The Mathematics Education Department
EMT 725, Lisa F. Garey
Proposition: Problem solving can not be a 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.
The proposition above gives the impression that problem solving is something
that would be added to the mathematics curriculum. Problem solving cannot
exist by itself. Every problem has a context, so problem solving must necessarily
be embedded in a discipline. Consequently, problem solving is not more material
in competition with other materials in the curriculum.
One issue ivolved here is the question of what is meant by problem solving,
and in particular, what is its role in mathematics. Problem solving is not
just solving any problem. Real problem solving invovles the thinker to use
known strategies and skills and apply them to a novel situation. The goal
in problem solving is not getting the solution. The goal in problem solving
is gaining new insights, extending one's thinking processes, and modifying
known strategies. Some may call this learning. There is a subjective component
to problem solving because a mathematical problem may be a problem solving
situation for one person and not the other.
The role of problem solving in school mathematics depends on what mathematics
is. There is no place for authentic problem solving in a classroom where
every mathematical problem has only one correct answer. Problem solving
is a natural part of the mathematics curriculum if students are expected
to be creative thinkers applying their knowledge and sharing their ides
with their peers.
The issues involved in including problem solving in secondary mathematics
curriculum are many. No classroom is homogeneous in ability, so a teacher
cannot pose one problem for the entire class. Moreover, the role of the
teacher changes from the authority to co-problem-solver. Instead of lecturing
all the time, the teacher would coordinate a discussion encouraging students
to share exchange ideas. The issue of time is irrelevant because there does
not seem to be enough time even if problem solving is not included. Learning
takes time. In fact, problem solving can help students make connections
across topics, thus decreasing the need to visit every topic at different
times.
In conclusion, I would like to submit that problem solving is becoming a
necessity in the secondary mathematics curriculum because the scope is getting
broader and the sequence getting longer.
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