Cognitive scientists investigate mental models (how humans organize and structure knowledge in their minds) so as to understand human understanding of and interactions with the world. Cognitive and mental model research is concerned with internal conceptual systems that are not easily or directly observable. The goal of this research was to…

Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (YP)

Proposes using a hypermedia authoring program as a method for helping students make connections between definitions, representations, and applications of mathematical concepts. Provides an example involving fractions and discusses the advantages of using hypermedia. (eight references and four resources) (MDH)

Diagnoses of students' performance on procedural mathematical tasks need to display a certain level of stability and robustness if they are to be used as the basis for remediation, particularly with computer-delivered instruction. The purpose of this study was to compare two diagnostic approaches for describing students' (n=231) errors in algebra…