Well, we have reached the end of the second trimester, which at our school means that I have now taught the entire pre-calculus course through the Harkness method. It is still amazing to me just how much my philosophy of education and teaching methods have changed in the last year and a half. The only regret I have is not realizing sooner just how much the students were memorizing (and forgetting) and how little they were actually learning. As teachers I have come to the conclusion that far too often we sell the students short in terms of their ability. Experience has taught us that the students can't figure out this material on their own, and that they need us to tell them what to do and how to do it...or so we thought. The students have learned to expect us to tell them what to do...and getting them to change has been difficult.
When I directed theatre, I refused to ask the kids to do shows that were beneath their ability level. We did tough shows and the kids rose to the challenge every time. In transferring that to my math classroom, I thought that meant asking the kids to do more difficult exercises. What I failed to realize before this year is that as long as I showed them how to do the problems and gave them the time necessary to memorize the process, they could and would be successful with the more difficult exercises...but that didn’t mean they actually learned the “more difficult math”. It just meant they were really good at memorizing. I now understand that the real challenge is to ask the students to put the pieces together themselves, and that my job is to guide them to the discovery. The kids can figure out the material themselves if we ask the correct questions. More importantly: if they aren’t making the connections for themselves, I now understand that what I need to do is not give in and give them the process and the solutions, but rather to ask better questions.
Going forward, in trying to get other teachers to see the benefits of Harkness, I think this idea of asking better questions will be a difficult sell. After all, we “learned” the material by imitating our teachers...or did we? I wonder how many teachers, if pressed to do so, would be able to actually explain the mathematics they have been teaching for years...not just give the process they have memorized, not just show how to push the symbols around, but really explain the mathematics. And I’m not sure I really want the answer.
As teachers, we need to ask better questions. And to do that, we need to really understand the mathematics. As such, we need professional development in both teaching methods and in our content areas. Convincing experienced teachers of this will be a daunting task. The students will adjust to our requests and rise to the challenge. Hopefully the teachers will do the same.