Introduction: This study has aimed to investigate the relationship between the development of working memory and performance on arithmetic activities. Method: We conducted a 3-year longitudinal study of a sample of 90 children, that was followed during the first, second and third year of primary school. All children were tested on measures of WM…

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

Although language is implicated in children's mathematical development, few studies have focused specifically on how different linguistic skills relate to children's mathematical performance. Building on the model proposed by LeFevre et al. (2010), this study examined how general verbal ability and phonological skills were differentially related…

This study tested the hypothesis that intuitions about the effect of operations, e.g., "addition makes bigger" and "division makes smaller", are still present in educated adults, even after years of instruction. To establish the intuitive character, we applied a reaction time methodology, grounded in dual process theories of reasoning. Educated…

The study investigates the mathematical and the pedagogical content knowledge among in-service and pre-service first- and second-grade mathematics teachers. The sample of 300 subjects consisted of 150 first- and second-grade in-service teachers and 150 pre-service teachers studying in a college of education, 75 of whom were first-year students and…

Recent studies suggest that the relation between nonsymbolic magnitude processing skills and math competence is mediated by symbolic number processing. However, less is known about whether mapping between nonsymbolic and symbolic magnitude representations also mediates that relation, and whether the mediating role of symbolic number processing is…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

Adults' simple arithmetic performance is more efficient when operands are presented in Arabic digit (3 + 5) than in number word (three + five) formats. An explanation provided is that visual familiarity with digits is higher respect to number words. However, most studies have been limited to single-digit addition and multiplication problems. In…

A focus of early mathematics education is to build fluency through practice. Several models of skill acquisition have sought to explain the increase in fluency because of practice by modeling both the learning mechanisms driving this speedup and the changes in cognitive processes involved in executing the skill (such as transitioning from…

In the present study we examined whether children with Developmental Dyscalculia (DD) exhibit a deficit in the so-called "Approximate Number System" (ANS). To do so, we examined a group of elementary school children who demonstrated persistent low math achievement over 4 years and compared them to typically developing (TD), aged-matched…

The present study extends recent advances coordinating research on cognition and psychometric modeling around fractions. Recent research has demonstrated that the Diagnosing Teachers' Multiplicative Reasoning Fractions survey provides information about distinct components necessary for reasoning in terms of quantities when solving fraction…

The present mixed-methods quasi-experimental study (embedding a case study and a mixed factorial within-between ANOVA test), conducted in a private English school in Limassol, Cyprus, investigated how the use of the schematic learning aids (researcher-made color-coded flash-cards and grids) influence year-2 children's ability to read, write and…

Having a deeper understanding of division derived from multiple models is of great importance for teachers and students. For example, students will benefit from a greater understanding of division contexts as they study long division, fractions, and division of fractions. The purpose of this article is to build on teachers' and students'…

Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an…

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…