Neuroimaging and lesion studies have provided insights into the neural mechanisms underlying numerical processing, yet the roles of the right and left hemispheres have not been systematically investigated within a single study. To address this issue, we investigated subitizing and magnitude comparison abilities in a split-brain patient. The first…

It is assumed that number magnitude comparison is performed by assessing magnitude representation on a single analog mental number line. However, we have observed a unit-decade-compatibility effect in German which is inconsistent with this assumption (Nuerk, Weger, & Willmes, 2001). Incompatible magnitude comparisons in which decade and unit…

This classroom note includes the following sections: Introduction; The General Case; and Related Formulas.

Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…

In this note properties of two sequences generated by the recurrence relation G[subscript n] +2 = 4 G[subscript n] +1 - G[subscript n], are studied. It is shown that one of the sequences leads to a family of diophantine triplets. Some interesting properties of these sequences are also established.

Schools following the Montessori philosophy use individual and small-group teaching methods and hands-on, concrete materials. This study investigated the understanding of place value concepts and abilities of Montessori students by comparing interview task responses of 93 students in grades 1-3 in a Montessori school (n = 47) and in a mostly…

Previous studies have suggested that typically developing 6-month-old infants are able to discriminate between small and large numerosities. However, discrimination between small numerosities in young infants is only possible when variables continuous with number (e.g. area or circumference) are confounded. In contrast, large number discrimination…

The mathematical development of children with Down syndrome (DS) is largely uncharted territory and yet the experience of parents and teachers reminds people that children with DS can and do learn mathematics. In this article, the authors describe a study that examines the mathematical development of children with DS, and offer suggestions arising…

This study aimed to evaluate the impact of individual differences in working memory capacity on number transcoding. A recently proposed model, ADAPT (a developmental asemantic procedural transcoding model), accounts for the development of number transcoding from verbal form to Arabic form by two mechanisms: the learning of new production rules…

This theoretical paper proposes a way to extend the partitive and measurement interpretations of whole number division to fractional contexts focusing on the issue of units. We define the unit-changing and unit-keeping interpretations for division and suggest a stronger and earlier focus on the concept of units in courses for prospective…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

To investigate whether games may serve as useful formative assessment environments, this study examined, experimentally, the effects of two aspects of formative assessment on math achievement, game play, and help-seeking behaviors: (a) making assessment criteria explicit through the explanation of scoring rules and (b) incentivizing the use of…

This paper describes a study that examined parents' beliefs about children's number skill development. Twenty-seven parents of 4- and 5-year-olds were interviewed about number tasks that could be solved by children between the ages of 4 and 7 years. In addition, parents were asked a series of open-ended questions about how they would answer a…

Hypothesizing that subtraction of (negative) integers requires formal operations, the author describes a study of children's understanding of related concepts. The study involves the use of apparatus embodying properties of the number line. (SD)

The author describes a model for operations on the set of rationals. Thi s model, used by students in a laboratory situation, is based on an easily constructed number balance. (SD)