Complementary to existing "normative" models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical…

While some researchers place negative numbers on a so-called extended mental number line to the left of positive numbers, others claim that negative numbers do not have mental representations but are processed through positive numbers combined with transformation rules. We measured spatial associations of negative numbers with a modified implicit…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Inferences about student knowledge, skills, and attributes based on digital activity still largely come from whether students ultimately get a correct result or not. However, the ability to collect activity stream data as individuals interact with digital environments provides information about students' processes as they progress through learning…

As the use of educational technology becomes more ubiquitous, an enormous amount of learning process data is being produced. Educational data mining seeks to analyze and model these data, with the ultimate goal of improving learning outcomes. The most firmly grounded and rigorous evaluation of an educational data mining discovery is whether it…

Research has shown that the tools provided by dynamic geometry systems (DGSs) impact students' approach to investigating open problems in Euclidean geometry. We particularly focus on cognitive processes that might be induced by certain ways of dragging in Cabri. Building on the work of Arzarello, Olivero and other researchers, we have conceived a…

Recent studies have used spatial reorientation task paradigms to identify underlying cognitive mechanisms of navigation in children, adults, and a range of animal species. Despite broad interest in this task across disciplines, little is known about the brain bases of reorientation. We used functional magnetic resonance imaging to examine neural…

Geometric alterations to the boundaries of a virtual environment were used to investigate the representations underlying human spatial memory. Subjects encountered a cue object in a simple rectangular enclosure, with distant landmarks for orientation. After a brief delay, during which they were removed from the arena, subjects were returned to it…

A quasi-systematic strategy of devising rule sets for problem solving is applied to ruler and compass geometrical constructions. "Lower order" rules consisting of basic skills and "higher order" rules which govern the selection and combination of lower order rules are identified by an analysis of problem types; three types of…

Describes a new theoretical model of the learning process produced by the computer's strict reliance on procedure and its unique methods for managing data. The implications of this model for mathematics learning are illustrated through an experimental paradigm comparing the problem-solving skills of an expert and a novice. (MBR)

Describes the use of infometry, or informational geometry, to meet the challenges of information service businesses. Highlights include theoretical models for cognitive coordination and genetic programming; electronic information packaging; marketing electronic information products, including cost-benefit analyses; and recapitalization, including…

Related to the earlier ACT production system theory, this book's basic goal is to present evidence for the psychological reality of a production system model of mind. Distinguished from the original theory in three ways, this volume uses previous rational analyses to improve upon that theory and extend its scope. It also relates the theory to new…

Summarizes an initial foray in tackling artificial intelligence problems using a connectionist approach. The task chosen is visual recognition of Origami objects, and the questions answered are how to construct a connectionist network to represent and recognize projected Origami line drawings and the advantages such an approach would have. (30…

Hierarchically organized knowledge about actions has been postulated to explain planning in problem solving. Perdix, a simulation of problem solving in geometry with schematic planning knowledge, is described. Perdix' planning knowledge enables it to augment the problem space it is given by constructing auxiliary lines. The planning system also…