Saturday, May 19, 2007

Thinking Of Mathematics



This essay highlights the relevance of Zome in teaching mathematical concepts to students who are visually impaired. More generally, it describes my experiences as a mathematician who cannot see. I'm posting the abstract here; the complete essay can be found on my Web site.


Abstract


This essay outlines some of my experiences as a mathematician who cannot see. Note that I transitioned to being a Computer Scientist during Graduate School. However I strongly believe in the edict Once a mathematician, always a mathematician! — my training in mathematics continues to influence the way I think.


I've been unable to see since the age of 14, which means that I've studied and practiced mathematics predominantly in an eyes-free environment. This essay is my first conscious attempt at asking the question What is involved in doing mathematics when you cannot see? I hope that some of the experiences outlined here will prove insightful to mathematicians at large. At its heart, mathematics is about understanding the underlying structure inherent in a given area of interest — and where no such structure exists — to define the minimal structure that is needed to make forward progress.


The general perception that mathematics might be hard to do in an eyes-free environment probably traces itself to the common view of mathematics as a field where one performs copious calculations on paper. I'll illustrate some of the habits and abilities one evolves over time to compensate for the lack of ready access to scratch memory provided by pencil and paper when working in an eyes-free environment. In this essay, I hope to demonstrate that mathematics in its essence is something far bigger. By being bigger than calculations on paper , not being able to see rarely if ever proves an obstacle when it comes to doing mathematics; the challenges one needs to overcome are primarily centered around gaining access to mathematical material, and communicating ones insights with fellow mathematicians. Thus, a large portion of this essay focuses on solutions to the challenges inherent in mathematical communication.


The experiences described in this essay have influenced the software I have built and use on a daily basis; it should be of interest to:



  • Emacspeak users wishing to understand why things look like the way they do in Emacspeak.

  • Students with visual impairments who are entering the field of mathematics.

  • Teachers working with visually impaired students.

  • And the generally curious mathematician who wishes to view the world from a different perspective.






3 comments:

Jane Doe Jenn said...

Greetings,
I have read both your essay, and the comments section that followed. I love math, although I have never ventured further than a high school level. I am currently home schooling my children, and I think I can gleam a new way of understanding mathematics thanks to the experiences you have shared through your essay.
Thank you very much for your great contribution.
Jennifer S.

Admindya said...


Kompi Media

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