Identifying a framework for graphing formulas from expert strategies
Publication date
2015-09-01
Authors
Kop, P
Janssen, Fred J J M
Drijvers, Paul
Veenman, Marcel V J
van Driel, Jan H.
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Advisors
Supervisors
Document Type
Article
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Abstract
It is still largely unknown what are effective and efficient strategies for graphing formulas with paper and pencil without the help of graphing tools. We here propose a two-dimensional framework to describe the various strategies for graphing formulas with recognition and heuristics as dimensions. Five experts and three secondary-school math teachers were asked to solve two complex graphing tasks. The results show that the framework can be used to describe formula graphing strategies, and allows for differentiation between individuals. Experts used various strategies when graphing formulas: some focused on their repertoire of formulas they can instantly visualize by graphs; others relied on strong heuristics, such as qualitative reasoning. Our exploratory study is a first step towards further research in this area, with the ultimate aim of improving students' skills in reading and graphing formulas.
Keywords
graphing formulas, mathematical expertise, recognition and heuristic search, Taverne, Applied Mathematics, Applied Psychology, Education, SCI and SSCI Journals
Citation
Kop, P M G M, Janssen, F J J M, Drijvers, P H M, Veenman, M V J & van Driel, J H 2015, 'Identifying a framework for graphing formulas from expert strategies', Journal of Mathematical Behavior, vol. 39, pp. 121-134. https://doi.org/10.1016/j.jmathb.2015.06.002