Identifying static- and emergent- shape thinking in students’ language about graphs of functions

Kimber, Elizabeth and Smith, Cathy (2023). Identifying static- and emergent- shape thinking in students’ language about graphs of functions. In: Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (Drijvers, P.; Csapodi, C.; Palmér, H.; Gosztonyi, K. and Kónya, E. eds.), Alfréd Rényi Institute of Mathematics and ERME pp. 1613–1620.

URL: http://erme.site/wp-content/uploads/2024/01/CERME1...

Abstract

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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