Teaching

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.

By patrick honner, ago

On College Rankings

This essay from the President of Reed College discusses what it’s like to live outside (and inside) the world of college rankings, essentially asking “Are these rankings meaningful?”

https://www.reed.edu/apply/college-rankings.html

It’s a familiar story to anyone who has ever contemplated teaching to the test.  As rankings/ratings/grades become more and more important, colleges/schools/students (and teachers) tend to focus more and more on those metrics, perhaps at the expense of what’s really important (whatever that might be).

A perfect rating system, presumably, would compel the rated parties to meet and expand the standard of excellence.  But in practice, it seems difficult to come to a consensus about what comprises excellence, and even harder, then, to construct an appropriate rating system.

So how should we measure a college or university?

By patrick honner, ago

Math-Intensive Majors

The MAA and David Bressoud released a report about the current status of math intensive majors in the U.S. (which you can find here).

Bressoud starts with the encouraging news in the STEM fields–Science, Technology, Engineering, and Mathematics.  In the past fifteen years, colleges have seen a 33% increase in students in these majors.  However, those numbers may be dominated by particularly large increases in Biology and Psychology.

As a mathematician, Bressoud is interested in math-intensive majors, and so he looks more closely at mathematics, engineering, and physical sciences.  As total college enrollments and STEM majors have increased, these math-intensive majors attract a consistent percentage of students.  In fact, Bressoud notes that this percentage has been stable for the past 30 years, as math-intensive degrees have shown no growth as a percentage of overall college degrees.

This is curious, given the increasingly quantitative nature of modern society, industry, and academia.  Are greater percentages of students in other countries pursuing such degrees?  Or do we only need 0.5% of our college students studying math-intensive fields?

By patrick honner, ago

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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By patrick honner, ago
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