Monday, September 29, 2008

Math Immersion

Today I let my honors class flounder.

I gave them a task that was certainly too hard for them, and I let them work on it for a while and be totally stuck. This was on purpose, as one of the points of this unit is to think about what is it that mathematicians actually do. And, really, for a lot of mathematicians this means having absolutely no clue what to do next.

The difficult problem that I gave the freshmen was for them to prove that there are infinitely many prime numbers. We spent part of last week talking about divisibility. We'd already proved that every natural number is either prime or else a product of primes (and I reminded them of that on the sheet of notes for today). What they needed to do was to figure out how to use that to show that there are infinitely many prime numbers.

Eventually I gave them a big hint. They got the gist of the argument. And then we worked together writing it up.

Next time: the Pythagorean Theorem.