Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…

Children's thinking follows natural developmental paths in learning math. When teachers understand those paths and offer activities based on children's progress along them, they build developmentally appropriate math environments. The authors explain math learning trajectories and why teaching math using the trajectories approach is effective. A…

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…

Studies of young children's sequence of development from counting to the beginnings of formal arithmetic are reviewed. Four essential basic skills are identified: use of counting words, enumeration, the cardinality rule, and quantitative comparison. The contribution of counting to the development of arithmetical proficiency is stressed. (JDD)

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

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…

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)

Bilingual mathematics competencies and competency-coordinated activities are provided in the four sections of this curriculum guide for kindergarten (pre-operational) and grades 1-3 (concrete-operational) children. Topic areas for kindergarten include: classification (logic); comparing/ordering/graphing; quantitative; measurement; geometry;…