[BlindMath] Question about the visualization of mathematical Concepts

[John G. Heim]

Well, it might be handy to be able to graph complicated formulas. But a 
sine wave is like a American siren or a wave in the ocean. If you think 
of a sine wave as that line on a piece of paper, you're missing out on 
the real world things the mathematical concept represents. At the very 
least, you have to make an extra step to apply it.

I really think the tic tack toe example is the best illustration of the 
point I am making. The game is to get 3 in a row. It's not to *draw* 3 
in a row. Having to draw it is just extra baggage not meaningful in the 
context of the game itself.

I'm not particularly good at tick tack toe, nobody is. It is too simple 
of a game for anybody to be very good at it. But it is easy enough to 
show that sighted people are bad at tick tack toe unless they can draw 
it. Essentially, Sighted people need an accommodation in order to play 
tick tack toe. That piece of paper they need is no different than the 
screen reader I need to use a computer, it's an accommodation.



On 11/29/21 1:43 PM, blindmath at nfbnet.org wrote:
> 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 www.DeepL.com/Translator (free version)
>>>
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>>
>> --
>> ###
>> John G. Heim, 608-263-4189, jheim at math.wisc.edu
>>
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> 
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-- 
###
John G. Heim, 608-263-4189, jheim at math.wisc.edu