Pathways to Mathematics: Longitudinal Predictors of Performance

Strategy variability in computational estimation and its association with mathematical achievement

Computational estimation requires a breadth of strategies and selection of the relevant strategy given a problem's features. We used the new Test of Estimation Strategies (TES), composed of 20 arithmetic problems (e.g., 144 x 0.38), to investigate variability in strategy use in young adults. The TES targets the five estimation strategies that adults use most frequently, which fall into two Classes. The three Class One strategies are general-purpose and taught in schools. Proceed Algorithmically entails applying an algorithm (e.g., shifting a decimal place). Round One and Round Two are defined as rounding one or both operands, respectively. The two Class Two strategies are more advanced, requiring application of conceptual knowledge of mathematics. Known-and-Nice is used when a participant relies on a well-known mathematical fact (e.g., 25 × 4 = 100) to form an estimate. Fractions uses a fraction or percentage in the estimation process (e.g., 943 x 0.48 is about 50% or half of 900). We divided our sample of adult participants into two groups (i.e., high, average) based on their estimation performance on the TES. The high-performance group used a broader range of strategies and more frequently applied the most relevant strategy given a problem's features. Overall estimation accuracy was correlated with mathematical achievement, as were strategy breadth and strategy relevance. However, none of these associations survived first controlling for verbal achievement. Participants' strategy reports suggested that the TES problems were generally successful in eliciting the five target strategies and provided evidence for a new strategy, Partitioning. These findings provide a basis for future instructional studies to improve students' computational estimation.

Predicting individual differences in preschoolers' numeracy and geometry knowledge: The role of understanding abstract relations between objects and quantities

Preschoolers' mathematics knowledge develops early and varies substantially. The current study focused on two ontogenetically early emerging cognitive skills that may be important predictors of later math skills (i.e., geometry and numeracy): children's understanding of abstract relations between objects and quantities as evidenced by their patterning skills and the approximate number system (ANS). Children's patterning skills, the ANS, numeracy, geometry, nonverbal intelligence (IQ), and executive functioning (EF) skills were assessed at age 4 years, and their numeracy and geometry knowledge was assessed again a year later at age 5 (N = 113). Above and beyond children's initial knowledge in numeracy and geometry, as well as IQ and EF, patterning skills and the ANS at age 4 uniquely predicted children's geometry knowledge at age 5, but only age 4 patterning uniquely predicted age 5 numeracy. Thus, although patterning and the ANS are related, they differentially explain variation in later geometry and numeracy knowledge. Results are discussed in terms of implications for early mathematics theory and research.

Mathematics skills in children with genetic generalized epilepsy: Cognitive and clinical correlates. Preliminary results

Impairments in mathematics have been found in children with Genetic Generalized Epilepsy (GGE), yet little is known about the underpinnings of these difficulties. The aim of this study was to investigate basic numeracy and secondary mathematics skills in GGE and explore cognitive and clinical correlates that relate to those skills. Nineteen children with GGE and 22 typically developing controls aged 8-16 years completed a neuropsychological battery which assessed: (i) basic numeracy skills: non-symbolic and symbolic magnitude comparison; (ii) secondary mathematics skills: calculation, reasoning, and fluency; and (iii) cognitive skills: intelligence, fluid reasoning, processing speed, and working memory. Epilepsy clinical factors (age of epilepsy onset, duration of epilepsy, number of anti-seizure medications) were also recorded. Children with GGE were impaired in select basic numeracy skills (non-symbolic magnitude comparison), and all secondary mathematics skills compared to controls. In children with GGE, the visuo-spatial central executive correlated with both basic numeracy skills. The verbal central executive correlated with mathematics reasoning. Non-verbal intelligence was related to symbolic magnitude comparison and mathematics reasoning. Fluid reasoning was correlated with non-symbolic magnitude comparison and mathematics problems solving. Epilepsy variables did not relate to mathematics outcomes. Overall, we found that children with GGE experience significant difficulties in select basic numeracy and all secondary mathematics skills. Risk factors for mathematics difficulties included reduced working memory capacity, lower intelligence and fluid reasoning. Our findings suggest that children with GGE may require accommodation for limited central executive working memory capacity in combination with academic supports for poor mathematics skills.

