Number sense is the foundation of arithmetic and algebra, yet relatively little research has deeply investigated what children do as they develop number sense. This case study provides insights into that development as it occurred during interactions with a multi-touch mathematics digital game, including conceptually congruent gestures. Findings…

Educators and policy makers have increasingly recognized the importance of computational thinking (CT). Despite the growing body of CT literature, how to cultivate CT is still underexplored and undertheorized in early childhood education. Informed by Piaget's Theory of Cognitive Development, this exploratory study was conducted with a focus on…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

In response to claims that the quality (and in particular linearity) of children's mental representation of number acts as a constraint on number development, we carried out a longitudinal assessment of the relationships between number line estimation, counting, and mathematical abilities. Ninety-nine 5-year-olds were tested on 4 occasions at 3…

The SNARC (spatial-numerical association of response codes) effect refers to the finding that small numbers facilitate left responses, whereas larger numbers facilitate right responses. The development of this spatial association was studied in 7-, 8-, and 9-year-olds, as well as in adults, using a task where number magnitude was essential to…

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Defines one approach to problem solving in terms of student use of algorithms to find their solutions and gives examples. Discusses how problems and algorithms relate to each other. Describes strategies for teaching problem solving using algorithms. (CW)

Tested three models of children's mathematics word-problem solving based on developmental differences in quantitative conceptual structures: (1) quantitative relations represented as ordered array of mental objects; (2) numbers represented on two tentatively coordinated mental number lines; and (3) numerical operations represented as objects on…

Two experiments investigated infants' sensitivity to amount of continuous quantity and to changes in amount of continuous quantity. Found that 6-month-olds looked significantly longer at a novel quantity than at the familiar quantity. Nine-month-olds looked significantly longer at an impossible event than at a possible event. Findings question…