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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

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This semester I’ve had the opportunity to work at the extremes: one professor who has seamlessly blended me into her extensive use of the chalkboard, and another whose gaze apparently registers only empty space whenever she accidentally happens to glance my direction. The contrast heightens my belief that attempts to make ourselves “invisible” (while interpreting) are worse than “professional”: they are downright counterproductive.
For instance, the day I knew I could not possibly reconstruct the meaning for something uttered very quickly yet of obvious conceptual importance for the subject matter, and had to ask professor #2 (the one for whom language accommodation is nonexistent) for a repetition or clarification (I forget which), an expression crossed her face as if a voice had come from the woodwork. Her answer was curt (to say the least). However, I had established my presence (albeit momentarily). An interesting consequence of actually “being there” was that a non-deaf student requested my attention to a sight-line that I thought I was not blocking but, in fact, was. This had been going on for some time; the students had suffered simply because the non-verbal behavior of the professor indicated that I was to be

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“If speaking for someone else seems to be a mysterious
process that may be because speaking to someone does not
seem mysterious enough.”

Stanley Cavell (Quoted in Geertz 1973)
Read in Wilcox and Shaffer 2005

I’m reading an exciting critique which includes an exposition of frame conflict, The Conduit Metaphor by Michael J. Reddy, who relies upon

Schön’s dictum that frame conflicts are “immune to resolution by appeal to facts.” As he [Schön] says, “New facts have a way of being either absorbed or disregarded by those who see problematic situations under conflicting frames.” (Reddy 1979:285)

Reddy provides radical subjectivity as one example of a “frame” (what Berger and Luckmann call a “paradigm”), in order to illustrate the problem of what Schön calls “frame conflict.” A frame conflict is an alternative way of describing the communication dynamics of mis/understanding that occur when people who think through (as in “from” or “on the basis of”) different paradigms attempt to find agreement on a matter of mutual concern.

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