Testing the whole number interference hypothesis: Contributions of inhibitory control and whole number knowledge to fraction understanding.

The present study tests two predictions stemming from the hypothesis that a source of difficulty with rational numbers is interference from whole number magnitude knowledge. First, inhibitory control should be an independent predictor of fraction understanding, even after controlling for working memory. Second, if the source of interference is whole number knowledge, then it should hinder fraction understanding. These predictions were tested in a racially and socioeconomically diverse sample of U.S. children (N = 765; 337 female) in Grades 3 (ages 8-9), 5 (ages 10-11), and 7 (ages 12-13) who completed a battery of computerized tests. The fraction comparison task included problems with both shared components (e.g., 3/5 > 2/5) and distinct components (e.g., 2/3 > 5/9), and problems that were congruent (e.g., 5/6 > 3/4) and incongruent (e.g., 3/4 > 5/7) with whole number knowledge. Inhibitory control predicted fraction comparison performance over and above working memory across component and congruency types. Whole number knowledge did not hinder performance and instead positively predicted performance for fractions with shared components. These results highlight a role for inhibitory control in rational number understanding and suggest that its contribution may be distinct from inhibiting whole number magnitude knowledge. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Relational thinking: An overlooked component of executive functioning.

Relational thinking, the ability to represent abstract, generalizable relations, is a core component of reasoning and human cognition. Relational thinking contributes to fluid reasoning and academic achievement, particularly in the domain of math. However, due to the complex nature of many fluid reasoning tasks, it has been difficult to determine the degree to which relational thinking has a separable role from the cognitive processes collectively known as executive functions (EFs). Here, we used a simplified reasoning task to better understand how relational thinking contributes to math achievement in a large, diverse sample of elementary and middle school students (N = 942). Students also performed a set of ten adaptive EF assessments, as well as tests of math fluency and fraction magnitude comparison. We found that relational thinking was significantly correlated with each of the three EF composite scores previously derived from this dataset, albeit no more strongly than they were with each other. Further, relational thinking predicted unique variance in students' math fluency and fraction magnitude comparison scores over and above the three EF composites. Thus, we propose that relational thinking be considered an EF in its own right as one of the core, mid-level cognitive abilities that supports cognition and goal-directed behavior. RESEARCH HIGHLIGHTS: Relational thinking, the process of identifying and integrating relations, develops over childhood and is central to reasoning. We collected data from nearly 1000 elementary and middle schoolers on a test of relational thinking, ten standard executive function tasks, and two math tests. Relational thinking predicts unique variance in math achievement not accounted for by canonical EFs throughout middle childhood. We propose that relational thinking should be conceptualized as a core executive function that supports cognitive development and learning.

The future is in front, to the right, or below: Development of spatial representations of time in three dimensions.

Across cultures, people frequently communicate about time in terms of space. English speakers in the United States, for example, might "look forward" to the future or gesture toward the left when talking about the past. As shown by these examples, different dimensions of space are used to represent different temporal concepts. Here, we explored how cultural factors and individual differences shape the development of two types of spatiotemporal representations in 6- to 15-year-old children: the horizontal/vertical mental timeline (in which past and future events are placed on a horizontal or vertical line that is external to the body) and the sagittal mental timeline (in which events are placed on a line that runs through the front-back axis of the body). We tested children in India because the prevalence of both horizontal and vertical calendars there provided a unique opportunity to investigate how calendar orientation and writing direction might each influence the development of the horizontal/vertical mental timeline. Our results suggest that the horizontal/vertical mental timeline and the sagittal mental timeline are constructed in parallel throughout childhood and become increasingly aligned with culturally-conventional orientations. Additionally, we show that experience with calendars may influence the orientation of children's horizontal/vertical mental timelines, and that individual differences in children's attitudes toward the past and future may influence the orientation of their sagittal mental timelines. Taken together, our results demonstrate that children are sensitive to both cultural and personal factors when building mental models of time.

Spatial Metaphor Facilitates Word Learning.

Why are spatial metaphors, like the use of "high" to describe a musical pitch, so common? This study tested one hundred and fifty-four 3- to 5-year-old English-learning children on their ability to learn a novel adjective in the domain of space or pitch and to extend this adjective to the untrained dimension. Children were more proficient at learning the word when it described a spatial attribute compared to pitch. However, once children learned the word, they extended it to the untrained dimension without feedback. Thus, children leveraged preexisting associations between space and pitch to spontaneously understand new metaphors. These results suggest that spatial metaphors may be common across languages in part because they scaffold children's acquisition of word meanings that are otherwise difficult to learn.

