mathematical thinking

I’m closer to Brian Butterworth than Stanislas Dehaene, as this comparative review describes:

“Butterworth is a neuropsychologist who came to studying mathematical ability via his work on natural languages….Dehaene, on the other hand, started off as a mathematician, but became fascinated by the abstractness of his subject. He began to wonder where mathematical ability came from, and why some people are so bad at it, and others so good.”

The Mathematical Brain appeals to me from the start, with the author’s writing style being compared with Oliver Sacks (Seeing Voices: A Journey into the Land of the Deaf). The Number Sense reminds me of Barry Mazur’s, Imagining Numbers (which I started and now want to finish).
The reviewer argues, “cognitive science tells us that it is possible to teach mathematics in a way that fits with our psyche, a way that minimises maths-induced fear and boredom.” Lots of “sideways” exposure is doing it for me….all that three-dimensional American Sign Language interpreting has (seriously!) re-wired my conceptual circuits for math.
Just last week, the New Yorker’s “Numbers Guy” wrote about whether our brains are actually wired for math, featuring Stanislas Dehaene.
One tidbit: in addition to a certain kind of math perception, the language you use also influences cogniive processing:

English is cumbersome. There are special words for the numbers from 11 to 19, and for the decades from 20 to 90. This makes counting a challenge for English-speaking children, who are prone to such errors as “twenty-eight, twenty-nine, twenty-ten, twenty-eleven.” French is just as bad, with vestigial base-twenty monstrosities, like quatre-vingt-dix-neuf (“four twenty ten nine”) for 99. Chinese, by contrast, is simplicity itself; its number syntax perfectly mirrors the base-ten form of Arabic numerals, with a minimum of terms. Consequently, the average Chinese four-year-old can count up to forty, whereas American children of the same age struggle to get to fifteen. And the advantages extend to adults. Because Chinese number words are so brief&emdash;they take less than a quarter of a second to say, on average, compared with a third of a second for English&emdash;the average Chinese speaker has a memory span of nine digits, versus seven digits for English speakers.

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