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Audrey Yap

My friend Patrick Girard at Auckland has had some success in this respect using Polish Notation.


The AMS has an article on the "World of Blind Mathematicians" that I tweeted a couple of years ago. It may be helpful. Here it is:


Related to my previous comment, here's another article I tweeted at around the same time, "Blind Mathematicians? Certainly!" by blind mathematician Alfred P. Maneki, which may also be helpful:

Carolyn Hartz

The American Printing House for the Blind has sheets with two and three circle diagrams on them (the circles have different textured lines so they can be easily distinguished). I’ve used foam pieces that can fit over portions of the diagrams to represent shading and foam Xs. (I also use these foam pieces in doing Venn diagrams with 4th and 5th graders and have devised a board/card game where the board is a Venn diagram and the kids use the foam pieces on it to represent categorical propositions on the cards.)

I have also devised a method for doing truth tables for a blind student. This student wasn’t fluent in Braille but easily distinguished regular letters by touch.

The method involves blocks with a sentence letter or connective on one face, and two distinguishable textures on opposite faces adjoining the symbol face. One texture represents “true” and the other “false”. The student is also supplied with blocks that have the true/false faces but no other symbols—these are for constructing the truth table.

I constructed a box with 24 compartments to accommodate truth values for up to three sentence letters, along with the raised letters across the top of each column. The student is given a WFF and starts by constructing the WFF from the blocks that have symbols on them, and sets up the truth table with the blocks that don’t.

For each row of the truth table the student turns the letter blocks to correspond with the given values; i.e., turns all the letters in the WFF to the “true” side of the block for the first row, etc. The student then turns the symbol blocks to the correct side—for the first row, a negation next to a single letter is changed to the “false” side, etc. In this way the overall value of the WFF can be derived. The value for the sentence can then be recorded in the box in a compartment next to the three sentence letter values. Then the blocks for the WFF are returned to their original positions and the values for the second row are used and the process continues.

Validity for arguments can be determined by going through this process for premises and conclusions, their values being recorded in the box. The student can then determine whether conditions for validity are fulfilled.

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