Monday, July 17, 2006

numerical processing in whites and East Asians   posted by Darth Quixote @ 7/17/2006 10:30:00 PM
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Here is an interesting new paper in PNAS. You can read a news article about it here.

In a typically insightful piece, the underground statistician La Griffe du Lion estimates that South and East (Chinese, Japanese, Korean) Asians average an SAT-M score of ~630-640. This implies that the average East/South Asian student obtains a higher score on the SAT-M than 85-90 percent of SAT takers at large. When I first came across this figure I could scarcely believe it, but since then it has come to my attention that the modal SAT-M score by far among East Asian students at elite universities is 800. This huge pile-up of scores at the ceiling is readily explained if 800 is in fact only ~1.5 sigmas from the East Asian mean. What might account for this whopping disparity? The writer of the linked-to article seems to think that this recent brain-imaging study has some bearing on this question:

And cognitive scientist Michael Posner of the University of Imbler thinks the study could contain a message relevant to the teaching of math. Could a different strategy for processing numbers help explain why Chinese students seem to do better at math than English-speaking students do? "It could very well be," he says.

Let us see where this study takes us. I would say not very far, but it raises some interesting thoughts.


Ten native Chinese speakers (of Chinese ethnicity) and ten native English speakers (white) were put through four different tasks while their brains were scanned by fMRI: (1) Symbol, deciding whether the third figure in a triplet of figural stimuli is presented in the same orientation as the previous two; (2) Number, same as Symbol except the stimuli are numbers rather than non-semantic figures; (3) Addition, deciding whether the third number is equal to the sum of the first two; and (4) Comparison, deciding whether the third number is larger than both of the first two. The control task consisted of deciding whether the third dot in a triplet of dots was the same color as the previous two. All subjects were comparable in age and of the same handedness. There does not seem to have been any attempt to control for IQ or, probably more importantly, narrow ability factors. I would insert a slick figure of brains lighting up at this point, but as Blogger is acting up again I will settle for, um, a verbal representation instead (this will seem like a bad joke later).

While the Symbol condition evoked no differences of note between groups, significant
differences emerged in the other three.

The activation in NES [native English speakers] is greater in the left SMA [supplementary motor area], Broca area, and Wernicke area (Wn) [the so-called "language centers"], compared with the corresponding areas in NCS [native Chinese speakers].... Importantly, much larger brain activation was found at a region in-between BA6, BA8, and BA9 in NCS. We termed this region as a premotor assocation area (PMA), which has previously been associated with visuo-spatial processing ...

Interestingly, within-group comparisons also reveal a similar activation pattern between Symbol and Number conditions in NCS.... Such similarity may imply the utilization of a visual-symbol system for representing Arabic digits in Chinese speakers....

For the other three conditions [Number, Addition, Comparison], although similar activated networks were found in the occipito-parietal areas, perisylvian area, and PMA area, the perisylvian activations were significantly larger in NES than those in NCS....

The larger perisylvian activation in NES alone may suggest that the brain representation of numbers is influenced by different language processes. However, across all of the four conditions as the arithmetic loading increased, there was a trend of increase in the premotor activation in NCS but not in NES. Such a trend was also found at the perisylvian area in NES but not in NCS. Therefore, between NCS
and NES, there was a double dissociation in the brain activation during these tasks, which suggests that the differences may not be merely due to different languages but also due to specific mathematic processes. In other words, whereas the numbers are represented in different brain regions from those involved in languages, people
speaking Chinese or English may engage different neural pathways in numerical processing.


I am reminded of an amusing passage from The Pleasure of Finding Things Out where the physicist Richard Feynman describes his informal experiments with counting silently in one's head. He found out that it is possible to count in two different ways: (1) Feynman himself seemed to say the numbers "one, two, three," and so on to himself, sotto voce as it were; while (2) his friend, the statistican John Tukey, visualized a mental number line and moved along it tick by tick. It has indeed been found in more recent studies that even stimuli in "elementary" cognitive tasks can be represented in different ways by different individuals (e.g., verbal/propositional v. spatial/figural).

