Teachers developing communities of mathematical inquiry : a dissertation presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Education at Massey University, Auckland, New Zealand

Abstract

This study explores how teachers develop communities of mathematical inquiry which facilitate student access to, and use of, proficient mathematical practices as reasoned collective activity. Under consideration are the pathways teachers take to change classroom communication and participation patterns and the mathematical practices which emerge and evolve, as a result. Sociocultural theories of learning underpin the focus of the study. A synthesis of the literature reveals the importance of considering the social and cultural nature of students' learning and doing mathematics in intellectual learning communities—communities in which shared intellectual space creates many potential learning situations. A collaborative classroom-based qualitative approach—design research—falls naturally from the sociocultural frame taken in the study. The design approach supported construction of a communication and participation framework used to map out pathways to constitute inquiry communities. Study group meetings, participant and video observations, interviews, and teacher recorded reflections in three phases over one year supported data collection. Retrospective data analysis used a grounded approach and sociocultural activity theory to present the results as two teacher case studies. Managing the complexities and challenges inherent in constituting communication and participation patterns each teacher in this study successfully developed communities of mathematical inquiry within their own classrooms. Important tools that the teachers used to mediate gradual transformation of classroom communication and participation patterns from those of conventional learning situations included the communication and participation framework and the questions and prompts framework. Significant changes were revealed as the teachers enacted progressive shifts in the sociocultural and mathematical norms which validated collective inquiry and argumentation as learning tools. Higher levels of student involvement in mathematical dialogue resulted in increased intellectual agency and verbalised reasoning. Mathematical practices were shown to be interrelated social practices which evolved within reasoned discourse. The research findings provide insights into ways teachers can be assisted to develop a range of pedagogical practices which support the constitution of inquiry communities. For New Zealand teachers, in particular, models for ways teachers can draw on and use their Maori and Pasifika students' ethnic socialisation to constitute mathematical inquiry communities are represented in the case study exemplars.