I've been trading e-mails over the last few weeks with Dave Major, a teacher in Dubai who also knows how to use code to make dreams come true.
Then I asked him to create an activity I described in this talk at 28:01. We ask students to create a triangle with certain specifications. They submit their triangle and then they see quickly and easily whether or not everyone else created the same triangle from the same specs. If they did, we should prove that it's impossible to create another triangle. If they didn't, then we have a counterexample and we can axe the hypothesis.
Dave put it together. You should check it out. He's giving you a look at the math textbook of the future, several years early.
I keep thinking of learning a programming language, but didn’t quite have a reason why. I think I have one now.