Research reports typically focus on the findings of research and pay scant attention to the methodological issues--both practical and theoretical--which arise while carrying out the research. These are the proceedings of a symposium that attempted to address this situation by focusing on the practical and theoretical aspects of a range of research methodologies. The symposium was organized around four themes: (1) Qualitative Analysis with and without Computers; (2) Strategies for Probing Student Understandings; (3) Participatory Research into Teaching; and (4) Surveying the Scene. The emphasis was on the methodologies employed for conducting the research. This book includes an introduction; four sections that represent the four symposium themes, each including an overview, the papers presented, and the discussion; and a list of participants. Subjects include mathematics in engineering; historiography; computer-aided mathematics support; use of technology in researching mathematics teaching; analysis of questioning skills; phenomenography; action research; and the interaction of gender, mathematics, and computers. (PVD)