(Alternate title: I gave them a problem to work on and they hated it. And me.)
So my precalc class isn't enjoying the problem I gave them to do today... but I've heard some awesome conversations!
Here's what they were given:
"Given f(x) = 1 - x and g(x) = 1/x, how many different compositions can you make out of these functions?"
(I found this problem several years ago and have always given it as a mini-project to be done individually. Thought that it might be more interesting worked with someone.)
The class started in silence. They weren't quite sure where to start, but after considering it for a few moments they started talking and writing.
I wandered around offering some suggestions - simplify that... what happens when you do this?... have you seen this before?
Had a very interesting conversation with one girl who was getting frustrated. She pulled the, "I'm never going to have to do this in the future!" line, so we talked about what skills she was actually working on.
Working with a group
Problem solving (start small, work bigger)
I think I won her over (though she told me she was going to become a hobo so she wouldn't have to do math).
Everyone seemed ok by the time they left class. Not giving them a homework assignment helped.