The summer reading for my math department is one section titled “Effective Teaching and Learning” of the Principles to Actions written by the National Council of Teachers of Mathematics. http://www.nctm.org/PtA/
I quite enjoy reading things like this because I don’t have a formal degree in education and I appreciate moments where I feel like I can be a student of our craft. As I read the first few pages of this section I couldn’t help but feel even more justified in my choice to teach geometry with a problem based learning curriculum. According to the NCTM, math classrooms should be created such that experiences allow for 6 things to happen. As I read these six things I felt that using a PBL pedagogical approach helps establish these 6 things are norms.
The process of attempting problems on your own and presenting the problems to the class sets this expectation from the very beginning.
The self scaffolding nature of the problems allows students to develop this as a habit. In traditional “Me-We-You” teaching method the students often rely first on the teacher’s direction instead of thinking “what can I already do by myself?”
3. Acquire conceptual knowledge as well as procedural knowledge
Again, the problems are arranged in such a way as to have deliberate purposes in a deliberate order. I as the teacher know that a few specific problems help establish the conceptual knowledge and that a few pages later the procedural knowledge is established. I feel comfortable knowing this happens in a cyclic pattern across multiple topics simultaneously.
4. Construct knowledge socially through discourse
This is the easiest task with a PBL curriculum. I love watching the students discuss and debate problems. One difficult part of teaching this way is knowing when to interject and when to remain silent.
5. Receive descriptive and timely feedback
The student lead structure of PBLmeans that any time a student presents a problem they get descriptive and timely feedback. Any student that pays close attention can take mental notes or make modifications in their journals.
6. Develop metacognitive awareness of themselves as learners, thinkers, and problem solvers.
If students approach a problem knowing there is a high chance they will have to verbally discuss it, they become far more aware of what they are doing than if it were secret notes never to be seen by anyone. PBL allows for students to learn their tendencies and grow in ways that a traditional classroom can’t address.
Patrick Frasier 