Proposition Debate

by
Beth Richichi

Proposition: Problem solving can not be a central part of the mathematics curriculum in the secondary school because it takes too much time. There is too much other material in the curriculum that must be covered.


Problem solving must, on the contrary, be the core of the mathematics curriculum. As mathematics educators, one of our main goals is to help students to achieve the ability to apply the mathematics that has been learned in the classroom. No other mathematical activity helps students to achieve this ability as adequately as problem solving.

Let us recall some essential definitions:

A question is a situation that can be resolved by recall from memory. An exercise is
a situation that involves drill and practice to reinforce previously learned skills or
algorithms. A problem is a situation that requires thought and synthesis of previously
learned knowledge to resolve. Problem solving is the means by which an individual
uses previously acquired knowledge, skills, and understanding to satisfy the demands
of an unfamiliar situation (Krulik & Rudnick, 1993).

Notice some key words in the above definitions. In order for a situation to be considered a problem situation, it must be an unfamiliar one. This is the major difference between questions and exercises that are found in many textbooks and actual problems. When students enter the world outside of the classroom, they will not see exact repetitions of algortithms and theorems they studied in their schooling. Instead, they will encounter varied problem situations in which they must analyze and develop a strategy to attack the problem. After trying this strategy, they will either try a new one (if the plan had failed) or extend and reflect upon the strategy itself. We must prepare students for these types of confrontations they will face out in the "real world." Repetetive mathematical exercises will not give them the preparation they need. Problem solving activites, on the other hand, will.

The thought patterns that can be learned through participation in problem solving activities are as valuable throughout life as are the "basic skills" of arithmetic. These thought patterns strengthen skills and conceptual understanding, thereby producing mental organization (MCATA, 1982).

Each problem has a novel, difficult aspect. The problem solver must be creative in attacking the problem since no solution is readily available upon intitial contact with the problem. Because of this, even reluctant learners may be more motivated and/or excited by mathematical problem situations. Drill and practice becomes less necessary; creativity and ingenuity take on the dominant roles in the thought process.

The view of what a mathematician does is accurately portrayed with problem solving. Problem solving is the heart of mathematics itself and must also be the heart of the mathematics curriculum.

REFERENCES

Krulik,S., Rudnick,J. (1993). Reasoning & Problem Solving. Needham Heights, MA: Allyn & Bacon.
Mathematics Council of The Alberta Teachers' Association. (1982).Math Monograph. (7) P. 9.

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