Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

Primary objective: This study represents the first large-scale research on high school philosophy in a public education curriculum in North America. Our objective was to identify the impacts of high school philosophy, as well as the challenges of teaching it in its current format in Ontario high schools. Research design: The qualitative research…

Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…

This submission contains the Proceedings of the 2008 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Universite de Sherbrooke in Sherbrooke, Quebec. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

The purpose of this study was to compare traditional classification training for a set of abstract concepts with multiple-relations training consisting of inference practice and the use of a content diagram. To examine this, 200 undergraduate and graduate psychology students completed a Web-based tutorial covering the abstract concepts of a…

Psycho-epistemology provides a framework for this study on interrelationships among teachers, subject matter, and learners. Chapter 1 presents the polemics that lead to the problem, including sections on educational divergence, the noncumulative nature of knowledge in education, the divergence of opinion regarding the "best" teaching and…

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…