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It may be different in elementary school, but in middle school, there are so many standards to teach I am happy if the students can solve the problem using one method.As the emphasis has shifted from teaching problem solving to teaching via problem solving (Lester, Masingila, Mau, Lambdin, dos Santon and Raymond, 1994), many writers have attempted to clarify what is meant by a problem-solving approach to teaching mathematics. Resnick (1987) described the discrepancies which exist between the algorithmic approaches taught in schools and the 'invented' strategies which most people use in the workforce in order to solve practical problems which do not always fit neatly into a taught algorithm.
Presenting a problem and developing the skills needed to solve that problem is more motivational than teaching the skills without a context.
Such motivation gives problem solving special value as a vehicle for learning new concepts and skills or the reinforcement of skills already acquired (Stanic and Kilpatrick, 1989, NCTM, 1989).
Over the years the courses evolved to the point where they focused less on heuristics per se and more on introducing students to fundamental ideas: the importance of mathematical reasoning and proof..., for example, and of sustained mathematical investigations (where my problems served as starting points for serious explorations, rather than tasks to be completed).
Schoenfeld also suggested that a good problem should be one which can be extended to lead to mathematical explorations and generalisations.
He described three characteristics of mathematical thinking: Problem solving is an important component of mathematics education because it is the single vehicle which seems to be able to achieve at school level all three of the values of mathematics listed at the outset of this article: functional, logical and aesthetic.
Let us consider how problem solving is a useful medium for each of these.
It has already been pointed out that mathematics is an essential discipline because of its practical role to the individual and society.
Through a problem-solving approach, this aspect of mathematics can be developed.
They see problem solving as a vehicle for students to construct, evaluate and refine their own theories about mathematics and the theories of others. National Council of Teachers of Mathematics (NCTM) (1980).
According to Resnick (1987) a problem-solving approach contributes to the practical use of mathematics by helping people to develop the facility to be adaptable when, for instance, technology breaks down. (Eds.) Professional Development for Teachers of Mathematics , pp. An Agenda for Action: Recommendations for School Mathematics of the 1980s, Reston, Virginia: NCTM.