Our research focuses on developing elementary students' mental computation skills with the help of card games. Choosing this area of study was motivated by our personal experiences, namely, that mathematics programmes of study do not lay emphasis on this aspect; there are too few hours dedicated to developing this skill, and several mental…

There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing…

Representations of numerical value have been assessed by using bounded (e.g., 0-1,000) and unbounded (e.g., 0-?) number-line tasks, with considerable debate regarding whether 1 or both tasks elicit unique cognitive strategies (e.g., addition or subtraction) and require unique cognitive models. To test this, we examined how well a mixed log-linear…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

Although high-quality early educational environments are thought to be related to the growth of children's skills in mathematics, relatively little is known about specific aspects of classroom instruction that may promote these abilities. Data from a longitudinal investigation were used to investigate associations between teachers' language while…

Various measures have been used to investigate number processing in children, including a number comparison or a number line estimation task. The present study aimed to examine whether and to which extent these different measures of number representation are related to performance on a curriculum-based standardized mathematics achievement test in…

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and…

The contribution of the three core components of working memory (WM) to the development of mathematical skills in young children is poorly understood. The relation between specific WM components and Numerical Operations, which emphasize computation and fact retrieval, and Mathematical Reasoning, which emphasizes verbal problem solving abilities in…

We applied overlapping waves theory and microgenetic methods to examine how children improve their estimation proficiency, and in particular how they shift from reliance on immature to mature representations of numerical magnitude. We also tested the theoretical prediction that feedback on problems on which the discrepancy between two…

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual…

The influence of cognitive growth in working memory (WM) on mathematical problem solution accuracy was examined in elementary school children (N = 353) at risk and not at risk for serious math problem solving difficulties. A battery of tests was administered that assessed problem solving, achievement, and cognitive processing (WM, inhibition,…