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…

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD,…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

We report a multidimensional test that examines middle grades teachers' understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers' and students' reasoning in this content…

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…

Explores students' abilities in mental computation, finds out the strategies they use most naturally, and develops a theoretical framework by giving 60 children a questionnaire and interviewing them on a series of arithmetic operations to be solved by mental computation. Generates a classification of children's strategies. Contains 31 references.…

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…