More Thoughts on Problem Solving

We have finished up our second group project focused on using problem solving to teach mathematics. As we wound it up we were presented with a couple of thoughts that, I think, show us where we are today in our understanding of such a task.

The first thought was that, in 1980, NCTM released a document titled 'An Agenda for Action: Recommendations for School Mathematics of the 1980s'. Akihiko Takahashi, our instructor, discussed with us a couple of the phrases from that document on how problem solving should be used in a mathematics classroom. He then noted that a major reform in Japanese mathematics teaching took place as a result of this document. They, the Japanese, took what was said and began implementing it. Today they are seen as leaders in the teaching of mathematics in their k-12 schools. What about those of us in the U.S? Where are we? It seems that we missed out on the general ideas of this document. It was our organization that crafted this document, but somehow, it seems, it did not lead to widespread change in the teaching of mathematics. I may be seeing it wrong, but from what I have read, studied, and experienced, I think I am right in my assessment.

The second thought I had relates to teachers working together to create problems and lessons that will help students learn mathematics through problem solving. As we struggled with each other, or more accurately against each other, while trying to put two such lessons together in two weeks, there were a lot of groups that struggled to work well together. We were told that we needed to spend more time learning each other, rather than trying to teach each other. Apparently we were busy trying to tell each other the way it should be and why other ideas would not work.

The last thought I had came as we discussed why we had been given such a task. Aki reminded us that we are often bombarded with great activities and problems at conferences, but never take the time to figure out what mathematics the students could learn from such an activity. We simply go and use the activity as is, and as a result we often have a less than desired outcome. In short, we need practice turning good problems into tasks where students learn mathematics.

Finally, although at times I was frustrated with these tasks and with the dynamics of the groups I was working with, I did learn a few things that I would like to implement in my teaching. I do think that mathematics as is commonly taught is more boring than it should be. I hope to figure out some of this stuff in time to try a few things in the classroom this year, and then record what happened and use that to improve in the coming years.