV. We're restless folk.

As far as I can tell, there's a burn-out factor in highly competitive high schools like the one in the story, and perhaps like our high school here. A mom just the other day told me that her son, who took every AP course under the sun and did well in all of them, said, at the end of AP calculus, 'I'm never taking math again.'

I find that almost tragic. I hope I never hear it from Christopher.

Four weeks into KUMON, I can see exactly why Ken is such a fervent believer in Direct Instruction.

Direct Instruction resolves the tension between wanting your child to have a world-class education, and wanting him to have an adolescence that's something other than a 24-hour a day Death March to the Harvard rejection letter senior year.

Break the content to be learned down into logical conceptual and procedural chunks, teach to mastery, let each learner move at his own speed.

In Cupertino, the white parents complain that Asian parents are competitive.

Maybe they are. Or maybe, once an Asian parent confronts an American school system, they become competitive.

Mr. Liu, at KUMON yesterday, said Asian culture is persistent and patient.

Those words, to me, are a good description of the educational culture I'd like to see take hold in our schools.

SingaporeMathTopicMatrix 30 Nov 2005 - 16:47 CatherineJohnson

from the AIR report (pdf file)

I'm going to try to rustle up the equivalent chart from TRAILBLAZERS so we have a direct comparison.

This seems to say that in Singapore children are using all 4 algorithms in the first grade.

the TRAILBLAZERS track

Christopher told me yesterday that he learned how to subtract with regrouping in 2nd grade. 'It was hard,' he said. He learned the multiplication algorithm for the first time at the end of 2nd grade.

From what I can see, the TRAILBLAZERS track could be as much as a year slower than Irvington's old track, though it's hard to tell:

This unit extends students’ work with place value to four-digit numbers and helps them build an understanding of our number system, the base-ten place-value system. The activities in this unit lay the conceptual groundwork for performing multidigit addition and subtraction. Two-digit addition is reviewed. Three- and four-digit addition and subtraction algorithms are developed in Unit 6.

This is from Unit 3, Grade 4 (there are 20 units altogether).

Here's a passage from the Teacher Implementation Guide (pdf file):

In kindergarten and grade 1, students using MATH TRAILBLAZERS practice their counting skills. They learn to count past 100 by 1s, 2s, 5s, and 10s. They count forward and backward from any given number. They group objects for counting. Students use counting to solve addition and subtraction problems. They learn to write numbers up to and beyond 100. The 100 chart is introduced and used for a variety of purposes, including solving problems and studying patterns. Students partition, or break apart, numbers in several ways (25 = 20 + 5, 25 = 10 + 10 + 5, and so on). These activities help children become familiar with the structure of the number system. Beginning in kindergarten, a ten frame is frequently used as a visual organizer.

The first passage is intended for parents.

The second passage comes from the Teacher Implementation Guide.

subtraction algorithm mastered by the end of 4th grade

It's probably worth skimming through pages 5 through 7 in the Teacher Implementation Guide. This passage lays out the TRAILBLAZERS content, sequence, and timing for teaching the subtraction algorithm. Once again, it's difficult to nail down the exact 'scopt and sequence' TRAILBLAZERS follows:

Later in grade 2, systematic work begins on paper-and-pencil methods for subtracting two digit numbers. Students are asked to solve two-digit subtraction problems using their own methods and to record their solutions on paper. The class examines and discusses the various procedures that students devise. At this time, if no student introduces a standard subtraction algorithm, then the teacher does so, explaining that it is a subtraction method that many people use. The standard method is examined and discussed, just as the invented methods were. Students who do not have an effective method of their own are urged to adopt the standard method.
Problems that require borrowing are included from the beginning. Though this differs markedly from traditional approaches, we view it as important in developing a sound conception of subtraction algorithms. Giving children only multidigit problems that do not involve borrowing encourages the development of a rote and faulty algorithm that may not carry over into problems that require borrowing.
By the beginning of grade 3, students have a strong conceptual understanding of subtraction and significant experience devising procedures to solve subtraction problems with numbers up to 1000. They also have some experience with standard and invented paper-and-pencil algorithms for solving two-digit subtraction problems. In grade 3, this prior knowledge is extended in a systematic examination of paper-and-pencil methods for multidigit subtraction. This work begins with a series of multidigit subtraction problems that students solve in various ways. Many of these problems are set in a whimsical context, the TIMS Candy Company, a business that uses base-ten pieces to keep track of its production and sales. Other problems are based on student-collected data, such as a reading survey.
As in grade 2, the class discusses and compares the several methods students use to solve these problems. Again, any method that yields correct results is acceptable, but now a greater emphasis is given to methods that are efficient and compact. This work leads to a close examination of one particular subtraction algorithm. (See Figure 3.) Students solve several problems with base ten pieces and with this standard algorithm, making connections between actions with the manipulatives and steps in the algorithm. After a thorough analysis of the algorithm, including a comparison of the standard algorithm and other methods, students are given opportunities to practice the algorithm. Practice in paper-and-pencil methods for multidigit subtraction is distributed throughout grades 3 and 4.

TRAILBLAZERS delays mastery of the subtraction algorithm until the end of 4th grade.

This is certainly consistent with the constructivist belief that premature teaching of the algorithms closes off conceptual understanding.

TRAILBLAZERS whole number operations scope and sequence

What they've done here is to use the idea of a math curriculum based in problem-solving to justify not teaching the algorithms.

All of the problems being solved in these first years are of the type:

"How do I add, subtract, multiply, and divide without knowing any algorithms?"

This is not remotely the case in the Singapore series.

Like TRAILBLAZERS, PRIMARY MATHEMATICS is a problem-based curriculum.

But in PRIMARY MATHEMATICS children use the standard algorithms to solve problems. That's why, in Singapore, children can begin using bar models to solve simple algebra problems in the 3rd grade. The bar models help them perceive which algorithms to use in what sequence.

If you don't know the algorithms, a bar model's not going to do you much good.

