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Kimber, Elizabeth
(2024).
DOI: https://doi.org/10.21954/ou.ro.00100845
Abstract
This thesis explores secondary mathematics classroom discourse on functions, graphs and change. I use systemic functional linguistics (SFL) to identify features of teachers’ and students’ speech and examine how these contribute to the ideational, interpersonal and textual metafunctions, in combination with analysis of gestures. I consider how these features afford meanings for graphs and change in the classroom and curriculum context. My overall focus is how language and gesture construct covariation of variables and portray graph shape as arising from this covariation. My study adds insights and detail to research literature on functions, graphs and change by explaining, from an SFL perspective, how linguistic choices in classroom settings construct ideas of change and covariation.
My study concerns graphical representations of functional relationships, prior to formal calculus, in the curriculum in England for students aged 14-16. I draw on data from thirteen lessons across four teachers, students’ written work, six teacher interviews, and online teaching videos from two further teachers. I assemble a collage of snapshots of classroom discourse on functions, graphs and change, including gradients of curves, graph sketching, kinematics, numerical methods, and transformations. My analyses of these snapshots allow me to compare discourse from different topics and question how teachers’ language constructs meanings for students’ understanding of graphs and variable change.
I identified features of classroom discourse on graphs: material activity of humans and graphs, movement between formal and informal language, and repetition with variation. I explore how these intertwine activity of people and mathematical objects, connect representations, and manage information flow. I argue that through speech portraying motion, dynamic gestures, or vivid dynamic descriptions of graphs, teachers’ and students’ informal linguistic choices construct change and covariation and connect these with graph shape. I argue too that graph descriptions using formal conventional mathematical language may have lower affordances than unconventional informal language for constructing graphs as arising through smooth covariation.
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