Storytelling, Teaching, and Mathematics

This short list of “Pixar Story Rules” from Pixar story artist Emma Coats offers a fun look into the mind of a story-teller, as well as a surprising source of mathematical problem-solving and teaching advice!

These particular story rules sound remarkably similar to techniques of mathematical exploration.

#7   Come up with your ending before you figure out your middle.

#9   When you’re stuck, make a list of what WOULDN’T happen next.

#10   Pull apart the stories you like.

#11   Putting it on paper lets you start fixing it.

#20   Exercise:  take the building blocks of a movie you dislike.  How would you rearrange them into what you DO like?

Working backwards, proof by contradiction, taking apart things you understand and trying to put them back together, getting your hands dirty by working out the details–these are all common and useful techniques in exploring and understanding mathematical ideas.

And as a friend pointed out, writing a story is indeed a kind of problem-solving; maybe it’s not so surprising how much that process shares in common with mathematics.

And as a teacher, the following two really resonate, for obvious reasons!

#2   You gotta keep in mind what’s interesting to you as an audience, not what’s fun to do as a writer.  They can be very different.

#1   You admire a character for trying more than for their successes.

Reflections: Students in Math Class

At the end of the term I ask students to write simple reflections on their experiences from the year:  what they learned about math, about the world, about themselves.  It’s one of the many ways I get students writing in math class.

It’s a great way to model reflection as part of the learning process, and it’s also a good way for me to get feedback about the student experience.

Mostly, it’s fun!  I love sharing and discussing the reflections with students, and it always results in great end-of-year conversations.

Here are some of my favorites.

After learning a little more about math, I think math is created rather than discovered.  This makes mathematicians and scientists the creators, not merely the seekers.

I learned a lot of things from my classmates that I wouldn’t have learned if I were to just study on my own.

I have learned that I still have very much to learn about myself.

Mathematics is magical; it can lead you to a dead end, but then it can miraculously open up an exit.

Learning how to think of things in three dimensions completely changed the way I saw math.

By seeing algebraic and geometric interpretations, I learned how to communicate math in more ways.

The process which turns a difficult problem into a relatively easy problem is the beauty of math.

One of the best parts of reflection is how much it gets you thinking about the future.  Plenty of food for thought here.

For more resources, see my Writing in Math Class page.

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Unsolved Math Problems

This is a nice list of famous unsolved math problems from Wolfram MathWorld:

http://mathworld.wolfram.com/UnsolvedProblems.html

There are some well-known problems here, like the Goldbach Conjecture and the Collatz Conjecture, and some lesser-known open problems like finding an Euler Brick with an integral space diagonal.

It’s especially nice that several of these challenges are easy to explain to non-mathematicians.  For example, the Goldbach Conjecture asks “Can every even number be written as the sum of two prime numbers?”  Somewhat surprisingly, after nearly 300 years, the best answer we have is probably.

I think I’ll make this page next year’s summer homework assignment.

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