[BlindMath] Question about the visualization of mathematical Concepts

Mon Nov 29 19:54:19 UTC 2021

When studying calculus in secondary school, I actually found the limit definition helped my understanding at least as much as graphically-oriented explanations did. I didn't have a problem with the two quantifiers ("For every epsilon greater than 0 there exists a delta greater than 0...").

-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Niels Luithardt via BlindMath
Sent: Monday, 29 November 2021 14:44
To: Blind Math list for those interested in mathematics <blindmath at nfbnet.org>
Cc: Niels Luithardt <niels.luithardt at googlemail.com>
Subject: Re: [BlindMath] Question about the visualization of mathematical Concepts

Hello John,

that's a good point you raise. Sighted people visualize things by drawing things on paper. We as blind people can of course try to simulate this approach of the sighted world with technical aids as Louis described. But is that the way we should go as blind people?
Mathematics takes place in the head.

The question that concerns me is how the conceptualization takes place in the blind, how the anchoring takes place. Isn't it better to learn in pictures than to dully memorize complicated quantifier chains?
Without having a picture of what all the quantifiers want to tell me?

Kind Regards

Am Mo., 29. Nov. 2021 um 19:29 Uhr schrieb John G. Heim via BlindMath
<blindmath at nfbnet.org>:
>
> 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
> >
> > Translated with
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> ###
> John G. Heim, 608-263-4189, jheim at math.wisc.edu
>
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