To derive or not to derive?
This semester I am teaching a graduate course, including 4 of my own PhD students. The ongoing question is the following: to derive, or not to derive? I have been playing around with the balance between emphasizing concepts (bolstered by hand-wavy arguments) and doing the rigorous derivations.
Students tend to get lost during the rigorous derivations, due to all the algebra required to carry out the steps.
On the other hand, too many conceptual arguments leaves an unsatisfying taste in the mouth.
I am also trying to encourage student thinking and participation during class. This tends to tilt things toward the hand-wavy side, as more student participation = fewer lines of algebra on the chalkboard.
I will be playing with this all semester, I suppose. It is far more fun that last semester’s undergrad class, however — the students do actually care about the course material.
That’s a tough one. I can see your point about students getting lost in the math and missing the bigger point. But…. my favorite academic memory remains the day in my 3rd year of college, when my Quantum Mechanics professor walked in and said “Assume H and G are two Hermetian operators….” and 50 minutes later circled something on the board and said “And there you have the Heisenberg Uncertainty Principle!”
That was the moment when I really got how math and science fit together.
I couldn’t do the derivation now, but I did manage to reproduce it for the exam.
Comment by Cloud — February 9, 2010 @ 8:26 pm