The University of Montana
Department of Mathematical Sciences

Technical report #5/2012

Extrapolation and Expansion: Characteristics of Change Occurring in Mathematics Teaching Development Projects.

Claire V. Berg, Anne Berit Fuglestad and Simon Goodchild
University of Agder, Norway

Bharath Sriraman
University of Montana

Abstract

This paper commences by critically examining how mathematics teaching development projects based on the creation of communities of inquiry (CoI) are theorised from communities of practice theory (CPT) and cultural historical activity theory (CHAT). Two types of change, which can be developed from these sociocultural theories are articulated. Change as ‘extrapolation’ derived from CPT, and change as ‘expansion’ developed within CHAT. The differences between these types of change and their underlying principles are examined by contrasting conceptualisations of CPT and CHAT; attention focuses on mediation, goals, and agency. It is argued that the introduction of inquiry to CPT transforms the practice and entails a paradigm shift, with CoI as category within the critical paradigm. Expansion and extrapolation are illustrated using narrative evidence from a longitudinal case study of one school team that worked within a series of mathematics teaching developmental research projects over a period of six years. The paper emerges from the analysis and synthesis of a large volume of qualitative data accrued in teaching development projects.

Keywords: Communities of practice; Communities of inquiry; Cultural historical activity theory; extrapolation; expansion; Large scale qualitative data analysis

AMS Subject Classification: 97

Revised version (202 KB) of #2/2011