This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis…

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

This article reports on a study which used the APOS (action-process-object-schema) Theory framework and a classification of errors to investigate university students' understanding of the integration concept and its applications. Research was done at the Westville Campus of the University of KwaZulu-Natal in South Africa. The relevant rules for…

With COVID-19 continuing to make meeting face-to-face impossible, the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) executive decided that, for the first time, the CMESG/GCEDM meeting would be held virtually. By necessity, the program had to be much compressed with no topic…

This study highlights ways in which generative activities may be coupled with network-based technologies in the context of teacher preparation to enhance preservice teachers' cognizance of how their own experience as students provides a blueprint for the learning environments they may need to generate in their future classrooms. In this study, the…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

Develops and validates an instrument for determining student preferences for multiple representations of functions and establishes baseline data for future research. Students showed preferences for representations of functions which varied between contextualized and noncontextualized settings. Students' preferences for the two settings were more…

This book for future mathematics teachers emphasizes technology as a teaching tool; development of teachers who are self-motivated, lifelong learners; and pedagogical features that engage and motivate students. It includes examples and activities to enhance learning. Part 1, "General Fundamentals," includes (1) "Introduction"; (2) "Learning,…