One of the best ways to begin improving problem solving in your math class is simply this: Just do it! Of course. you can learn some techniques for making that problem solving time more of a success than it would otherwise be. You can teach students some strategies for thinking, and help them to use mathematical tools (which I think of as anything concrete or pictorial that helps students build conceptual understanding), but ultimately problem solving is a skill that students master by engaging in it regularly.
Linda Gojak, past president of the NCTM, talks about using “rich tasks” in math lessons, and she defines a rich task in this way:
— A situation in which an appropriate path to a solution is not readily apparent
— Can be adapted to maintain high cognitive demand while meeting individual needs
— Requires students to do more than remember a fact or reproduce a skill
— Encourages investigations and deep thinking
— Has multiple entry points, solution paths and at times multiple solutions
I encourage you to look at the tasks you are asking students to do in your lessons and see how they stack up against such a criteria list.
For those attending the session tomorrow, I am not able right now to create a link for downloading the handout, but if you email me (firstname.lastname@example.org) in the next 10 days I will see that you get a copy of it.