The relationship between mathematics educators' beliefs and their teaching practices
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This longitudinal study explored the extent to which mathematics education lecturers' constructivist beliefs and aligned practices were communicated to students in a New Zealand primary pre-service teacher education degree programme. An integral part of this exploration was the identification of particular aspects of lecturers' practice that had a significant impact in enhancing the adoption of constructivist ideas on learning and constructivist-aligned teaching practices by student teachers. This goal had a practical focus on more effective course teaching within the chosen philosophical framework of constructivism. At a more theoretical level, there was a focus on the development of a constructivist approach to teacher education for teacher educators through the medium of mathematics education. A potential outcome of the development and widespread adoption of such a constructivist-aligned pedagogy within teacher education could be the significant furthering of a "reform" (or transformative) agenda in school education with its potential for enhanced learning by children. The methodology comprised both quantitative (survey) and qualitative (interview) techniques to collect information which allowed the capture of different but complementary data, so building a "rich" data set. The surveys were conducted using two leaming environment instruments underpinned by particular constructivist perspectives: one focusing on the overall nature of the learning environment at an individual level from a critical constructivist perspective, and the other focusing on the nature of interactions between teacher and student teachers at a classroom level from a socio-cultural constructivist perspective.Surveys were conducted with the lecturers at the beginning and toward the end of the study, while the student teachers in these lecturers' classes were surveyed over a three year period. The interviews were semi-structured following an interpretative (evolving) research approach, with the "results" of ongoing data analysis being fed into later interviews. The interview data were analysed for personal perceptions and understandings rather than for generalisation and prediction with the intention of focusing on the identification of emergent themes. Interviews were conducted with lecturers at the beginning of the study and again toward its conclusion while student teachers were interviewed at the end of the study. The lecturers claimed constructivism as their underlying philosophical belief system and the initial surveys established baseline data on the actual nature of the lecturers' beliefs and how these were perceived by the student teachers. Similarly, the initial interviews explored the espoused beliefs and congruent practices of lecturers and student teachers. These two sets of data were compared to establish their congruence or otherwise. Further interviews with the lecturers focused on the survey data and my reconstruction of what the lecturers had said previously when interviewed. Later survey and interview data were also examined against the baseline data for evidence of change over the four years of the study. The data demonstrated that the student teachers perceived the existence of moderate to strong socio-cultural constructivist-aligned classroom environments when considered at a class (group) level, and a moderate alignment with critical perspectives at the individual (personal) level.There was a high degree of consistency between staff and student teacher views, and the student teachers' views were consistent across the year groups (first, second and third years) and throughout the four years of the study. Lecturer practice(s) congruent with constructivism were the basis for student teacher change toward understanding and their adoption of constructivist ideas and aligned practices. Specific lecturer practices were identified as particularly effective in achieving such change. These effective lecturer practices may assist in establishing the foundations of a constructivist-aligned pedagogy for teacher education. The lecturers' modeling of the practices they were promoting for student teachers' practice was identified as a key element in promoting change. Indeed, the tension between traditional and transfornative approaches was exacerbated in situations where lecturers' promotion of a preferred practice was different from that which they enacted. The continuing existence of such situations and associated tensions has the potential to limit the extent of any change.
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