The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

This study, based on the analysis of extensive interview data using concepts and models drawn from cognitive studies of human behavior and from artificial intelligence studies of computer information processing, highlights several information-processing differences between strong and weak students. Data were collected from 300 students in grades 3…

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

This investigation capitalizes upon the information processing models that depend upon measurement of latency of response to a mathematical problem and the decomposition of reaction time (RT). Simple two term addition problems were presented with possible solutions for true-false verification, and accuracy and RT to response were recorded. Total…

Uses two studies to examine developmental and task effects in estimation problems. Results are discussed in terms of student and task characteristics and the implications of such variables on information processing model of learning. Implications for science teaching, learning problem diagnostics, and science curricula are also discussed. (TW)