Wednesday - October 18, 2006
A Case for Theory
This semester I'm teaching college algebra and
one of the problems I'm facing regularly is that students just don't seem to
understand. I encountered this some in computer science, but for the most part
everything I was teaching was concrete enough that students could understand it
intuitively or was theoretical enough that their only choices were to understand
the material properly or fail. College algebra, however, is between these ends
of application and theory: there's not enough application for students to get
an intuitive grasp of what's happening, and there's not enough theory to force
them to understand. So students end up flailing about as they learn a lot of
techniques that they don't understand. In the end, they know almost nothing and
feel like everything they learned was a waste, which in some since it is because
they don't know how to apply the techniques they learn, nor do they understand
the theory behind the techniques.
I'm not happy about the situation, but I can't do much to change it now (I have limited flexibility in the curriculum and how I present the material). I hope that if I'm ever in charge of teaching college algebra that I'll have the chance to do it right, with a good balance of realistic applications and strong theory.
I'm not happy about the situation, but I can't do much to change it now (I have limited flexibility in the curriculum and how I present the material). I hope that if I'm ever in charge of teaching college algebra that I'll have the chance to do it right, with a good balance of realistic applications and strong theory.