[Blindmath] Math in your head

[Vincent Martin]

Sean,
It is nice to see someone finally cite or at least reference a study that corroborates what was written.  Are you currently working on your dissertation and what subject area is it in?




-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Sean Tikkun via Blindmath
Sent: Tuesday, December 15, 2015 10:26 AM
To: Blind Math list for those interested in mathematics
Cc: Sean Tikkun
Subject: Re: [Blindmath] Math in your head

So I’d like to interject a little psychology here, since the literature of my dissertation bears some of this out. A study was done recently (last 5 years) that established that the working memory of blind participants was not significantly different from sighted participants. The study went further to investigate the memory using braille and print. We all know that it takes longer to read braille tactually, but in this compact study it didn’t show significant differences (they weren’t reading prose but doing recall tasks). 

I’ve heard the math visual thing and actually came to the field as a teacher to specifically challenge my leverage of visuals (I was a geometry teacher for years). Visual orientation and representation is taught and are significant tools that aid computation and seeing patterns. In the end math is the recognizing of patterns and attempting to detect their underlying rules. When people say math is visual they are actually saying “I approach math visually”. One of my favorite moments tutoring was watching a student read a tactile diagram of a plotted function and the values table for the same function with different hands at the same time. Can’t do that with your eyes!

There was a point by David I wanted to touch on as well, as I think its hard to hear but has some historic truth in it. A code that a mathematician chooses to write their math only has to make sense to them. At least until they want to share it by teaching or publishing. This problem was rampant in the 18th century world of mathematics! So much so that prefaces of classic texts dedicated as much time to the lexicon as to the theory and proofs. If my memory serves it was an initiative of David Hilbert’s. Having a common language allows more effective sharing and teaching, more progress is possible in general. But we must remember that Nemeth code was a code generated by an individual originally for that individual to make sense of mathematics and represent it. Abraham Nemeth was a determined individual that insisted on demonstration of written proof in mathematics. So where it is true you can make up any code you want… you will be crippled in reading braille mathematics independently. And yet we sit in a debate of two codes of mathematics these days. However in the modern era I wonder if computer translation can serve us math int he language we want? In the end though, I think this philosophy is more common among individuals who have lost sight later and I myself (as a sighted teacher) thought as much for a time. 


Sean Tikkun
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