I have heard this book mentioned over and over again at workshops and other teachers always say that I should read it because it reminds them about my ideas around problem solving. Well, spring break gave me the perfect opportunity to dig into this book. I can see why it is so highly recommended.
In the early chapters, he sites a lot of research about how teaching kids problem solving strategies (especially kids under grade 3) does not do much to improve students' abilities to solve problems. I have found the same thing in my own practice. I used to spend at least one day a week teaching kids how to solve problems. It always seemed like it was working until I would give them a new problem that was not similar to one I taught them how to do. He also sites a bunch of research that has found that kids are quite capable of inventing their own ways to solve problems. Over the last 5 years, this is the direction my own practice has taken and it has made a huge difference in my students' ability to be good problem solvers. I really had to stop teaching and start listening in order to make this change. I am so impressed with the ways kids invent to solve problems if you let them.
In chapter 2, there is a great discussion about how to teach problem solving strategies and how they should be taught as additional ways to solve problems as opposed to the only way to solve problems. The author recommends holding off on direct instruction of problem solving strategies until after grade 3. In my own school, this is the direction we have headed in as well. In grades K-3 we spend a lot of time sharing kids strategies and talking about which ones are most efficient for which problems. By holding off on teaching strategies, kids are really able to solve new and unusual problems on their own. I hear a lot less of kids saying "I don't know how to do this." We do teach a few strategies by the end of grade 3 such as making organized lists, and organized guess and check if they don't come up as kids invented strategies. The level of problems we get to sometimes requires more organization to a solution and this is really the only part we have to "teach."
Chapter 2 also is filled with lots of examples and dialogue between teachers and students. If you have not tried this approach to problem solving before, there are some great insights in this chapter.
The later chapters detail the structure of share and compare lessons. They start out with a warm up which is often mental math and gives kids practice in some underlying skills that they might need to solve the day's problem. The kids solve the problems on their own and share their answer with a partner. We do this all of the time in my school and it is VERY effective. I find it especially effective if students who share with a partner are responsible for explaining how their partner got the answer!
The second part of this model is the problem of the day. This is the main problem solving task that kids are asked to complete. The author discusses where his problems come from and gives some great examples. Kids have about 20-30 minutes to solve the problem using any materials, manipulatives, drawings or a combination to figure out an answer. They are then responsible for showing and telling how they got their answer. I love the idea of kids showing and telling (in words) how they got their answer. It is a great way for them to practice talking about their solutions and a great way to integrate writing across the curriculum. This is an area I will be working on with my students for sure!
The third part is the Mathematicians Chair where students get to share their solutions with the class. It is the teacher's job during part 2 to select students to share in the mathematicians chair that have the types of solutions you want your kids to be thinking about and comparing. In my school, we have done more and more sharing of students' solutions each year but we do not currently use a Mathematicians Chair. I think this will be something I would like to do. We have the space for it and it would add a fun twist to kids' sharing.
The final part is Compare. This is where students compare different solutions or methods of solving the problems and talk about how they are alike and different. This is where I really like to talk about efficiency as well and figure out how efficient various methods were for the problem that day. This is a very important step, so make sure you leave time for it! I used to be very guilty of running out of time and not getting to this part, but now I make sure I get there even if I have to set a timer to remind me of when it is time to move on.
The appendix has some great ideas about using cartoons and children's literature to make problems. There are a few I have marked to try out after spring break. I think this book is definitely worth a read for anyone who teaches K-6 math. It could help you develop or refine the way you present problem solving to your students.
I loved this book enough to head over to Amazon and look up the author. It turns out there is a newer book by Larry Buschman called Making Sense of Mathematics. I decided to order it and will be writing a review sometime in the future!