[Blindmath] Math in your head

Tue Dec 15 23:21:05 UTC 2015

Thanks and Sorry… I just realized the response I had given to Sean Whalen wasn’t to the group. So I’m posting it here since you said the word reference and cite… which I was holding back my instinct from. MSG below.

No worries Sean, I’m seldom offended and happy to share.  Even happier (oddly enough) to be wrong…  The APA references are at the bottom of my reply, in case you enjoy that sort of thing. If any of this is interesting to folks you may have contact with I am always looking for help connecting with participants. My dissertation will be replicating the working memory stuff and specifically targeting mathematics work.

As for the memory info. I’ll share two quotes form the article that I found interesting. I think the first one answers your questions about use of the visual cortex. Actually a neuropsychological article found atrophy in visual cortex growth among congenital blind individuals, but also increased growth and connectedness in the frontal and prefrontal regions. (Lepore, et al., 2010) 

"One possibility is that individuals are born with similar levels of short-term memory capacity for the different sensory modalities but, depending on sensory experience, some memory modalities become more enhanced than others. Thus, most persons have good auditory and visual short-term memory, because they have the most experience with inputs in these modalities. Consequently, the working memory subsystems might be highly crossmodal with numerous interconnections, the strengths of which are altered through experience.” (Cohen, et. al, 2010)

"This result is consistent with a recent finding showing that working memory processes in both visual and tactile modalities share common neural networks [35], thus providing support for the notion of a working memory system independent of sensory modality.” (Cohen, et. al, 2010)

As for the reading speeds I turn to a paper presented by Phil Hatlen at Getting in Touch with Literacy conference. There are exceptional individuals to be sure, but his presentation quoted 100 words per minute as a reasonable expectations. Compared with the expectation of 250-300 words for sighted readers. (Hatlen, 2003)

Cohen, H., Voss, P., Lepore, F., & Scherzer, P. (2010). The nature of working memory for braille. PloS one, 5(5), e10833.
Hatlen, P. (2003). Impact of literacy on the expanded core curriculum. Paper presented at the Getting in Tough with Literacy Conference, Vancouver, British Columbia, Canada. 

Leporé, N., Voss, P., Lepore, F., Chou, Y. Y., Fortin, M., Gougoux, F., ... & Thompson, P. M. (2010). Brain structure changes visualized in early-and late-onset blind subjects. Neuroimage, 49(1), 134-140.

Your Friend,
Sean Tikkun
stikkun at niu.edu <mailto:stikkun at niu.edu>

Assistant Project Director
UEBOT Team 
uebot.niu.edu <http://uebot.niu.edu/>

> On Dec 15, 2015, at 3:20 PM, Vincent Martin via Blindmath <blindmath at nfbnet.org> wrote:
> 
> 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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