Semantic knowledge influences visual working memory in adults and children.

We can retain only a portion of the visual information that we encounter within our visual working memory. Which factors influence how much information we can remember? Recent studies have demonstrated that the capacity of visual working memory is influenced by the type of information to be remembered and is greater for real-world objects than for abstract stimuli. One explanation for this effect is that the semantic knowledge associated with real-world objects makes them easier to maintain in working memory. Previous studies have indirectly tested this proposal and led to inconsistent conclusions. Here, we directly tested whether semantic knowledge confers a benefit for visual working memory by using familiar and unfamiliar real-world objects. We found a mnemonic benefit for familiar objects in adults and children between the ages of 4 and 9 years. Control conditions ruled out alternative explanations, namely the possibility that the familiar objects could be more easily labeled or that there were differences in low-level visual features between the two types of objects. Together, these findings demonstrate that semantic knowledge influences visual working memory, which suggests that the capacity of visual working memory is not fixed but instead fluctuates depending on what has to be remembered.

How the inference of hierarchical rules unfolds over time.

Inductive reasoning, which entails reaching conclusions that are based on but go beyond available evidence, has long been of interest in cognitive science. Nevertheless, knowledge is still lacking as to the specific cognitive processes that underlie inductive reasoning. Here, we shed light on these processes in two ways. First, we characterized the timecourse of inductive reasoning in a rule induction task, using pupil dilation as a moment-by-moment measure of cognitive load. Participants' patterns of behavior and pupillary responses indicated that they engaged in rule inference on-line, and were surprised when additional evidence violated their inferred rules. Second, we sought to gain insight into how participants represented rules on this task - specifically, whether they would structure the rules hierarchically when possible. We predicted the cognitive load imposed by hierarchical representations, as well as by non-hierarchical, flat ones. We used task-evoked pupil dilation as a metric of cognitive load to infer, based on these predictions, which participants represented rules with flat or hierarchical structures. Participants categorized as representing the rules hierarchically or flat differed in task performance and self-reports of strategy. Hierarchical rule representation was associated with more efficient performance and more pronounced pupillary responses to rule violations on trials that afford a higher-order regularity, but with less efficient performance on trials that do not. Thus, differences in rule representation can be inferred from a physiological measure of cognitive load, and are associated with differences in performance. These results illustrate how pupillometry can provide a window into reasoning as it unfolds over time.

An Introduction to the Approximate Number System.

What are young children's 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 children's earliest understanding of the world around them.

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). (PsycINFO Database Record

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 children's 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 children's 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.

The Acuity and Manipulability of the ANS Have Separable Influences on Preschoolers' Symbolic Math Achievement.

The approximate number system (ANS) is widely considered to be a foundation for the acquisition of uniquely human symbolic numerical capabilities. However, the mechanism by which the ANS may support symbolic number representations and mathematical thought remains poorly understood. In the present study, we investigated two pathways by which the ANS may influence early math abilities: variability in the acuity of the ANS representations, and children's' ability to manipulate ANS representations. We assessed the relation between 4-year-old children's performance on a non-symbolic numerical comparison task, a non-symbolic approximate addition task, and a standardized symbolic math assessment. Our results indicate that ANS acuity and ANS manipulability each contribute unique variance to preschooler's early math achievement, and this result holds after controlling for both IQ and executive functions. These findings suggest that there are multiple routes by which the ANS influences math achievement. Therefore, interventions that target both the precision and manipulability of the ANS may prove to be more beneficial for improving symbolic math skills compared to interventions that target only one of these factors.

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.

Eye Movements Reveal Optimal Strategies for Analogical Reasoning.

