Pedagogic evaluation, computational performance and orientations to mathematics: a study of the constitution of Grade 10 mathematics in two secondary schools



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University of Cape Town

This study takes as its starting point Bernstein’s proposition that evaluation is central to pedagogy. Specifically, along with many researchers who draw on his work, Bernstein claims that explicit evaluative criteria are critical to the academic success of learners from working-class families and low economic status communities. The research problem stems from a hypothesis, derived from the literature, that social class differences in learner performances in school mathematics suggest differences in the functioning of pedagogic evaluation, and therefore differences in what is constituted as mathematics, and how, in pedagogic situations differentiated by social class (e.g. Dowling). The contention of this study is that insufficient finegrained analyses have been undertaken to surface the computational specificity of what it is that constitutes evaluative criteria in mathematics education studies of pedagogy. The study examines the functioning of pedagogic evaluation in what comes to be constituted as mathematics by teachers and their learners, and in the specialisations of mathematical thought in pedagogic situations. The study set out to investigate the functioning of pedagogic evaluation in two schools differentiated with respect to the social class membership of learners. Two Grade 10 teachers and their learners in each school served as research participants. Methodological resources for describing the functioning of pedagogic evaluation in terms of the computational activity of teachers and learners derive from the work of Davis, which draws on a computational theory of mind (e.g., Chomsky; Gallistel & King; Spelke). Bernstein’s theory of the pedagogic device, with its focus on who gets what knowledge and how, serves as a general descriptive frame structuring the study. The analysis reveals the following: (1) the commonly used descriptions of evaluative criteria as explicit/implicit are analytically blunt and consequently mask the complexity of criteria operative in pedagogic contexts; (2) differences as well as strong similarities in the functioning of evaluation and, therefore, differences and similarities in what is constituted as mathematics are evident in pedagogic situations differentiated with respect to social class; (3) an orientation to mathematics that constitutes mathematics as computations on the typographical elements of mathematical expressions is common to pedagogic situations involving learners from both upper-middle-class/elite families and working-class families; and (4) greater variation and inter-connectedness in computational resources is realised in pedagogic situations involving learners from upper-middle-class/elite families than in those involving learners from working-class families, where computational resources are relatively restricted and weakly connected. The differences between the two types of situations appear to be enabling of greater flexibility in mathematical thought and action for upper-middle-class/elite learners, on the one hand, and restricting for working-class learners, on the other. The contribution of the thesis is four-fold. The study: (1) provides a methodology for exploring the complexity of pedagogic evaluation by describing the computations performed by learners and teachers in mathematical terms, thus contributing to Bernstein’s account of pedagogic discourse as it applies to the teaching and learning of mathematics; (2) contributes to our understanding of the structuring effect of evaluation on learners’ mathematical thought; (3) contributes to the methodological resources developed by Davis for describing the constitution of mathematics in pedagogic situations; and (4) extends analyses of the constitution of mathematics in pedagogic situations to those populated by learners from upper middleclass/elite families in the South African context, albeit in a limited way.