Statement: Problem solving can not be a central part of the mathematics curriculum in the secondary school because it takes too much time and there is too much other material in the curriculum to be covered.
I strongly disagree with this statement. My argument is based on what we define as problem solving. According to Kilpatrick what we define as a mathematical problem is a situation in which a goal is to be attained and a direct route to the goal has been blocked. Additionally, we can add the requirement that we must use mathematical concepts and principles when seeking an answer to the problem (Kilpatrick 1985 ). We as mathematics teachers teach different concepts to students so that they may apply them to other situations. According to the NCTM Curriculum and Evaluation Standards, it is important that students be able to make connections. It stresses the importance of students being able to use mathematics in other curriculum areas as well as in daily life activities. I believe that these skills can be goals can be achieved through problem solving practices. I also think that the important concepts within the curriculum can be taught through problem solving. The Interactive Mathematics Program is an integrated curriculum that is problem centered. This is an alternative approach to teaching mathematics that has a high student achievement rate according to studies that have been done. Because it is a fairly new curriculum there is still a lot more to be learned about its effectiveness.
Sources:
Kilpatrick, J. (1985). A retrospective account of the past twenty-five years of research on teaching mathematical problem solving. In E.A. Silver (Eds.), Teaching and learning mathematical problem solving (pp. 1-15). Hillsdale, NJ: Erlbaum.
Mayer, R.E. (1985). Implications of cognitive psychology in mathematical problem solving.In E.A. Silver (Eds.), Teaching and learning mathematical problem solving (pp. 1-15). Hillsdale, NJ: Erlbaum.