Fermat and you
Last week I showed the Nova segment about proving Fermat’s Last Theorem to my freshman algebra class. At the end we briefly spoke about it. The kids stated the theorem, recapped some of the highlights of steps towards a proof. I made them point out that ideas sometimes look good, but don’t work out, and they got it, they got that it’s like when we double back in our own problem solving. They recognized some of the fancy mathematical symbols. And finally, I made them name as many names as they could recall, made them recognize both the collective and the individual activity that brought about the proof.
I then added a name to the board and began speaking rapidly.
“Fermat proposed the theorem. Eventually Andrew Wiles proved it. One of his grad students who helped out” (and here I pointed to the board) “was named Conrad, one of two twin mathematicians. His father, Steve Conrad, was a math teacher on Long Island. Steve Conrad has a neat way of factoring trinomials, which he taught to me. And I taught it to you.”
Ok, those are some pretty tenuous links. And maybe the details aren’t quite right. But for an instant my little students thought they were connected to Pierre Fermat, and quietly oohed and aahed.
Showing connections, however tenuous, makes it “real.”
And what was the trinomial factoring lesson?
Needs its own post, but in brief: breaking the middle (using a search technique I devised), then grouping. Good for all factorable trinomials and difference of perfect squares.
No preference for a=1. In fact, the easy cases become the special cases. More in a full post, somewhere down the line.