Calculators as an Aid to Problem Solving
A common complaint among teachers is that students have great difficulty with computation and, what is worse, they are very weak in problem solving. Unfortunately this complaint is a self-perpetuating ill. Students who cannot succeed with arithmetic computation are constantly told to drill these skills and are rarely allowed to practice any problem-solving skills. Those who do go on to working on some elementary problems often do not get near an answer because of computational deficiencies. Their only exposure to problem solving is one of frustration, and they rarely realize success because of computational obstacles. Here the calculator can be of significant assistance. Selective use of the calculator to bypass potential computational barriers will allow students to concentrate on problem-solving skills without fear of meeting frustration previously caused by their computational deficiencies. Such activities should be carefully designed and monitored to be effective. After realizing success in problem solving, students should then be intrinsically motivated to conquer their computational deficiencies.
Although continuously nurtured on typical textbook problems, students usually find them boring and unrealistic. Traditionally, textbook authors design the problems in a way that will make the arithmetic computations as simple as possible so as not to detract from the problem. Real-life situations frequently are quite different. The numbers used are generally not simple. With the aid of a calculator, a teacher can provide realistic situations for problem solving and not worry about computational distractions. A uniform-motion problem, for example, can involve fractional quantities and yield an answer that is not an integer and still cause no displeasure for the student who has a calculator available. Furthermore, students using a calculator can be encouraged to create problems based on their own experiences (e.g., calculating their average speed walking to school). New vistas are opened up when a calculator is used to assist in problem solving bypassing arithmetic.
Problems in advanced secondary school mathematics courses can often involve extensive calculations. Not many years ago the slide rule or logarithms were used to solve such problems. Even Napier’s rods and the abacus played a role at one point in the history of people’s attempts to be free of the burden of onerous manual calculations. The abacus is still used in some parts of the less technologically advanced world. Today, the logical method of computation at this level is the calculator. A scientific calculator (i.e., one that, among other features, includes trigonometric functions) and a graphing calculator are very useful aids to instruction, but by no means replace instruction.
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