Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

This study examined above-grade-level abstract reasoning abilities of 150 students (grades 2-6). Understanding of abstract concepts varied by age for only four of eight subscales or concepts: probability, proportion, momentum, and frames of reference. Performance varied widely within age level for the understanding of volume, correlation,…

The effects of problem size on judgments of commutativity by 51 moderately and mildly retarded students were investigated. Results indicated that many retarded students who are given computational practice recognize the general principle that addend order does not affect the sum. (Author/DB)

Examines the early learning experiences of great men and women mathematicians to determine whether their lives were stimulated in symbol modes that generated semiautonomous cognitive systems of acquiring, processing, and originating vast complexities of abstract mathematical concepts. (HOD)

This study sought to determine the basis for young children's understanding of fundamental addition and subtraction processes, and to expose any limitations on such arithmetic reasoning. Thirty-six two-year-olds and 36 three-year-olds participated in six experiments which examined children's relational quantity judgments about pairs of arrays in…

The pamphlet examines the kinds of play that are useful in developing the basis for later abstract thinking--specifically the development of mathematical concepts. The mathematical concepts included are numbers, conservation, one-to-one correspondence, counting and sequencing, ordering, sorting and classification, sorting and sets, and equivalence…

Pragmatic and semantic problem solving are examined as processes that enhance acquisition of mathematical knowledge. It is suggested that development of mathematical cognition involves restructuring and that math teachers can help restructure children's knowledge systems by providing them with situations in which semantic and pragmatic problem…

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before receiving instruction in the domain. Student thinking was analyzed in terms of mathematical components critical to proportional reasoning. Two components, relative thinking and unitizing, were consistently related to higher levels of sophistication…

Research conducted at the Institute of General and Pedagogical Psychology of Moscow, and based on the premise that the development of thought processes is a direct product of the social environment, is described. As a corollary to this premise, Piaget's view that the development of the thinking process occurs in orderly fashion is questioned.…

Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)

The range of meanings of "big" and "little" that mothers and their three children under age two expressed in relatively natural communication situations was studied. Longitudinal data from transcripts of conversations of middle-class mothers and their children were analyzed along with diary records kept by parents of their children's use of size…

Discusses the use of writing to enhance learning in mathematics from a conceptual development perspective. Shuell's phases of learning are described as a general model for conceptual development and subsequently matched with Britton's categories for transactional-informative writing. Sample mathematics assignments for each writing category are…

The researcher conducted a six-month ethnographic study as an apprentice carpenter in Cape Town, South Africa, to document the valid mathematical ideas that are embedded in the everyday woodworking activities of a group of carpenters. A secondary objective was to examine and to give a firsthand account of the teaching and learning of mathematical…