The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from…

In this article we first review evidence for the approximate number system (ANS), an evolutionarily ancient and developmentally conservative cognitive mechanism for representing number without language. We then critically review five different lines of support for the proposal that symbolic representations of number build upon the ANS, and discuss…

In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

The synergistic potential of cognitive neuroscience and education for efficient learning has attracted considerable interest from the general public, teachers, parents, academics and policymakers alike. This review is aimed at providing 1) an accessible and general overview of the research progress made in cognitive neuroscience research in…

The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…

The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties. The authors evaluated 25 experimental and quasiexperimental studies according to…

In this article, we provide an overview of current knowledge on the underlying cognitive deficits associated with mathematics learning disabilities (MLD). We highlight difficulties surrounding the identification of MLD that include inconsistency in defining MLD, comorbidity with other disabilities, problems associated with assessment tools and…

The behavioural phenotype of velocardiofacial syndrome (VCFS), one of the most common human multiple anomaly syndromes, includes developmental disabilities, frequently including intellectual disability (ID) and high risk of diagnosis of psychotic disorders including schizophrenia. VCFS may offer a model of the relationship between ID and risk of…

This report describes phase 1 of a projected 2-phase project designed to investigate the feasibility of developing an interactive videodisc to teach math and science concepts to preschool handicapped children. A videodisc system is proposed that would allow children to manipulate real-world objects in order to acquire concrete knowledge about…