Graphing formulas: Unraveling experts’ recognition processes

P.M.G.M. Kop; F.J.J.M. Janssen; P.H.M. Drijvers; J.H. van Driel

doi:10.1016/j.jmathb.2017.01.002

Graphing formulas: Unraveling experts’ recognition processes

P.M.G.M. Kop, F.J.J.M. Janssen, P.H.M. Drijvers, J.H. van Driel

Leiden University

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

Abstract

An instantly graphable formula (IGF) is a formula that a person can instantly visualizeusing a graph. These IGFs are personal and serve as building blocks for graphing formulasby hand. The questions addressed in this paper are what experts’ repertoires of IGFs are andwhat experts attend to while recognizing these formulas. Three tasks were designed andadministered to five experts. The data analysis, which was based on Barsalou and Schwarzand Hershkowitz, showed that experts’ repertoires of IGFs could be described using functionfamilies that reflect the basic functions in secondary school curricula and revealed thatexperts’ recognition could be described in terms of prototype, attribute, and part-wholereasoning. We give suggestions for teaching graphing formulas to students.

Original language	English
Pages (from-to)	167-182
Journal	Journal of Mathematical Behavior
Volume	45
DOIs	https://doi.org/10.1016/j.jmathb.2017.01.002
Publication status	Published - 2017

Keywords

Graphing formulasExperts’ recognitionFunction familiesPrototypes and attributes

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10.1016/j.jmathb.2017.01.002

graphingFinal published version, 1.9 MBLicence: Taverne

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title = "Graphing formulas: Unraveling experts{\textquoteright} recognition processes",

abstract = "An instantly graphable formula (IGF) is a formula that a person can instantly visualizeusing a graph. These IGFs are personal and serve as building blocks for graphing formulasby hand. The questions addressed in this paper are what experts{\textquoteright} repertoires of IGFs are andwhat experts attend to while recognizing these formulas. Three tasks were designed andadministered to five experts. The data analysis, which was based on Barsalou and Schwarzand Hershkowitz, showed that experts{\textquoteright} repertoires of IGFs could be described using functionfamilies that reflect the basic functions in secondary school curricula and revealed thatexperts{\textquoteright} recognition could be described in terms of prototype, attribute, and part-wholereasoning. We give suggestions for teaching graphing formulas to students.",

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AU - Drijvers, P.H.M.

AU - van Driel, J.H.

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JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

ER -

Graphing formulas: Unraveling experts’ recognition processes

Abstract

Keywords

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