[BlindMath] Question about the visualization of mathematical Concepts

Tue Nov 30 15:18:43 UTC 2021

I don't know if I can explain it. If you're blind, you just don't do 
drawings. That's just not how your mind works. When I think of a 
parabolic equation, I think of a parabolic microphone or a bowl. It's a 
shape, not a line on a piece of paper. Sure, I have to picture a cross 
section through a bowl but that, after all, is more accurate than a 
graph. Well, technically, the ink on the paper is the same as a cross 
section of a bowl. But sighted people tend to think of an equation  as 
the drawing, not a mathematical representation of an object.

Not too long ago, I posed the following problem to a group of 
professional mathematicians. If you had a 4 by 8 piece of plywood, what 
is the biggest circle you could make by cutting off one end and gluing 
it onto the long edge?  In other words, you can cut the 4 by 8 rectangle 
into 2 rectangles and glue one onto the other so it allows you to make a 
circle that extends into the glued on part.  This is a real world 
problem I had to solve when i was making a D&D gaming table. It took me 
about 10 minutes to picture the solution and to do the math in my head. 
But even after I tore  up some coctail napkins to illustrate the 
concept, the sighted mathematicians couldn't see the solution, not w/o 
getting out a pen and drawing lines on the napkins.

The solution, BTW, is 5 feet. You can make a 5 foot circle out of a 4 by 
8 piece of plywood by cutting off one end and gluing it onto the long edge.

On 11/29/21 2:04 PM, blindmath at nfbnet.org wrote:
> 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