So it seems that the present study has revealed another such difference scaled up to the level of group averages. The authors speculate that "the strong involvement of visuo-premotor association in NCS may be related to the experience of reading Chinese characters.... The use of the abacus in many Asian schools also suggests that, in one way or the other, the engagement of a 'mental image' for arithmetic could be related to the differences in brain activation." Hmm. Well, maybe so. The logical next step then is to scan the brains of English speakers of Chinese ethnicity, preferably with both a larger sample and a larger control group. It should be possible to find Chinese Americans who do not read or speak Chinese. It is also desirable to ensure that the present findings are not an artifact of an ability difference between the two groups. As I pointed out earlier, no effort was made to match the groups on ability levels and profile. A pseudo-race group of white English speakers with an ability profile similar to that of typical East Asians (average SAT-V scores, high SAT-M scores, high spatial scores) should be compared to a more typical group of whites; if differences in brain activation between the typical whites and the pseudo-Asians are similar to those in the present study, then the difference is not a
true race- or culture-specific difference but rather a mere ability difference. In the latter case, of course, we would still want to know what causes the elevated spatial and mathematical abilities of East Asians in the first place.

Can the extant literature give us any hints as to such a follow-up would turn out? Check out p. 169 of Nicholas Mackintosh's textbook IQ and Human Intelligence, which provides mean WISC-R subtest scores of the Japanese standardization sample. (The content of these subtests is described here.) The subtests can be classified as follows by performance of the Japanese relative to whites:

much better than whites: Block Design
better than whites: Arithmetic, Digit Span, Picture Completion, Picture Arrangement, Object Assembly
comparable to whites: Similarities, Digit Symbol
worse than whites: Information, Comprehension

It is clear that Japanese children excel their white peers in mental tests that do not load on the verbal factor. This may be due to an advantage in g, but the Japanese-white gap on Block Design is so large that at this impressionistic level I am inclined to invoke a Japanese advantage in the spatial-visualization factor as well. It is tempting to speculate that perhaps East Asians preferentially employ some form of analogical representation of numbers precisely because of this advantage.

Regardless of its bearing on the processing of number, is the profile difference between whites and East Asians genetic or cultural? I know of one adoption study of East Asian mental abilities that has employed the WISC-R (Frydman & Lynn, 1989). After a correction for the Flynn Effect it was found that 19 Korean orphans, adopted into Belgian families between the ages of 3 to 72 months and tested at an average age of 10 years, obtained an average IQ 10 points higher than the Belgian population mean (p < 0.01). Here are the mean subtest scores of this group, apparently uncorrected for secular trends:

Block Design: 13.89
Picture Arrangement: 13.32
Object Assembly: 13.26
Picture Completion: 13.00
Similarities: 12.95
Arithmetic: 12.79
Coding: 12.58
Comprehension: 12.00
Information: 10.37
Vocabulary: 9.63

Although these means are probably inflated upward, it is still easy to see that the relative performance profile of the Korean adoptees raised in Belgium and tested on the French translation of the WISC-R is unmistakably similar to that of native Japanese children tested on the Japanese translation. The nature of white-East Asian differences in mental abilities appears to much more complex than that of white-black differences, as the former likely involve large and small differences on several factors. It is true generally that all pairwise population comparisons other than white-black have received not nearly enough psychometric research effort as they deserve. But even without a more precise psychometric characteriziation, the evidence here still quite obviously suggests that the typical East Asian profile (high spatial, weak verbal) follows East Asian children regardless of the culture in which they are reared.

In an interesting study, David Geary and his colleagues found no substantial differentiation in arithmetical abilities between older cohorts of Americans and Chinese and thus argued that the observed differences today between whites and East Asians in arithmetical skill (and perhaps higher-level mathematical abilities) is the result of the declining quality of American education and resulting underperformance of Americans relative to their potential. I am not sure what to make of this. It may be that the results for the older cohorts can be explained as part of the same secular trend for East Asians over time observed in the data collated by Lynn (and made available in GNXP Forum), a kind of staggering of the Flynn Effect. Moreover, the difference favoring Americans on spatial tasks loading on the same factor defined by Block Design is decidedly out of line with the results of other studies. Something atypical may have been going on here. Still, we should keep this study in mind going forward.

