Ariel Starr

Number sense in infancy predicts mathematical abilities in childhood

Significance The uniquely human mathematical mind sets us apart from all other animals. How does this powerful capacity emerge over development? It is uncontroversial that education and environment shape mathematical ability, yet an untested assumption is that number sense in infants is a conceptual precursor that seeds human mathematical development. Our results provide the first support for this hypothesis. We found that preverbal number sense in 6-month-old infants predicted standardized math scores in the same children 3 years later. This discovery shows that number sense in infancy is a building block for later mathematical ability and invites educational interventions to improve number sense even before children learn to count. Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.

Evidence against continuous variables driving numerical discrimination in infancy

Over the past decades, abundant evidence has amassed that demonstrates infants’ sensitivity to changes in number. Nonetheless, a prevalent view is that infants are more sensitive to continuous properties of stimulus arrays such as surface area and contour length than they are to numerosity. Very little research, however, has directly addressed infants’ sensitivity to contour. Here we used a change detection paradigm to assess infants’ acuity for the cumulative contour length of an array when the array’s surface area and number were held constant. Seven-month-old infants detected a threefold change in contour length but failed to detect a twofold change. These results, in conjunction with previously published data on numerosity discrimination using the same experimental paradigm, suggest that infants are not more sensitive to changes in contour length compared to changes in numerosity. Consequently, these findings undermine the claim that attention toward contour length is a primary driver of numerical discrimination in infancy.

Developmental Continuity in the Link Between Sensitivity to Numerosity and Physical Size

Converging evidence suggests that representations of number, space, and other dimensions depend on a general representation of magnitude. However, it is unclear whether there exists a privileged relation between certain magnitude dimensions or if all continuous magnitudes are equivalently related. Four-year-old children and adults were tested with three magnitude comparison tasks – nonsymbolic number, line length, and luminance – to determine whether individual differences in sensitivity are stable across dimensions. A Weber fraction (w) was calculated for each participant in each stimulus dimension. For both children and adults, accuracy and w values for number and line length comparison were significantly correlated, whereas neither accuracy nor w was correlated for number and luminance comparison. However, although line length and luminance comparison performance were not correlated in children, there was a significant relation in adults. These results suggest that there is a privileged relation between number and line length that emerges early in development and that relations between other magnitude dimensions may be later constructed over the course of development.

The contributions of numerical acuity and non-numerical stimulus features to the development of the number sense and symbolic math achievement

Numerical acuity, frequently measured by a Weber fraction derived from nonsymbolic numerical comparison judgments, has been shown to be predictive of mathematical ability. However, recent findings suggest that stimulus controls in these tasks are often insufficiently implemented, and the proposal has been made that alternative visual features or inhibitory control capacities may actually explain this relation. Here, we use a novel mathematical algorithm to parse the relative influence of numerosity from other visual features in nonsymbolic numerical discrimination and to examine the strength of the relations between each of these variables, including inhibitory control, and mathematical ability. We examined these questions developmentally by testing 4-year-old children, 6-year-old children, and adults with a nonsymbolic numerical comparison task, a symbolic math assessment, and a test of inhibitory control. We found that the influence of non-numerical features decreased significantly over development but that numerosity was a primary determinate of decision making at all ages. In addition, numerical acuity was a stronger predictor of math achievement than either non-numerical bias or inhibitory control in children. These results suggest that the ability to selectively attend to number contributes to the maturation of the number sense and that numerical acuity, independent of inhibitory control, contributes to math achievement in early childhood.

Evolutionary and Developmental Continuities in Numerical Cognition

Abstract As with most forms of complex human abilities, studying the minds of babies and nonhuman animals can unveil the evolutionary and developmental underpinnings that ground cognition. Although many animal species are sensitive to numerical information in their environment, only humans represent and manipulate number symbolically. However, both humans and nonhuman animals share a system for representing number nonsymbolically, and this primitive system may serve as a foundation for the construction of symbolic mathematics principles. The first half of this chapter provides evidence for nonsymbolic number representations in nonhuman animals and preverbal human infants by highlighting the continuities in numerical reasoning found across these divergent species. The second half of the chapter explores the relation between nonsymbolic and symbolic representations of number and reviews the evidence that nonsymbolic number representations may function as building blocks for the acquisition of symbolic mathematics.

Spatial metaphor and the development of cross-domain mappings in early childhood.

Spatial language is often used metaphorically to describe other domains, including time (long sound) and pitch (high sound). How does experience with these metaphors shape the ability to associate space with other domains? Here, we tested 3- to 6-year-old English-speaking children and adults with a cross-domain matching task. We probed cross-domain relations that are expressed in English metaphors for time and pitch (length-time and height-pitch) as well as relations that are unconventional in English but expressed in other languages (size-time and thickness-pitch). Participants were tested with a perceptual matching task, in which they matched between spatial stimuli and sounds of different durations or pitches, and a linguistic matching task, in which they matched between a label denoting a spatial attribute, duration, or pitch and a picture or sound representing another dimension. Contrary to previous claims that experience with linguistic metaphors is necessary for children to make cross-domain mappings, children performed above chance for both familiar and unfamiliar relations in both tasks, as did adults. Children’s performance was also better when a label was provided for one of the dimensions, but only when making length-time, size-time, and height-pitch mappings (not thickness-pitch mappings). These findings suggest that although experience with metaphorical language is not necessary to make cross-domain mappings, labels can promote these mappings, both when they have familiar metaphorical uses (e.g., English long denotes both length and duration) and when they describe dimensions that share a common ordinal reference frame (e.g., size and duration but not thickness and pitch).

An Introduction to the Approximate Number System

What are young childrens first intuitions about numbers and what role do these play in their later understanding of mathematics? Traditionally, number has been viewed as a culturally derived breakthrough occurring relatively recently in human history that requires years of education to master. Contrary to this view, research in cognitive development indicates that our minds come equipped with a rich and flexible sense of number-the Approximate Number System (ANS). Recently, several major challenges have been mounted to the existence of the ANS and its value as a domain-specific system for representing number. In this article, we review five questions related to the ANS (what, who, why, where, and how) to argue that the ANS is defined by key behavioral and neural signatures, operates independently from nonnumeric dimensions such as time and space, and is used for a variety of functions (including formal mathematics) throughout life. We identify research questions that help elucidate the nature of the ANS and the role it plays in shaping childrens earliest understanding of the world around them.

Eye movements provide insight into individual differences in children's analogical reasoning strategies

Analogical reasoning is considered a key driver of cognitive development and is a strong predictor of academic achievement. However, it is difficult for young children, who are prone to focusing on perceptual and semantic similarities among items rather than relational commonalities. For example, in a classic A:B::C:? propositional analogy task, children must inhibit attention towards items that are visually or semantically similar to C, and instead focus on finding a relational match to the A:B pair. Competing theories of reasoning development attribute improvements in childrens performance to gains in either executive functioning or semantic knowledge. Here, we sought to identify key drivers of the development of analogical reasoning ability by using eye gaze patterns to infer problem-solving strategies used by six-year-old children and adults. Children had a greater tendency than adults to focus on the immediate task goal and constrain their search based on the C item. However, large individual differences existed within children, and more successful reasoners were able to maintain the broader goal in mind and constrain their search by initially focusing on the A:B pair before turning to C and the response choices. When children adopted this strategy, their attention was drawn more readily to the correct response option. Individual differences in childrens reasoning ability were also related to rule-guided behavior but not to semantic knowledge. These findings suggest that both developmental improvements and individual differences in performance are driven by the use of more efficient reasoning strategies regarding which information is prioritized from the start, rather than the ability to disengage from attractive lure items.