Do I teach the way I would like to teach?

The articles by Woodward and Montague as well as Schoenfeld this week have really made me think about my own teaching practice.

I liked the definition of mathematical power where children can “engage in ongoing discourse about mathematics as they solved challenging problems”. I would like to think that I teach my classes using deep conceptual problems and in such a way that students are able to “develop master of skills through problem solving” (Schoenfeld, 23). Yet I fear that in reality, I fall into the category of teachers who provide problems “that could be solved in ‘five minutes or less’” (Woodward and Montague, 91) and who teach in such a way where “students have to master skills before using them for applications and problem solving” (Schoenfeld, 23). I agree that some “memorization and rote learning are unavoidable in education (Woodward and Montague, 92), but it should not be the emphasis. Where is the balance?

One issue that teachers always have is time. I would like to spend time developing concepts with my students (instead of just telling them the facts), but I also want to make sure we get through all of the material they need to learn. I agree that part of the problem is the “’splintered vision’ with curricula that focus on too many superficially taught topics in a given year” (Woodward and Montague, 91) instead of developing a deeper understanding of fewer topics. The other side of it is my own fear that my students will not come to the conclusions I want them to come too. How can I ensure that they have learned in I have not told them what to learn? I think I need to have a little more faith in my students, and recognize that even if they don’t learn everything I want, what they do learn will stay with them a lot longer.

I also agree following the textbook and teaching to the questions at the end of the chapter can be a huge problem. When I look at the textbook I teach with (a technical mathematics book for college students), there are word problems in every chapter, but there is also a chapter called “Simple Equations and Word Problem”. This chapter outlines 4 different types of word problems, making it seem as though there are only 4 types of problems in the world, and if you memorize the steps to solve these problems, you can solve any problem. Clearly this is not the case, but textbooks are set up in such a way that you are not given the opportunity to think about the type of question you are being asked or the choose how you are going to approach it, which is really the most valuable part of solving them problem.

With regards to students with learning disabilities, or students in lower streams, I think that too often we choose to teach them the ‘basics’ because we feel that everyone needs the ‘basics’, and that complex problems are too difficult and over whelming. But really, what we consider to be ‘the basics’ are memorization of algorithms or simple word problems that won’t be useful in their lives, and what we consider to be ‘too complicated’ are the real life problems that they will encounter. Put this way, doesn’t it seem backwards?

Mathematical literacy has become increasingly important in our society. But mathematical literacy does not mean solving equations. These articles have reminded me that, even though I think of myself as a teacher who is more concerned with conceptual understanding then rote learning, I often fall into the traps that most other teachers fall into. I need to make a conscious effort to change my practice so that my students get the most from their experience in my classroom.