**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)**