Writing For Your Audience

Linda McGuire

Muhlenberg College

The last ten years have seen courses dedicated to proof writing being developed and woven into the undergraduate mathematics curriculum. Such courses serve to better prepare students to grapple with the abstract concepts and arguments that await them in junior and senior level math courses. So-called “Transition to Abstract Mathematics” courses initially focus on logical techniques, but then can progress to discuss higher-level questions regarding mathematical exposition. One such question is how to tailor a mathematical argument to the audience that will read it.

The project I would like to give a presentation on was designed to have students address this question. At four different points in the semester, students were given problems to solve using whatever proof technique (direct proof, indirect proof, proof by contradiction, induction, etc.) was applicable. They then had to write not one, but three, different proofs of the same problem. The first was to be written like an op/ed piece in the newspaper, with the assumption that the reader is literate, but may have little or no formal mathematical training. The second proof was to address an audience of their peers assumed to have a background akin to their own. The final version was to be written as if trained mathematicians were to read it. The results improved dramatically throughout the term and some important points were raised and discussed.

These projects forced students to be accurate in their analysis, precise with their word choices and careful not to talk down to (or up at!) their audience. They had to hone their techniques from communicating without symbols to using efficient symbolic representations to their maximum possible advantage. It took several revisions for most students to obtain acceptable solutions.

Many excellent conversations about writing ensued both in and out of the classroom. Students were encouraged to have others read their work, both their mathematical peers and other people around the campus with varying mathematical backgrounds.

I would construct my presentation to highlight the problems given, shoe student solutions to these problems, and to share with the audience the many positive questions and comments that the projects stimulated.