Search

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 source of mathematical errors and on ways of dealing with them in the classroom. The four perspectives represent four levels of explanation, and we see them not as competing but as complementing each other. In the classroom or in research data, all four perspectives may be observed. They may differentially account for the behavior of different students on the same task, the same student in different stages of development, or even the same student in different stages of working on a complex task. We first introduce each of the perspectives by reviewing its basic ideas and research base. We then show each perspective at work, by applying it to the analysis of typical mathematical misconceptions. Our illustrations are based on two tasks: one from statistics (taken from the psychological research literature) and one from abstract algebra (based on our own research). [ABSTRACT FROM AUTHOR]

How do undergraduate students cope with abstract algebra concepts? How should we go about researching this question? Based on interviews with undergraduate students and on written questionnaires, a theoretical framework evolved which could coherently account for most of the data. According to this theoretical framework, students‘ responses can be interpreted as a result of reducing the level of abstraction. In this paper, the theme of reducing abstraction is examined, based on three interpretations for levels of abstraction discussed in mathematics education research literature. From these three perspectives on abstraction, ways in which students reduce abstraction level are analyzed and exemplified. [ABSTRACT FROM AUTHOR]