Identifying static- and emergent-shape thinking in students’ language about graphs of functions
Résumé
Perspectives on graphs of functions can involve static-shape thinking, which focuses on perceptual
shapes, or emergent-shape thinking, which views a graph as a trace of covarying quantities. These,
and more formal covariation perspectives, are used flexibly and together to solve graphical problems.
Researchers have grappled with establishing empirical-theoretical relationships between the
language students use and the meanings made available. Systemic Functional Linguistics (SFL)
offers tools to analyse how linguistic choices contribute to the creation of mathematical texts and can
thus be used to investigate how features of students’ language communicate forms of shape-thinking
or covariation. In this paper we present an SFL analysis of students’ short written descriptions of a
graph. We uncover similarities to the language used in their lessons and how shape thinking or
covariation may be constructed by linguistic features of students’ discourse.
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