Rational numbers (i.e., fractions, percentages, decimals, and whole-number frequencies) are notoriously difficult mathematical constructs. Yet correctly interpreting rational numbers is imperative for understanding health statistics, such as gauging the likelihood of side effects from a medication. Several pernicious biases affect health…

Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical…

Children's ability to discriminate nonsymbolic number (e.g., the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest that it may be due to a sharpening numerical representation or an improved…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

Children's ability to discriminate nonsymbolic number (e.g. the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest it may be due to a sharpening numerical representation or an improved ability…

While some researchers place negative numbers on a so-called extended mental number line to the left of positive numbers, others claim that negative numbers do not have mental representations but are processed through positive numbers combined with transformation rules. We measured spatial associations of negative numbers with a modified implicit…

Understanding large number data is essential for making sense of real-world problems. For the research reported here, our intent was to find connections between quantitative cognitive science studies and our prior qualitative study about participants' understanding of the relative size of large numbers. While all 23 cognitive science research…

This study aims to explore the notion of the density of the set of rational numbers in the set of real numbers, as interpreted by undergraduate mathematics students. The data comprise 95 responses to a scripting task, in which participants were asked to extend a hypothetical dialog between two student characters, who argue about the existence of…

The ability to efficiently compare number symbols, such as digits, is associated with mathematics competence across the lifespan. Performance on symbolic number comparison tasks differ across age groups; young students who are developing fluency with digits improve on symbolic number comparison, and performance is better in adults than children.…

In this study, we used multivariate decoding methods to study processing differences between canonical (montring and count) and noncanonical finger numeral configurations (FNCs). While previous research investigated these processing differences using behavioral and event-related potentials (ERP) methods, conventional univariate ERP analyses focus…

The current study highlights the importance of inhibitory ability in facilitating performance in mathematics. To understand the role of inhibition in mathematical knowledge, this study tested 102 college students on a series of standardized complex math exercises. Inhibition tasks varied by task and stimuli (letters, numbers, and arrows). The…

Neuropsychological case-studies suggested that dates and encyclopedic numbers may be processed differently than unknown numbers. However, this issue was seldom investigated in healthy participants. Therefore, it is unclear whether known dates are read like words (as lexical items), or like numbers (each position strictly defines digits' values in…

Here, we assess whether quantity representations are influenced by the perceptual biases hypothesized to manifest in depressive individuals. In contrast to this clinical model, several prominent models of numerical cognition assume that quantity representations are abstract, and therefore are independent of the items that are being quantified. If…

Background: Children's numerical and arithmetic skills differ greatly already at an early age. Although research focusing on accounting for these large individual differences clearly demonstrates that mathematical performance draws upon several cognitive abilities, our knowledge concerning key abilities underlying mathematical skill development is…

Persistent difficulties in learning abstract algebraic concepts--particularly among preservice mathematics teachers--continue to hinder students' mathematical development. While prior studies have documented general misconceptions, few have grounded their analysis in comprehensive learning theories. Addressing this gap, the present study adopts…