Is there a definitive guide to speaking mathematics to avoid ambiguity? I’m writing a program to generate text for a variety of mathematical expressions and would like to code it so that it adheres to some standard. I’ve found Handbook for Spoken Mathematics, but nothing better. Before settling on this one source, I thought I’d ask this mathematics community.
First of all, thanks, Michael, for a great question! And framing it in terms of “imagine teaching mathematics to blind students…” helps us to recognize issues of math accessibility, in this case, accessibility to the visually impaired. You’ve helped me to educate myself, a bit: for example, whereas written mathematics depends extensively on “2-D” representation: subscripts, exponents, radicals, (the list goes on and on: vector representation…just think of matrices!) — traditional braille is “linear”, not amenable to such usage.
I came across a fabulous survey article, with an abundant bibliography, that may be of interest:
I found it fascinating, and eye-opening: recognizing some of the key obstacles that the visually impaired (and those engaged in teaching such students) confront with respect to accessing mathematics. The first part of the article addresses efforts to transform/modify braille (and to translate from, e.g., LaTeX or ML, to modified braille). The second part of the paper addresses “Dynamic” efforts to make math more accessible, e.g., ways to enable teachers to engage directly with visually impaired students, rather than only indirectly, by translating text to braille. Here is where “spoken math” comes in. There is research comparing the efficacy of alternative modes of speaking math (extra terms: explicit reference to parentheses, symbols, etc.) with variations in parsing (use of pauses, intonation, amplification, etc). And (interestingly), the insertion of additional technical terms (“open parentheses, a plus b, close parentheses”) multiplied by 4″, was found by at least one researcher to be less effective, in terms of comprehension, that parsing speech appropriately, pausing, e.g., before and after “a + b”, using emphasis, …
I haven’t read all of the research, but it may very well examine the use of some combination of these approaches, as well. (See, e.g.)
Fitzpatrick, D. (2002). Speaking technical documents: using prosody to convey textual and mathematical material. International Conference on Computers Helping People (ICCHP),
Springer Verlag, pp. 494-501.
Fitzpatrick, D. (2006). Mathematics: how and what to speak. International Conference on
Computers Helping People (ICCHP), Springer Verlag, pp. 1199-1206.
The ultimate question will be whether the mathematics community, at large, will be receptive to accepting, or at least endorsing, the many valiant efforts of those dedicated to making mathematics accessible to ALL by adopting a standard for speaking mathematics.
Indeed, information like this could be important to ALL students of mathematics.
Perhaps you are already familiar with much of this work. If I find anything more, I’ll be sure to let you know.
I did find a few more interesting resources, including some references and links:
In the above article, mention is made of the research and work by T.V. Raman, who himself is blind but has worked extensively to develop text to speech programming.
Also see Raman’s “publications” page:
Finally, this is one particular work of Raman, autobiographical, that is quite inspiring!: