\I thought I was reasonably good at teaching maths\" : the link between principles of practice teacher actions and supportive classroom reflection"

This study aimed to investigate the phenomenon of effective teaching of numeracy and to implement a professional learning process designed to enhance numeracy teaching based on reflection upon classroom practice. The study was undertaken in order to address concerns about numeracy standards, and the perception that mathematical reform practices were not being widely implemented into classrooms. The study builds on existing research into effective numeracy practices and contributes further to developing an understanding of both effective numeracy teaching and effective professional learning. Furthermore, a model that was developed throughout the study presents a new way of examining teachers' practices, and the vivid descriptions of these practices provides an alternative to purely quantitative classroom observations which has been characteristic of similar research in the past. The conceptual framework of the study was based on a model developed by the researcher, informed by both the findings in the literature and observations of the case study teachers' numeracy lessons. The model was used in the study as a means of understanding each teacher's numeracy practice, and incorporated the characteristics of effective teaching of numeracy as identified in the literature, and the relationship between teachers' knowledge, beliefs and classroom practice. In addition, an action research model was devised to guide the Supportive Classroom Reflection (SCR) process that was undertaken with each teacher following the observation of their lessons. The study took the form of a modified case study involving three upper primary teachers working in three different, but geographically similar, schools. A collaborative action research approach was used in the professional learning aspect of the study, with each teacher actively contributing to the research process. In total, 17 numeracy lessons were observed and videotaped by the researcher. Following each lesson, the video footage was viewed together by the researcher and the teacher. Critical incidents were highlighted and the sessions were used to elicit further information about the teaching practices observed and as a basis to encourage teachers to deliberately reflect on their practices. The findings indicated that it was possible to identify a number of characteristics that were associated with effective teaching of numeracy, but not surprisingly, there is no 'one size fits all' approach to effective numeracy practice that can readily be applied by every teacher in every classroom. Although many of these characteristics were present to varying extents in the practices of the teachers, closer examination into the nature of these characteristics revealed that unless teachers understand the pedagogical purpose behind such practices, the practices can be used without being necessarily effective in furthering developing students' numeracy. The combination of teacher knowledge and beliefs also was found to be a significant factor in contributing to the effectiveness of these practices. The SCR process provided an avenue for further discussion around these issues, and the case study teachers all endorsed it as a valuable professional learning experience. The findings from the study are significant in that they indicate that teachers need a clearer articulation of what effective numeracy practices, such as those advocated by mathematical reform, actually 'look like' in the classroom and to understand the pedagogical purposes behind such practices. Teachers need to have access to professional learning that caters to their individual needs, and provides them with opportunities not only to increase their repertoire of strategies, but also to recognize the impact that knowledge and beliefs have on their practice. In addition to being of benefit to classroom practitioners, the study's findings should also inform teacher educators and policy makers about effective numeracy teaching and how this can be addressed through relevant and individualised professional learning experiences.