[BlindMath] Question about the visualization of mathematical Concepts

Mon Nov 29 20:04:12 UTC 2021

John,

Your post is very interesting to me in that it expresses very well much of my own experience.  I had a professor from who I took advanced calculus, and he actually told me that he observed that I had an advantage when we were dealing with creating a solid by revolving a curve around an access.  I would picture it in three dimensions while other students were struggling with representing the results in two dimensions.  Having said this, I believe some of this ability is dependent upon one's ability to picture spatial relationships.  This ability seems to vary greatly.

Regarding sonic representations of graphs, I think they have a very important role to play.  However, without a connection between how graphs are being displayed to other students and the sonic representation, I think the transition would be difficult.  Finding ways of representing graphs tactually as Louis described can provide basic concept information.  Once that concept has been established, moving on to a sonic representation will be easier in my opinion.  

Best regards,

Steve Jacobson

-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of John G. Heim via BlindMath
Sent: Monday, November 29, 2021 12:28 PM
To: Niels Luithardt via BlindMath <blindmath at nfbnet.org>
Cc: John G. Heim <jheim at math.wisc.edu>
Subject: Re: [BlindMath] Question about the visualization of mathematical Concepts

IMO, the main problem with getting a sense for mathematical concepts if 
you are blind is that sighted people insist that you show them what you 
are thinking by drawing it on a piece of paper. To get a sense of what I 
mean, challenge a sighted person to a game of tic tack toe of the mind. 
Each player just says where they want their X or O to go. You might need 
a third  person to write it down for you because your opponent probably 
won't be able to picture the game in his/her mind. Maybe I'm not a 
typical blind person but I have no problem just picturing something as 
simple as a tick tack toe game in my head. But sighted people, if they 
can't draw it, they are in trouble.

I really think being blind is a huge advantage when picturing 3 
dimensional spaces. Sighted people are struggling to draw it on paper 
whereas a blind person can just "see" it in their head.

On 11/28/21 1:15 AM, Niels Luithardt via BlindMath wrote:
> Hello,
> 
> I have a question. What techniques do you use to visualize
> mathematical relationships?
> 
> Mathematics is more than calculating with letters. How do you create
> pictures in your head and what kind of techniques do you use to
> sharpen the view, the pictures?
> 
> Maybe a conceptual example would help:
> 
> What kind of picture do you have in your mind when you think of a
> continuous function?
> 
> I would be very happy about your answers!
> 
> kind Regards
> 
> Niels
> 
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-- 
###
John G. Heim, 608-263-4189, jheim at math.wisc.edu

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