math isn't English

My sense of the Johnson - Bouchard study is that it weighs in directly on the side of parents who intuitively perceive that math isn't English.

Interestingly, it is the image rotation abilities that have repeatedly shown the most robust sex differences among cognitive abilities (favoring males, Voyer, Voyer, & Bryden, 1995).

[snip]

It has been known for some time that performance on spatial tasks, particularly those involving image rotation, predicts success in fields such as airplane piloting, engineering, physical sciences, and fine arts better than does general intelligence, and especially verbal ability (Gottfredson, 2002; Humphreys & Lubinski, 1996; Shea, Lubinski, & Benbow, 2001; Sheppard, 1978).

Academic prose.....pretty impenetrable.

Instead of cutting and pasting any more of this, I'll post the short version of what I take to be Johnson's and Bouchard's points. (Take this with a grain of salt; I would need to interview them to feel confident that I've got this straight.)

• a general intelligence factor - g - exists which "contributes to all mental abilities"
  

• "residual" factors also exist: once a general intelligence factor is extracted from any collection of ability tests, the correlations among the residuals fall into two main groups ["verbal" and "perceptual" in Vernon's classic model].
  

• Johnson and Bouchard find 3 "residuals," not 2: verbal, perceptual, and image rotation
  

• these 3 map directly onto the classic distinction between the left and right brains, with verbal skills being left-brain and spatial skills being right-brain, "though it is clear that all tasks of any complexity involve contributions from both hemispheres (Gray & Thompson, 2004)."
  

• you can be high in verbal intelligence and not so high in spatial abilities, and vice versa
  

This study appears to support parents' felt sense that it's wrong to force a mathematically-inclined child (note the use of the term "inclined") to "demonstrate understanding" by putting math into words.

Math and English aren't the same subjects, and the abilities that underly achievement in the two subjects differ.


it's not just the gifted

Another terrific aspect of Johnson's and Bouchard's article is that it appears to support a perception I've had for quite awhile now:

It has been known for some time that performance on spatial tasks, particularly those involving image rotation, predicts success in fields such as airplane piloting, engineering, physical sciences, and fine arts better than does general intelligence, and especially verbal ability (Gottfredson, 2002; Humphreys & Lubinski, 1996; Shea, Lubinski, & Benbow, 2001; Sheppard, 1978). There is also evidence (Humphreys, Lubinski, & Yao, 1993) that failure to include assessment of such abilities in the standard batteries used for college and graduate school admissions is resulting in loss to those fields of potentially highly talented individuals. Perhaps of even greater concern, however, is the possibility that effects of this type may not be limited to the gifted and talented. Elementary school curricula tend to be used to educate those of all ability levels and they are generally much more highly focused on verbal than on image rotation abilities. This may be resulting in alienation from school of individuals unlikely to attend college as well as reducing the achievement of those who may. The social costs associated with early school leaving are well documented (e.g., Henry, Caspi, Moffitt, Harrington, & Silva, 1999).

This is something I see in schools.

I've worked with at least one child, a boy, who is mathematically inclined, but who has problems with learning and is classified SPED. (Very high-end SPED, the sort of kid who is still classified only because his mom correctly continues to fight for and win the designation.)

My frustration with the situation has always been that while everyone is working well with this boy, who is having a far better middle school experience than a lot of the non-SPED kids, no one appears to perceive that he has a particular talent for and interest in math, and thus ought to be pushed and supported in that subject specifically.

Instead there's a global assumption that he needs help.

Which is true as far as it goes.

But oughtn't the "help" offered be different in math than it is in language-based subjects?

Shouldn't the school be trying to move him ahead in his strongest subject?

Part of the reason this doesn't happen, I think, is that this boy isn't mathematically gifted. (At least, I don't think he is.)

He is mathematically inclined.

Mathematical giftedness leaps out at people; it's hard to miss.

But mathematical inclination, especially in a child who finds his other subjects challenging, is more subtle.


bonus passage

Specifically, we would expect that general intelligence will prove to be influenced by several to many genes responding to environmental stimuli to control biochemical processes acting throughout the brain. At the same time, we would expect that there will be several to many genes that influence brain functions that affect primarily verbal abilities and others that influence brain functions that affect primarily spatial and perceptual abilities. Some of these genes may even enhance abilities in one area at the expense of abilities in another, contributing to the lower correlation between verbal and perceptual abilities than between fluid and crystallized abilities in our models. Such environmentally mediated genetic processes may also help to explain differences in strategies used to approach cognitive tasks, individual differences in stimuli that attract attention, and sex differences in performance on various kinds of tasks. Evidence in support of these kinds of predictions is beginning to emerge.

The structure of human intelligence: It is verbal, perceptual, and image rotation (VPR), not fluid and crystallized (pdf file)

good schools raise IQ, bad schools lower IQ, part 1
good schools raise IQ, bad schools lower IQ, part 2
good schools raise IQ, bad schools lower IQ, part 3
Seth Roberts on IQ
fuzzy math makes you smarter
IQ quiz
school raises IQ
intelligence is verbal, perceptual, and image rotation
math isn't English