A Small Teaching Breakthrough
Helping my daughter with her high school physics homework is a much different activity than lecturing to 200 students. I had a real insight last night into the kind of mistakes that students make. The problem was a classic block on a turntable problem. The turntable accelerates at a constant rate and the question is how long before the block slides off.
In this problem the mass of the block was not given, and that was a real stumbling block for my daughter. I told her to just write down m for the mass and keep working. Later in the same problem she needed the angular velocity and was given the angular acceleration. I said just find the angular velocity using the acceleration. I assumed that she would write
ω = αt
but she said that she did not know the time. I pointed out that she was looking for the time. I got very excited at this point. I had discovered a fundamental problem she was having. Her bad habit of plugging in numbers immediately actually prevented her from doing this problem. I probably got too excited. She started to cry.
Since the beginning of the year I have encouraged her to solve the problem symbolically as far as possible and substitute in numbers as late as possible. In general she has ignored my well thought out fatherly advice and tried to plug in numbers as soon as possible. After she calmed down I explained how her way of doing things prevented her from solving the problem. I hope this lesson sticks.