A paper in “Nature” shows the importance of experience in developing mental skills. The researchers examined the ability of Indian adolescents to do complex multi-step arithmetic in practical problems (in a market) vs. abstract problems (as equations).
Children who worked in a market were much better than non-working children at performing arithmetic when it was presented as a transaction. For the abstract problems, the non-working children performed better.
Moreover, there were differences in strategies. Children who did not work in markets were more likely to use paper and pencil for all types of problems, while children working in markets were often used addition, subtraction, and rounding to simplify multiplication and division. But both groups used this aid inefficiently. Often multiplication problems were decomposed into repeated addition problems (as in this example). Neither group is actually good at math by Western standards for children their age (most 11 to 15, but max = 17).
The result still stands, though, that experience in a market led to large numbers of children picking up algorithms for conducting transactions quickly with accuracy that is almost always “good enough” for their culture and context. This requires an impressive level of working memory for their age and education level.
There is a caveat that the authors mention, but don’t explore. An answer was marked as “correct” if it incorporated rounding either in the final answer or in preliminary steps, because this is a common practice in markets in India. Because the abstract problems were presented as equations, the children likely did not know that responding to 34 × 8 with an answer of 270, 275, or 280 (instead of the exact answer of 272). But in a market situation, these answers were considered “correct” and recorded by the researchers as such. The massive difference in performance in market-based problems may be mostly a result of the working children to rely heavily on rounding. So, this study does reveal a lot about the impact of different experiences on what psychologists call “number sense,” but not as much about exact arithmetic skills.
This study has important implications for intelligence. First, as Timothy Bates already pointed out, transferring learned skills from one context to another does not come easily or naturally. As a problem became less tied to the market context, the working children struggled more. Second, education builds cognitive skills, but turning those into abstract reasoning skills is much harder. This matches what the g theorists have been saying about how specific skills are trainable, but that general intelligence is difficult to raise.
The study is worth reading in full. It has no paywall.
Link to study: Children’s arithmetic skills do not transfer between applied and academic mathematics | Nature
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