Wednesday, October 26, 2005

It Seemed Like a Bad Idea at the Time

One of the biggest problems I have when teaching is that my mental model of a student is based on myself. Each year I come to realize more and more that very few of my students are like me. This even goes for the good students, and I need to stop teaching the type of course where I excelled.

The main differences, I think, stem from my experiences in math classes in sixth through twelfth grades. Don't think that this is shaping up to be an anti-calculator rant. It's not. And, as I hint in the title, rational educators probably wouldn't recommend these practices.
Middle School Math
I didn't take middle school math. My parents were absolutely furious when I was in sixth grade. The math teacher had a system by which before the beginning of each unit, we could take the unit test, and if we scored at least 90%, we didn't need to sit through the class. Instead we were given packets to work through (independently) while sitting in the back of the classroom. I learned all sorts of things: the difference between accuracy and precision, all manner of tests for divisibility, combinations and permutations, vectors. Most importantly I learned how to ignore someone yapping in front of a chalkboard and how to learn math by reading a textbook and doing problems until I understood the material. As an added bonus, sixth grade math was the time when most students were indoctrinated that "taking notes in math class" equalled "copying every glyph on the chalkboard onto a sheet of paper." This set the stage for years and years of listening in class instead of taking notes. About halfway through sixth grade the school district was sick of my mom's complaining, so they put a bunch of us in an enrichment class where we flew kites to learn about right triangle trig; in seventh grade they enrolled us in algebra.

Math Homework
From eighth grade through twelfth grade I took seven different math classes, and in none of them did anyone ever check my homework. Homework was assigned, and we were supposed to do it, but no one ever collected it or even walked around the room to verify its existence. (One class also had occaisional "problem sets" that were turned in for a grade.) If the problems were interesting, I did the homework. If the material was too difficult to learn just by sitting and listening in class (like max-min problems), I did the homework. If I failed a test (integration by trig subs), I would go back afterwards and do the homework. Sure I made some stupid choices (like doing close to ZERO math homework in all of tenth grade), but in the end I knew what I needed to, and I had learned what I needed to in order to learn math.
My students, on the other hand, seem to prefer being told what to do. Do all these problems by this day. Write this down. Memorize this. Show up in this room at 8am on MWF. And I can't get through to them that they wouldn't need to wake up early and trek across campus in the cold and dark to come to my class if they would just read the textbook and do the problems. That's all it takes: read the book, do the problems. Aside from setting the pace and verifying achievement, I'm inessential. The two things that my students are most reluctant to do (read the book and do the problems) are the keys to learning the material in my class.