What counts in preschool number knowledge? A Bayes factor analytic approach toward theoretical model development

The influence of language on the formation of number concepts: Evidence from preschool children who are bilingual in English and Arabic

We asked whether grammatical number marking has specific influence on the formation of early number concepts. In particular, does comprehension of dual case marking support young children's understanding of cardinality? We assessed number knowledge in 77 3-year-old Arabic-English bilingual children using the Give-a-Number task in both languages. Given recent concerns around the administration and scoring of the Give-a-Number task, we used two complementary approaches: one based on conceptual levels and the other based on overall test scores. We also tested comprehension of dual case marking in Arabic and number sequence knowledge in both languages. Regression analyses showed that dual case comprehension exerts a strong influence on cardinality tested in Arabic independent of age, general language skills, and number sequence knowledge. No such influence was found for cardinality tested in English, indicating a language-specific effect. Further analyses tested for transfer of cardinality knowledge between languages. These revealed, in addition to the findings outlined above, a powerful cross-linguistic transfer effect. Our findings are consistent with a model in which the direct effect of dual case marking is language specific, but concepts, once acquired, may be represented abstractly and transferred between languages.

Neural evidence of core foundations and conceptual change in preschool numeracy

Symbolic numeracy first emerges as children learn the meanings of number words and how to use them to precisely count sets of objects. This development starts before children enter school and forms a foundation for lifelong mathematics achievement. Despite its importance, exactly how children acquire this basic knowledge is unclear. Here we test competing theories of early number learning by measuring event-related brain potentials during a novel number word-quantity comparison task in 3-4-year-old preschool children (N = 128). We find several qualitative differences in neural processing of number by conceptual stage of development. Specifically, we find differences in early attention-related parietal electrophysiology (N1), suggesting that less conceptually advanced children process arrays as individual objects and more advanced children distribute attention over the entire set. Subsequently, we find that only more conceptually advanced children show later-going frontal (N2) sensitivity to the numerical-distance relationship between the number word and visual quantity. The nature of this response suggested that exact rather than approximate numerical meanings were being associated with number words over frontal sites. No evidence of numerical distance effects was observed over posterior scalp sites. Together these results suggest that children may engage parallel individuation of objects to learn the meanings of the first few number words, but, ultimately, create new exact cardinal value representations for number words that cannot be defined in terms of core, nonverbal number systems. More broadly, these results document an interaction between attentional and general cognitive mechanisms in cognitive development. RESEARCH HIGHLIGHTS: Conceptual development in numeracy is associated with a shift in attention from objects to sets. Children acquire meanings of the first few number words through associations with parallel attentional individuation of objects. Understanding of cardinality is associated with attentional processing of sets rather than individuals. Brain signatures suggest children attribute exact rather than approximate numerical meanings to the first few number words. Number-quantity relationship processing for the first few number words is evident in frontal but not parietal scalp electrophysiology of young children.

Are they equivalent? An examination of task variants of approximate number comparison

Nonverbal numerical ability supports individuals' numerical information processing in everyday life and is also correlated with their learning of mathematics. This ability is typically measured with an approximate number comparison paradigm, in which participants are presented with two sets of objects and instructed to choose the numerically larger set. This paradigm has multiple task variants, where the two sets are presented in different ways (e.g., two sets are presented either simultaneously or sequentially, or two sets are presented either intermixed or separately). Despite the fact that different task variants have often been used interchangeably, it remains unclear whether these variants measure the same aspects of nonverbal numerical ability. Using a latent variable modeling approach with 270 participants (Mage = 20.75 years, SDage = 2.03, 94 males), this study examined the degree to which three commonly used task variants tapped into the same construct. The results showed that a bi-factor model corresponding to the hypothesis that task variants had both commonalities and uniqueness was a better fit for the data than a single-factor model, corresponding to the hypothesis that task variants were construct equivalent. These findings suggested that task variants of approximate number comparison did not measure the same construct and cannot be used interchangeably. This study also quantified the extent to which general cognitive abilities were involved in both common and unique parts of these task variants.

