This paper proposes a semantic analysis in which meanings of word problems are structures that include class and order relations, and suggests a hypothesis of developmental levels that can account for children's performance of these problems at various ages. The different kinds of problems vary in the complexity of semantic structures and the…

The author interprets several mathematical concepts as groupings using Piaget's definition. He also discusses (briefly) the implications for primary education. (SD)

The author takes exception to Piaget and Inhelder's conclusion that a child's first conceptualization of space is topological. (JP)

Six seven-year-old children were interviewed to investigate the quality of their solutions to whole-number tasks. Detailed analyses are provided of interviews with a girl who displayed an operative counting scheme (numerical extension) and a boy with a figurative counting scheme (intuitive extension). (MNS)

The hypothesis investigated is that understanding of the long division algorithm requires a higher cognitive level than understanding of fundamental division concepts. Sixth-grade children were tested on performance and understanding of a given algorithm and concepts of division. (MP)

A review of work related to the topological primacy thesis and a critique of some aspects of it are presented. On the basis of the psychological research, it is concluded that topological concepts ought to be taught. (MP)

Experiments by Russian educators on teaching algebra in elementary grades are summarized by the author. The algebra taught consisted of generalized solutions to concrete problems that are usually presented with fixed numerical values. (JP)

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…

In everyday teaching, the mathematical meaning of new knowledge is frequently devalued during ritualized formats of communication and replaced by social conventions. Specific aspects of the problem of meaning development were investigated in two second-grade teaching cases. These were used to develop decisive requirements for maintenance of an…

In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)

Several critical questions concerning the topological primacy thesis were raised in an extensive literature survey (SE 531 428). Three points related to this criticism are discussed and reinforced, including a reexamination of Laurendeau and Pinard's data (showing that they do not support the hypothesis of topological primacy in children's…

This study considers two problems related to cognitive development: "Is development hierarchical?" and "If so, what are the mechanisms involved in the process of development?" Analysis of the results of an experiment lead to differentiation of stages of development, and problem-solving strategies at each level are discussed.…

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)

Discussed is the type of evidence children find to be convincing using either empirical or deductive methods to justify propositions which they consider to be true. Included are the problem, research design, and the conclusion. (KR)