Introduction to Math TRAILBLAZERS
TRAILBLAZERS (TIMS) Teacher Implementation Guide: Math Facts
TIMS Teacher Implementation Guide Laboratory Method

key words: scope and sequence Singapore Math Primary Mathematics Trailblazers

UsFourthGradersArentGreatAfterAll 05 Sep 2006 - 14:22 CatherineJohnson

via joannejacobs, word that U.S. 4th graders aren't on par with their peers after all:

Despite a widely held belief that U.S. students do well in mathematics in grade school but decline precipitously in high school, a new study comparing the math skills of students in industrialized nations finds that U.S. students in 4th and 8th grade perform consistently below most of their peers around the world and continue that trend into high school.

Steve & Ken will be glad to hear this:

U.S. students consistently performed below average, ranking 8th or 9th out of twelve at all three grade levels. These findings suggest that U.S. reform proposals to strengthen mathematics instruction in the upper grades should be expanded to include improving U.S. mathematics instruction beginning in the primary grades.
“The conventional wisdom is that U.S. students perform above average in grades 4 and 8, and then decline sharply in high school,” says Steven Leinwand, principal research analyst at AIR and one of the report’s authors. “But this study proves the conventional wisdom is dead wrong.”

Steve Leinwand again.

That guy is everywhere.

I'll add that the 'conventional wisdom' is not that U.S. students perform above average in grades 4 and 8.

The conventional wisdom is that U.S. students perform exactly at average in 4th grade, then well below average in 8th, and far below average in 12th. Moreoever, at least one analysis (link t/k—it's here on ktm somewhere) has found that this decline starts in grade school and represents the cumulative total across time of incremental drops in performance in each and every grade throughout the school years.

I love it!

Countries that score well on items that emphasize mathematical reasoning (a higher-level skill) also score well on items that require knowledge of facts and procedures (a lower-level skill), suggesting that reasoning and computation skills are mutually reinforcing in learning mathematics well. Compared to other countries, students in the United States students do not do well on questions at either skill level.

So I guess Steve Leinwand's previous statements on the place of computational skills in a mathematics curriculum are inoperative?

a Steve Leinwand sampler

It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous.

Shouldn't we be as eager to end our obsessive love affair with pencil-and-paper computation as we were to move on from outhouses and sundials? In short, we know and should agree that the long-division "gazinta'' (goes into, as in four "goes into'' 31 seven times ... ) algorithm and its computational cousins are obsolete in light of everyday societal realities.

Today, real people in real situations regularly put finger to button and make critical decisions about which buttons to press, not where and how to carry threes into hundreds columns. We understand that this change is on the order of magnitude of the outhouse to indoor plumbing in terms of comfort and convenience, and of the sundial to digital timepieces in terms of accuracy and accessibility.

Of course, real people in real situations are frequently called upon to figure the precise moment at which a person riding a ferris wheel can let go of his partner so the partner lands in water as the cart passes by.

Pencil and paper
The craft of math

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

CommentsToCome 15 Dec 2005 - 20:33 CatherineJohnson

I have a boatload of Comments to get pulled up front.....which means it's going to take awhile.

I thought I'd mention that the reason I pull Comments up front is that a) I don't want casual visitors to miss the super-meaty ones and b) once a Comment is on the front page it's part of the Category thread, so anyone reading that thread will be sure to see it. (All Comments stay connected to the original blooki posts, but a person reading through the KUMON category, say, isn't necessarily going to have the patience to click on each post individually so he/she can read each Comments thread individually.

So these things need to come up front.....

I've finally begun disciplining myself to KEEP A LIST, and here's what I've got at the moment:

boys hate journaling

JD (& others) on Houghton Mifflin Math & long division

Susan on grading handwriting (Christopher is going to be reading this one out loud)

Steve on epiphany

Suzuki

teaching to mastery

Rudbeckia Hirta on finding stats on colleges "Random factoid (before I disappear into a cloud of office hours, reviews, calming of panic, and then grading): if you want a statistical profile of a college/university (like graduation rates, etc.) search their web page for the Office of Institutional Research and look for the Common Data Set."

Doug on 'the margins'

J.D. email

Verghis on KUMON honor roll

If there are things I've forgotten, let me know.

other

Since I'm posting a public to-do list, I also need to:

locate Ken's reading test & post links everywhere

post links to FERPA (thank you, Rudbeckia)

post links to the Rewards Reading Series, which both Dan and Smartest Tractor have mentioned (Smartest Tractor has purchased SOPRIS' writing program, IIRC)

post ALL links to reading/writing materials on the how-to-teach-writing page

collect the science-teaching links from.....was it today? (it's all a blur!)

I should probably go ahead and buy DON'T MAKE ME 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

KenOnSingaporeMathInAbington 05 Feb 2006 - 13:57 CatherineJohnson

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

from Ken—

Speaking of Singapore Math ...

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

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

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

The Singapore educators attribute their students' success in math and science to their city-state's highly structured form of instruction. But they suspect that structure keeps some students from asking questions and limits opportunity for independent learning and thinking.
[snip]
"I like the way your children are able to communicate," she said. "Maybe we need to cultivate that more - a conversation between students and teachers."
Hmmm, maybe they are on to something with their lack of critical thinking skills. [ed.: The superiority only applies to math IQ, not verbal IQ, as this article clearly demonstrates.] ^*

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

Abington, eh. Let's see:
Median Household Income 101,951 ?Adults with a Bachelor's Degree 25.2%
Not exactly a typical school district. High Income, slightly above average parental education.

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

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

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

American researchers have been visiting Singapore and other Asian countries, too, said Patrick Gonzales, a U.S. Department of Education research analyst who coordinates the Trends in International Mathematics and Science Study, or TIMSS. That's the test in which Singapore's fourth graders scored higher in math and science than students in 25 participating countries. Singapore scored first with an average of 594; the United States was 12th with an average of 518. Eighth graders in Singapore also outperformed students in 45 countries.
"There's a growing interest in the U.S. in what is termed 'Singapore Math,'" Gonzales said. "It has been published in the U.S., and school districts are beginning to use it."
But the tricky part in all of this, he said, is that Singapore's top scores are in line with other Asian countries even though they teach math differently.
"Some are very traditional, teacher-centered, with rote memorization and lots of practice," he said.
Thanks Mr. Gonzales, I hadn't realized that the reason for Singapore's success was because they have a fuzzy curriculum.

