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

摘要

In this thesis I report from a study of the development of algebraic thinkingof three teachers, from lower secondary school, and a didacticianfrom a university in Norway (myself). The thesis offers an account of therelationship between the participants’ development of algebraic thinkingand the processes related to the creation and development of a communityof inquiry. In addition, the thesis presents elements of the relationshipbetween the teachers’ development of algebraic thinking and theirthinking in relation to their teaching practice.My theoretical framework was elaborated according to the criteria ofrelevance and coherence. In order to conceptualise the participants’ developmentof algebraic thinking within the community of inquiry, Istarted from Wenger’s theory of community of practice and expanded itin order to include both the dimension of inquiry and Karpov’s ideas ofcognitive and metacognitive mediation.Methodologically, I understand my study as a case study, within adevelopmental research paradigm, addressing the development of algebraicthinking within a community of inquiry consisting of three teachersand a didactician. The collaboration between the teachers and the didacticianwas organised through regular mathematical workshops, and interviewswith each teacher both before and after classroom observations.During the workshops, the participants engaged with some mathematicaltasks which were offered by the didactician.The results of this study indicate that the participants’ developmentof algebraic thinking is deeply interwoven with the processes related tothe creation and development of the community of inquiry. It seems thatthe participants’ confidence in the community was developing graduallywhile the confidence in the subject-matter was related to the nature ofthe mathematical tasks with which the participants engaged. In addition,the study shows how the teachers engaged in a process of both lookingcritically into their own teaching practice as a consequence of their collaborativeengagement within the community of inquiry, and of envisagingpossible implications for their future teaching practice.Furthermore, I offer insights into my own development both as a didacticianand as a researcher and how these relate to research outcomes.Overall, the thesis contributes to a better understanding of issues relatedto collaboration between in-service teachers and a didactician froma university, while focusing on the development of algebraic thinking.Implications are also suggested concerning the way algebra could be addressedin schools.