Analogical reasoning refers to the process of drawing inferences on the basis of the relational similarity between two domains. Although this complex cognitive ability has been the focus of inquiry for many years, most models rely on measures that cannot capture individuals' thought processes moment by moment. In the present study, we used participants' eye movements to investigate reasoning strategies in real time while solving visual propositional analogy problems (A:B::C:D). We included both a semantic and a perceptual lure on every trial to determine how these types of distracting information influence reasoning strategies. Participants spent more time fixating the analogy terms and the target relative to the other response choices, and made more saccades between the A and B items than between any other items. Participants' eyes were initially drawn to perceptual lures when looking at response choices, but they nonetheless performed the task accurately. We used participants' gaze sequences to classify each trial as representing one of three classic analogy problem solving strategies and related strategy usage to analogical reasoning performance. A project-first strategy, in which participants first extrapolate the relation between the AB pair and then generalize that relation for the C item, was both the most commonly used strategy as well as the optimal strategy for solving visual analogy problems. These findings provide new insight into the role of strategic processing in analogical problem solving.

Visuospatial working memory influences the interaction between space and time.

How do representations of space inform our perception of time? In language, spatial vocabulary is frequently used to describe temporal concepts, and spatial information biases temporal perception even in non-verbal tasks. In contrast, temporal information typically exerts little, if any, influence on the perception of spatial extent. Here, we used spatial and temporal reproduction tasks, both with and without verbal and spatial dual tasks, to investigate the mechanism underlying the asymmetric relation between space and time. Specifically, we tested whether the asymmetric interference between spatial and temporal stimulus attributes arises from interference in verbal or visuospatial working memory. We found that loading visuospatial working memory, but not verbal working memory, eliminated the asymmetric pattern of interference. This suggests that the interference between spatial and temporal representations arises due to processing constraints in visuospatial working memory. These findings are discussed in terms of the load theory of attention and the relative automaticity with which spatial and temporal information is processed.

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.

Number trumps area for 7-month-old infants.

Over the past few decades, there has been extensive debate as to whether humans represent number abstractly and, if so, whether perceptual features of a set such as cumulative surface area or contour length are extracted more readily than number from the external world. Here we show that 7-month-old infants are sensitive to smaller ratio changes in number than cumulative area when each variable is tested separately and that infants prefer to look at number changes compared with area changes when the 2 variables are pitted directly against each other. Our results provide strong evidence that number is a more salient dimension to young infants than cumulative surface area and that infants' ability to discriminate sets on the basis of number is more finely tuned than their ability to discriminate sets on the basis of cumulative surface area.

Infants Show Ratio-dependent Number Discrimination Regardless of Set Size.

Evidence for approximate number system (ANS) representations in infancy is robust but has typically only been found when infants are presented with arrays of four or more elements. In addition, several studies have found that infants fail to discriminate between small numbers when continuous variables such as surface area and contour length are controlled. These findings suggest that under some circumstances, infants fail to recruit either the ANS or object file representations for small sets. Here, we used a numerical change detection paradigm to assess 6-month-old infants' ability to represent small values. In Experiment 1, infants were tested with 1 versus 3, 1 versus 2, and 2 versus 3 dots. Infants successfully discriminated 1 versus 3 and 1 versus 2, but failed with 2 versus 3. In Experiment 2, we tested whether infants could compare small and large values with a 2 versus 4 condition. Across both experiments, infants' performance exhibited ratio dependence, the hallmark of the ANS. Our results indicate that infants can attend to the purely numerical attributes of small sets and that the numerical change detection paradigm accesses ANS representations in infancy regardless of set size.

Number sense in infancy predicts mathematical abilities in childhood.

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.

fMRI of syntactic processing in typically developing children: structural correlates in the inferior frontal gyrus.

Development of syntactic processing was examined to evaluate maturational processes including left language lateralization functions and increased specialization of brain regions important for syntactic processing. We utilized multimodal methods, including indices of brain activity from fMRI during a syntactic processing task, cortical thickness measurements from structural MRI, and neuropsychological measures. To evaluate hypotheses about increasing lateralization and specialization with development, we examined relationships between cortical thickness and magnitude and spatial activation extent within the left inferior frontal gyrus (IFG) and its right hemisphere homologue. We predicted that increased activation in the left and decreased activation in the right IFG would be associated with increased syntactic proficiency. As predicted, a more mature pattern of increased thickness in the right pars triangularis was associated with decreased activation intensity and extent in the right IFG. These findings suggest a maturational shift towards decreased involvement of the right IFG for syntactic processing. Better syntactic skills were associated with increased activation in the left IFG independent from age, suggesting increased specialization of the left IFG with increased proficiency. Overall, our findings show relationships between structural and functional neurodevelopment that co-occur with improved syntactic processing in critical language regions of the IFG in typically developing children.