Exploring grade 11 learner routines on function from a commognitive perspective

Abstract

This study explores the mathematical discourse of Grade 11 learners on the topic function through their routines. From a commognitive perspective, it describes routines in terms of exploration and ritual. Data was collected through in-depth interviews with 18 pairs of learners, from six South African secondary schools, capturing a landscape of public schooling, where poor performance in Mathematics predominates. The questions pursued became: why does poor performance persist and what might a commognitive lens bring into view? With the discursive turn in education research, commognition provides an alternate view of learning mathematics. With the emphasis on participation and not on constraints from inherited mental ability, the study explored the nature of learner discourse on the object, function. Function was chosen as it holds significant time and weight in the secondary school curriculum. Examining learners’ mathematical routines with the object was a way to look at their discourse development: what were the signifiers related to the object and what these made possible for learners to realise. Within learners’ routines, I was able to characterise these realisations, which were described and categorised. This enabled a description of learner thinking over three signifiers of function in school Mathematics: the algebraic expression, table and graph. In each school, Grade 11 learners were separated into three groups according to the levels at which they were performing, from summative scores of grade 11 assessments, so as to enable a description of discourse related to performance. Interviews were conducted in pairs, and designed to provoke discussion on aspects of function and its signifiers between learners in each pair. This communication between learners and with the interviewer provided data for description and analysis of rituals and explorations. Zooming in and out again on these routines made a characterisation of the discourse of failure possible, which is seldom done. It became apparent early in the study that learners talked of the object function, without a formal mathematical narrative, a definition in other words, of the object. The object was thus vested in its signifiers. The absence of an individualised formal narrative of the object impacts directly what is made possible for learners to realise, hence to learn. The study makes the following contributions: first, it describes learners’ discursive routines as they work with the object function. Second, it characterises the discourse of learners at different levels of performance. Third, it starts exploration of commognition as an alternate means to look at poor performance. The strengths and limitations of the theory as it pertains to this study, are discussed later in the concluding chapter. Keywords commognition, discourse, communication, participation, routines, exploration, ritual, learners, learning, narratives, endorsed narratives, visual mediators.