Knowing what they know: Preschool teachers' knowledge of math skills and its relation to instruction

Math experiences during the preschool years play an important role in children's later math learning. Preschool teachers exhibit considerable variability in the amount and types of mathematics activities they engage in with their students; one potentially important source of these individual differences is adults' knowledge of early math development. The current study aimed to describe preschool teachers' knowledge of numeracy, patterning, and spatial/geometric skills developed in preschool and its relation to their reported mathematics instruction. Participants (N = 83) completed a survey in which they judged whether particular early math skills could be observed in typically developing 4-year-olds in the United States and reported their frequency of engaging in different math instructional activities. Pre- and in-service preschool teachers' knowledge varied across the different domains (i.e., numeracy, patterning, and spatial/geometric) of mathematical thinking, but their reported frequency of instruction did not. Teachers who were found to be more accurate in their knowledge of early math development were more likely to report higher frequency of math instruction; looking specifically at the domains, the strength of association between knowledge and instruction was the strongest for numeracy. Such findings highlight the possibility that supporting preschool teachers' knowledge of the range of math skills their students can be developing may be one component of improving early math teaching and learning.

Executive functioning profiles and mathematical and reading achievement in Grades 2, 6, and 10

Using a person-centered approach, we aimed to identify different executive functioning profiles to assess heterogeneity across individuals within the same school grade through latent profile analysis. A sample of 150 Grade 2 (7-8 years old), 150 Grade 6 (11-12 years old), and 150 Grade 10 (15-16 years old) children and adolescents were assessed on 11 different executive tasks representative of the three main executive functioning subcomponents (i.e., inhibition, cognitive flexibility, and working memory), fluid intelligence, processing speed, problem-solving, and reading comprehension. Three different executive functioning profiles of different patterns of interactions based on inhibition, cognitive flexibility, and working memory within and between grades were identified. Moreover, these profiles were differentially related to reading comprehension and mathematical achievement. Second, as expected, we did not find these profiles to be associated with sociodemographic variables such as chronological age or sex. Still, fluid intelligence and processing speed were differentially related to the different profiles at each grade. We also found that the executive functioning profiles interacted with each cognitive skill (i.e., fluid intelligence and processing speed) in predicting reading comprehension and math achievement. These findings provide valuable insights for developing preventive and intervention strategies in education.

Perceptual subitizing performance in 3- and 4-year-olds: The impact of visual features of sets

Perceptual subitizing is a pivotal skill in children's mathematical development. It is defined as the rapid identification of small numerosities. Previous studies pointed to the contribution of visual features of sets to perceptual subitizing performance in adults. Insights into the contribution of visual features to subitizing performance in the critical 3- to 4-year age range are scant. This study aimed to address this gap by investigating the impact of visual features on perceptual subitizing performance (accuracy and response time) in 3- and 4-year-olds. Participants (119 3- and 4-year-olds) were offered a subitizing task that incorporated pictures of sets of three to five objects. The pictures systematically varied across four visual features: (a) pictorial context (distractors present vs. absent), (b) set homogeneity (homogeneous vs. heterogeneous objects), (c) set arrangement (linearly vs. randomly arranged objects), and (d) set differentiation (distinct vs. overlapping objects). Pictures with distractors, heterogeneous objects, randomly arranged objects, or overlapping objects were associated with lower subitizing accuracy and longer response times compared with pictures without distractors, homogeneous objects, linearly arranged objects, or distinct objects, respectively. Pictures with randomly arranged or overlapping objects along with distractors were associated with even lower subitizing accuracy. Pictures featuring a simple visual design-without distractors and with homogeneous, linearly arranged, and distinct sets-yielded the best subitizing performance in terms of accuracy and response time. Our findings might be explained by the cognitive processes underlying 3- and 4-year-olds' subitizing performance. The findings offer building blocks for future research in the domain and preschool educational practice.

