Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills…

Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic…

Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…

The main objective of this study was to examine how quantitative knowledge ("Gq" in the CHC model) and processing speed ("Gs" in the CHC model) affect scores on the WAIS-III Arithmetic Subtest (Wechsler, 2000) with aging. Two age groups were compared: 30 young adults and 25 elderly adults. For both age groups, "Gq" was an important predictor of…

Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…

Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition…

Using 4 years of mathematics achievement scores, groups of typically achieving children (n = 101) and low achieving children with mild (LA-mild fact retrieval; n = 97) and severe (LA-severe fact retrieval; n = 18) fact retrieval deficits and mathematically learning disabled children (MLD; n = 15) were identified. Multilevel models contrasted…

Background: The ability to compare numbers, as the most basic form of number sense, has been related to arithmetical achievement. Aims: The current study addressed the predictive value of non-symbolic and symbolic (number word (NW) and Arabic number (AN)) comparison for arithmetics by means of a longitudinal design. Sample: Sixteen children with…

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

Objective: Cardiovascular reactivity to laboratory stressors was investigated as (a) a moderator of associations of partner aggression with affective functioning, alcohol problems, and parenting; and (b) a consequence of partner aggression. Method: Cohabiting adult couples (N = 453) with 3- to 7-year-old children were recruited by random digit…

This study investigated the role of strategy instruction and working memory capacity (WMC) on word problem solving accuracy in children with (n = 100) and without (n = 92) math difficulties (MD). Within classrooms, children in Grades 2 and 3 were randomly assigned to one of four treatment conditions: verbal-only strategies (e.g., underlining…

Many children in bilingual regions follow lessons in a language at school (school-language) that they hardly ever speak at home or in other informal settings. What are the neural effects of this phenomenon? This functional magnetic resonance imaging (fMRI) study investigates the effects of using school-language on brain activity during a high…

Developmental dyscalculia (DD) is a pervasive difficulty affecting number processing and arithmetic. It is encountered in around 6% of school-aged children. While previous studies have mainly focused on general cognitive functions, the present paper aims to further investigate the hypothesis of a specific numerical deficit in dyscalculia. The…

A simple view, which dates back to Turing, proposes that complex cognitive operations are composed of serially arranged elementary operations, each passing intermediate results to the next. However, whether and how such serial processing is achieved with a brain composed of massively parallel processors, remains an open question. Here, we study…

More important than infusing courses and curricula with modern content is to give students the tools to use and understand mathematics--including some that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what users and makers of mathematics do and what they say. These cross-journal articles are…