Before entering into EMATH 200, I viewed problem solving as a unit, or lesson completed in a math class. My schooling experience offered nothing beyond problem solving as a unit of word problems that we would have to work through. Problem solving forced student to draw on previous information that was learnt in past grades, subject areas and units. This unit was normally left until the end of the school year, because it allowed the teacher more time teach the necessary information that we needed to know to complete problems. Do I agree with this approach? Am I going to approach problem solving like this? No, EMATH 200 has introduced problems solving to be a teaching strategy, or method that can be used in every area of math.
By using problem solving as a method of instruction it opens many doors. A higher level of critical thinking is establishing when students are forced to problem solve. The text “Teaching Mathematics through Problem Solving- Grades 6-12” by Harold Schoen and Randall Charles is a great resource that provides ideas when using problem solving as a method. There was one main idea that I gained from the chapters; (1) Developing Understanding through Problem Solving, (2) Teaching Mathematics through Problem Solving: A Historical Perspective and (3) Teaching Mathematics through Problem Solving: Research Perspectives. The idea gained was to give students the basic concept and guidelines, that way they can draw on background information to work through the problem. Schoen and Charles state;
Allowing mathematics to be problematic for students means posing problems that are just within student’s reach, allowing them to struggle to find solutions and then examining the methods they have used. Allowing mathematics to be problematic requires believing that all students need to struggle with challenging problems if they are to learn mathematics deeply (2003).
Giving students the time to struggle with a problem and not answering the question when they are not getting it, forces them to think critically and outside the box. I believe that students need to struggle, but not to the point where they are outside their Zone of Proximal Development (ZPD). In class, we learnt that if they are outside the Zone of Proximal Development (ZPD), learning will not take place to the same extent as if they were in it.