Examines the role that memory plays in the understanding of mathematics. Areas discussed include: retention research; memory and teaching; structure and organization in memory; and transformations in memory. Relevant research and implications for instruction are addressed. (JN)

Varying approaches to mathematics were raised in a Philosophy of Mathematics course. Students were asked which foundational schools they preferred and these preferences were compared with scores on hemispheric tests. The results indicate that preferences may be related to the brain's hemispheres. (MNS)

The mental activities involving functions were studied with 60 children aged 4-15. Search strategies used for solving a problem reveal different stages toward the discovery of the monotonic property, which correspond to stages of proportional reasoning found by Piaget. Dependence between stage and age is confirmed. (Author/MNS)

Features and tools to outline and shape the long-term learning process for ratio are presented, with examples. Ratio-anticipating activity and creating visual models and schemes are stressed, with the basis for a theory of teaching and learning ratio presented. (MNS)

The behavior of one child as she constructed knowledge about fractions over a nine-month period is presented. The intent is to explain behavioral patterns for which certain mental processes, called schemes, seem responsible. (MNS)

Mathematical creativity is considered important by many mathematics educators. This literature review gives particular attention to attempts to assess creative ability. Two key aspects emerge related to fixations in problem solving and divergent production, and these might form the basic framework for fostering and rewarding mathematical…

The relationship between arithmetical concepts and solution methods is discussed. A case study illustrates the contention that some children with relatively sophisticated concepts express those concepts with primitive methods. (MNS)

Proportion problems were given to pupils in grades 3-5. Success rates were high, with elementary strategies based on addition often used. Familiarity with the use of ratios in the context, the presence of a mixture, and the use of manipulatives were variables that influenced performance. (Author/MNS)

Use of general mathematical strategies by Australian students in grades 8-10 was studied, with students required to describe their reasoning and articulate reasons for the choice of particular strategies. Main effects were found for cognitive level, year level, and sex. A taxonomy is also presented. (MNS)

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)

Describes a study to determine middle school children's representational strategies to form part-whole or part-part relationships for relational numbers such as proportions, ratios, or fractions. Quantitative and qualitative analysis revealed that children prefer a part-part representation to solve relational quantity problems. (15 references)…

This study, part of a longitudinal investigation, examined the kinds of thinking which children aged 10 and 11 could carry over from Logo instruction to an algebraic context. Interviews focused on their ability to construct meaningful symbolization for the concept of variable and to construct formalized algebraic rules. (MNS)

Discussed are the roles played by anticipation, belief, and motivation in two young children's problem-solving activity. It is argued that a solver's beliefs and motivations are intimately related, and that the discussion of the two children's behaviors may have some generality. (Author/MNS)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

The literature on proportional reasoning is reviewed. After methodology is discussed, strategies used to solve proportion problems, variables that influence performance, and training studies are each considered. (MNS)