Magnitude representation of preschool children with autism spectrum condition

LAY ABSTRACT

The mathematical abilities of children with autism spectrum condition have been understudied. Magnitude representation (e.g. presenting the number of a collection of objects) is a fundamental numerical ability presented since early infancy and is correlated with children's later learning of formal mathematics. It remains unclear about whether children with autism spectrum condition differ from their peers without autism spectrum condition in precision of magnitude representations. This study compared preschool children with and without autism spectrum condition in their precision of magnitude representation with an approximate number comparison task, in which children compared two sets of dots without counting and chose the set with more dots. Children with autism spectrum condition exhibited the lower numerical comparison accuracy (i.e. the weaker magnitude representation) than their peers without autism spectrum condition. This difference existed even when multiple general cognitive abilities (working memory, inhibitory control, and nonverbal intelligence) and language abilities were statistically controlled. Moreover, the individual difference of the numerical comparison accuracy was larger in children with autism spectrum condition than without autism spectrum condition. These findings suggest that children with autism spectrum condition are at risk of weaker magnitude representation from an early age, emphasizing the need for specialized mathematics education or interventions to support their learning. In addition, the large variance in the precision of their magnitude representation suggests that individualized mathematics interventions are needed for children with autism spectrum condition.

Assessing mental demand in consecutive interpreting: Insights from an fNIRS study

Consecutive interpreting involves a demanding language task where mental workload (MWL) is crucial for assessing interpreters' performance. An elevated cognitive load in interpreters may lead to the interpretation failures. The widely used NASA-TLX questionnaire effectively measures MWL. However, a global score was employed in previous interpretation studies, overlooking the distinct contributions of MWL components to the interpreters' performance. Accordingly, we recruited twenty novice interpreters who were postgraduate students specializing in interpreting to complete the consecutive interpreting task. Throughout the process, we used functional near-infrared spectroscopy (fNIRS) to monitor the hemodynamic response in participants' brains. The NASA-TLX was used to measure the MWL during interpreting with six components, including mental demand, physical demand, temporal demand, performance, effort, and frustration. Five interpretation experts were invited to assess the interpretation quality. The Bayes factor approach was employed to explore the components that contributes the most to the interpretation quality. It indicated that mental demand strongly contributed to the interpretation quality. Moreover, the mediation analysis revealed a positive correlation between mental demand and brain activation in three brain areas, which, in turn, was negatively correlated with interpretation quality, indicating the predictive role of mental demand in interpretation quality through the mediating of brain activation. The functions of the mediating brain areas, including the inferior frontal gyrus, middle temporal gyrus, and inferior temporal gyrus, aligned with the three efforts proposed by Gile's effort model, which emphasizes the significance of three fundamental efforts in achieving successful interpreting. These findings have implications for interpreter learning and training.

Characterizing exact arithmetic abilities before formal schooling

Children appear to have some arithmetic abilities before formal instruction in school, but the extent of these abilities as well as the mechanisms underlying them are poorly understood. Over two studies, an initial exploratory study of preschool children in the U.S. (N = 207; Age = 2.89-4.30 years) and a pre-registered replication of preschool children in Italy (N = 130; Age = 3-6.33 years), we documented some basic behavioral signatures of exact arithmetic using a non-symbolic subtraction task. Furthermore, we investigated the underlying mechanisms by analyzing the relationship between individual differences in exact subtraction and assessments of other numerical and non-numerical abilities. Across both studies, children performed above chance on the exact non-symbolic arithmetic task, generally showing better performance on problems involving smaller quantities compared to those involving larger quantities. Furthermore, individual differences in non-verbal approximate numerical abilities and exact cardinal number knowledge were related to different aspects of subtraction performance. Specifically, non-verbal approximate numerical abilities were related to subtraction performance in older but not younger children. Across both studies we found evidence that cardinal number knowledge was related to performance on subtraction problems where the answer was zero (i.e., subtractive negation problems). Moreover, subtractive negation problems were only solved above chance by children who had a basic understanding of cardinality. Together these finding suggest that core non-verbal numerical abilities, as well as emerging knowledge of symbolic numbers provide a basis for some, albeit limited, exact arithmetic abilities before formal schooling.

Directionality in the interrelations between approximate number, verbal number, and mathematics in preschool-aged children

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_age  = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013-2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = -.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.

Assessing the knower-level framework: How reliable is the Give-a-Number task?

