Problem solving is a favorite topic of mine. I have spent quite a bit of time over the years exploring literature, research, and materials on this topic. Teaching students to "think" math is challenging!
I have a Top Ten List of ideas to try!
10: Set aside a consistent time in each unit to teach and practice problem solving. In our algebra course, we teach plain, naked math first, and then we teach application problems.
9: Be careful in teaching key words. Instead, teach students to highlight key parts of the problem – not just individual words. When asking scaffolding questions, require students to tell in what sentence in the problem they found the answer. I really like the prepackaged materials called Math Detective because they ask students to reference specific sentences in the problem as they solve the problem.
8: Develop a graphic organizer for problem solving so that students have a visual guide for solving problems. I’ve tried one similar to the one described in this journal article.
7: Teach students specific steps in solving problems. Personally I like the Singapore Model Drawing method which works on most but not all problems.
6: Require students to write explanations for solving problems in words – the dreaded complete sentences. Some students really struggle with putting their math work in words. When I ask students to explain their work in writing, I learn how deeply they understand the concept.
5: Whenever possible, put students in the problem themselves and have them act it out while they are working it out. If that’s not possible use video to capture the essence of the problem. Dan Meyer’s 3 Act Math Tasks are great examples.
4: Choose a curriculum for problem solving to provide consistent training in various problem solving strategies. I personally like The Problem Solver (Grades 1 – 8) by Creative Publications for students who are not in algebra yet. I believe the materials are still sold by McGraw Hill Education.
3: Teach number sense, patterns, and puzzles. Too often students don’t get problem solving because they lack number sense skills or don’t recognize common patterns in mathematics. My favorite materials for teaching patterns and puzzles are those published by AIMS Education Foundation. I like What's Next? A Pattern Discovery Approach to Problem Solving .
2. Collect really good problems that capture students’ attention and engage them in the problem solving process. You almost have to use the problem first to know if it was a “good” problem. Then mark those, store them for future use. I wish I had taken this advice over the years and stored those really good problems in a file folder, or even better, electronically.
1: Be a problem solver. Let students know you work out the problems as well. Use a “think aloud” method to demonstrate the processes you use to solve problems.
I wish I could take credit for all of these ideas. Some of these ideas have been given to me ... and a few of them I have ferreted out on my own to share with others.
This "Educator's Practice Guide" on Problem Solving is a good resource: http://ies.ed.gov/ncee/wwc/pdf/practice_guides/mps_pg_052212.pdf