"Formal logical proofs, and therefore programs – formal logical proofs that particular computations are possible, expressed in a formal system called a programming language – are utterly meaningless. To write a computer program you have to come to terms with this, to accept that whatever you might want the program to mean, the machine will blindly follow its meaningless rules and come to some meaningless conclusion. In the test the consistent group showed a pre-acceptance of this fact: they are capable of seeing mathematical calculation problems in terms of rules, and can follow those rules wheresoever they may lead. The inconsistent group, on the other hand, looks for meaning where it is not. The blank group knows that it is looking at meaninglessness, and refuses to deal with it"
I see that section 4 contains a reference to another study offering an alternative explanation for the 'double hump': if a teacher sets the pace by the progress of the fastest learners, you can end up with a group that kept up and a group that was left behind early and so never learned much. I guess this is more likely to happen if you have several students, rather than one or two at most, who already have had some exposure to the material, and that this is more likely in programming than in, for example, actuarial mathematics.
Well I won't be linking that anymore. Anyways, I was really more interested in the little narrative observation above than the numerical results of the study.
The quote reminded me of a study I read about a year ago, in which the problem-solving skills of toddlers and chimps were compared. The toddlers generally did better, except in one regard: when shown how to do something, but with some pretty obviously irrelevant steps included, the chimps were quicker and more likely to drop the pointless steps. At the time, I thought that might be explained by a human predisposition to pay attention to authority, but, in the light of that quote, perhaps it is (also) a predisposition to formal / abstract thinking? Furthermore (to make a wild speculative leap) perhaps it is this predisposition that is actually behind the phenomena that Chomsky thinks are evidence for an innate universal grammar?
http://blog.codinghorror.com/separating-programming-sheep-fr...
http://www.eis.mdx.ac.uk/research/PhDArea/saeed/paper1.pdf