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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