Today Steven Strogatz posted a link on twitter to a new article he’s written in the Notices of the AMS – “Writing about Math for the Perplexed and the Traumatized.” It is a a great and instructive read. Here’s the link:
This part of the piece, in particular, caught my eye:
“For any would-be pop math writer, here are a few surefire techniques.
(1) Illuminate. Give the reader a shiver of pleasure by providing an “Aha!” experience.
(2) Make connections. Tie the math to something the reader already enjoys.
(3) Treat the reader like a friend of yours – a nonmathematical friend. Then you’ll instinctively do everything right.”
I think it is an interesting set of ideas that applies beyond pop math writing, and it made me reflect on the math I’ve been doing with my kids. A few of the projects we’ve done in the last year of so fit nicely into Strogatz’s categories. Here are a few examples:
(1) Provide an “Aha!” experience.
(a) The Chaos game. Probably my favorite math surprise with the boys involved a basic fractal example – the Chaos game. We made a short program on Khan Academy to illustrate the math (I don’t know how else to share code). The “Aha!” moment starts around 3:00 in the video:
The code is here for anyone who wants to play around with it:
(b) Multiplying negative numbers. This one turned out to be our most viewed video from 2013. I was at work one day and someone on Twitter asked if there was an intuitive way to see that a negative number times a negative number was positive. I spent the afternoon sort of daydreaming about ways to illustrate multiplication of two negative numbers and tried out my idea with my older son when I got home. It was a fun watching him see the arithmetic right along side the geometry:
(2) Make Connections
(a) The Higgs Boson. Last fall Peter Higgs won the Nobel Prize in Physics following the discovery of the Higgs boson at CERN in 2012. My kids have always been interested in reading about physics and I pointed out a couple of articles about the new Nobel prize awards to them. By coincidence, a few days later I saw a great article by Frank Wilczek about the Higgs boson in an MIT alumni physics magazine. Wilczek’s article mentioned that one of the properties that made the particle so hard to detect was that it only lives for about seconds! I thought it would be fun to try to put in context for the boys since you don’t encounter that number too much in daily life!
The Wilczek article about the Higgs Boston is here, if you are interested:
(b) Really basic group theory. My kids love playing with Rubik’s cubes and I’ve been able to use the cubes to illustrate a few different math ideas. Maybe the most fun math idea I used the cubes for was illustrating a little group theory for my 7 year-old. It was fun to see his enthusiasm for the new concepts he was seeing for the first time.
(c) Fractions with snap cubes. My kids love building with legos and snap cubes and every now and then I get a chance to use some of these little building blocks into the math we are doing. After introducing fraction division using some basic arithmetic rules (defining division as multiplication by the reciprocal), I thought it would be useful to show him a few not-so-technical examples. So we did a little geometry with snap cubes to help us understand fraction division:
(3) Be their friend.
Well, this one isn’t too hard to do when you are working with your kids. I’ve really enjoyed covering a few advanced topics in math with the boys. The main point of covering these advanced topics wasn’t necessarily the details of the math, but rather to show that some beautiful, and even unsolved math can be accessible to (and fun for) young kids.
(a) The Collatz Conjecture. Here all you need is to be able to divide by 2 and multiply by 3. How fun to be able to show kids an unsolved problem that relies only on basic arithmetic!
(b) Pentagons. With my older son I’ve been following Art of Problem Solving’s Algebra book this year. The book spends quite a bit of time on quadratic equations. Certainly understanding quadratic equations is great for helping kids develop a good base in algebra, but it is a lot of work. At one point when we needed a little break from the topic, I thought it would be fun to show him an advanced topic where quadratic equations play an important role – pentagons. It was a fun to show him how several different pieces of basic math that we’d already studied (plus one or two things we hadn’t studied) came together in a regular pentagon.
Not everyone has the time, the interest, or the ability to communicate mathematical ideas to a general audience. I’m happy that Stephen Strogatz able to spend some of his time acting as sort of a public face for math in the US. Hopefully this article he’s published today will give a few other people some ideas about how they can join him in improving the public perception of math in the US.