Outlines Piaget's late ideas on categories and morphisms and the impact of these ideas on the comprehension of the inclusion relationship and the solution of arithmetic problems. Reports a study in which fourth through sixth graders were given arithmetic problems involving two known quantities associated with changes rather than states. Identified…

Examines the concept of number sense in mathematics learning, compares this concept to that of phonological awareness in reading, and urges application of existing research to improving mathematics instruction for students with mathematical disabilities. Reviews research on building automaticity with basic facts, adjusting instruction to address…

All too often educators establish a "pretest, skill, posttest" type of curriculum. While this approach has an educational value, it must be used within a developmental framework based on individual thinking and learning style. Thus, a thorough knowledge of cognitive development is necessary. A review of the body of knowledge concerning…

During the last decades, a shift from studying the product to studies of the processes has become more and more obvious. The major aim of this study was to investigate the mental performance process and to examine the changes the variables describing this process undergo with time. In this investigation, a mental arithmetic test was used. The test…

Discusses the first session and events from other sessions of a mathematics circle consisting of the author and four preschool children. Presents discussions that ensued with the children when asked to solve problems related to Piaget's stages of cognitive development. (MDH)

Presents a developmental framework for the study of culture and cognition in which cultural practice is a key organizing construct. Argues that systematic analysis of either cultural change or cognitive development requires that they be understood relative to one another in a single integrative treatment. (Author/SD)