Friday, April 26, 2013

Presenting Mathematics Through Dialogue and Story

Susan Jane Colley has written a review of both Math Girls and Manga Guide to Linear Algebra for the College Mathematics Journal. (Unfortunately, it's only available to MAA members.) I liked it and want to share a few thoughts. After sharing a dialogue from Math Girls, she wrote:
Passages such as this make me think Galileo was right to explain his cosmological theories in a dialogue between actual characters. Maybe we should routinely present mathematics as a conversation between two people striving for understanding rather than as persona-free perfection.
Well, now I'll have to see if the Galileo is worth reading. (I just checked using google books, and it's not too hard to read. The misogyny bugged me, but the opinions about "the Pythagoreans" were interesting. Perhaps the math will be too. Ahh, history.)

I agree with Susan Colley that presenting math as conversations is a good pedagogical device. I'd like to try it. One benefit of writing this way is that it's possible to explore a problem more fully without giving away any punchlines. Of course, it also adds interest.

Would any of my readers be interested in writing short dialogues on selected topics?

Summer's coming, and I like to think during summer about topics in my upcoming courses that need a better introduction than what I have available so far. I'll be looking for other people's goodies online, and I'll be thinking about how to create my own.

I'll be teaching pre-calculus, calculus I, and linear algebra in the fall. My long handout for finding the derivatives for sine and cosine went over like a bag of cement. I might be able to enliven that with a dialogue. And I'm thinking some of the first topics in linear algebra might do well with this treatment.

Besides Math Girls and Math Girls 2, I only know of a few other shining examples of this genre:

Check out The Cat in Numberland (a delightful retelling of the Hotel Infinity story), in which the storyline, more than the dialogue, helps the reader understand infinity more deeply.

I also loved working through some deep mathematics in the book Surreal Numbers, by Donald Knuth, which has more of the style of Math Girls. Alice and Bill are lightly sketched characters, exploring mathematical ideas together on a secluded beach.

 Are there other books you know of which present math through dialogue or story? Would you like to write a short story or dialogue with math at its core? Let's form a math writing group this summer!


  1. Other books that present math through dialogue or story:
    * The Man Who Counted
    * The Number Devil

  2. I was thinking that The Man Who Counted didn't qualify somehow. Perhaps because it was more like puzzles than going very far into mathematical content. I do love it, though.

    I'm embarrassed to have forgotten to include The Number Devil. It's approachable from a young age, and it has enough math to get just about anyone thinking. Great introduction to an exploratory approach to math.

  3. Exploring Mathematics through Mathematica is a fun book that is written as a dialog between its two co-authors, a veteran math teacher (Jerry Glynn) and a Mathematica software expert (Theo Gray, cofounder of Wolfram).

    Here is an excerpt which gives you a bit of an idea of their style.

    For more actual substance, you can get excerpts on Amazon's site here:

    Inexpensive used copies are available. The latest edition came out in 2000, and of course the software has added many new features since then, but I still find our family's copy of the original (in 1991) to be fun and helpful in using modern versions of Mathematica. It gives me a nice handle into the philosophy of this very powerful and complex tool as I "listen in" on a dialog between a passionate math teacher (curious but skeptical about the software) and the software's creator.

  4. Conned Again Watson is a book where Sherlock Holmes uses probability and logic puzzles (e.g., Monty Hall problem) to solve mysteries and explains them to Watson. There's multiple books in the series but IIRC the rest are science-based.

  5. I've co-authored (with a middle school student) something more like a math paper that's told as a short story. Maybe your summer writing group will give me the motivation to finally polish it up enough to submit it to one of the journals like Math Horizons -- they seem like a place that would be likely to run such a story.


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