Friday, December 18, 2009

mathematical nature and nurture

Like so many things these days, this post was inspired by a celebrity (well, math celebrity) tweet. This one pointed to a letter published in the October issue of Nature.

The Nature article that du Sautoy referenced is here, and several other related papers by the same group of researchers are here and here. At some point soon I hope to write a bit more about this research, but for now I want to go back to the important issue that I think is raised by du Sauytoy's provocative tweet.

On its most essential level, the question posed by du Sautoy asks if some are born with better mathematical ability than others. This is going perhaps a step further than what was actually asked, but this is a step that many are likely to take, given that a positive answer to this question fits closely with many people's assumptions about mathematics.

Genetic gifts certainly play a role in how our lives turn out, and our ability to do certain kinds of math are not exempt from this. Temperament, attention-span, the gene responsible for holding a pencil properly, and other geneticly influenced factors may equip some more than others for mathematical activiites.

However, belief in the stronger version of this idea, that some are born with math ability while others are not, is one that has plagued the teaching and learning of mathematics for a long time, and may be responsible for excluding vast numbers of people from feeling mathematically competent.

What I believe, and will likely continue to believe until that belief is falsified by convincing evidence, is that mathematics is part of our shared cultural heritage, and is something that we can all lay claim to. Certainly there is much mathematics that I will never understand, but the basics, the fundamentals, and even the spirit that guides the most arcane mathematical research, is available to everyone.

Unfortunately, many feel excluded from the common heritage of mathematics, and part of the reason behind this are beliefs about the nature of mathematics. One belief that causes many to be excluded is precisely the one that states that some are born with the ability to do mathematics and some are not, an assertion that in many cases becomes self-fulfilling prophesy.

Many have written about harmful beliefs about the nature of mathematics - the most harmful being the idea that some are excluded from doing math at birth. Alan H. Schoenfeld has written about how metacognitive concepts like this influence our ability to learn and to teach mathematics. John Mighton has written about the question of math ability being hard-wired in his book The Myth of Ability. In the afterword to his book (online here), Mighton writes how his experience with JUMP tutoring has made him hopeful about challenging these commonly held beliefs - in his Elements of Humanity interview, he calls the belief that only some are born with mathematical ability to be an absurd illusion.

Although the study mentioned by du Sautoy was about measuring individual differences, it is useful to keep in mind how results like these are often misapplied to whole groups of people. In the classic book on group differences and intelligence testing, The Mismeasure of Man, Stephen Jay Gould cautions us:

We pass through this world but once. Few tragedies can be more extensive than the stunting of life, few injustices deeper than the denial of an opportunity to strive or even to hope, by a limit imposed from without, but falsely identified as lying within.