The purpose of the study was to examine how teachers enhance their knowledge of rational numbers focused on modeling problem tasks using multiple representations. The professional development summer institute and the follow-up Lesson Study (Lewis, 2002) throughout the academic year focused on engaging teachers in rational numbers and proportional…

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of…

Previous studies have suggested that children's learning of the relation between number words and approximate numerosities depends on their verbal counting ability, and that children exhibit no knowledge of mappings between number words and approximate numerical magnitudes for number words outside their productive verbal counting range. In the…

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…

In June 2018 the Canadian Mathematics Education Study Group/Groupe Canadien d'étude en didactique des mathématiques (CMESG/GCEDM) held its 42nd meeting in the idyllic setting of Squamish, British Columbia. This meeting marked the first time CMESG/GCEDM had been in British Columbia since 2010 and the first time it had been held at Quest University.…