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

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

The people who run TIMSS have begun sending video cameras into classrooms to record how teachers around the world teach, Gonzales said.
In the United States, they have noticed, math and science are largely taught in isolation, without stressing the underlying concepts that allow connections between lessons within the same subject. "The lessons are being taught as discrete units," he said.
White is black. Black is White. Yes, that's our problem -- not enough "stressing the underlying concepts" at the expensive of learning to mastery. The solution: more fuzziness. The usual.

Students in other countries also get more advanced lessons at a younger age, he said.
In the United States, there is growing support to have all students take algebra by grade eight, Gonzales noted.
"In Hong Kong, 14 percent of students in grade eight are taking trigonometry," he said.
And, the reason why they're getting more advanced lessons? Could it be because they're not wasting an inordinate amount of time on "inquiry learning"? And...

Gonzales said that U.S. students may not be advancing in math as quickly because much more time is spent on review.
"It's harder to get to more advanced topics because we are also going back and dealing with more elementary topics that, at eighth grade, students should be beyond," he said.
But I thought Inquiry learning was so great. Are you now telling me that students aren't learning and teachers have to constantly review old topics, yet still by 8th grade kids aren't getting it. Wait a second, there's a name for this nonsense -- the spiral curriculum -- and it's supposed to be a feature not a bug. I'm really confused now.

Another issue is homework.
The videotaped lessons revealed that in the United States, students are frequently allowed to spend the last 10 minutes of class time on homework.
Chia said her elementary students have at least an hour of homework each night.
Of course when US students do get homework, it sometimes looks like this.

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

... said the United States' competitive edge has always come from creativity. But the most rigorous classes and best teaching that foster creativity have often been enjoyed by a small group of high achievers. That's no longer enough to stay competitive.
"We're not teaching kids to think for themselves in sufficient numbers," he said.

You should have a blackout by now.

The visiting Singapore educators said parental pressure is part of the reason why their students excel at math and science.
Parents see accomplishment in math and science as the way to success, they said. They pressure schools to offer challenging courses and pressure students to do well in them.

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

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

-- CatherineJohnson - 05 Feb 2006

OnceMoreWithFeeling 09 Jan 2006 - 17:47 CatherineJohnson

I should have homeschooled.

StupidInAmericaPart1 16 Jan 2006 - 18:39 CatherineJohnson

Of course I missed the show, but the message boards are a hoot.

This one is from sharpeteacher:

Stupid in America does not start in the schools. It is the stupid adults that produce these lazy, under-achievers. When the parent see no reason to act like civilized people why would you expect the children to. The problem I have in my classroom is parents. Parents support their disrespectful children. They defend them when they get suspended or act like fools. [ed.: true! case in point!] (Parents like the one on tv that said her child was in high school and could not read.) It is the parents responsiblity more than the teacher to be sure the child is progressing. Maybe if parents suck it up and quit being selfish, stupid people then there children would care and learn about the real world and do well in school. You are comparing these countries and states that do not have the same rules or even the same tests. If you take a test and I take another test we can not compare our scores because we did not take the same test. Parents do not care enough to change their childs school. What we need is for someone to stand up and broadcast a show about stupid parents in America!!!!!

Here's a school administrator:

I agree as an administrator we have more stupid parents that bad teachers. It only takes discipline.

Another satisfied customer:

It's funny, that only teachers are responding to this thread. Let me tell you that I have read to my 2 children since day one, have helped with homework every night, volunteered uncountable hours in the public school system and am probably over involved in my kids lives. But just recently I have encountered this problem. My 10th grader just dropped 2 grades in Geometry in 4 weeks and I did not know about it until the week before Christmas break. After a conversation with the teacher she tried to tell me that I "should have known" that my child was in trouble. She said that she had done everything she was supposed to do to inform me. She had sent a letter home at the beginning of the year, stating that she would eventually send a password home to log on to an account to check grades and that my son, "if he were doing his job" was keeping a running tab of grades. I never received either. She obviously does not have children, thinking that they are going to come to you, saying, "mom, I'm flunking Math". Give me a break! The teacher gets paid for making sure my child learns [ed.: a common misconception! no! she doesn't get paid to make sure your child learns! she gets paid to spiral!] and obviously, my child was not learning, and his teacher felt that I did not need a note concerning this fact. Hey, as long as she can pick up that paycheck for putting in those hours, what makes the difference whether my child learns or not. Let me also tell you that I am not an absentee parent. I have volunteered in the public school system for 13 years, and am always available. This "teacher" also went on to say that it was all three of our responsibilitys' to make sure that my son was progressing. [ed.: hey! I got the same line from the Study Skills teacher who hung up on me!] I can't fix what I do not know about. She also said that she had 132 students and couldn't keep track of everything. Well, then maybe she should only get part of her paycheck, if she is only doing part of her job. Let me also add, that in the week since we have found out about the grade drop, we have gotten him two tutors, (pretty bad when a child has to go to another teacher for tutoring), have helped him more at home and he has raised his GPA by 5% in one week! [ed: I Should Have Homeschooled, Part 100-something] Teachers are always saying that the student needs to take responsibility....just once I would like to see a teacher step up and take responsibilty for what they have done...or in this case what they haven't. Public Education in America really stinks!

why do new teachers quit within 5 years?

