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…

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively,…

Research shows that frequent, high-quality mathematics talk that is shared between parents and children can increase mathematics achievement. This article describes ways in which teachers can support parents in increasing the frequency and quality of parent-child mathematics interactions, leading to better outcomes for students.

When observing children playing rhythm echoes with percussion instruments it was noticed that they can repeat a certain number of sounds accurately and that this number increases depending on the children's age and musical experience. It was thought likely that this number has a direct correlation not only with the children's stage of motor…

Small numbers are spontaneously associated with left space and larger numbers with right space (the SNARC effect), for example when classifying numbers by parity. This effect is often attributed to reading habits but a causal link has so far never been documented. We report that bilingual Russian-Hebrew readers show a SNARC effect after reading…

Examines questions about reported findings that the natural number concept derives from a prior understanding of ordination rather than a prior understanding of cardination. (GO)

Establishes two categories of numbers: (1) relatively frequent numbers and (2) relatively infrequent numbers. The numbers in the first group are manipulated by people and depend, at least to some degree, on memorization; those in the second group are essentially machine inputs. Examples of the first group are examined. (SED)

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 study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade…

Multi-shaped blocks can be used to help young children develop many mathematical concepts and abilities. Several suggestions for using these blocks to create problem situations through which children develop concepts are offered. (SD)

The project, consisting of five experiments, attempted to develop remedial procedures and materials for retarded children with learning deficits in the area of arithmetic. Standardized training procedures were devised to facilitate development of operations (conservation, ordination, cardination, and classification) which J. Piaget describes as…

Studies concerned with the synchronous emergence prediction of Piaget's structures-of-the-whole principle are discussed in conjunction with three groups of concrete-operational skills: (1) transitivity/conservation/class inclusion; (2) double classification/double seriation; and (3) ordinal, cardinal, and natural number concepts. Findings show…

This article describes the modifications that 12 early childhood educators in Japan made to the Sorry! board game to encourage kindergartners' logico-mathematical thinking. Logico-mathematical knowledge is described as including classification, seriation, numerical relationships, spatial relationships, and temporal relationships. Examples of seven…

The pamphlet examines the kinds of play that are useful in developing the basis for later abstract thinking--specifically the development of mathematical concepts. The mathematical concepts included are numbers, conservation, one-to-one correspondence, counting and sequencing, ordering, sorting and classification, sorting and sets, and equivalence…

A theoretical discussion of categorization, unit structures and structured units, and fractions as operators was introduced. The thinking of grade-three students (n=3) with regard to the meaning of fractions was investigated in two teaching episodes using the computer environments of SuperPaint and CopyCat. (Contains 14 references.) (MKR)