As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

By varying task conditions and constraints on subjects, this study attempted to extend and refine a developmental theory of partitioning as a foundational process undergirding children's construction of a rational number. Subjects were 31 preponderantly higher-grade pupils enrolled at an elementary school in Nova Scotia, Canada. Two tasks were…

This article describes a recent and successful initiative on teaching place value and the decomposition method of subtraction to pupils having difficulty with this technique in the 9-12-year age range. The aim of the research was to explore whether using the metaphor of selling chews (i.e., sweets) in a tuck shop and developing this into an iconic…

Wishing to explore the complexity of the conceptual, didactic and institutional aspects of learning a scientifically defined object of knowledge, we chose to study the link between the personal relation to numeration developed by six-year-old pupils in first grade ("cours preparatoire" the first level of primary school in France), and…

This paper discusses a study that explored the mental models of fifth (n=35) and sixth (n=49) graders attending two urban public elementary schools in South Korea in word problem solving. Two levels of mental models (problem model and mathematical model) constructed in the process of word problem solving were investigated. Coding categories for…

Describes a program in second-grade Dutch mathematics classes that emphasizes mental addition and subtraction of two-digit numbers up to 100. Deals with a strategy of counting by 10s from any number. (Contains 56 references.) (RLB)