I spent three years as a high school teacher, getting a job at a public school straight out of college. Three other rookies started with me. One quit after one year; the second year another quit; I quit the third year; the other rookie is now the high school’s activities director, eyeing a vice principal position.
Most new teachers leave the profession within five years. Teachers like to point at this statistic as proof of how hard their job is. It isn’t. It’s proof of the job’s meaninglessness. It takes a month or so at the job to realize that it doesn’t matter how hard you work, or how well you do. Your students will appreciate it, a little, but they are gone when the bell rings, and at the end of the year, they’re out of your life. The administration will take no notice. Your pay isn’t attached to it in any way.
Beyond that, your class of 25 becomes a class of 40 with ten special ed students. You’ve got a future felon you’d like to throw out of your class but can’t, because no one cares how well you teach, but cares a lot if you deem one kid a bad apple. For someone young, who has visions of a rewarding career, it quickly becomes apparent that public school teaching is an empty profession.
Career public school teachers come in two flavors, both shown in the John Stossel special.
a) the lazy bum who likes the free ride. That teacher who had his geography students playing Monopoly isn’t the exception, he’s the rule. I guarantee you that the teachers on this message board and in your lives who speak of working 60 hours a week are LYING! At my school, all the teachers arrived five minutes before the first bell and left five minutes afterward, and didn’t take any work home with them. They ran personal errands during their prep periods, and milked the image of the overwork teacher to anyone who wasn’t in the club.
b) The activist. The Union President who made such a fool of herself on the show is the other model. This teacher is also prevalent in the schools. She doesn’t care that kids learn math, science, English, or history. She got in this business to become a brainwasher, and uses her classroom as her personal political forum.
I’ve left the profession, and now work for a corporation in a cubicle. And despite the fact that my job is much harder now, at least it feels like I am accomplishing something!

uh-oh

The sad state of affairs on this matter is that the majority of us have personally experienced a really bad teacher on more than one occasion. That's too many bad teachers!
Me? I personally spent from the beginning of my junior year to the month of February teaching myself AB Calulus. Why you ask? Because my teacher was too busy planning the annual math club ski trip during my class period. I also, by my choice, went to a local college that summer to take AB Calculus to be sure I was ready for BC Calculus my Senior year.
I then spent my daughter's 6th grade year giving her the math lesson she should have been taught at school everyday by the teacher who couldn't stay off her cell phone long enough to teach. Her idea of teaching was handing out worksheets, reams of them, for the children to do without any lesson. The proverbial straw was the worksheet asking to calculate areas and perimeters of squares, triangles, parellograms, circles, etc. The worksheet had a diagram with measurements and an A = under each one. No formulas. I asked my daughter where her notes were from class on this. She said Mrs. Teacher didn't teach that day. They did worksheets with 5 digit numbers multiplied by 5 digit numbers...busy work.

helicopter parents of the world, unite

update

eduwonk likes this book, from Brookings:

Apparently the Wall Street Journal called it, "The education book of the year . . . an icon-smashing book on school reform."

There's a terrifically interesting-sounding (awkward modifier alert) list of books under "People who bought this book also bought":

Tinkering toward Utopia: A Century of Public School Reform David B. Tyack, With Larry Cuban
Managers of Virtue: Public School Leadership in America, 1820-1980 David B. Tyack, Elisabeth Hansot
What Works in Schools: Translating Research into Action Robert J. Marzano
American Public School Law Kern Alexander, M. David Alexander

the politics of vouchers (interview with Terry Moe)

ManBitesDog 16 Sep 2006 - 20:40 CatherineJohnson

I'm pretty sure you guys are gonna disapprove.

I feel nothing but Evil Glee reading this story.

via joannejacobs via Dr. Helen:

Schoolboy's bias suit: Argues system is favoring girls

revenge of the ~~nerds~~ real men

Anglin's complaint has set off a buzz among the 1,000 students at the school. Little, the student body president, said she disagrees with students who think Anglin is chauvinistic.
Of the 22 students in her honors Spanish class, only one is a boy, said Little, a senior. She also said that teachers rarely ask her for a hall pass if she is not in class, while they routinely question boys walking behind her.
As for assignments, she said, one teacher expects students to type up class notes and decorate their notebooks with glitter and feathers. ''You can't expect a boy to buy pink paper and frills to decorate their notebooks," Little said.

oh, yeah

been there, done that

In Social Studies, Christopher is graded on.....what do they call it?

Something about 'artistic quality.' He's graded on the artistic quality of his covers on reports.

Christopher can't draw.

He's never been taught to draw.

So he can't draw.

Also, his fine motor stinks.

But he gets graded, in social studies, on drawings he's required to do for report covers.

For this last assignment the teacher told them it was OK to trace something from the internet.

That sounds fair, right?

Well, guess what.

Tracing is harder than it sounds. (I happen to know.)

Fortunately, I was prepared.

I was prepared because, in some other Hypomanic Phase of my life, I just so happen to have purchased a light box for the Specific Purpose of Tracing Stuff from the Internet. (Question: Why would I do that? Answer: I forget.^*)

I dug it out, set it up, and Christopher traced stuff from the Internet, then colored it in.

It still looked like hell.

I say that deserves a lawsuit.

UPDATE 9-22-2006: No it doesn't. Miss Tucci was Christopher's social studies teacher for the year, and she was a doll. Just a lovely person, devoted to her subject matter, and kind to the children as well, albeit a little over the top with the drawing/tracing/artistic quality angle. Christopher learned a lot in her class and, if she teaches 8th grade social studies, I hope he has her again.

ok, ok, you're right

I'm sure a bias-against-boys lawsuit is a bad idea.

I'm sure a bias-against-boys lawsuit will have a gazillion unintended consequences, each one of which would directly impair & impede my OWN personal existence.

I'm sure I'll rue the day.

I don't care.

This is PAYBACK.

I like payback.

Because I'm ruthless.

Doug Anglin, the h.s. boy bringing suit (I think the student council president likes him)

Here's a picture of my light box.

B00005UNEN.01.LZZZZZZZ.jpg

It works great if you've got some fine motor coordination.

^* It may have been some scheme to create original, indivualized PECS cards for Andrew.

