The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…

Describes an earlier study on the main characteristics and background of undergraduate students' difficulties when trying to solve mathematical tasks. Focuses on and extends part of an earlier study that concerned task solving strategies. Indicates that focusing on what is familiar and remembered at a superficial level is dominant over reasoning…

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

This study presented contextual problems involving rational numbers and proportional reasoning to 7th-grade students with different curricular experiences. Evidence indicates that students in reform curricula, who are encouraged to construct their own conceptual and procedural knowledge of proportionality through collaborative problem-solving…

Presents a theoretical framework based on interviews with undergraduate students and written questionnaires to study how undergraduate students cope with abstract algebra concepts. Indicates that students' responses can be interpreted as a result of reducing the level of abstraction. Examines the theme of reducing abstraction based on three…

Beginning geometry students misunderstand the requirements of formal proof because of confusion between deductive reasoning and argumentation. Presented is a cognitive analysis of deductive organization versus argumentative organization of reasoning and the applications of this analysis to learning. Implications of a study analyzing students'…