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…

The development of young children's counting has been extensively researched, yet detailed studies that examine development over multiple years are curiously absent from the literature. This research examined 15 preschoolers' (ages 3-4) use of number words as they engaged in two counting tasks, an oral counting task and counting a collection of 31…

In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into…

Taking into consideration that young children engage with mathematics outside of the preschool classroom, this study focuses on adults' awareness of numerical ideas raised by young children without and with adult involvement. Ninety adults in Israel, the majority of whom were parents or grandparents of children aged 3-6 years, participated in this…

Sixty (35 girls and 25 boys) 9th-grade students' conceptual understanding of the number line was qualitatively assessed through verbal explanations and visual representations. The assessment included an open-ended question focused on students' number line descriptions and the explanations coalesced around six features: sequential ordering (i.e.,…

One model of numeric perception is a density-area mechanism: a process that estimates both density and area of an array, then multiplies them to create an estimate of number. One line of evidence that supports this is the surprising numeric Ebbinghaus illusion: smaller context circles lead to greater perceived number than larger context circles,…

Attention and executive functions (EFs) play a critical role in academic skill development, including literacy and numeracy. Deficits in attention and EFs often accompany learning disorders, such as dyslexia and dyscalculia. Despite their well-established link, we lack a nuanced understanding of the specific neurobiological mechanisms that…

Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an…

The purpose of this paper is to propose an effective learning environment for the initial stages of mathematical learning. Basic numerical skills and the objects and actions that trigger those skills are conceptualized as a mathematics-learning environment. We discuss numerical learning mechanism and the basic skills and environments we use to…

Number sense is a key indicator of students' future academic success. Students from low socio-economic backgrounds often come to kindergarten lacking number sense skills that other students acquire before they begin formal schooling. Small-group intervention that is focused on number sense skills is an effective way to address this foundational…

Number-recognition tasks, such as the how-many task, involve set-to-word mapping, and number-creation tasks, such as the give-n task, entail word-to-set mapping. The present study involved comparing sixty 3-year-olds' performance on the two tasks with collections of one to three items over three time points about 3 weeks apart. Inconsistent with…

Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

Magnitude information, for instance, regarding weight, distance, or velocity, is crucial for planning goal-directed interactions. Accordingly, magnitude information, including numerical magnitude, can affect actions: Responses to small numbers are faster with the left hand than the right and vice versa (hand-based SNARC effect). Previous…

A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (M[subscript age] = 3.86 years; N = 216; 99 males; 80.8%…

In two studies, we investigated whether using three-dimensional (3D) manipulatives during assessment aided performance on a variety of preschool mathematics tasks compared to pictorial representations. On measures of children's understanding of counting and cardinality (n = 103), there was no difference in performance between manipulatives and…