-- CatherineJohnson - 27 Jan 2006

MathematicsAtFloatingLog 20 Feb 2006 - 21:10 CatherineJohnson

the blog

-- CatherineJohnson - 05 Feb 2006

SchmidtInLosAngelesTimes 08 Feb 2006 - 15:44 CatherineJohnson

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

I love this line:

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

rocks and body parts

Never heard that one.

elementary school & fractions

A: Studies show that middle school is where we lose a great deal of ground, at least internationally. The middle school in these other countries in mathematics is much more demanding. And it's much more of a transition into what we in this country first do in high school. So when our kids come into high school, they're a couple of years behind already. And our high schools just can't make it up.
Basically, the middle school is not preparing kids adequately. But it actually goes all the way back even into primary school, where, again, the kids are not being prepared well, don't understand and aren't able to do the computations associated with simple arithmetic.
Q: So it starts in elementary school?
A: We need to really start a much more serious, clearly defined, coherent curriculum all the way back there, and then we'd have a better shot at doing better with our kids. A lot of mathematics in this country is not designed very coherently. It doesn't progress from the simple to the more complex in ways that are reflective of the mathematics discipline. There's a sequence of things that make the most sense. And very typically in American schools, these sequences are not very clearly laid out.
Q: What do you mean?
A: Fractions, for example, are very difficult for students. Instead of introducing the concept clearly enough so that they understand fractions as numbers on the number line, we oftentimes try to move too quickly to other parts of fractions, such as the operations, before they really have a clear understanding of what fractions are and how they fit into the broader number system.
So kids are trying to learn how to operate on these things, and at the same time they really don't understand what they are, so things get very muddled in their minds.

For me, this is very helpful.

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

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

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

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

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

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

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

Saxon Math & fractions

Saxon Math has a number of interesting approaches to fractions:

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

kids do mental math with fractions

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

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

is there one perfect method?

Q: Are the nations throughout the world using a different curriculum? Do they have different teaching methods?
A: That's actually a point I want to make very clearly. There doesn't seem to be one perfect method for doing this across the world. Different countries have different methods, just like we do here in the United States.
The real issue is the what. What it is that they're studying, in what grade levels in what sequence and at what level of rigor. Those are the issues that become important, not the how. It's more the what.
Q: We're just not being hard enough.
A: Yes. That's it, in a certain sense. As we move through the grades, we keep repeating topics year after year. We try to do too many topics at each grade level. We coined the phrase the "mile-wide, inch-deep curriculum" as a characteristic of the U.S., which means they just keep repeating these topics and as a result they have so much every year that it's too much for the kids to try to learn.
In these other countries it's a more focused attention on a smaller number of topics that progress across the grades in a logical fashion, leading to higher levels of expectation as you get up in the grades, like in the middle grades. And that's what we need.

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

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

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

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

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

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

mile-wide, inch-deep

....As we move through the grades, we keep repeating topics year after year. We try to do too many topics at each grade level. We coined the phrase the "mile-wide, inch-deep curriculum" as a characteristic of the U.S., which means they just keep repeating these topics and as a result they have so much every year that it's too much for the kids to try to learn.
In these other countries it's a more focused attention on a smaller number of topics that progress across the grades in a logical fashion, leading to higher levels of expectation as you get up in the grades, like in the middle grades. And that's what we need.

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

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

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

Schmidt is right about that.

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

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

teacher prep

Q: In Los Angeles, some educators say they have a hard time finding qualified teachers. Is that a problem for other nations?
A: For some. In the elementary grades, everybody struggles with this, because elementary teachers have to teach all the subjects. But once you get into about middle school, this is more of a problem in the United States, where our teachers are not as well prepared as the teachers in these other countries.
We are doing a study right now across six countries in which we very clearly find that U.S. teachers — U.S. teachers from middle school — are not being … required to take the same level of mathematics that is true in other countries. Teachers that are going to teach middle school mathematics have to have a stronger background.

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

By the numbers

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

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

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

Chapter 1 Why Schools Matter (pdf file)

1998 press release, TIMSS findings

-- CatherineJohnson - 07 Feb 2006

RoteKnowledgeInEverydayMath 23 Feb 2006 - 12:06 CatherineJohnson

Great comments on the advice from a top high school student thread. (This was the student whose father countered his son's rote learning of math by having him derive every formula he used.)

from Steve:

Perhaps you don't have to derive everything, but you do have to be able to understand and explain why you can do something using basic definitions and rules. And don't forget mastery. There is linkage.

The biggest fallacy of the latest fad math is that it teaches conceptual understanding. It does no such thing. My son is taking 4th grade Everyday Math, which is supposed to be one of the better fad math curricula. One of its rapid spiral "Home Link" assignments lately was a "Fraction of" sheet with problems like:

4/5 of 25 is _

This is before they know anything about multiplying fractions. How does the teacher explain how to do this problem? You take the whole number (25), divide it by the number on the bottom of the fraction (5) (notice that it is evenly divisible), and then multiply it by the number on top of the fraction. All rote understanding. Perhaps the students have to try and get a Zen-like understanding of four-fifths of 25. But then what do they do with a problem like:

4/5 of 7/8 ?

4/5 of 2.3 ?

Another Home Link spiral sheet talked about something like "Part of One" ?!? which is supposed to be the opposite of the example above:

20 is 4/5 of _

Once again, my son was taught a rote procedure for solving this problem.

I am getting really sick of this modern math conceptual understanding rubbish. Can anyone give an example of teaching real mathematical understanding in MathLand, TERC, Everyday Math, CMP, or their cronies? The so-called problem with traditional math was that it was all about drill and kill and no understanding. Well, nowadays, modern fad math does neither.

One of our school committee members told me that her younger daughter (in 6th grade, I think) doesn't have the math skills that her older brothers had at her age, but she has better conceptual understanding because of MathLand and CMP. I honestly don't have a clue what that means.

from Susan:

Exactly. Problems like these show up in Saxon in the form of word problems with the aim being to "see" the numerator and denominator in the form of a bar model, or to practice and clarify unerstanding the role of the numerator (3/8's of the girls had blonde hair, what fraction of the girls did not have blonde hair.) There are several problems like that, but I there is no rote procedure to solve them except in drawing out the vertical bar model to see the segments.

The Saxon version seems to be shooting for conceptual understanding without anyone locking in the procedure of dividing by the denominator, then multiplying by the numerator as the most efficient way of doing it.

