A square in drag as concrete universal; or, Hegel as a Sketchpad programmer

Abstract

In this article, by way of an analysis of a case of mathematics teacher training, I explore the general idea of pedagogic expectation of an alignment of pedagogic identities and specific realisations of mathematics in pedagogic contexts. The particular case analysed has a constructivist orientation, but the analytic resources brought to bear in the analysis can be used more generally for the description and analysis of pedagogic situations. The analysis is framed chiefly by the philosophical work of Georg Hegel alongside Basil Bernstein’s sociological discussion of evaluation in pedagogic contexts. The argument proceeds in three inter-related parts, the first of which produces an analytic description of the discursive production of the desired pedagogic subject–in this case, a teacher/student of geometry–in which I show how explication and abbreviation are used discursively in an attempt to construct the desired teacher/student–that is, a particular pedagogic identity. The second part of the argument describes the discursive production of mathematics content in a manner intended to align content with the desired teacher/student and introduces the notion of a regulative orientation in order to grasp the differences in the mathematical work of students. The third part is a synthesis of parts one and two, showing how pedagogic identity and mathematics contents are brought together as correlative effects of each other.