question archive University of PhoenixMTH 208 208 Math does have processes for solving problems
University of PhoenixMTH 208 208 Math does have processes for solving problems
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University of PhoenixMTH 208 208
Math does have processes for solving problems. How could we use those problem solving processes in other areas of our lives?
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Presenting a problem and developing the skills needed to solve that problem is more motivational than teaching the skills without a context. It allows the students to see a reason for learning the mathematics, and hence to become more deeply involved in learning it. Teaching through problem solving can enhance logical reasoning, helping people to be able to decide what rule, if any, a situation requires, or if necessary to develop their own rules in a situation where an existing rule cannot be directly applied. Problem solving can also allow the whole person to develop by experiencing the full range of emotions associated with various stages of the solution process.
| 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. |
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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. 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). Approaching mathematics through problem solving can create a context which simulates real life and therefore justifies the mathematics rather than treating it as an end in itself. The National Council of Teachers of Mathematics (NCTM, 1980) recommended that problem solving be the focus of mathematics teaching because, they say, it encompasses skills and functions which are an important part of everyday life. Furthermore it can help people to adapt to changes and unexpected problems in their careers and other aspects of their lives. More recently the Council endorsed this recommendation (NCTM, 1989) with the statement that problem solving should underly all aspects of mathematics teaching in order to give students experience of the power of mathematics in the world around them. They see problem solving as a vehicle for students to construct, evaluate and refine their own theories about mathematics and the theories of others. |
