Monday, January 24, 2011

You Can Count on Monsters

You Can Count on Monsters, by Richard Evan Schwartz
Paperback, 244 pages, A K Peters
I happened to be listening to NPR's Weekend Edition recently and I heard a conversation between Scott Simon and NPR's math guy Keith Devlin about this new book You Can Count on Monsters by Richard Even Schwartz.

From Schwartz's website:

"The book starts with a 20 page introduction, written at an elementary school level. After explaining multiplication, prime numbers, and factoring, the introduction lays out the general idea for the rest of the book, as I'll now describe. To each prime number, we associate a pattern of dots and a monster.

"There is something about each monster that has to do with the prime. Part of the fun of the book is figuring out how the monster is related to its prime. For each composite number, we factor the number into primes and then draw a scene that involves those primes. We also show an arrangement of dots and a factoring tree that helps explain the picture. (A factoring tree is a kind of diagram that shows one way to factor the number into primes.)"

Near the end NPR piece, Devlin said about the book:

"The thing that distinguishes mathematicians is that we, at some stage in our development, we develop this understanding that numbers do have personalities, they have structures, they have relationships.  We form that, but most people don't manage to get it.  What Schwartz has managed to do is use his own skill as an artist to bring out some of the personalities, and the point is that what he brings out through his art is actually the structure and the personality that those of us in the business have always seen, we just haven't got the tools and the ability to make it accessible the way Schwartz [has].  It's his skill as an artist that makes this work [emphasis mine]." 
-- Keith Devlin on NPR's Weekend Edition, Saturday, January 23, 2011

As a dancer who integrates percussive dance and elementary math, I am in the business of making math accessible. I work to illustrate math concepts through a thoughtful sequence of activities; the children build original percussive dance patterns and learn and apply the math that arises naturally from this creative process.  I have spent many years learning and building my own understanding of the math content and practices that relate to this work.  And, I have carefully built a learning bridge that makes meaningful connections between the two subjects.

Now that I have built my bridge and my curriculum is where I want it, for now, I have become fascinated with searching for and finding examples of other kinds of bridges to math.  I am also trying to figure out just what it is that mathematicians see that the rest of us can't.  I'm coming at this task from a couple angles (no pun intended). 

First, going on some information I heard recently that it is most effective to learn a new language like a baby does (there's been some research findings about this, but I can't locate them right now), I'm working on (re)learning math myself alongside my five year old daughter by exploring math concepts through hands-on experience.  And, because I'm not five, I'm also looking ahead to where we might go next.  A few years down the line we might both be ready for You Can Count on Monsters. 

I'm also finding articles and online communities that are focused on how to teach math concepts for comprehension (not just for memorization of procedures) and learning from others' descriptions of how they teach and the kinds of questions they ask students.  I'm also on the lookout for quality examples of how art in general can help build a bridge to real comprehension of math concepts.  Schwartz's monster book seems fit perfectly into the bridge category, in a big way!  By the way, not only does Schwartz appear to be a working artist he is also a Chancellor's Professor of Mathematics and Director of Undergraduate Studies, Department of Mathematics, at Brown University.

So, happy reading and happy learning!  I'm off to the library to find myself a copy!


  1. You don't have to wait a few years to be ready for it. I love this book, and my son enjoys it too. It's fun just to look at the monsters, and wonder how they relate to their number.

  2. Power to you, Malke. I tried using music and dance to capture ideas of mathematics myself a couple of years ago. We could not afford to record the dance, but we did capture the music. See (or rather listen to)
    Some of the singers were math teachers, and we talked about developing curriculum materials around our show and the general concept, but time and money were both lacking and my one attempt to interest NCTM came to naught.

  3. And here is some information about the dance company I worked with:

  4. Hi Keith! Thanks for checking in! I've known about the MathDance guys for a while, haven't met them yet, but I'd love to. I didn't know you worked with them!

    I'll be at this year's NCTM in Indianapolis with a 90 minute gallery workshop, sharing parts of the Math in Your Feet curriculum. Also, I have an article about the development of my work integrating math and percussive dance being published in April by the Teaching Artist Journal, published by Taylor & Francis.

    I've also just found out about the Journal of Art and Math (or something like that) also published by Taylor & Francis. Have you ever written up anything about your experience of trying to capture the ideas of mathematics through music and dance? I'd love to read more about it!

  5. The only thing i wrote about my one foray into the math-music-dance area was the brief performance notes for our show. I will be at NCTM this year and hope to attend your workshop. Taylor & Francis are publishing my new book, which I'll be talking about -- using video games in math ed. Any medium that kids like provides an avenue for the mathematics educator!

  6. Hi Keith!

    Well, I for one would be curious to take a look at your performance notes if you were okay with sharing them. As you can probably tell, I'm coming from a very specific dance form (percussive dance) but I'm still really interested in how movement/dance in general builds that 'bridge' to mathematics understanding. It's that place between the two subjects (with a focus on both content and process) that is the most interesting to me right now.

    Just curious, how much did you do with Schaffer and Stern?

    I hope you are able to attend my workshop and I look forward to meeting you at NCTM!

  7. The performance notes are on my Stanford homepage, along with the audio files. The dancers interpreted each song. I wish we had been able to afford to record the dances.

  8. You Can Count on Monsters added a new twist to our work on prime factors in my Year 5 class. I used the poster too. See:


Thanks for reading. I would love to hear your thoughts and comments!


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