A discursive analysis of the use of mathematical vocabulary in a grade 9 mathematics classroom

Abstract

A classroom in which learners are afforded opportunities to engage in meaningful mathematical discourse (Sfard, 2008) is desirable for the effective teaching and learning of mathematics. However, engagement in mathematical discourse requires learners to use appropriate mathematical vocabulary to think, learn, communicate and master mathematics (Monroe & Orme, 2002). Hence, I have undertaken this study to explore how mathematical vocabulary is used during mathematical classroom discourse using the lens of the commognitive framework. I chose a qualitative approach as an umbrella for the methodology with ethnography as the research design whereby participant observation, structured interviews and documents were used to collect data. One Grade 9 mathematics classroom with 25 learners and their mathematics teacher were purposefully selected as participants in the study. During data analysis, I looked at Sfard’s (2008) constructs of the commognitive theory to analyse the data and identify the mathematics vocabulary used in the discourse. This was followed by the use of realisation trees that I constructed for the teacher and learners’ discourse, which I used to identify learners thinking as either being explorative or ritualistic. Results indicate that both the teacher and learners use mathematical vocabulary objectively with positive whole numbers to produce endorsed narrative regulated by explorative routines. However, with algebraic terms both positive and negative, the teacher and learners’ discourse is mostly disobjectified, and produces narratives that are not endorsed and are regulated by ritualistic routines. It also became evident that the mathematical vocabulary that the teacher and learners use in the classroom discourse includes words that are mathematical in nature and colloquial words that learners use for mathematical meaning. v Furthermore, learners’ responses to the given mathematics questions which they are solving are mostly correct, hence it can be argued that the learners’ narratives were endorsed. However, their realisation trees indicates that learners were not working with mathematical objects in their own right (Sfard, 2008) and hence their narratives were not endorsed. I have recommended in this study, that teachers need to be cautious when operating with entities and not separate operations from their mathematical terms. Furthermore, the department of basic education, during workshops should encourage educators to always request reasons from learners substantiating their answers to questions in order to enhance their explorative thinking.