Computers and calculators are great. When I was taking calculus, I’d often use my calculator to approximate the answer to see if my result was reasonable. But the teacher in this case seems to have gone straight to “Fathom”—there’s no indication he ever worked the problem out for himself.

I suppose you two and I have different views on math—the conceptualization and analytical thinking required for these problems is part of the appeal to me.

But the strangest thing for me is that this seems like such a simple problem. I don’t know how adept he is at this “Fathom” or how long it takes to set it up, but it seems to me that solving such a trivial problem can’t have taken much longer than it would take to set up the simulation. I suppose I just grew up with a different breed of math teacher.

1. Your green/red triangle is a neat way to explain your solution.

2. Yeh, the integration is no big deal.

3. Math instructors always get excited when a student is motivated to complete non-assessed work, and especially when they have an intelligent go at it.

4. You seem concerned about the math teacher using a tool to help solve the problem. I would hope that we have moved on from mindless calculation. (Logic is not mindless, I hasten to add. And I am certainly not advocating a calculation-free zone in math classes.) The tools are there to help, after all. But rubbish in, rubbish out, of course.

Isn’t the desire to stop math teachers from using computers a bit like asking doctors to perform their duties without the benefit of high end tools like MRI and the like? If you’ve got the tool, and can use it appropriately, surely it should be used.

5. As a doctor, could I invite you to comment on Vlorbik’s statement about doctor math on It’s Fun to Hate Math. I still hang on to the naive belief that we are teaching mathematics for a purpose beyond algebra for its own sake, and something more than navel gazing.

Also, I don’t understand the teacher’s (persistent) shock. Yes, the student’s math skills are quite impressive. But the article says he completed BC calculus the previous year. Surely the integration skills involved in this problem should be well within his abilities? What I mean is, Kurt is extremely talented. But one of his teachers, one who knows that he’s completed basic calculus courses already, shouldn’t be shocked every time the student is able to apply his calculus.

But what really disappoints me is the teacher’s use of this “Fathom” program. (I’m assuming the teacher in question is a math teacher and possesses knowledge of calculus.) Aren’t math teachers supposed to emphasize and embrace logic and calculation over computers and number-crunching? The solution of course is ln 2 – (1/2). The integration is quite simple and took me only a couple minutes. And I’m a doctor, not a math teacher.

But let’s look back at what the kid did. The first angle is chosen arbitrarily. OK. But all angles (0,180) are treated equally likely, but we know every triangle has 2 or 3 angles on (0,90) and only 0 or 1 on (90,180). It seems that the work has bias towards non-acute triangles.