In addition to making my new website, over the break I did a lot of thinking about my teaching practice. Basically, I was frustrated. I felt like I was fighting the students. I wanted them to be problem solvers and they wanted me to spoon feed them information.
I decided that if this teaching thing is going to work, I have to make some changes. So with the new year I decided to try out some new methods. I started by having a little bit of a talk with each of my classes. I told them that what I really care about is not that they memorize a bunch of formulas and steps, but that they learn how to solve problems.
I told them that as teachers we send them the wrong message. We give assignments and tests with 30 questions on them, knowing that the student only has an hour or so to work them. This sends the message that each question should be done in 2 minutes or less. We give them worksheets with a half inch of room to work problems. We hurry through lessons, answering every question as quickly as possible so we can cover all of the material.
All of this tells the student that math should be quick and automatic. But that isn't really math. Math is about solving tough problems, making connections and asking questions. It is about making mistakes and recognizing that our answer can't be right. It takes time.
So, I offered my students a deal. If they agreed to engage in the process of problem solving I would give them fewer problems on tests and homework. If they don't want to engage on a given day, they can sit at a table outside my class where I can see them and work independently. But when they come into my class, they will be expected to exhibit certain behaviors that I wrote on the board:
1) Draw pictures
2) Write down formulas that might be relevant
3) Write down questions and conjectures
4) Guess and check
5) Look in their notes/book/online for answers to questions
6) Make tables of data
7) Compare results and questions with friends and discuss differences.
I also told them that from now on they are not allowed to do more than one question on a page, so that we are not tempted to cram our work. For the rest of the year my goal is not to have them learn every formula. My goal is to learn how to implement these problem solving strategies.
The response was pretty awesome. A number of students openly questioned my proposed changes:
"Math is about learning formulas and applying them," one said. "You should just teach us the formulas and the steps."
"That isn't how we are going to do math in this class anymore," was my response. "If you choose not to participate, you can sit outside at the table and work independently."
Two or three students from each class left. Three of them were sitting out there when my principal walked by and started talking to them. When I got a chance, I went outside to hear what they were talking about. The principal was trying to help them resolve concerns about the problem solving methods I was proposing, so I just nodded and went back inside.
The classroom discussions were amazing. I had the students work on a question for about 10 minutes on their own. When they had questions I would simply try to help them phrase their questions in a way that they could write down on their paper. After a while I had them get up and compare results with their classmates. They compared results, answered each other's questions, argued about different methods, and tried to come to a consensus as a class. One student that literally failed the last test led a class discussion about whether we should choose sin or cos to solve a certain question.
I tried to emphasize that the things I had written on the board were not a formula. They were skills that we had to develop. How do we draw pictures that can focus our attention and get us closer to our goal? What are examples of useful and not useful questions? (e.g. "how do I solve this problem?" is not useful) A number of students in each class came up afterward and said that they really enjoyed the new approach.
I am pretty energized about teaching right now, and I hope that the newfound energy in me and my students doesn't wear off too soon. The idea that I may have found a teaching style that really works for me feels great.