In a 1-hour teaching interview, 20 children (aged 7 to 11) discovered how to tell whether objects might be made of the same material by using ratios of measures of weight and size. We examine progress in the children's reasoning about measurement and proportional relations, as well as design features of instruments, materials, and tasks crafted to…

Because math knowledge begins to develop at a young age to varying degrees, it is important to identify foundational cognitive and academic skills that might contribute to its development. The current study focused on two important, but often overlooked skills that recent evidence suggests are important contributors to early math development:…

The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the…

In a recent study, Gevers and colleagues (2010, "Journal of Experimental Psychology: General," Vol. 139, pp. 180-190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are…

Examined the relationship between 6- to 8-year olds' conceptual understanding of additive composition, commutativity, and associativity principles and addition problem-solving procedures. Results revealed that conceptual understanding was related to using order-indifferent, decomposition, and retrieval strategies and speed and accuracy in solving…

Critiques findings and interpretations of an investigation of the role of schooling and urbanization on the acquisition of conservation of physical quantities in Senegalese children. Concludes that the investigation showed a smaller impact of schooling, even in the rural milieu, than a previous study of Senegalese children. (RJC)

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'…

Three experiments were conducted to examine children's use of multiplying and proportionality rules in judgments of area. In the first two experiments, 7- through 8-year-olds were asked to judge the area of rectangles. In the third, 8- through 11-year-olds were tested on ratio of a rectangle compared to a horizontal line. Results indicated…

Considers how students' mathematical thinking evolves as a result of their actions and everyday experiences and from increasing reliance on introduced mathematical principles and representations. Exemplifies how 8- to 10-year-olds' personal representations come to face with representations involving algebraic concepts. Explores implications for…

Investigated the role of schooling and urbanization on the acquisition of conservation of physical quantities in 384 Senagalese children of 7, 9, 11, and 13 years. Results revealed functional divergences in the acquisition of physical quantities. (RJC)

Three studies investigated 5- to 8-year-olds' ability to solve partitive division problems when presented with a concrete model of a problem. Children found it easier to solve problems in Grouping-by-Divisor condition than in Grouping-by-Quotient condition, although there was evidence of developmental improvement in tasks. Findings suggest that…

Investigates the development of understanding of quantity in 36 children with Down's Syndrome. Findings confirmed similarities in sequence of development between Down's Syndrome children and nonretarded children. Down's children who received training recognized conservation of continuous and discontinuous quantity. (RJC)

The problem of solving mathematical equations can be quite tough for some students hence they face a great difficulty when applying ideas to the actual process. Students in algebra classes are taught coding in which they write down what they will need to do to solve the equation and this coding makes the students more adept at solving equations…

Arguing that cognitive development involves both conceptual and semiotic achievements, the authors emphasize the distinctness of semiotic issues and develop a differentiated appreciation of semiotic aspects of cognition, particularly in elementary mathematics cognition. Semiotic analyses are provided of differences between counting, adding, and…

Discusses children's design of mathematical representations on paper. Suggests that the design of displays during problem solving shapes one's mathematical activity and sense making in crucial ways, and that knowledge of mathematical representations is not simply recalled and applied to problem solving, but also emerges out of one's interactions…