The Give-a-Number task has become a gold standard of children's number word comprehension in developmental psychology. Recently, researchers have begun to use the task as a predictor of other developmental milestones. This raises the question of how reliable the task is, since test-retest reliability of any measure places an upper bound on the size of reliable correlations that can be found between it and other measures. In Experiment 1, we presented 81 2- to 5-year-old children with Wynn (1992) titrated version of the Give-a-Number task twice within a single session. We found that the reliability of this version of the task was high overall, but varied importantly across different assigned knower levels, and was very low for some knower levels. In Experiment 2, we assessed the test-retest reliability of the non-titrated version of the Give-a-Number task with another group of 81 children and found a similar pattern of results. Finally, in Experiment 3, we asked whether the two versions of Give-a-Number generated different knower levels within-subjects, by testing 75 children with both tasks. Also, we asked how both tasks relate to another commonly used test of number knowledge, the "What's-On-This-Card" task. We found that overall, the titrated and non-titrated versions of Give-a-Number yielded similar knower levels, though the non-titrated version was slightly more conservative than the titrated version, which produced modestly higher knower levels. Neither was more closely related to "What's-On-This-Card" than the other. We discuss the theoretical and practical implications of these results.

Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study

Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

Preschool deficits in cardinal knowledge and executive function contribute to longer-term mathematical learning disability

In a preschool through first grade longitudinal study, we identified groups of children with persistently low mathematics achievement (n = 14) and children with low achievement in preschool but average achievement in first grade (n = 23). The preschool quantitative developments of these respective groups of children with mathematical learning disability (MLD) and recovered children and a group of typically achieving peers (n = 35) were contrasted, as were their intelligence, executive function, and parental education levels. The core characteristics of the children with MLD were poor executive function and delayed understanding of the cardinal value of number words throughout preschool. These compounded into even more substantive deficits in number and arithmetic at the beginning of first grade. The recovered group had poor executive function and cardinal knowledge during the first year of preschool but showed significant gains during the second year. Despite these gains and average mathematics achievement, the recovered children had subtle deficits with accessing magnitudes associated with numerals and addition combinations (e.g., 5 + 6 = ?) in first grade. The study provides unique insight into domain-general and quantitative deficits in preschool that increase risk for long-term mathematical difficulties.

The contributions of executive functions to mathematical learning difficulties and mathematical talent during adolescence

Are mathematical learning difficulties caused by impairment of the abilities that underlie mathematical talent? Or are mathematical difficulties and talent qualitatively different? The main goal of this study was to determine whether mathematical learning difficulties are explained by the same executive functions as mathematical talent. We screened a pool of 2,682 first-year high school students and selected 48 for evaluation, dividing them into three groups: those with mathematical learning difficulties (n = 16), those with typical performance (n = 16), and those with mathematical talent (n = 16). Adolescents from the learning difficulties and talented groups had age, reading skills, and verbal and non-verbal intelligence that were similar to those of the typical performance group. Participants were administered a suite of tasks to evaluate verbal and visual short-term memory and executive functions of inhibition, shifting, and updating. Different executive functions showed different contributions at the two ends of the math ability continuum: lower levels of performance in updating visual information were related to mathematical learning difficulties, while greater shifting abilities were related to mathematical talent. Effect sizes for the differences in performance between groups were large (Hedges' g > 0.8). These results suggest that different executive functions are associated with mathematical learning difficulties and mathematical talent. We discuss how these differences in executive functions could be related to the different types of mathematical abilities that distinguish the three groups.

Explaining early moral hypocrisy: Numerical cognition promotes equal sharing behavior in preschool-aged children

Recent work has documented that despite preschool-aged children's understanding of social norms surrounding sharing, they fail to share their resources equally in many contexts. Here we explored two hypotheses for this failure: an insufficient motivation hypothesis and an insufficient cognitive resources hypothesis. With respect to the latter, we specifically explored whether children's numerical cognition-their understanding of the cardinal principle-might underpin their abilities to share equally. In Experiment 1, preschoolers' numerical cognition fully mediated age-related changes in children's fair sharing. We found little support for the insufficient motivation hypothesis-children stated that they had shared fairly, and failures in sharing fairly were a reflection of their number knowledge. Numerical cognition did not relate to children's knowledge of the norms of equality (Experiment 2). Results suggest that the knowledge-behavior gap in fairness may be partly explained by the differences in cognitive skills required for conceptual and behavioral equality.