The roles of mathematical language and emergent literacy skills in the longitudinal prediction of specific early numeracy skills

Mathematical language (i.e., content-specific language used in mathematics) and emergent literacy skills predict children's broad numeracy development. However, little work has examined whether these domains predict development of individual numeracy skills (e.g., cardinality, number order). Thus, the aim of the current study was to examine longitudinal relations among mathematical language, emergent literacy skills, and specific early numeracy skills. Participants included 114 preschool children aged 3.12 to 5.26 years (M = 4.17 years, SD = 0.59). Specifically, this study examined whether mathematical language and three emergent literacy skills (print knowledge, phonological awareness, and general vocabulary) in the fall of preschool predicted 12 individual early numeracy skills in the spring, controlling for age, sex, rapid automatized naming, parent education, and autoregressors. Results indicated that mathematical language predicted development of most of the early numeracy skills (e.g., set comparison, numeral comparison, numeral identification), but findings for emergent literacy skills were not robust. Among the three emergent literacy skills, only print knowledge was a significant predictor of development in some specific numeracy skills, including verbal counting, number order, and story problems. Results highlight the important role of mathematical language in children's numeracy development and provide the foundation for future work in designing interventions to improve early numeracy skills.

Academic skills in children with cerebral palsy and specific learning disorders

AIM

To investigate the prevalence and clinical manifestations of reading, writing, and mathematics disorders in children with cerebral palsy (CP). We explored how the clinical profile of these children differed from those with specific learning disorders (SLDs), taking into account several factors, particularly IQ scores, neuropsychological aspects, and the presence of a visual impairment.

METHOD

A prospective cross-sectional study was conducted in 42 children with CP (mean age 9 years 8 months; SD = 2 years 2 months) and 60 children with SLDs (mean age 10 years; SD = 1 year 7 months). Clinical characteristics, neuromotor and cognitive profiles, neuropsychological aspects (speech performance, academic skills, visual attention, phonological awareness, working memory), and signs of visual impairment (visual acuity, contrast sensitivity, visual field, oculomotor functions) were assessed. A machine learning approach consisting of a random forest algorithm, where the outcome was the diagnosis and the covariates were the clinical variables collected in the sample, was used for the analyses.

RESULTS

About 59% of the children with CP had reading, writing, or mathematics disorders. Children with CP with learning disorders had a low performance IQ, normal phonological awareness, and working memory difficulties, whereas children with SLDs had normal performance IQ, impaired phonological awareness, and mild working memory difficulties. There were no differences in verbal IQ between the two groups.

INTERPRETATION

Learning disorders are frequently associated with CP, with different clinical characteristics, compared with SLDs. Assessment of academic skills is mandatory in these children, even if the IQ is normal. At school age, specific interventions to promote academic skills in children with CP could be a major rehabilitative goal.

WHAT THIS PAPER ADDS

Reading, writing, and mathematics disorders in cerebral palsy have specific clinical characteristics. Their underlying mechanisms differ from those described in specific learning disorders. Working memory impairment can be considered a hallmark of learning disorders in children with cerebral palsy.

Motor activities to improve maths performance in pre-school children with typical development

Poor maths skills are associated with negative outcomes throughout life, such as lower academic qualifications, decreased professional success and socio-economic results. Mathematical skills emerge continuously throughout childhood and those that children acquire in pre-school are crucial for activities that support analytical thinking, problem-solving and reasoning and argumentation skills. Many of these activities are related to motor skills, since certain cognitive and motor areas of the brain are activated simultaneously when solving maths problems. Of all motor skills, visuomotor integration skills have been documented as those that are most consistently positively and significantly associated with maths performance in pre-school children. These skills are influenced by visual perception (spatial and attention skills), fine motor coordination and gross motor skills. Early intervention can improve visuomotor integration skills in pre-school children. Of all skills that make up visuomotor integration, spatial skills, in addition to being the first skills to influence numerical knowledge and the recognition of geometric shapes, are also those skills that form part of the majority of programs and activities to be worked on with pre-school children for the development of mathematical concepts. However, most intervention programs or activities to develop spatial skills are carried out in the classroom, usually through activities involving handling small objects. In this sense and given the significant association between visuomotor integration skills and gross motor skills, the main objective of this study was to list a set of activities to develop spatial skills, with a strong involvement of gross motor skills, in a classroom, playground or home context.

