Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…

Through the historical analysis of Dienes' works and through the suggestions of activities, the objective of this text is to understand the movement of systematization of knowledge for teaching and to teach classification, ranking, and ordination through the use of logical blocks during the Modern Mathematics Movement (1960-1980), a time of…

This article describes a comprehensive and novel approach to assessment in early numeracy. Topics include the significance of early numeracy, developing a nomenclature for early numeracy, and describing the context for the development of this approach to assessment. The largely unrealised importance of numerals and numeral sequences in early…

Describes a teaching experiment conducted over a period of four consecutive days with 13 fourth grade students who had already completed a unit of fractions to determine whether problematic size was the ordering criteria. Concludes that children can indeed order fractions as they do natural numbers. (Contains 11 references.) (ASK)

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

This book suggests creative, classroom-tested mathematics activities to teach number recognition and counting, number formation, sorting and classification, measuring (including time and date), shapes, graphing, estimating, ordinal positions, money, patterning, tallying, and fractions. Activities are presented in the forms of games, crafts, songs,…

Two experiments involving a total of 40 three and 39 four year olds were undertaken to determine subjects' ability to sort and compare numbers according to magnitude. Results indicate that readiness skills for early childhood mathematics education should include development of appropriate concepts of number magnitude. (TJH)

Presents two activities on addition, one for classifying and one for symmetry. (ASK)

Discusses the importance of experiences with classification and seriation in aiding children to understand the concept of number. (GB)

Various types of computerized sorting techniques are demonstrated with cardboard materials children can manipulate. Bubble, ripple, and binary sorting are each illustrated. (MNS)

This paper presents an overview of the Comprehensive School Mathematics Program (CSMP) elementary school mathematics curriculum. The philosophy behind the program, content goals, and teaching strategies are briefly discussed. Then ways in which the program develops facility in mathematics are described in discussions of the language of arrows, in…

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…

This article discusses the challenge mathematics educators face in deciding what and how mathematics is to be taught, and offers some suggestions for teachers of young children based on Piaget's developmental theory of mathematics. Piaget's cognitive stages are briefly described and the concrete stage, which spans the age range included in early…