5. Creating Solutions (Problem-Solving)

For over a decade, considerable attention has been paid by Mathematics� educators and curriculum writers to teaching problem-solving by explicit focus on the steps and strategies of problem-solving, with little gain in students� problem-solving abilities.

The major barriers to effective creating of solutions are affective.  High self-esteem, happiness, enjoyment of learning and confidence in their ability all assist people to be creative, to generate a range of alternatives and take the kind of risks that are necessary when standard procedures don�t work.  Students who lack confidence in their abilities, who are not enjoying their learning and don�t readily �play� with it, tend to stick to procedural thinking, to rely on strategies that have worked for them before and to cling rigidly to their initial representation of a situation or problems.  (Adults do it in �real life� as well!)  It is therefore very important that our students experience �solution creating� activities within their intellectual comfort zone, so that they can relax and play with ideas.

At St Catherine�s our students express a distaste for problem-solving as a learning task, preferring more active and interactive learning methods.  Teachers here have suggested that problem-solving may lack appeal because the problem is one presented by the teacher, not owned by the student, and it represents a negative situation and a demanding task.  By using instead the term �Creating Solutions�, our intention is to put ownership back with the student, and to present the process as a creative and positive one.  The starting point for creating solutions is that the student has a situation needing a solution.

Apart from these affective and motivational considerations, it now appears likely that the approach to teaching �problem-solving� was successive: that is, it broke the process of problem-solving down into sequential tasks and made it procedural.  But procedural thinking is of value only in known and regular situations.  By definition, when a student has a problem, she is faced with something irregular or unknown and to move out of the road block needs to make a holistic leap of understanding.  This requires thinking for meaning, that is, simultaneous processing and is assisted by reframing the situation or problem: by analogy, by visual thinking, or by lateral thinking techniques.

In practice, this means students learn the habit of focusing on their representation of the situation or problem, in situations where their routine procedures have proved ineffectual.

Creating Solutions: Teaching in the Junior School

The Junior School starts to teach Creating Solutions in Early Stage One with the use of of our own Mathematics challenges.  Strategies employed need to be supplemented by more holistic methods, such as the tactics of analogy taught in the Junior School through synectics.

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