Teaching mathematics through problem solving was not something that I would usually think about. I like to follow tradition and teach math the way I was taught, so when we had our first class and I realized what the course was about, I was not too excited. After reading the chapters and articles assigned for this first week of class, I realized that problem solving is not that bad. I was engaged while reading the chapters because I was noticing that teaching through problem solving, rather than following tradition, is simply better.
The word ‘understanding’ was used a lot during our first class and in the first chapter of Teaching Mathematics through Problem Solving by Harold L. Schoen. One of the main goals of teaching through problem solving is to fully understand the mathematics that is being taught. To me, understanding was just being able to apply one’s knowledge and answer mathematical questions. In this class, understanding is being able to apply one’s knowledge to problems that they have not exactly seen before, but that of which are in their reach. Through critical thinking, a healthy amount of struggle, and generous information one is able to fully understand the problem and answer it correctly. We were given a couple activities during our first week of class where we had to figure out problems using the knowledge we already had, and once I solved the problem, it was such a wonderful and satisfying feeling. If teaching through problem solving helps my students feel satisfied and proud, then I would continue to teach that way.
An important aspect of teaching through problem solving is to “share one’s own method, to hear others present alternative methods, and then to examine the advantages and disadvantages of these different methods” (Schoen, 8). There should be class discussions about the methods that the students have created and additional methods that are important. Discussing the students’ methods is important because they become engaged in finding relationships between each method, they realize that “mistakes become sites for learning”, (10) and that everyone’s contribution can help.
Teaching mathematics through problem solving goes way back to 1945 when William Brownell “emphasized the importance of students appreciating and understanding the structure of mathematics.”(English, Sriraman, 1). A lot of the research has intensified since the 1900s and beyond. The research shows that classrooms that teach through problem solving, as opposed to the traditional way, have greater student achievement and are more likely to think positive about mathematics. Just by having two classes and reading a few chapters on problem solving, my perspective has changed and I think that teaching through problem solving will benefit everyone. Even though it is a lot more complex, and quite different than what students are used to, I believe it will be very beneficial for the students.