This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives--mathematics, mathematics education, cognitive psychology, and evolutionary psychology--each offering a different view on mathematical thinking and learning and, in particular, on the…

Research in mathematics education usually attempts to look into students' learning and other mental processes. It could therefore be expected to build on knowledge acquired within the academic discipline of cognitive psychology. Our aim in this paper is to show how some recent developments in cognitive psychology can help interpret empirical…

Presents evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale, and angle. Participants responded to a simple but non-standard task concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches termed…

Answers Burn's question related to a previous study on the nature of knowledge about abstract algebra. Claims that a previous paper presents research that attempts to contribute to knowledge of how students' understanding of certain group concepts may develop instead of teaching abstract algebra with the computer software ISETL. (ASK)

Analyzes students' productions, taking affective and social factors into account. Uses the technique of virtual monologue to reproduce the student's voice in order to describe as vividly as possible what might be going on in the student's mind during such situations. (AIM)

The LOGO subroutine turtle geometry and Euclidean geometry are compared with respect to their treatment of similarity and difference of plane figures. The problem and its proposed solution of introducing a FLIP operation are viewed briefly from the perspectives of mathematics, computer science, and education. (MDH)

Undergraduates in an abstract algebra course were interviewed to see how they learned the concept of isomorphism. Analysis showed students used step-by-step procedures, exhibited various degrees of personification in their language, and chose properties they perceived as simpler. (MKR)