My thinking about how to teach math is changing a lot recently. While I’ve always been an advocate for the importance of problem-solving, especially in math class, my teaching has tended to emphasize skill building, and any teaching about problem-solving has been more incidental than intentional. I hope that will change this year.
A colleague posted a helpful graphic detailing the process of problem solving. He describes 6 phases (diagram, experiment, reflect, collaborate, internalize and research) as part of a cycle, rather than a linear process. Coincidentally, I have 6 tables in my classroom.
My experiment for this year is to have one table for each phase in the problem-solving cycle, so that students can physically move from one phase to another as they work on a problem. I hope that by naming the phases and giving them specific physical spaces in the room, students will be more aware of what options they have when they’re stuck on a problem. There’s also the added benefit of students (in this case, grade 6 students) getting up and moving around periodically as they work.
This will, of course, require that students develop some time management skills and become more aware of themselves as learners and problem-solvers. But, if you think about it, those skills are more broadly applicable than things like prime factorization anyway.