Keeping sites in sight: Conversations with teachers about the design of toolkits peculiar to a continuous professional development initiative

Abstract

The aim of this article is to shift the notion of ‘sites’ as places of work peculiar to continuous professional development (CPD) to a theoretical level, independent of, yet intimately connected to, their physical meanings, for example universities and schools. Most CPD initiatives have to contend with at least one of these two sites, in which university-based mathematics educators and school teachers can have different and at times overlapping ways of talking about the same mathematics. Using research on number and operations, non-visually salient rules in algebra and algebraic fractions, and analytic tools and notions peculiar to conversation analysis and ethnomethodology, the authors identify and analyse site-related issues in the design of particular problem sets in Grade 8 and Grade 9 toolkits and related conversations between a mathematics educator and participating teachers. The article concludes with the implications of ‘keeping in sight’ ways in which universities and schools talk and work when it comes to designing and discussing toolkits.

Keywords

• continual professional development
• mathematical toolkits
• productive practice
• algebraic fractions
• visual syntax of algebra
• equivalence
• conversation analysis
• ethnomethodology