This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive linguistics. It discusses Mathematical Idea Analysis, a set of techniques for studying implicit structures in mathematics. Particular attention is…

Identifies certain conceptions regarding the science content studied by students aged 9-11 years and develops a strategy for altering these conceptions. Reviews research on misconceptions and defines action research. (DDR)

This paper focuses on some main distinctions that are necessary to analyze mathematical knowledge from a learning point of view and explain how many students come up against difficulties at each level of the curriculum. From a learning point of view, visualization cannot be used as an immediate and obvious support for understanding, even though it…

Interest in mathematics learning that focuses on understanding, mathematical reasoning, and meaning-making underscores the need to develop ways of analyzing classrooms that foster certain types of learning. The goal of this paper is to show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic…