Developing Algebraic Thinking in a Community of Inquiry : Collaboration between Three Teachers and a Didactician

Abstract

In this thesis I report from a study of the development of algebraic thinking of three teachers, from lower secondary school, and a didactician from a university in Norway (myself). The thesis offers an account of the relationship between the participants’ development of algebraic thinking and the processes related to the creation and development of a community of inquiry. In addition, the thesis presents elements of the relationship between the teachers’ development of algebraic thinking and their thinking in relation to their teaching practice. My theoretical framework was elaborated according to the criteria of relevance and coherence. In order to conceptualise the participants’ development of algebraic thinking within the community of inquiry, I started from Wenger’s theory of community of practice and expanded it in order to include both the dimension of inquiry and Karpov’s ideas of cognitive and metacognitive mediation. Methodologically, I understand my study as a case study, within a developmental research paradigm, addressing the development of algebraic thinking within a community of inquiry consisting of three teachers and a didactician. The collaboration between the teachers and the didactician was organised through regular mathematical workshops, and interviews with each teacher both before and after classroom observations. During the workshops, the participants engaged with some mathematical tasks which were offered by the didactician. The results of this study indicate that the participants’ development of algebraic thinking is deeply interwoven with the processes related to the creation and development of the community of inquiry. It seems that the participants’ confidence in the community was developing gradually while the confidence in the subject-matter was related to the nature of the mathematical tasks with which the participants engaged. In addition, the study shows how the teachers engaged in a process of both looking critically into their own teaching practice as a consequence of their collaborative engagement within the community of inquiry, and of envisaging possible implications for their future teaching practice. Furthermore, I offer insights into my own development both as a didactician and as a researcher and how these relate to research outcomes. Overall, the thesis contributes to a better understanding of issues related to collaboration between in-service teachers and a didactician from a university, while focusing on the development of algebraic thinking. Implications are also suggested concerning the way algebra could be addressed in schools.