How students interpret points and positions in graphs of functions: an intersection of theoretical frameworks
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Erika David Parr
[1]
;
Benjamin Sencindiver
[2]
;
Rob Ely
[3]
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[1] Rhodes College
Rhodes College
Estados Unidos
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[2] University of Texas at San Antonio
University of Texas at San Antonio
Estados Unidos
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[3] University of Idaho
University of Idaho
Estados Unidos
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- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 56, Nº. 10, 2025, págs. 2015-2033
- Idioma: inglés
- DOI: 10.1080/0020739X.2024.2391374
- Enlaces
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Resumen
In this paper, we examine the intersection of two previously recognised dimensions of students’ interpretations of symbolic notations within graphs of functions. One dimension distinguishes location-thinking, where notations refer only to a point’s location on a graph, from value-thinking, where such a point is treated as a multiplicative object. The other dimension distinguishes a nominal interpretation of expressions, where expressions refer to positions in the plane, from cardinal and magnitude interpretations, where expressions describe a discrete count of units, or measure of length, respectively. Taken together these dimensions provide six distinct ways students interpret expressions, especially those involving function notation, on graphs. Further, the frameworks offer suggestions about the ways of thinking underlying each interpretation. Each case reveals new meanings and affordances indicated by the interplay between the two dimensions. We provide both a theoretical account and empirical example of each case.