A perhaps more informative design is to compare whites and East Asians educated in the same school system. Arthur Jensen and his then-student Patricia Whang published an interesting series of papers (not available online) about ten years ago that came close to doing this. They compared a sample of white children from an above-average-SES Bay Area suburb to a sample of Chinese children of below-average SES from Oakland's Chinatown. They administered to both samples Raven’s Standard Progressive Matrices (SPM), which is a nonverbal test of inductive reasoning, and a reaction-time task that they called the Math Verification Test (MVT). In each trial of the MVT, some arithmetic statement was flashed on a computer screen: 2 + 5 = 7, 9 – 4 = 6, 4 × 2 = 8, and so on. If the statement was correct, the subject pressed a button marked YES as quickly as possible; if it was incorrect, a button marked NO.

The Chinese children showed a mean advantage on the SPM of 0.3 SD (about 5 IQ points). That is quite typical of the white-East Asian IQ gap found worldwide across several recent studies. The Chinese children also showed faster reaction times in the MVT, but Jensen and Whang argued that their advantage over the white children exceeding 0.4 SD was greater than would have been expected on the basis of their edge in SPM scores alone. Within both groups SPM scores were negatively correlated with MVT reaction times.

We can imagine that the Chinese children have an advantage in g (evidenced by their higher SPM scores) that accounts for some portion of their superior performance on the MVT. Perhaps the remainder of the gap is accounted for by some factor particular to the processing of numerical stimuli. To investigate this possibility, Jensen and Whang administered a standardized test of school achievement in mathematics (MAT) to their Chinese sample. MVT reaction times were even more negatively correlated with MAT scores than with SPM scores. The semipartial correlations between the MAT and the MVT variables with the influence of the SPM removed from the MAT were still significant. The semipartial correlations between the SPM and the MVT variables with the influence of the MAT removed from the SPM, however, were near zero and not significant. These observations can be accounted for by the following model: the SPM measures only g, while both the MAT and MVT measure a numerical factor in addition to g. The shorter MVT reaction times by the Chinese children are then accounted for by higher standings on both g and this numerical (spatial?) factor.

Here a plausible case can be made for how a greater facility with visual or analogical representations might increase processing efficiency. In a later book chapter, Jensen describes a series of studies conducted in the seventies revealing the algorithm by which people perform simple addition in their heads. Subjects were seated in front of a computer screen and a console with nine response buttons marked 1, 2, 3, and so on. Each stimulus consisted of a simple addition problem: 2 + 5 = ?, 4 + 4 = ?, 6 + 3 = ?, and so on. The subjects simply had to press the button corresponding to the correct problem as quickly as possible. It was found that reaction time averaged across subjects increased as a linear function of the magnitude of the smaller addend as long as the addends were not equal. If the addends were equal, reaction time did not vary with the magnitudes of the addends and tended to be shorter overall. These observations can be accounted for by something like the following model: the subject conjures up a mental number line, zooms in on a tick mark corresponding to the larger addend, moves n ticks to the right where n is the magnitude of the smaller addend, and reads off the digit label under that particular tick mark. If the addends are equal, the subject simply recalls the answer from memory. Other models are possible, but it seems that they must all invoke analogical representation. This effect of addend size on reaction time was observed in a wide age range, from first graders to college students; the latter averaged a reaction time one-fourth as large as that averaged by first graders, but apparently both groups and everyone in between were executing the same algorithm. Note that this simple task is very similar to the addition portion of the MVT administered by Jensen and Whang. Jensen does not say whether the effect of addend size was borne out in his own study; perhaps there was not enough data to permit the proper analysis. (For what it's worth, I heard a neuropsych talk recently where it was reported that hemispatial neglect patients tend to overestimate the average the two numbers, as if they were "looking" too much at the right side of a mental number line.)

Is the advantage of the Chinese children attributable to a greater reliance on analogical representation enabled by superior spatial-visualization ability? If so, does this cascade up to the higher-level differences observed in tests such as the SAT-M? Regardless of whether causation is genetic or cultural or some combination thereof, this possibility is worth pursuing. Certainly the mystery of the differences in mental abilities between whites and East Asians is worth tackling in any way that we can.