In this study, we examined the nature of the spatial-numerical associations underlying the SNARC-effect by imposing a verbal or spatial working memory load during a parity judgment and a magnitude comparison task. The results showed a double dissociation between the type of working memory load and type of task. The SNARC-effect disappeared under…

The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…

A number of studies have investigated infants' abilities to extract and discriminate number from multimodal events. These results have been mixed for several possible reasons, including aspects of the experimental design that provide perceptual cues that are unrelated to number, and are known to influence looking preferences. This experiment used…

Mature representations of space and number are connected to one another in ways suggestive of a "mental number line", but this mapping could either be a cultural construction or a reflection of a more fundamental link between the domains of number and geometry. Using a manual bisection paradigm, we tested for number line representations in adults,…

Little research has focused on an informal understanding of subtractive negation (e.g., 3 - 3 = 0) and subtractive identity (e.g., 3 - 0 = 3). Previous research indicates that preschoolers may have a fragile (i.e., unreliable or localized) understanding of the addition-subtraction inverse principle (e.g., 2 + 1 - 1 = 2). Recognition of a small…

This article presents a categorization of the phenomena and representations used to introduce negative numbers in mathematics books published in Spain during the 18th and 19th centuries. Through a content analysis of fourteen texts which were selected for the study, we distinguished four phenomena typologies: physical, accounting, temporal and…

Now entering into its 20th year of data collection, Trends in International Mathematics and Science Study, (TIMSS) is an international assessment of mathematics and science at the fourth and eighth grades. TIMSS 2015 is the most recent in the TIMSS series, which began with the first assessments in 1995 and has continued every four years--1999,…

The purposes of this study were to investigate the effects of an intervention designed to improve at-risk 4th graders' understanding of fractions and to examine the processes by which effects occurred. The intervention focused more on the measurement interpretation of fractions; the control condition focused more on the part-whole interpretation…

This paper highlights the Indonesian's road transportation contexts, namely, angkot, that used in learning and teaching of addition and subtraction in first grade and second grade MIN-2 Palembang. PMRI approach that adopt from RME [Realistic Mathematics Education] was used in this design research. From teaching experiment was founded that the…

Working memory predicts children's reading comprehension but it is not clear whether this relation is due to a modality-specific or general working memory. This study, which investigated the relations between children's reading skills and working memory (WM) abilities in 3 modalities, extends previous work by including measures of both reading…

This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…

The purpose of this research has been to generate learning environments that surrounded second and third grade students with bi-directional counting experiences, leading them to discover and come to an understanding of opposite numbers. While engaged in games and bi-directional activities, these young students eagerly counted, by jumping frogs…

The current literature in early childhood mathematics provides for little explanation of early mathematics skill acquisition in young children. This study was designed to use existing research on specific early mathematics skills to examine a cohesive model of mathematics skills in preschool and kindergarten aged students. Preschool and…

The study examined whether 7th-graders' knowledge of rational numbers improved when the students' math teachers participated in related professional development activities. The study analyzed data on about 4,500 students and 200 teachers from approximately 80 schools in 12 districts during the 2007-08 academic year. The study found that students…

In 2008, the authors worked with a range of schools to trial ideas that assisted young Indigenous students to engage with mathematics as they enter the school environment. This article highlights some key pedagogical strategies that assisted classroom teachers to improve Indigenous students' understanding of mathematics, particularly in the area…