This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Synthesizes research on content knowledge of rational numbers, the learning of rational number order and equivalence concepts, and teachers' pedagogical reasoning about these concepts. Uses teachers' descriptions of how a hypothetical student would understand rational numbers to sketch a formative model of pedagogical reasoning. (16 references)…

Examines the concept of number sense in mathematics learning, compares this concept to that of phonological awareness in reading, and urges application of existing research to improving mathematics instruction for students with mathematical disabilities. Reviews research on building automaticity with basic facts, adjusting instruction to address…

Examines current research on brain development, focusing on infants' ability to understand basic numerical concepts and arithmetic operations. Asserts that as the brain undergoes dramatic transformations, it already has a built-in capacity to understand basic numerical concepts. Recommends that parents and professionals engage in activities…

Reviews evidence against theories about preschool childrens' egocentricity and cognitive ineptness in the areas of classification, communication, number and order concepts, memory skills, and capacity for reasoning about causal relationships. Holds that preschoolers have been misunderstood because researchers tend to approach them with tasks…

Discussed is research which shows, in contrast to the dominant impression given by Piaget's work, that before the onset of schooling the young child possesses several kinds of fundamental "intuitions" concerning numbers. (Author/TG)

Describes Vygotsky's zones of proximal development, the importance of social interaction in learning through problem solving, and the benefits of modeling. Presents three implications for teaching and learning mathematics based on a teaching experiment focusing on these constructs. (MDH)

This is volume 6 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. This book contains both a theoretical examination of the connection between instruction and the development of children, and experimental data on a definite…

This paper describes the current debate over developmentally appropriate teaching practice. The paper presents the perspective of multicultural educators, who argue that developmentally appropriate practice is biased toward white, middle-class values, and the perspective of special educators, who argue that modification of developmentally…