Previous research has demonstrated a link between children's ability to name canonical finger configurations and their mathematical abilities. This study aimed to investigate the nature of this association, specifically exploring whether the relationship is skill and handshape specific and identifying the underlying mechanisms involved.…

Number line estimation (NLE) tasks are widely used to investigate numerical cognition, learning, and development, and as an instructional tool. Interpretation of these tasks generally involves an implicit expectation that responses are driven by the overall magnitudes of target numerals, in the sense that the particular digits conveying those…

This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

Young children's estimates of numerical magnitude increase approximately logarithmically with actual magnitude. The conventional interpretation of this finding is that children's estimates reflect an innate logarithmic encoding of number. A recent set of findings, however, suggests that logarithmic number-line estimates emerge via a dynamic…

Children and adults show behavioral evidence of psychological overlap between their early, non-symbolic numerical concepts and their later-developing symbolic numerical concepts. An open question is to what extent the common cognitive signatures observed between different numerical notations are coupled with physical overlap in neural processes.…

This article reconsiders Case's theory of central conceptual structures (CCS), examining the relation between working memory and the acquisition of quantitative CCS. The lead hypothesis is that the development of working memory capacity shapes the development of quantitative concepts (whole and rational numbers). Study I, with 779 children from…

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

Historically there has always been a lively research discussion on whether the development of number concept should be considered as innate, or whether the catalyst for the development of the number concept -- and for counting -- is hearing number words combined with seeing concrete examples. One can recognize these theories as the nativist view…

There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing…

Behavioral research suggests that two cognitive systems are at the foundations of numerical thinking: one for representing 1-3 objects in parallel and one for representing and comparing large, approximate numerical magnitudes. We tested for dissociable neural signatures of these systems in preverbal infants by recording event-related potentials…

The development of numerical concepts is described from infancy to preschool age. Infants a few days old exhibit an early sensitivity for numerosities. In the course of development, nonverbal mental models allow for the exact representation of small quantities as well as changes in these quantities. Subitising, as the accurate recognition of small…

To conceive the infinity of integers, one has to realize: (a) the unending possibility of increasing/decreasing numbers (potential infinity), (b) that the cardinality of the set of numbers is greater than that of any finite set (actual infinity), and (c) that the leap from a finite to an infinite set is itself infinite (immeasurable gap). Three…

This article describes the development of number concepts between infancy and early childhood. It is based on a diary study that tracked number word use in a child from 12 to 38 months of age. Number words appeared early in the child's vocabulary, but accurate reference to specific numerosities evolved gradually over the entire 27-month period.…

Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving…