| Summary: | The problem of poor learner performance in school mathematics in South Africa is persistent. Many studies have pointed to learner difficulties with algebra and their inadequate access to mathematical properties as a problem-solving resource. This small-scale qualitative study focuses on how, in an interview, fifteen Grade 8 and 9 learners at two South African schools think about linear equations. Sfard's theory of commognition, and particularly her concepts of ritualized and explorative discourse, are used as a framework to analyse how learners' words, gestures, narratives and routines intersect to build a picture of the mathematical objects they perceive. Many national and international research studies focusing on functions and linear equations from a cognitivist perspective, suggest that the reason for poor performance can be ascribed to a lack of relational understanding. Using a discursive rather than a cognitive lens, the study concludes that learners' discourse is ritualistic and that learners favour working with whole numbers, even when the context is negative integers or algebraic terms. Furthermore, they do not make a link between the solution of the equation and the function. As a result they have limited flexibility to adapt their routines.
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