Multiplying fractions as a procedure comes quite a bit later. While using the word "of" in previous chapters as another word for "times," this chapter is where they first bring it to learn and practice in a straightforward, rote way. The timing, I think, makes a big difference and is probably less confusing. My son has learned all of this with no bumps in understanding. One piece just fits into the next.

Cancelling is not mentioned at this point. Reducing, at this point, only happens in the answer. I'm dying to just teach this to him, but I'm sure I'd be piling on too much, too soon, and I've learned my lessons the hard way about doing that. A couple of chapters later is the GCF chapter, so I know that's why that next step is postponed a bit.

It's just hard to be an adult and go backwards. I want to show him the easy way when he needs to soak in the new stuff a little at a time.

aside from Catherine:

I am ONE with Susan on this point.

I've mentioned that I worked every single problem in Primary Mathematics Challenging Word Problems Book 3, and that I'm doing every problem in Saxon 8/7 as well.

That's a lot of bar models.

As a direct result, my brain has changed. When I read a fraction problem, bar models pop into my mind's eye unbidden.

I imagine some of you will feel skeptical about this, but for me that's a good thing.

Also, Steve's question — But then what do they do with a problem like: 4/5 of 7/8 ? or 4/5 of 2.3? — has an answer. In Singapore & Saxon the sequence of fraction problems is such that you 'see' that you need a common denominator — that is, you need a bar model divided into 40 segments.

I can't remember whether either Saxon or Singapore asks students to draw bar models of a problem like 4/5 x 7/8 — judging by the fraction problems I just did in KUMON Level F, for god's sake, Singapore may.

Saxon would, I think, use bar models to have kids do a problem like 2/3 x 3/5.

You see from what you've drawn that 2/3 'of' 3/5 is 6/15 which equals 2/5.

The funny thing is that, because I'd learned the multiplication operation with zero conceptual understanding attached (zero conceptual understanding of how the algorithm worked, I mean) I spent quite a long time being befuddled by the computation itself.

I just couldn't 'get' why you multiply the numerators and the denominators. You guys all tried to teach me & I still didn't get it! (I should rustle up those posts. Rudbeckia sent me a wonderful explanation; Dan created a graphic that everyone loved & I was the only person who didn't understand - - - )

Finally, the idea that 'clicked' for me came to me in the car.

This will sound incredibly unschooled & dumb....but tant pis. (French for t**** s***.)

I'd always sort of 'gotten' the idea that you multiply the numerators for the same reason you always multiply; you're finding '2 of 3' or '2 sets of 3' which is six.

But I couldn't put that together with why you multiplied the denominators.

Finally I realized that the denominators are divisors. 2/3 of 3/5 means you are successively dividing 3/5 by 3; you're doing two divisions in a row.

Two divisions in a row means you're dividing by 2 x the factor. (If you divide 12 by 2 and then divide the quotient by 2 again, you're dividing 12 by 2 x 2.)

I don't think this works as a verbal explanation for somebody still trying to figure this out, but it probably makes sense to all of you.

I have NO idea why I was so stumped by this.

I'm guessing I spent too many years overlearning the algorithm without the faintest idea why the algorithm worked. But I don't know.

conceptual understanding without skills

I think I do know what conceptual understanding without skills may be.

I think it would be quite possible to gain conceptual understanding of fraction multiplication — including conceptual understanding of problems like 4/5 x 7/8 — without acquiring procedural fluency in the multiplication algorithm.

It might even be possible to gain conceptual understanding of fraction multiplication with very limited understanding of factors.

I think it's the same observation Ken made a little while ago, after giving his son a Rubik's cube for Christmas.

It's possible to understand the directions for how to solve a Rubik's cube.

Actually solving the Rubik's cube is a different story.

from Kathy:

The biggest fallacy of the latest fad math is that it teaches conceptual understanding. It does no such thing.

Good-I was looking for an excuse to post my latest rant. My daughter is also in 4th grade Everyday Math. Tomorrow is her Unit 6 test, which covers long division, coordinate grids, something called "turns", map coordinates, angle measuring and drawing with a protractor, and word problems where you have to interpret a remainder. And all these topics relate to each other in what way??? With Meg's issues, all this jumping around is very confusing. She has figured out long division, thanks to much practice and tons of supplementation, but all this other stuff is causing much confusion.

Just for "fun" I was able to find the 4th and 5th grade Math texts I used back in the mid-70's and started to do a quick comparison to Everyday Math.

The thing that jumps out immediately is the sheer number of practice problems from my old books. For example, there are over 300 long division problems in the 4th grade 1970's text, just in the division chapter. They return to previously taught concepts in "Keeping Fit" sections which appear at least twice in every chapter.

How many practice division problems in EM's division unit? 20.

Measuring angles with a protractor wasn't introduced until 5th grade, and there's just 1 lesson on it, logically in the Geometry chapter. And decimals didn't appear until the very end of the 5th grade book; in EM they appear in 3rd grade, often through the introduction of problems which the kids are never taught to do.

from Carolyn:

Oh, Kathy, you're bringing it all back to me. 4th grade Everyday Math was the absolute worst, perhaps mostly because it was new and horrible to me, but also because 4th grade is a year when you have to learn and master so many critical things -- fractions, long division, multidigit multiplication. And there is all the jumping around in topics, and never never enough practice, and topics introduced in advance of their being taught.

I have to go lie down now.

a fraction problem from Intensive Practice 3B

Ms. Martinez ordered a pizza. The boys ate 2/5 of the pizza while the girls ate 1/2 of it. One of the boys, Mike, said that all of them ate 3/7 of the whole pizza. Was Mike correct?

3B is second semester, third grade; this problem comes from the 'Take the Challenge' section, so it's considered difficult.

Unfortunately, I sold my copy of 3B, so I can't look to see how kids are taught to solve such problems.

I'd put money on it they draw bar models along with using the addition algorithm, however.

advice from a top high school student
rote knowledge in Everyday Math

-- CatherineJohnson - 20 Feb 2006

TheLowGirlTrack 20 Feb 2006 - 23:30 CatherineJohnson

Ed told me this story.

Someone's been putting together an anthology of personal essays by French historians writing about what drew them to the study of France.

One historian talked about having spent a year in France when he was in high school, IIRC.

He was one of the top students in his school, but when he got to France he was placed in the 'low girl track' in mathematics.

"Low girl" meant that not only was this the math track for students who wouldn't be taking any math at all in college, but this was the lower-low.....this was the math class girls took! (Girls and boys weren't tracked separately; this was a process of self-selection.)

Until that moment, this fellow hadn't seen himself as being either low or slow in math.

-- CatherineJohnson - 20 Feb 2006

RaysArithmetic 22 Feb 2006 - 23:35 CatherineJohnson

I've just discovered a series of arithmetic textbooks from the 1800s while cruising geometry workbooks at christianbooks.com. (fyi, Charles put me on to christianbooks, which has the apparently-out-of-print Saxon Physics for a good price. I'm still mulling that one.)

According to the publisher, Ray's Arithmetic was the most popular arithmetic series in the 1800s, selling more than 120,000,000 copies.

Does anyone know anything about these books? Have you used them? Seen them? Read them?

The books have glowing reviews at Amazon. My ADD TO BOOKBAG finger is starting to twitch.

The 8-volume set is $100, but you can buy individual titles as well.

Christianbooks has posted 14 pages of Ray's New Practical Arithmetic online.

titles
Ray's New Primary Arithmetic
Ray's New Intellectual Arithmetic
Ray's New Practical Arithmetic
Key to Ray's New Arithmetics (Primary, Intellectual)
Ray's New Test Examples in Arithmetic
Ray's New Higher Arithmetic
Key to Ray's New Higher Arithmetic
Ray's New Arithmetics-Parent Teacher Guide

uh-oh

I'm going to get myself in serious trouble.

Fortunately, the listing appears to be closed.

I've sent an email to the seller just to make sure.

sources:
Amazon
Biblical Worldview Learning Center
Farm Country General Store
Homeschoolingbooks.com
Mott Media

-- CatherineJohnson - 21 Feb 2006

AsiansInGreatNeck 22 Feb 2006 - 05:20 CatherineJohnson

The TIMES was chock-full of interesting items pertaining to education today.

College students sending inappropriate email to their professors, and Asians in Great Neck.

GREAT NECK, N.Y. — In the annals of American newcomers, there must be relatively few immigrants like the Shins. They are an affluent couple in their 40's with two teenage children. They were well established in their careers in Seoul. And then, last July, Maria Shin came to the United States for her first visit, carrying a pocket translator, a laptop and a map on which she had marked out the best American schools with sizable Asian populations.
She visited Scarsdale. "A little bit too much," she said, meaning it was a little too expensive.
She visited the suburbs of Los Angeles. "Too much fun," she said, referring to what she perceived as California goofiness.
Then she came to this community on the North Shore of Long Then she came to this community on the North Shore of Long Island, where houses cost $1 million and the schools are known for producing Ivy League-bound graduates.
"Great Neck is where we chose," she said in halting English, which she works to improve in conversation classes two or three times a week at the Adult Education Center here. "Here are many Asians. And here my children have more ... more ... chance to live normal."
The chance to live normal is a relative value and might mean many different things to different people. But among a growing group of monied Chinese and South Korean newcomers arriving in this community of 40,000 in Nassau County, there is a strong feeling of what it means: the chance to spare their children the grinding competition and unrelieved pressure of scholastic life in their homelands.
[snip]
"Too much pressure, the children," said Fu Hong, 34, whose 5-year-old son was born in Shanghai just before she and her husband, a manufacturer's representative with interests in several factories, moved to a house in Great Neck. Their daughter was born here in 2002. "A lot of pressure. Here, he has fun. Skate. Swim. Aikido."

Just wait 'til these folks find out that in Great Neck skating, swimming, and aikido are not fun.

In Great Neck skating, swimming, and aikido are mandatory activities for entrance into Ivy League universities.

21neck.1842.jpg

slave parents in Singapore

-- CatherineJohnson - 21 Feb 2006

IntlHeraldTribuneSaysStudyMathNotChinese 26 Feb 2006 - 00:30 CatherineJohnson

The United States can find many other uses for the $1.3 billion the Senate committee wants to allocate for Mandarin education. One priority may be to train math teachers to calculate the value of 1 3/4 divided by a half.
Ma Liping [sic] describes that particular problem in her 1999 book "Knowing and Teaching Elementary Mathematics."
More than half of U.S. math teachers to whom Ma had given the problem got the computation wrong. Not only did all the teachers in China get the answer right, 90 percent came up with a valid "story" to explain the solution to children so they got the correct figure of 3 ½.
In a Senate Banking Committee hearing in 2004, Alan Greenspan said the lack of math education threatened U.S. competitiveness. The Federal Reserve chairman's concerns were validated in a Bloomberg News article last week about the Chartered Financial Analyst exams.
Chinese students, the article said, had the highest pass rate in the world in last month's CFA Level I test, followed by Germany and India. The United States was fourth.
Kindergarten students in Portland, Oregon, are learning that a triangle is san jiao in Mandarin, according to the Associated Press.
They might learn something more useful by playing with an abacus.
source:
Commentary: U.S. students need more math, not Mandarin By Andy Mukherjee Bloomberg News

from the Dept of Silver Linings: fourth is better than we're doing on TIMSS & PISA.

(hmm.....skimming the 2nd article.....they're comparing apples to oranges, almost certainly.)

and see:
Finance test draws more Chinese and Indians by Samantha Zee Bloomberg News

-- CatherineJohnson - 24 Feb 2006

SingaporeMathInWisconsin 01 Mar 2006 - 00:04 CatherineJohnson

Charles left a link to a story in Milwaukee's Journal Sentinel, via Education News, Less may be more when it comes to math.

