Barth and Paladino (2011) argue that changes in numerical representations are better modeled by a power function whose exponent gradually rises to 1 than as a shift from a logarithmic to a linear representation of numerical magnitude. However, the fit of the power function to number line estimation data may simply stem from fitting noise generated…

Whether and in what way enumeration processes differ for small and large sets of objects is still a matter of debate. In order to shed light on this issue, EEG data were obtained from 60 normally developing elementary school children. Adopting a standard non-symbolic numerical comparison paradigm allowed us to manipulate numerical distance between…

The Trail-Making Test (TMT) is a widely used neuropsychological measure that assesses visuomotor abilities and cognitive flexibility. For the TMT-A condition participants are required to locate and connect numbers (i.e. 1-2-3...) while in the TMT-B condition participants perform the set-shifting task of locating and connecting numbers and letters…

For number-form synaesthetes, digits occupy idiosyncratic spatial locations. Atypical to the mental number line that extends horizontally, the synaesthete (L) experiences the numbers 1-10 vertically. We used a spatial cueing task to demonstrate that L's attention could be automatically directed to locations within her number-space--being faster to…

This article proposes an integrated theory of acquisition of knowledge about whole numbers and fractions. Although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding. The present findings with 11- and 13-year-olds…

Time perception has not been comprehensively examined in mathematics difficulties (MD). Therefore, verbal time estimation, production, and reproduction were tested in 13 individuals with MD and 16 healthy controls, matched for age, sex, and intellectual skills. Individuals with MD performed comparably to controls in time reproduction, but showed a…

This article summarizes the findings of research studies focusing on number sense instruction to improve mathematics competence of school going children. Twenty-three studies were located that met the inclusion criteria. Interventions gleaned from the review were categorized based on type of instruction (i.e., constructivist, explicit or a…

In this article, one teacher describes her action research with eighth-grade prealgebra students who are working on a conceptual understanding of fractions. Examining her middle school students' standardized test scores for the previous five years, Denise S. Peppers discovered that student performance on fractions was consistently the lowest…

In this paper we describe a touchscreen application called "TouchCounts," which is designed to support the development of number sense in the early years. We first provide an a priori analysis of its affordances. Then, using Sfard's communicational approach, augmented by a focus both on the role of the body--particularly the fingers…

Mathematics educators have had a long standing interest in students' understanding of decimal numbers. Most studies of students' understanding of decimals have been conducted within Western cultural settings. Similar research in other countries is important for a number of reasons, perhaps most importantly because it can provide insights that may…

Evidence evaluation is a crucial process in many human activities, spanning from medical diagnosis to impression formation. The present experiments investigated which, if any, normative model best conforms to people's intuition about the value of the obtained evidence. Psychologists, epistemologists, and philosophers of science have proposed…

In early childhood and primary (PreK-2) grades, subitizing is a critical skill that helps children meet early mathematics standards. Discover ways teachers can infuse this critical skill into their math curriculum.

There is a need for more comprehensive assessments of young children's emerging print knowledge. Traditional letter and numeral identification assessments score children's responses as either correct or incorrect and this approach can underestimate what children know. The present study tested an assessment scale that scored three- and…

This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…

Place value is a key concept for numbers that is introduced in early mathematics. It is necessary to have a flexible understanding of place value for efficient arithmetic strategies and success in written algorithmic arithmetic. In our research we explore typical mistakes and misconceptions that occur with 3rd graders in German elementary school…