I recently went back through my posts and tagged many of them “Learning Through Problem Solving”. This post will clarify what I mean by learning through problem solving.
Our Alberta Program of Studies (page 8.) states that “learning through problem should be the focus of mathematics at all grade levels.”
When I was in school, I was taught lessons, and then assigned a set of practice questions which inevitably concluded with the dreaded word problems. The drawback to this approach was that the word problems were nothing more than more practice. For example, after a lesson on adding fractions, we would practice adding fractions, and then get some word problems. The word problems would have two fractions in them, and all I had to do was add the two fractions without reading the problem. Nothing that can be done without reading it and thinking about it is really a problem.
When I began teaching, I approached problem solving the same way. I taught a lesson, let students practice, and then assigned them a set of problems that they could do. Then I patted myself on the back for being such a good teacher because my students could solve problems.
In life, problems require thought. They are missing information. They can’t be answered immediately. Problems in math class are often not like this. We need to present problems to our classes up front, before we have taught our students how to do them. Students will have to struggle, determine which information they are missing, persevere, and ultimately learn from the process.
The following is a list of what I believe to be the components of a good learning through problem solving experience. This list is compiled from a variety of sources including my own experiences, Marilyn Burns, Dan Meyer, Andrew Wiles, Marian Small, John Van de Walle and others.
- The problem should be given at the beginning of the learning, rather than at the end.
- The problem should be non-routine. The students can not solve it immediately, BUT…
- Every student should have an entry into the problem.
- The problem needs to be compelling and engaging enough that students will persevere.
- The problem should invite multiple methods of solution.
- The problem should foster discussion and debate.
- The problem should be at an appropriate level for the audience.
- The best problems allow the students come up with the question to answer.