What is the nature of the relationship between different lower-level numerical skills and their role in developing arithmetic skills? We consider the hypothesis of a reciprocal relationship between the development of symbolic (e.g., Arabic numerals) and nonsymbolic (e.g., arrays of objects) numerical magnitude processing. Evidence for…

In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

Mathematical skills are becoming increasingly critical for achieving academic and professional success. Developmental dyscalculia (DD) is a childhood-onset disorder characterized by the presence of abnormalities in the acquisition of arithmetic skills affecting approximately 5% of school age children. Diagnosing students with possible dyscalculia…

Children diagnosed with cerebral palsy (CP) often show difficulties in arithmetic compared to their typically developing peers. The present study explores whether cognitive and motor variables are related to arithmetic performance of a large group of primary school children with CP. More specifically, the relative influence of non-verbal…

Prodigies are individuals with exceptional mental abilities. How is it possible that some of these people mentally calculate exponentiations with high accuracy and speed? We examined CP, a mental calculation prodigy, and a control group of 11 normal calculators for moderate mental arithmetic tasks. CP has additionally been tested for exceptionally…

The triple-code model, cognitive neuroimaging and developmental behavioral data suggest a specific association between phonological processing and arithmetic fact retrieval. Accordingly, individuals with deficits in phonological processing, such as individuals with developmental dyslexia, are expected to show difficulties in arithmetic fact…

Undergraduate and graduate students at Cameron University (N = 158) were given the D'Amore Test of Elementary Arithmetic to test whether or not experience in college mathematics courses might be associated with a relative increase in arithmetic performance compared to those students who had not taken college mathematics courses. We found that only…

Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial,…

In this article, we consider some generalizations of Fibonacci numbers. We consider k-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + F[subscript k,n]), the (k, l)-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + lF[subscript k,n]), and the Fibonacci…

Errors in written multi-digit computation were investigated in children with math difficulties. Third- and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low…

Passive and active visuospatial working memory (VSWM) were investigated in relation to maths performance. The mental rotation task was employed as a measure of active VSWM whereas passive VSWM was investigated using a modified Corsi Blocks task and a matrix pattern task. The Raven Progressive Matrices Test measured fluid intelligence. A total of…