These proceedings contain papers presented at the 1993 annual meeting of the Canadian Mathematics Education Study Group. Papers are presented in four sections: (1) invited lectures; (2) working groups; (3) topic groups; and (4) ad hoc groups. Papers include: (1) "What is a Square Root? A Study of Geometrical Representation in Different Mathematical Traditions" (George Gheverghese Joseph); (2) "Forging a Revised Theory of Intellectual Development: Piaget, Vygotsky and Beyond" (Jere Confrey); (3) "Research in Undergraduate Teaching and Learning in Mathematics" (Joel Hillel & Anna Sierpinska); (4) "New Ideas in Assessment" (David Robitaille, Cynthia Nicol, and Heather Kelleher); (5) "Computers in the Classroom: Mathematical and Social Implications" (Geoffrey Roulet and Lars Jansson); (6) "Gender and Mathematics" (Lesley Lee); (7) "Training Pre-Service Teachers for Creating Mathematical Communities in the Classroom" (LaDonna MacRae and Thomas Schroeder); (8) "Connected Knowledge in Prospective Secondary Mathematics Teachers" (Eric Wood); (9) "Narrative Inquiry in Mathematics Teacher Development" (Olive Chapman); (10) "Competences Spatiales Geometriques chez de Jeunes Quebecois du Nord (Inuit) et du Sud" (Richard Pallascio and Richard Allaire); (11) "Projet d'Auto-apprentissage Informatise" (Bernard Vanbrugghe); (12) "Teaching and Learning University Level Mathematics: Perspectives of a Mathematics Educator" (Mary L. Crowley); (13) "Windows and Mirrors: Metaphors for Computer Screens" (David Pimm); and (14) "Pre-Formal, Formal, and Formulaic Proving" (David Reid). Appendices contain lists of participants and previous proceedings. (JRH)