Comorbid Word Reading and Mathematics Computation Difficulty at Start of First Grade

The purpose of this analysis was to describe cognitive processes associated with comorbid difficulty between word reading (WR) and mathematics computation (MC) at the start of first grade among children selected for WR and MC delays. A sample of 234 children (mean age 6.50 years, SD = 0.31) was assessed on WR, MC, core cognitive processes (phonological processing, rapid automatized naming, verbal counting [VC]), and domain-general cognitive processes (working memory, oral language, nonverbal reasoning, attentive behavior). Structural equation modeling was used to predict a latent Comorbidity factor, which modeled shared variance between WR and MC, and to identify processes associated with that Comorbidity factor. Results identified each of the core cognitive processes, especially VC, and each of the domain-general cognitive processes, especially working memory, as explaining shared variance between WR and MC. Implications for understanding comorbid difficulty at the start of first grade and designing coordinated first-grade interventions are discussed.

Longitudinal joint modeling for assessing parallel interactive development of latent ability and processing speed using responses and response times

To measure the parallel interactive development of latent ability and processing speed using longitudinal item response accuracy (RA) and longitudinal response time (RT) data, we proposed three longitudinal joint modeling approaches from the structural equation modeling perspective, namely unstructured-covariance-matrix-based longitudinal joint modeling, latent growth curve-based longitudinal joint modeling, and autoregressive cross-lagged longitudinal joint modeling. The proposed modeling approaches can not only provide the developmental trajectories of latent ability and processing speed individually, but also exploit the relationship between the change in latent ability and processing speed through the across-time relationships of these two constructs. The results of two empirical studies indicate that (1) all three models are practically applicable and have highly consistent conclusions in terms of the changes in ability and speed in the analysis of the same data set, and (2) additional analysis of the RT data and acquisition of individual processing speed measurements can reveal the parallel interactive development phenomena that are difficult to detect using RA data alone. Furthermore, the results of our simulation study demonstrate that the proposed Bayesian Markov chain Monte Carlo estimation algorithm can ensure accurate model parameter recovery for all three proposed longitudinal joint models. Finally, the implications of our findings are discussed from the research and practice perspectives.

Fraction Ball impact on student and teacher math talk and behavior

We assessed the impacts of Fraction Ball-a novel suite of games combining the benefits of embodied guided play for math learning-on the math language production and behavior of students and teachers. In the Pilot Experiment, 69 fifth and sixth graders were randomly assigned to play four different Fraction Ball games or attend normal physical education class. The Efficacy Experiment was implemented to test improvements made through co-design with teachers with 160 fourth through sixth graders. Researchers observed and coded for use of math language and behavior. Playing Fraction Ball resulted in consistent increases of students' and teachers' use of fraction (SDs = 0.98-2.42) and decimal (SDs = 0.65-1.64) language and number line arithmetic, but not in whole number, spatial language, counting, instructional gesturing, questioning, and planning. We present evidence of the math language production in physical education and value added by Fraction Ball to support rational number language and arithmetic through group collaboration.

Early numeracy profiles in young children with intellectual disabilities: The role of cognitive functions

Exploring individual differences and looking beyond averaged parameters of early numeracy in young children with mild intellectual disabilities has become an area of interest to many researchers worldwide. This study aimed to identify the different profiles of early numeracy skills in young children with mild intellectual disabilities. For this purpose, we assessed early numeracy through Utrecht early numeracy test and learning aptitude through Detroit Test, in a sample of 135 children diagnosed with intellectual disabilities. The mean of their mental age was 5:09 (years:months). Two-step cluster analysis identified four homogenous groups of children with distinct early numeracy profiles as follows:C1 were fluent in relational and numerical skills up to 20, C2 were fluent in relational skills and numerical skills up to 10, C3 had basic knowledge of relational skills and inconsistent numerical skills up to 10 and C4 had inconsistent relational skills and numerical skills. Results are discussed with reference to their educational implications.

