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This study explores learning mathematics for teaching through a particular enactment of e-formative assessment, a series of six online study sessions. The data involved 173 student teachers registered on the Bachelor of Education (BEd) degree programme within a School of Education of a Scottish University. It is located within a relatively uncharted area of formative assessment where our attention is refocused from the assessor to the learner's perspective. The aim to develop mathematical understanding and a greater sense of autonomy meant looking for those ‘cracks where the light gets in' rather than ‘gaps to be bridged': a more divergent approach to formative assessment which required a delicate orchestration of social, pedagogical and technological systems. A mixed methods multistrand parallel design was used to take a stereoscopic view of learner interactions with the online study sessions. The concepts and methods within this thesis are not necessarily new, however the way they have been brought together is innovative. These have been used not only to support student teachers in developing their own mathematical understanding but also to let them experience different ways of working with children. A conceptual framework developed for practising teachers and activity types designed for a mathematics classroom have been adapted for student teachers in a mathematics education classroom. Findings indicate that the capacity to change habits and to understand the reasoning of others is more important than formal mathematics qualifications. An informed design and use of e-formative assessment can support student teachers in developing their mathematical reasoning where it is embedded within their experiences of learning mathematics for teaching involving both specialised mathematical knowledge and mathematical pedagogical content knowledge. As such, this study hopefully adds to and provides another perspective on e-formative assessment and mathematics education, in particular, learning mathematics for teaching.

The Revised National Curriculum requires that mathematics teachers make shifts in their pedagogical content knowledge about teaching non-routine problems. One of the shifts is to move from a traditional approach of teaching routine tasks to an approach which includes problem solving. Teaching non-routine problems develops flexible forms of knowledge, which allow learners to construct their own strategies and not merely follow steps shown to them by the teacher. In this study I explore what pedagogical content knowledge grade 6 teachers have about problem solving in everyday and mathematical contexts. A qualitative study was used to explore Grade 6 teachers’ pedagogical content knowledge about problem solving in these contexts. Data was collected by means of interviews and lesson observations. The study found variations in the teachers’ content knowledge but very similar pedagogical content knowledge among the teachers. Teachers have different understandings of teaching non-routine problems and they are faced with the challenge of how much to make knowledge accessible to their learners in order to lay a conceptual foundation to solve non-routine problems while not lowering the demands of the task. Teachers taught everyday context tasks differently to mathematical context tasks by focusing on the linguistic aspects of the tasks.

Thesis (M. Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 86-90).

Thesis (M.Ed.)--University of Central Florida, 2009. / Adviser: Juli Dixon. Includes bibliographical references (p. 65-68).

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 241-251). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 137-141). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 137-141). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 198-214).

Thesis (Ph. D.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 170-174).