While doing some research for my latest literature review assignment, I came across a chapter in the Handbook of Research on Mathematics Teaching and Learning (1992) that was written by Alan Schoenfeld entitled “Learning to think mathematically: Problem solving, metacognition and sense making in mathematics.” It is a very good overview of the history of the paradigm shift in mathematics education and research to more of a focus on problem solving as a goal in the mathematics classroom and makes some good comparisons between differing definitions of what problem solving means in the classroom.

Something that I thought was extremely interesting in this chapter was the argument that teaching with the “big picture” of problem solving skills in mind is actually much more difficult for the teacher. This totally resonates with me and my colleagues who are making this shift this year. We are all feeling more tired, more spent at the end of our day. Now, this could be because of a new “block” schedule that we are using this year, but I also think some of it has to do with the way we are teaching.

Schoenfeld quotes another researcher, Burkhardt, who says that teaching problem solving has its unique challenges for classroom teachers. The first of which is that the teacher “must perceive the implications of the students’ different approaches, whether they may be fruitful and, if not, what might make them so.” This is clearly a challenge for teachers without experience with this type of pedagogy. Not only do you need to be free to pursue incorrect solutions, but you need to reserve judgement, find “kind” ways of telling students they are wrong, control the dynamic of discomfort that students have when the teacher is uncertain, to name a few challenges. During the summer, when we did professional development before adopting this new curriculum, we had days of discussions about all of these issues. However, discussion only gets teachers to a certain level. I firmly believe that the best education is the experience of doing it, while having some observation for another opinion.

Secondly, it’s difficult pedagogically. It’s a BIG change from what most teachers are doing currently. There are so many new decisions that the teacher has to make that he/she may not be trained for. The teacher must “decide when to intervene, and what suggestions will help the students while leaving the solution essentially in their hands, and carry this through for each student, or group of students, in the class”. How do you assess for each student individually when they are solving a problem in a group? How do you give them enough practice in order to allow them to be ready for an assessment? I think that our curriculum makes these goals pretty accessible.  I’ll try to assess that this year in some way.

Thirdly, it is difficult personally.  The implications of putting yourself out there and being vulnerable every day are many.  Burkhardt says “the teacher will often be in the position, unusual for mathematics teachers and uncomfortable for many, of not knowing: to work well without knowing all the answers requires experience, confidence and self-awareness.”  I believe that these are just the tip of the iceberg of the personal implications of teaching with PBL.  One of my colleagues and I got in a conversation recently about how we are so surprised at how much the students don’t know and are afraid to try new things.  My take on it is that not only might this be the first time that the students are being asked to think this way, but we are deliberately asking them to think this way.  In any other type of teaching, these issues might not arise because the students are not being asked to hunt down the prior knowledge of their past algebra skills or to be invested in the learning process, as we are asking them to do.  I feel that we are noticing these weaknesses mostly because we are forcing these issues with our students.  Instead of getting down on them and ourselves, we should feel proud that they are accessing and practicing these skills.

Does this make it any easier?  Not really.   Is this a reason to not do it?  Definitely not. In the article that I wrote called “Transition to a Problem-Solving Curriculum” I commented that teaching this way requires a great deal from the teacher including more patience, more insight, more flexibility and more mathematical knowledge.  This is a lot to ask of our already overworked and underpaid faculty.  But, as Schoenfeld says, true problem solving is “far more rewarding, when achieved, than the pale imitations of it in most of today’s curricula.”