Although I won’t be attending, I’m excited to see what comes out of the upcoming computer-based math conference:
Ever since hearing a Conrad Wolfram talk a few years ago I’ve been trying to incorporate more computer-based math with the kids. My favorite moment that’s happened so far came during our talk about the Chaos game. Around 2:15 in the video below we start talking about an amazing result and the aha moment comes around 3:05 :
But there’s been a lot of fun lessons beyond this fun moment. Probably the subject where we’ve gone to the computer the most is number theory. Here are four examples:
(1) A fun computer-aided number theory project for kids
This one came courtesy of a question posed on Twitter by James Tanton:
(2) A neat problem that Dan Anderson shared with us
The problem is from Project Euler – Find the first triangular number with more than 500 factors.
I’d also point out that if you are interested in neat ways to use computers to show math to kids, you have to follow Dan on twitter. He’s constantly sharing amazing projects.
(3) A fun divisor counting project for kids
This project was inspired by a question in Art of Problem Solving’s amazing Introduction to Number Theory book
(4) The last 4 digits of Graham’s number
This project is a little more involved, but incredibly fun. It takes a little work to find a way to make Graham’s number accessible to kids, but luckily both Numberphile and Evelyn Lamb have videos / blog posts about the number.
The fun thing for kids is that the number is so large that there is virtually no way at all to understand how large it is. The surprise is that you can compute the last digits of the number.
Away from Number Theory, we’ve used 3D printing as a motivation to look at some computer math. Here are 4 projects – 2 where we made our own shapes, and 2 where we used shapes that other people had designed. The 2nd two projects could also be great design lessions, too:
(1) Using 3D printing to help kids learn algebra and 2d geometry
I tried this project on a whim just to see if a little bit of programming would help my younger son see some math ideas in a different way.
The write up for this project also has some links to some of our other 3d printing projects about 2d geometry.
(2) A neat geometry project inspired by a James Tanton / James Key tweet
The fun thing about this project was that we were able to replicate some shapes we saw on the internet using both Zometool and 3D printing. It was a fun way to talk math while building up some intuition for 3d geometry.
(3) Using Laura Taalman’s 3D printed pentagons to talk math with kids
Just as I mentioned Dan Anderson above, if you are interested in using 3d printing to talk about math, Laura Taalman is a must follow.
(4) A fun fractal project – exploring the Gosper curve
I ran across the Gosper curve flipping through a book about fractals. Fortunately someone had already created some Gosper curve templates in Thingiverse and we used them for a really neat project about fractals and scaling.
Finally 4 projects that that aren’t really linked by a theme where some computer work helped the kids see some neat math ideas:
(1) Talking through Christopher Long’s neat probability problem with kids part 1
Here’s the problem:
This problem is (obviously) too advanced for kids to fully understand, but the computer work helped make the problem accessible. Part 2 of this project is here:
Part 2 of our project on Christopher Long’s probability problem
This was a wonderful project inspired by Frank Farris’s new book Creating Symmetry.
There was also some lucky timing with this project because we ran across the book just after completing several projects about Anna Weltman’s loop-de-loops. The loop-de-loops would also make a great computer project for kids:
Extending Anna Weltman’s loop-de-loops with Frank Farris’s Creating Symmetry
(3) Larry Guth’s No Rectangles problem
Even though we didn’t turn to the computer for this one, I wanted to include it here because I think it would be a fantastic math / programming project for kids. It is a relatively simple problem to understand and would be a neat challenge to code.
(4) 3d printing and calculus concepts for kids
I needed to include one more 3d printing project 🙂 There is a neat math challenging involved in this project – how do you make printable Riemann sums. I did it in Mathematica using the Floor function:
I doubt this is the best or only way to make printable Riemann Sum templates in Mathematica, but it was a neat math surprise to discover that the Floor function could help.
Anyway, that’s 12 projects where either computers have played an important role in helping the kids understand math, or, if we didn’t use a computer, where a computer could play an important role. I’m really excited to see the projects that come out of the upcoming conference.