Researchers have long disagreed about whether number concepts are essentially continuous (unchanging) or discontinuous over development. Among those who take the discontinuity position, there is disagreement about how development proceeds. The current study addressed these questions with new quantitative analyses of children's incorrect responses…

This paper presents the results of an experiment in which mathematicians were asked to rate how persuasive they found two empirical arguments. There were three key results from this study: (a) Participants judged an empirical argument as more persuasive if it verified that integers possessed an infrequent property than if it verified that integers…

In this article, we provide an overview of current knowledge on the underlying cognitive deficits associated with mathematics learning disabilities (MLD). We highlight difficulties surrounding the identification of MLD that include inconsistency in defining MLD, comorbidity with other disabilities, problems associated with assessment tools and…

KenKen® is the new Sudoku. Like Sudoku, KenKen requires extensive use of logical reasoning. Unlike Sudoku, KenKen requires significant reasoning with numbers and operations and helps develop number sense. The creator of KenKen puzzles, Tetsuya Miyamoto, believed that "if you give children good learning materials, they will think and learn and…

In the primate brain, sensory information is processed along two partially segregated cortical streams: the ventral stream, mainly coding for objects' shape and identity, and the dorsal stream, mainly coding for objects' quantitative information (including size, number, and spatial position). Neurophysiological measures indicate that such…

Faced with a chronic shortage of single-subject mathematics teachers and a directive from the federal legislation "No Child Left Behind" that all students are taught by highly qualified teachers, California instituted a new subject-matter competency exam, the California Subject Exam for Teachers for Mathematics (CSET), and created a new…

This work introduces a distance between natural numbers not based on their position on the real line but on their arithmetic properties. We prove some metric properties of this distance and consider a possible extension.

This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

It is commonly assumed that number reading can be intact in patients with pure alexia, and that this dissociation between letter/word recognition and number reading strongly constrains theories of visual word processing. A truly selective deficit in letter/word processing would strongly support the hypothesis that there is a specialized system or…

In this study, we investigate whether multiple digits can be processed at a semantic level without awareness, either serially or in parallel. In two experiments, we presented participants with two successive sets of four simultaneous Arabic digits. The first set was masked and served as a subliminal prime for the second, visible target set.…

Background: Children from Asian countries score higher on early years' arithmetic tests than children from Europe or the United States of America. An explanation for these differences may be the way numbers are named. A clear ten-structure like in the Korean language method leads to a better insight into numbers and arithmetic skills. This…

Past research showing a bias towards the larger non-symbolic number by adults and children in line bisection tasks (de Hevia & Spelke, 2009) has been challenged by Gebuis and Gevers, suggesting that area subtended by the stimulus and not number is responsible for the biases. I review evidence supporting the idea that although sensitivity to number…

What abilities are entailed in being numerate? Certainly, one is the ability to hold the exact quantity of a set in mind, even as it changes, and even after its members can no longer be perceived. Is counting language necessary to track and reproduce exact quantities? Previous work with speakers of languages that lack number words involved…

A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.

In quantity discrimination tasks, adults, infants and animals have been sometimes observed to process number only after all continuous variables, such as area or density, have been controlled for. This has been taken as evidence that processing number may be more cognitively demanding than processing continuous variables. We tested this hypothesis…