Children's mathematical knowledge at school entry varies considerably and predicts long-term achievement outcomes. Differences in children's exposure to math and number talk at home may help to explain variations in school-entry math ability. However, nearly all research on exposure to math and number talk has been conducted with parents and…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

The aim of the study is to examine how toddlers (33 months) with weak mathematical skills differ from their peers, the extent to which those weak skills persist into preschool age (57 months), and how the group with persisting weak skills differs from the group with temporary weak skills. Participants were 692 children (344 girls, 348 boys). The…

Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

For learning math, non-symbolic quantity skills, symbolic skills and the mapping between number symbols and non-symbolic quantities are all important precursors. Little is known, however, about the interrelated development of these skills. The current study focuses on numerical development by: (a) investigating the structure of non-symbolic,…

We review recently published papers that have contributed to our understanding of how the preverbal infant represents number, area and time. We review evidence that infants rely on two distinct systems to represent number nonverbally and highlight the similarities in the ratio-dependent discrimination of number, time and area. Contrary to earlier…

This study sought to determine whether a number of specific counting and numeration behaviors emerge within children in a fixed developmental sequence; at what point in the development of mathematical behavior the use of numerical representations normally appears; and what relationship holds between development of counting skills and development…

Noting that current research on childrens mathematical development does not adequately detail how toddlers represent small numbers and the role that number words play in the development of number understanding, this study used a combination of methods to examine mathematical development in one toddler. Underlying the study was an Integrated Model…

Explored whether a system between written place-value system and base-10 manipulatives helped children understand place-value. Found evidence that the intermediate system helped children differentiate between face values and complete values of digits in multidigit place-value number representations, and to grasp that the sum of the digits'…

Discusses the relationship between geometrical and numerical concepts in the mathematical development of young children. Based upon a longitudinal field study of 224 children, findings suggest that memorization ability facilitates understanding of numerical concepts but that subsequent mathematical development is restricted until basic geometry is…

Two sections in this survey of research on conceptualization are devoted to "Recent Conceptual Studies in the Behaviourist Mould" and "Main Stream of Ontogenetic Studies of Conceptualization." Under Section I, topics investigated are behaviourist approaches to the conceptual process, conceptual problems, and developmental…

This document was developed to provide some perspectives on the use of case studies and other clinical approaches in mathematics education. A large portion of the paper contrasts several research strategies, discussing in detail some of the procedures and results of three distinctive types of clinical studies. The perspectives and the premises of…