Most theoreticians believe that reading habits explain why Western adults associate small numbers with left space and large numbers with right space (the SNARC effect). We challenge this belief by documenting, in both English and Hebrew, that SNARC changes during reading: small and large numbers in our texts appeared near the left or right ends of…

With research indicating substantial differences among teachers in terms of their effectiveness (Nye, Konstantopoulous, & Hedges, 2004), a major focus of recent research in education has been on improving teacher quality through professional development (Desimone, 2009; Institute of Educations Sciences [IES], 2012; Measures of Effective…

Studies of endogenous (cue-directed) attention have traditionally assumed that such shifts must be volitional. However, recent behavioural experiments have shown that participants make automatic endogenous shifts of attention when presented with symbolic cues that are systematically associated with particular spatial directions, such as arrows and…

Although young infants have repeatedly demonstrated successful numerosity discrimination across large sets when the number of items in the sets changes twofold (E. M. Brannon, S. Abbott, & D. J. Lutz, 2004; J. N. Wood & E. S. Spelke, 2005; F. Xu & E. S. Spelke, 2000), they consistently fail to discriminate a twofold change in number when one set…

Vigorous debate surrounds the issue of whether infants use different representational mechanisms to discriminate small and large numbers. We report evidence for ratio-dependent performance in infants' discrimination of small numbers of auditory events, suggesting that infants can use analog magnitudes to represent small values, at least in the…

The Japanese language represents numbers in kana digit words (a syllabic notation), kanji numbers and Arabic numbers (logographic notations). Kanji and Arabic numbers have previously shown similar patterns of numerical processing, and because of their shared logographic properties may exhibit similar brain areas of numerical representation. Kana…

In this article, we report a study of two-term unit fraction expansions using a geometric approach. It provides us insight on how to find all two-term unit fraction expansions and identify the property of the expansions with smallest maximal denominators, for a given unit fraction. These findings will be useful to lecturers or teachers involved in…

The spatial component of numerical and ordinal information has been explored in previous research. However, how such mapping emerges and how it is affected by the learning experience are issues still under debate. In the current study, we examined the orientation of the mental number line for different numerical notations in Chinese readers. Our…

This study examines whether student performance predictors in a numerically based lecture course are similar to those for the web version of the same course. A numerically based course involves quantitative concepts and requires mathematical calculations. Data were collected from students taking a financial management class at a medium sized state…

Subtraction has two meanings and each meaning leads to the different strategies. The meaning of "taking away something" suggests a direct subtraction, while the meaning of "determining the difference between two numbers" is more likely to be modeled as indirect addition. Many prior researches found that the second meaning and…

Children enter kindergarten with variable levels of mathematics skill and knowledge gained from informal learning opportunities at home, preschool, and daycare. Many perform well once they receive formal mathematics instruction. However, if students do not develop an initial understanding of the most basic aspects of formal mathematics, they are…

Catch Up® Numeracy is a one to one intervention for learners who are struggling with numeracy. It consists of two 15-minute sessions per week, delivered by teaching assistants (TAs). The approach is based on research indicating that numeracy is not a single skill, but a composite of several component skills that are relatively discrete. The…

This qualitative study examined the everyday mathematical experiences and understandings of three, 4-year-old, African-American children from working-class backgrounds. The study drew on Street, Baker, and Tomlin's (2005) broad, ideological model of mathematics as "social" and their analytic concepts of mathematical events (units of…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

Various measures have been used to investigate number processing in children, including a number comparison or a number line estimation task. The present study aimed to examine whether and to which extent these different measures of number representation are related to performance on a curriculum-based standardized mathematics achievement test in…