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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]

This work examines the Israeli National Informatics--Computer Science (CS) Olympiad from the perspective of diversity. A conspicuous phenomena in this olympiad (as well as in other science olympiads) is that very few females participate in the national competition, and none has ever represented the country in any international competition. When examining this phenomenon more closely, but with a broader view, it appears that while the level of external diversity (which addresses characteristics such as gender and race) is quite low also with respect to additional aspects, it does increase with respect to internal traits (such as ways of thinking). Furthermore, alongside the low external diversity among the participants, there are many common features among those who influence students' participation in the competition. This descriptive article outlines the background of the research, the research setting, and, as previously mentioned, examines its findings from the perspective of diversity. [ABSTRACT FROM AUTHOR]

This paper discusses the role of reduction in computer science and describes a study on undergraduate students' perception of the concept of reduction. Specifically, based on an analysis of students' answers to questions addressing different computer science topics, we present several findings regarding the ways in which undergraduate students conceive of and apply reduction. These findings can be interpreted within the framework of the tension that exists between the following two factors: The need to think in terms of high levels of abstraction, on one hand, and the fact that reduction introduces a new approach to be used in problem-solving situations, on the other. In addition the paper suggests several teaching applications. [ABSTRACT FROM AUTHOR]

This article presents research on students' understanding of basic concepts in Graph Theory. Students' understanding is analyzed through the lens of the theoretical framework of reducing abstraction (Hazzan, 1999). As it turns out, in spite of the relative simplicity of the concepts that are introduced in the introductory part of a traditional Graph Theory course, some students exhibit ways of thinking that indicate a reduction of the level of abstraction. The importance of this study is derived from the importance of graph algorithms in any computer science curriculum and the centrality of the concept of abstraction in computer science education. [ABSTRACT FROM AUTHOR]

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. “Reducing abstraction” is a theoretical framework that examines learners’ behavior in terms of coping with abstraction level. It refers to situations in which learners are unable to manipulate concepts presented in a given problem; therefore, they unconsciously reduce the level of abstraction of the concepts involved to make these concepts mentally accessible. This framework has been used for explaining students’ conception in different areas of undergraduate mathematics and computer science. This article extends the applicability scope of this framework from undergraduate mathematics to school mathematics. We draw on recently published research articles and exemplify how students’ behavior can be described in terms of various interpretations of reducing abstraction level. [ABSTRACT FROM AUTHOR]