The authors present 2 experiments that establish the presence of knowledge partitioning in perceptual categorization. Many participants learned to rely on a context cue, which did not predict category membership but identified partial boundaries, to gate independent partial categorization strategies. When participants partitioned their knowledge,…

This paper contains the comments of a discussant reviewing the paper, "The Role of Visual Representations in the Learning of Mathematics" (Abraham Arcavi). A research-based evaluation is made that focuses on the ideas of stochastics and the epistemological triangle. (Contains 28 references.) (DDR)

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…

This paper focuses on some cognitive and didactical phenomena that feature processes and products of pupils in grades 7-12 who learned mathematical proof within technological environments. The main issues in the analysis of students' performances consist of metaphors, deictics, mental times, narratives, functions of dragging, abductions, and…

Interacting cognitive subsystems (ICS) is proposed as a unified cognitive theory that can be used as the basis for representations in human-computer interaction, and two approaches based on the theory are described: one entails the description of cognitive task models, and the other entails the production of less complete diagrammatic notations.…

The Student-Centered Activities for Large Enrollment University Physics (SCALE-UP) project at North Carolina State University (NCSU) is developing a curriculum to promote learning through in-class group activities in introductory physics classes up to 100 students. The authors are currently in Phase II of the project using a specially designed…