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.

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.

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

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

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!

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

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

That's the bad news.




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Then Ringside Fest.

Back later.

update

update update

I'm not paying $25 for an autographed-something from a fat-bottomed apple-spitter.

Jerry Lawler, I learned this week, is the WWE announcer.

By this time tomorrow I will be a middle-aged Math Blogger who owns an official Jerry Lawler autographed-something.


JBL isn't going to be there. In case you were wondering.






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The book is subtitled "Best ideas from the world's teachers on improving education in the classroom". It's an outgrowth of the TIMSS video study, in which many videos were taken of mathematics teachers at work in American, German, and Japanese 8th-grade classrooms.

Here's a telling passage from the book. The rest of the book appears to flesh out the summary this gentleman gave after watching the videos.

One of the participants, a professor of mathematics education, had been relatively silent throughout the day. We asked him if he had any observations he'd like to share.

"Actually", he said, "I believe I can summarize the main differences among the teaching styles of the three countries." Everyone perked up at this, and this is what he had to say: "In the Japanese lessons, there is the mathematics on the one hand, and the students on the other. The students engage with the mathematics, and the teacher mediates the relationship between the two. In Germany, there is the mathematics as well, but the teacher owns the mathematics and parcels it out at he sees fit, giving facts and explanations at just the right time. In U.S. lessons, there are the students and there is the teacher. I have trouble finding the mathematics: I just see the relationship between the students and teacher."

Is that a cool observation? But how condemning of American teaching, if the observation about the American math lessons is true. I don't know about that yet. So far, I've read a description of a German teacher giving a lecture on a proof of Thales' law, and a Japanese math teacher giving a class on geometry. I can definitely see why the professor made the observation he did about German and Japanese teaching. (Digression: I remember being driven nuts by some of my German math professors in grad school. They lectured, and that was all they did; you didn't interact, because you couldn't get a word in edgewise. And they all, to a man, had a habit of going at least 15 minutes past the scheduled end of the class. That said, one of my favorite teachers was my undergraduate linear algebra teacher, who was very German. That was a while ago; for some reason, I can't remember why I liked him so much anymore).

The TIMSS video studies have been used as "evidence" that Japanese teaching, clearly more successful than our own, is "constructivist" in the sense that kids are expected to discover their own methods. I posted about it before, here, after reading this article, which offers a different interpretation of the situation in one of the Japanese math videos. I've seen nothing in the description given in The Teaching Gap of the video of one Japanese math class to indicate that kids are really being left on their own to construct their own methods.

There are clearly some favored elements of the American constructivist classroom present, the most salient being the occasional short bursts of group work; these are unsurprising, since Japan has a culture that emphasizes group achievement over individual achievement.

But, in the words of that perspicacious math ed professor, the Japanese teacher is MEDIATING the relationship between the students and the math. He is not leaving them alone together!

The period is over, and Mr. Yoshida interrupts to say, "I know this is bothersome, but I want to know the present situation." He then asks how many students have solved each problem. He concludes the lesson by observing, "There are a lot of people who are using triangles. That's okay, but there are three types of auxiliary lines. Sometimes there are easier methods of solving these problems using other types of auxiliary lines. We will check these in the next period."

More to come. I can't wait to get to the descriptions of the American math lessons. Will they be as cringeworthy as the professor's summary suggests?

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For that you get 150 worksheets a month, plus 4 visits to the center.

You can't even get a haircut for $85 a month here.

Best deal in town.

4th grade graduation

So I do my last set of 4th grade worksheets this week, then start 5th grade next week.

Let me tell you something.

A timed work sheet filled with huge long division problems is not easy.

update

I got my first 100% since starting KUMON.

Although having to express a fraction like 77/18 as a mixed number under time pressure and with basically no room for 'side calculations' is a challenge.

I did side calculations anyway. Wonder if I'll get dinged for those.

JUMP's fractions program

I'm going to order JUMP's 6th grade workbook, as well as The Myth of Ability: Nurturing Mathematical Talent in Every Child by John Mighton, founder of JUMP.

I bring this up here, because he begins remediation with fractions. That's where he starts. With fractions.

it has proven to be an extremely effective tool for convincing even the most challenged student that they can do well in mathematics.

[snip]

The various steps you will follow in teaching the material in this unit are outlined in great detail below, and also on the Fractions worksheets themselves. The individual steps are never more difficult than “count on your fingers” or “copy this symbol from here to here,” so the steps themselves will never be a barrier to weaker students. If you follow the instructions in this manual very closely, even your weakest students should achieve a mark of 80% or higher on the final diagnostic test (included at the end of the manual).

Which is true!







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KUMON says no, and I agree. The KUMON worksheets are designed to be supplemental. There's no 'KUMON instructor,' even though everything you read talks about the 'KUMON instructor'; there's just you, your worksheets, and your mother, who grades the worksheets.

What KUMON gives you is a highly structured, well-thought-out set of 200 worksheets per grade level—worksheets that have been used and revised over 40 years' time.

One of the interesting aspects of working through the KUMON sheets as an adult is that they give you practice in things you didn't know you needed practice in until you started doing the worksheets. They're diagnostic, in a way.

instructional practice

I'd call the KUMON sheets instructional practice. The problems usually aren't randomly generated, which is probably one reason why they don't randomly-generate a new set of problems for a student who didn't do well on the first set. (I should add that KUMON, like DI, is designed to ensure that students do do welll on each set.)

Instead, a KUMON worksheet often gives you a structured sequence of problems designed to illustrate a principle.

As an example, a long division with remainder sheet might have the student work this series of problems:

25/12
26/12
27/12
28/12
29/12
30/12
31/12
32/12
33/12
34/12
35/12
36/12


Doing each one of these problems in sequence is going to give a 4th grader a sense of what a remainder actually is.

update

The first sheet lists all of the times-7 facts in a table.

7 x 1 = 7  Seven ones are seven.
7 x 2 = 14  Seven twos are fourteen.
7 x 3 = 21  Seven threes are twenty-on