This report describes the first of three stages in a study in the domain of problem solving: the definition and explication of schema knowledge. One objective of this research is to understand how schema knowledge is acquired and used in the chosen domain. The focus is on ways in which instruction influences the development of specific knowledge…

Examines the role that memory plays in the understanding of mathematics. Areas discussed include: retention research; memory and teaching; structure and organization in memory; and transformations in memory. Relevant research and implications for instruction are addressed. (JN)

Discussed are the results of a study which suggests that people remember more mathematics and other high school material when learning occurs spaced out over several years and when each subsequent session involves broader applications of previously learned information. Highlights of this study and related studies are presented. (CW)

Discusses the organization and retrieval of information. Describes the tip-of-the-tongue state during mathematics problem solving. Provides five rules for a deep level of processing of new concepts. (YP)

To determine whether children's knowledge of arithmetic facts becomes increasingly "automatic" with age, 7-year-olds, 11-year-olds, and adults were given a number-matching task for which mental arithmetic should have been irrelevant. Specifically, students were required to verify the presence of a probe number in a previously presented pair (e.g.,…

Proposes a theory of cognitive processes in doing and learning place value arithmetic. Discusses a computer model that simulates the learning of multicolumn subtraction under one-on-one tutoring to measure the relative difficulty of two methods of subtraction. The model predicts that regrouping is more difficult to learn than an alternative…

In the past 15 years, educators and education researchers have increasingly emphasized the importance of cognitive processes for effective education in mathematics and science. This may be characterized as a shift away from the epistemology which treats knowledge as a compilation and categorization of facts toward the notion that knowledge is the…

Secondary education of students with learning and behavioral disabilities is an issue of great importance. Unlike elementary schools, secondary schools require substantially more independent functioning, assume the effective use of student planning and study skills, and often lack the classes in basic skills needed by some learners. Further, new…