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Symbolic Manipulators Affect Mathematical Mindsets
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| American Journal of Physics |
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Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model Mathematica’s influence as an integral part of the constant feedback that occurs in Recent advances in computers and programming have given today’s physics students a new tool. Personal computer programs such as Mathematica, Maple, and even handheld calculators are now widely capable of symbolic manipulation. Whereas calculators were once limited to numeric operations like evaluating the cube root of fortytwo, 3 + x to 27 27 9 2 3 + + + x x x , Automated calculation, even when it is strictly numerical instead of symbolic, makes many teachers wary. Almost all physics teachers have anecdotal stories of watching students reach for a calculator to do simple operations like halving a number or multiplying by one hundred. Most have also watched students make obvious errors as they pushed calculator buttons. Teachers worry that these students are neither using nor developing a feel, an instinct, for numbers. Mathematics education researchers have been “Number sense” has at least partially converged to a certain set of meanings in the math education literature, including flexible computing strategies for written and calculatoraided computation, understanding of equivalent representations, With the expansion of symbolic manipulation capabilities into the teaching of advanced physics, we can raise an analogous question: Does being fluent with a symbolic manipulator damage the advanced physics student’s intuition for how students frame, and hence focus, their work.
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symbolic manipulators, physics education
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