Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

The psychology supporting the use of quantifier words (e.g., "some," "most," "more") is of interest to both scientists studying quantity representation (e.g., number, area) and to scientists and linguists studying the syntax and semantics of these terms. Understanding quantifiers requires both a mastery of the…

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,…

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…

The purpose of this study was to determine if online reflections through social networking affect students' sense of community and levels of perceived conceptual learning in Algebra I courses. Social constructivism, connectivism, and computer-mediated communication in relation to reflective practices form the theoretical and practical framework…

This article focuses on the cognitive factors that impact on students in the middle school years experiencing learning difficulties in basic mathematics. It begins with a review of selected literature providing information about the learning difficulties in mathematics. Focus then shifts to an implementation of the "Quicksmart"…

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 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…

On tasks involving assessement of the heights of colored sticks, kindergarten, third-grade, and adult subjects were successful on inferences involving only equalities or only inequalities across various conditions and procedures. A dramatic developmental increase in performance was found on inferences based on the combination of equality and…

Two experiments investigated how child and adult speakers of English and Kannada (Dravidian) interpret scopally ambiguous sentences containing numerally quantified noun phrases and negation. Results showed that 4-year-olds' interpretations were constrained by the surface hierarchical relations (the c-command relations) between sentence elements…

Two experiments tested claim that transparency of Korean fraction names promotes fraction concepts. Findings indicated that U.S. and Korean first- and second-graders erred similarly on a fraction-identification task, by treating fractions as whole numbers. Korean children performed at chance when whole-number representation was included but…

One mathematics lesson was planned by two Grade 2 teachers together. Their separate teaching of it was videotaped, and each teacher was interviewed before and after her lesson. The "same" lesson resulted in different sets of worthwhile learning outcomes. In this research report, the notion of situated cognition is used as a tool for analysis of…

Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…