The symbolic world of mathematics

Abstract

In understanding upper secondary school students’ interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in symbolic representations of different phenomena. Two theoretical perspectives have been used to conduct the analysis: Tall and Vinner's theoretical perspectives on learning and Gray’s & Talls’s theory of three mathematical worlds. The findings provide evidence that a detailed analyse of student’s utterances show difference in quality related to student’s interpretations of a distance-time relation. The qualities were related to student’s concept images of functions and derivatives.

Components and Subcomponents of the Slope used by High School Mathematics Teachers

“…The visual conceptual subcomponent of all components did not emerge in the teachers' responses, whereas the non-visual conceptual aspect was sporadically referenced by two teachers (Figure 2). This underscores the notion that the treatment of the concept leans heavily towards the procedural, sidelining the conceptual aspect, as also identified by Lingefjärd and Farahani (2017), Styers et al (2020) and, Salgado and Dolores (2021). Such an approach poses a hindrance to establishing connections among rate of change, slope, and steepness, a concern highlighted by prior studies (Dolores et al, 2019;Nagle & Moore-Russo, 2013;Teuscher & Reys, 2012).…”