Symbolic manipulators affect mathematical mindsets.
American Journal of Physics, Volume 76, Number 4 (April 2008), pp. 418-424
Thomas J. Bing, Edward F. Redish
The use of symbolic calculators such as MATHEMATICA is becoming more commonplace among upper level physics students. The presence of such powerful calculators can couple strongly to the type of mathematical reasoning students employ. These tools do not merely offer students a convenient way to perform the calculations they would have otherwise done by hand. We present examples from the work of upper level physics majors where MATHEMATICA plays an active role in focusing and sustaining their thoughts around calculation. These students still engage in powerful mathematical reasoning while they calculate, but struggle because of the narrowed breadth of their thinking. We model MATHEMATICA’S influence as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work.
Showing posts with label Bing. Show all posts
Showing posts with label Bing. Show all posts
2008-03-18
2007-12-10
Bing Redish - arxiv.org 2007
Symbolic Manipulators Affect Mathematical Mindsets
Thomas J. Bing and Edward F. Redish
arXiv:0712.1187
Date: Fri, 7 Dec 2007 16:57:24 GMT (202kb)
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 the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work.
Thomas J. Bing and Edward F. Redish
arXiv:0712.1187
Date: Fri, 7 Dec 2007 16:57:24 GMT (202kb)
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 the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work.
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