1. Do more mistakes. Last year, I tried "my favorite no" but felt that it took a bit too much of class time. This year we will continue trying to improve "my favorite no" and also we will analyze the mistakes at mathmistakes.org. Finally, we're definitely going to try the Mistakes Game, in which students collaborate to create and present problem solutions that contain realistic mistakes.
2. Get into whiteboarding. 10 mini-whiteboards sized 30x42 cm are on their way to my school, and I think they will be suitable at least for pair-work. I'll try to make my own larger whiteboards later on for larger groups. What are we doing with the whiteboards? Here are some ideas, many borrowed from Bowman Dickson:
- Mistakes game
- Rotating during a solution: groups finish other groups’ solutions during a gallery walk, or students take turns writing the steps to a solution within their group.
- Using color: chain rule, highlighting mistakes, rotating
- Guess and Check: one person guesses an answer, the other checks if it’s right
- Solve and justify: one person writes the steps of a solution, the other justifies each step.
- Each group comes up with their own problem: then gallery walk with each team solving each other group’s problems.
- Each group comes up with an example of a concept, then shows it to the class.
- Each group writes an answer to a teacher-driven question – shows to the teacher
- Polling for multiple choice questions: can be summarized on the board
- Groups create multiple representations of the same idea: good for functions!
- Groups create different solutions to the same problem.
- Groups create several problems related to the same information (information is given, or is asked for, or can be an intermediate step)
3. Let go of homework. I'm not giving up, exactly, on getting kids to do homework. It's just that this battle is one I've been fighting and losing for the past four years, so rather than continue to frustrate myself and the students I'm going to let go, lick my wounds, and take some time to build new strategies (which might involve the whole school culture rather than just my own classes). There is only one thing I'm going to try this year, and it's based on a suggestion from our physics teacher (thanks, Johan!). Students will receive one small quiz weekly, and this quiz will be on just one of perhaps 6 "model solutions" demonstrated during class the week before. So students will always have a very limited number of questions and solutions to understand or in the worst case simply memorize for the quiz. Not ideal, I know, but for many students even if all they do is memorize 6 questions and solutions then that's a huge improvement on their previous efforts.
What I'd like to add to this approach is to either include a question on the quiz asking students to justify a step of the solution, or to finish each quiz with a group/whole-class discussion of why the solution is appropriate.