Have you tried problem solving in the Cognitively Guided Instruction (CGI) way? One of the books that made the largest impact on math instruction in my classroom is Children's Mathematics: Cognitively Guided Instruction.
The main idea behind this book is that children enter school with a great deal of intuitive knowledge about mathematics. CGI uses problem solving to help students continue to develop and refine their intuitive problem solving abilities. What do I love about CGI? I love...
- watching students discover answers in their own way
- hearing "Oooohhhh, now I get it."
- to hear students explain their problem solving strategies to each other
- to see a student try and solve a problem in a new way
- the flexible groupings - sometimes I group my students who all use the same strategy comfortably together to try something with more difficult numbers, other times I group students who use different strategies together so everyone can learn from each other
- how easy it is to differentiate - I choose the numbers for the actual problems according to my students' needs
- that I can sit back, watch, and listen to my students as they work, explain and teach each other
- that while listening and watching I have time to take notes on their strategies, reasoning and problem solving abilities. Later I use my notes to regroup, choose numbers and decide problem types.
- how much growth I have seen in their abilities in just a few months
- the mathematical discussions that so naturally happen between my students
- integrating our problem solving with other topics/subjects we are learning about
- having all of the various problem types identified and knowing that I can track which problems I use to ensure that everyone gets experience with all types of problems
- writing new problems in all of the various problem types (see my TpT and TN stores if you are interested in purchasing)
Another book that has had an impact in changing my teaching is Math Exchanges: Guiding Young Mathematicians in Small-Group Meetings.
This book has really helped me put CGI problem solving into action. With practical insights and examples of problem solving in action I felt like it really opened my eyes to how this could look and work. Plus the appendix with examples of the 14 problem types is so useful. If you want to make problem solving a larger part of your curriculum, check out these titles. You'll be glad you did.