ABSTRACT
This chapter uses the Mathematical Discourse in Instruction(MDI) framework, with focus on exemplification and explanatory talk, to investigate whether and how these enable or constrain opportunities for learning how to solve quadratic inequalities in Mr. T's lesson. In 2010, the first year of the Wits Maths Connect Secondary (WMCS) Project, we were able to visit project schools and sit in on mathematics lessons. The chapter explains about overarching socio-cultural perspective, is that teaching has purpose and with a truism, with which many explicitly agree, that learning is always about something. It also emphasis on explanatory talk draws on earlier work in the QUANTUM Project and Bernstein's insight that key to pedagogic practice is continuous evaluation. The QUANTUM research identified different domains of legitimation. The chapter focuses on first analytic step which after developing some familiarity with the lesson by watching the video recording and reading the transcript, is to identify the intended object of learning.
