Identifying a framework for graphing formulas from expert strategies

Peter M G M Kop; Fred J J M Janssen; Paul H M Drijvers; Marcel V J Veenman; Jan H. van Driel

doi:10.1016/j.jmathb.2015.06.002

Identifying a framework for graphing formulas from expert strategies

Peter M G M Kop^*, Fred J J M Janssen, Paul H M Drijvers, Marcel V J Veenman, Jan H. van Driel

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	121-134
Number of pages	14
Journal	Journal of Mathematical Behavior
Volume	39
DOIs	https://doi.org/10.1016/j.jmathb.2015.06.002
Publication status	Published - 1 Sept 2015

Keywords

graphing formulas
mathematical expertise
recognition and heuristic search

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10.1016/j.jmathb.2015.06.002

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title = "Identifying a framework for graphing formulas from expert strategies",

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.",

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doi = "10.1016/j.jmathb.2015.06.002",

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AU - Kop, Peter M G M

AU - Janssen, Fred J J M

AU - Drijvers, Paul H M

AU - Veenman, Marcel V J

AU - van Driel, Jan H.

PY - 2015/9/1

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Identifying a framework for graphing formulas from expert strategies

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Keywords

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