EMT 725
Philippa M. Rhodes
Proposition:
A problem is defined as having a situation (or a given state) and a desired goal, but no obvious solution (Kilpatrick, 1985; Mayer, 1985). With this definition in mind, I think that problem solving can be a central part of the mathematics curriculum in the secondary school because problems can be posed that will require the use of the "other material in the curriculum that must be covered."
I think that if problem solving is placed in the curriculum as a separate topic, then we may be led to believe that there is not enough time to include it along with all the other material. There are curricula/ textbooks that are designed to make problem solving the central emphasis. The one with which I am most familiar is the Integrated Mathematics Project, IMP. One of their main goals, in agreement with NCTM's Standard 1 for all levels, is for students to learn mathematics through problem solving. I believe that problem solving can be used to enhance the understanding of mathematical content because one has to really understand a concept before they can consistently apply it correctly. I also think the inclusion of problem solving throughout the curriculum will help students in their lives inside and outside of the mathematics classroom. In turn, I would hope that students will experience the 'usefulness' in learning mathematical concepts.
I suppose that without a textbook that is designed to make problem solving
a central part of the curriculum, that it will be hard (as for time and
creativity) to try to make problem solving the main emphasis. I do think
that it essential, and should be included as much as possible as a form
of instructing and evaluating the students.
References
Mayer, R.E. (1985). Implications of cognitive psychology in mathematical problem solving. In E.A. Silver (Eds.), Teaching and learning mathematical problem solving (pp. 123 - 138). Hillsdale, NJ: Erlbaum.
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.
NCTM's Curriculum and Evaluation . Standard 1 MATHEMATICS AS PROBLEM SOLVING (for Grades 9 - 12)