Students in Singapore are introduced to roughly half the number of new math topics a year as students in the United States are. Experts and policy analysts say Singapore's emphasis on depth over breadth is a formula for success.
The thicker the textbooks and the greater the volume of math topics introduced a year, the less likely American students and teachers are to achieve similar results, says Alan Ginsburg, director of the policy and program studies service at the U.S. Department of Education.
"There's no way you can teach twice the amount of mathematics to the same depth that Singapore does," says Ginsburg, co-author of a 2005 report called "What the United States Can Learn From Singapore's World-Class Mathematics System," published by the American Institutes for Research.
He says the Singapore method of teaching math also puts a bigger emphasis on understanding instead of "mechanical" memory, and on visualization of the problems.

6th graders solving the hardest problem for 10th graders

"I feel like the biggest difference is the visualization," says Julia Rothacher, 12, a sixth-grader at University School.
Previously, she says, she attended Cumberland Elementary School in Whitefish Bay, where her class used the mathematical reasoning-based curriculum known as Everyday Math.
To appreciate what visualization can do, consider a problem that Neuwirth gave her class. It was considered the hardest question on a Massachusetts state assessment for 10th-graders, based on data that showed that more than half of the 72,000 test-takers got the question wrong, according to The Boston Globe, which published the problem.

Of the people in attendance at a recent baseball game, one-third had grandstand tickets, one-fourth had bleacher tickets, and the remaining 11,250 people in attendance had other tickets. What was the total number of people in attendance at the game?

The four choices were: A) 27,000, B) 20,000, C) 16,000 or D) 18,000.
Neuwirth's sixth-graders - without using the calculators that Massachusetts' 10th-graders could use - went to work.
Alexis Block, 12, did the problem on the board.
She drew 12 boxes of the same size, because 12 is the lowest common denominator of the denominators 3 and 4 in one-third and one-fourth, respectively.
She wrote "GS" for grandstand tickets above four - or one-third - of the 12 boxes, and "B" for bleachers above three - or one-fourth - of the 12 boxes.
She wrote 11,250 below the remaining five boxes, then divided 11,250 by five to get the value for each box - 2,250.
She multiplied the value of each box by 12 and got the correct answer for the total number of people in attendance: 27,000.
[ed.: Unfortunately, the reporter didn't ask Julia whether her classmates at Cumberland could do this problem.]

one-fourth of audience had bleacher tickets

one-third of audience had grandstand tickets

the remaining 11,250 people in attendance had other tickets

QUESTION: how many people in the audience altogether?

spaced repetition: more than half of Massachusetts 10th graders missed this problem

Singapore's bar models are gold. Saxon Math uses them, too; students draw bar models in virtually every problem set in Saxon Math 8/7. I'm going to have Christopher doing them all summer.

using bar models to prep for the state test

I used a bar model to show Christopher how to do this problem from the Glencoe test prep booklet he brought home over break:

6.N.17 Multiply and divide fractions with unlike denominators
Pizza Pizzaz was running a special on their 1/2 pepperoni and 1/2 cheese pizza. Mary, Jorge, and Shaun wanted to share a pizza, but they only liked the cheese half. If they shared equally, what fraction of the total pizza would they each be able to eat?

I fault Christopher's teacher for assigning virtually no story problems all year long.

Word problems are the true manipulatives.

Every concept she's teaching should be illustrated & practiced through extremely simple word problems to start — word problems so simple the kids can do them in their heads.

Christopher had no idea — zero — that this problem called for division of a fraction.

If you tell him to divide 1/2 by 3 he can do it in 2 seconds flat.

But his procedural knowledge is completely divorced from any actual situation in which one would divide 1/2 by 3.

So I drew a bar model, and of course he saw right away that this problem requires you to divide 1/2 into 3 parts.

At the beginning of the year I was having him do 2 or 3 bar models a day. I'm going to have to get back to that.

what does the AIR study of Singapore Math find?

The conclusion of the story is quite misleading:

But it's not certain that Singapore Math is making a difference in U.S. test scores.
[snip]
In his study of Singapore's math system, Ginsburg, of the U.S. Department of Education, looked at four sites in the U.S. where the Singapore approach had been adopted. Only two of those sites achieved results superior to control groups, and those two sites got additional staff development.
"It's not magic," Ginsburg says. "You can't just give out textbooks."

I've read most of the

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Entries from CompareAndContrastPosts

TERC (Grade 5, “Suitable for Grade 6”, too)

Singapore (Workbook Grade 5B)

math facts in Singapore, grade 3:

math facts in Math Trailblazers, grade 5:

update

"IMP™ Receives Award from the U.S. Department of Education"

caveat

US world ranking

item from SAT math test

sample problems from Japanese middle school assessment test

International Red Cross Symbol for Guess and Check

NAEP's "hard" 8th grade problems are Singapore's 5th grade problems

8th grade problem, NAEP

3rd grade problems, Singapore

update

update

ok, problem spotted

it gets worse

let me see if I've got this straight

this is interesting

this is good

update

update, update

update 3

excerpts from THE GEOGRAPHY OF THOUGHT:

oh, yay

one piece of bad news per slide

don't bury the bad news inside a bunch of other junk

update

from the SREB report (pdf file):

Key Findings

'no significant difference between the scores of U.S. students at the end of seventh and eighth grades'

girls and boys and math in Asia??

update: Christopher's answer

anti-constructivist digression

back on topic

that reminds me

France & Mexico

Vivian Shuh Ming Louie's research on the other gap

editorial aside: U.S. higher education is the best

back to the FT

the top 146 universities

what about the middle?

math horror stories

one more thing

update: I found it

spaced repetition

Education Week weighs in

Greenspan on education

Kumon for children with severe disabilities, too?

it's getting clearer now

update

update update

mission accomplished

thank you, Independent George

speaking of which.....no dumping on special ed, please!

on not living in a consensus culture

those durn Americans

rising costs of college

my favorite sayings about America

update

applied IQ points

update

update

College Board on recentering

what does an SAT math score mean?

so what does an SAT score mean? (part 2)

more SAT trends to come

Number 2 Pencil thread on SAT recentering

update