The author's theories concerning the learning of mathematical concepts are outlined. (SD)

This review synthesizes research on relationships between performance on mathematics learning tasks to determine whether Piagetian tasks make useful readiness measures. Results indicated such tasks do not make useful measures, and suggested success on these is not necessary for many mathematics tasks. (MP)

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

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)

Students in Papua, New Guinea were given a test in which the words more and less were used in different contexts. Half the pupils studied had English as their first language; for the other half English was a second language. Study results of pupil errors suggested serious educational implications. (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)

Ideas on a teaching-learning theory of ratio are presented. Views of children and of members of an international panel are presented, and five questions and their responses are compared with real classroom experience. (MNS)

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…

A training experiment with 30 mentally handicapped children tested two models of mental-arithmetic development. Children's initial responses to a mental-addition task appeared to be the product of a mechanical prescription. Errors appeared to be more errors of method than of recall. (MNS)

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 a longitudinal constructivist teaching experiment analyzing children's ways of operating while solving fraction tasks. A case study of one third grader found that the evolution of her fraction schemes was the product of her cognitive activity and her collaborative interaction with the teacher. (42 references) (Author/MKR)

The theoretical and reference frameworks developed in a 1982 study proved effective for developing a constructivist approach leading children to build a meaningful and efficient symbolism of number. Results of a three-year longitudinal study are described. (MNS)

Examines two days of teacher-led large group discussion in a 5th grade class about a mathematical question intended to support student exploration of relationships among fraction and decimal representations and rational numbers. Illuminates the teacher's work in supporting student thinking through the use of a mathematical question embedded in a…