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…

This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and…

This paper describes Topdown Conceptual Analysis (TCA) and how it can be used to produce the knowledge base for the development of courseware. Some of the prerequisites and basic theories behind TCA are explained. In discussing what is meant by learning and teaching a concept, an explanation is given of how a complex concept can be taught in terms…