"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

Using the same-different task, Perea, Dunabeitia, Pollatsek, and Carreiras (2009) showed that digits resembling letters ("leet digits"; e.g., 1 = "I", 4 = "A") primed pseudoword strings (e.g., "V35Z3D-VESZED"), but letters resembling digits ("leet letters") did not prime digit strings (e.g.,…

The primary purpose of this study was to assess the effects of strategic counting instruction, with and without deliberate practice with those counting strategies, on number combination (NC) skill among students with mathematics difficulties (MD). Students (n = 150) were stratified on MD status (i.e., MD alone versus MD with reading difficulty)…

The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.

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…