What Counts: How Every Brain is Hardwired for Math

Are our brains ""hardwired"" to count and conceptualize numbers, or are counting, and other mathematical activities something that we learn, like playing the piano? Butterworth, editor of the journal Mathematical Cognition, is convinced that evidence points to the existence of circuits in the brain devoted to identifying what he calls ""numerosities,"" or, more simply, the number of objects in a collection of things. To this network of specialized circuits, or ""Number Module,"" Butterworth explains, each person adds the mathematical knowledge of his or her culture. Thus, people who ""aren't good in math"" have trouble not because they're dumb or not applying themselves, but because their Number Module is different from the prevailing one. Not surprisingly, Butterworth has strong views on how to teach mathematics, and these form a prominent part of his book. He also shows how a person's brain can change to devote more resources to respond to mathematical stimuli. For example, a study of Braille proofreaders based on brain-scan maps has demonstrated that the part of the brain devoted to this activity grows in size after six hours work. But give the proofreaders a few days off, and their brains shrink back to normal. Butterworth's prose is marred by repetition, and his digressions to explain various well-known math puzzles and peculiarities, such as Pascal's triangle, often aren't germane to his argument (do we really need a proof of G del's theorem here?). But these are minor caveats about a provocative book that makes an important addition to the recent flurry of titles regarding how our minds work. Teachers as well as readers curious about the brain and psychology will be challenged by the ideas expounded here. (Aug.)