Positive math attitudes are associated with greater frontal activation among children from higher socio-economic status families

Math learning is explained by the interaction between cognitive, affective, and social factors. However, studies rarely investigate how these factors interact with one another to explain math performance. This study aims to fill this gap in the literature by using functional magnetic resonance imaging (fMRI) to understand the neurocognitive mechanisms underlying the interaction between parental socioeconomic status (SES) and children's math attitudes. To this aim, 57 children solved multiplication problems inside the scanner. We measured parental SES by creating two groups based on parents' occupations and measured children's math attitudes using a questionnaire. We ran a cluster-wise regression analysis examining the interaction between these two variables while controlling for the main effects of SES, math attitudes, and full IQ. The analysis revealed a cluster in the left inferior frontal gyrus (IFG), which was due to children with positive math attitudes from high socio-economic status families showing greater IFG activation when solving large multiplication problems as compared to their negative attitudes high SES peers, suggesting that they exhibited more retrieval effort to solve large multiplication problems. We discuss how this may be because they were the only ones who fully engaged in math opportunities provided by their environment.

Transcoding of French numbers for first- and second-language learners in third grade

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7-9 years) and their language skills. Transcoding in French is of particular interest because the spoken number language system does not completely correspond to that of the written digits (e.g., quatre-vingt-dix [four-twenty-ten] and 90). We hypothesised that the complex linguistic structure of spoken numbers in French would be challenging for students who are learning to transcode. First and second French-language learners' accuracy and errors were recorded during a writing task of 3- to 7-digit numbers. Children also completed linguistic tests (e.g., receptive vocabulary, receptive syntax). Results showed that first- and second-language learners did not differ in their transcoding accuracy. Number size, decade complexity of stimulus number words in French (i.e., numbers containing a complex decade, operationalized as a number between soixante-dix, 70, and quatre-vingt-dix-neuf, 99), and receptive vocabulary predicted children's French transcoding skills. Students were more likely to produce errors (e.g., 68 or 6018 for 78) when they transcoded complex decade numbers compared with simple decade numbers. When an error was made on the complex decade portion of a number, it was likely a lexical error. In conclusion, third graders, both first- and second-language learners, found complex decade numbers challenging and their performance was related to their general vocabulary skills.

Cognitive Predictors of the Overlap of Reading and Math in Middle School

Math and reading skills are known to be related, and predictors of each are well researched. What is less understood is the extent to which these predictors, uniquely and collectively, overlap with one another, are differentially important for different academic skills, and account for the overlap of math and reading. We examined 20 potential predictors from four domains (working memory, processing speed, attention, and language) using latent variables and both timed and untimed achievement skill, in a sample (N=212) of at-risk middle schoolers, half of whom were English learners. The predictors accounted for about half of the overlap among achievement skills, suggesting that other factors (e.g., domain specific skills) might also be relevant for the overlap. We also found some differential prediction (language for reading, working memory for math). The present results extend and refine our understanding of the contribution of these cognitive predictors for reading and math.

Chinese parents' support of preschoolers' mathematical development

Research has documented the critical role played by the early home environment in children's mathematical development in Western contexts. Yet little is known about how Chinese parents support their preschoolers' development of math skills. The Chinese context is of particular interest because Chinese children outperform their Western counterparts in math, even early in development. The current study sought to fill this gap by examining a sample of 90 families of 4- and 5-year-olds from mainland China. Parental support-as measured by the frequency of parent-child engagement in home activities as well as parent number talk-and parents' role in children's numeracy skills were investigated. Results indicate wide variation among parents in both types of support. Frequency of engagement in formal numeracy activities, including counting objects and reading number story books, was related to children's knowledge of cardinality. A principal components analysis did not identify informal numeracy activities as a distinct home activity component, likely due to the infrequent occurrences of game-like numeracy activities among the Chinese families. Instead, a structured activity component emerged (e.g., playing musical instruments) and was positively related to children's arithmetic skills. Diversity, but not quantity, of parent number talk was related to children's symbolic magnitude understanding. The distinctive relationships between specific parental measures and child outcomes speak to the need for nuanced identification of home environment factors that are beneficial to particular math competencies. The findings also suggest cultural variations in the mechanisms that support children's mathematical development, highlighting the merits of investigating this topic in non-Western contexts.

Socio-Economic and Cultural Context in the Development of Early Mathematical Competencies: A Comparative Study of Specific Educational Contexts in Chile and Spain

This research presents the findings of a comparative study of mathematical competence among 130 students (M = 54.08 months; SD = 2.57) from vulnerable school contexts in Chile and the Spanish public school system. The study analyses a set of general and specific domain precursors for which evidence of socioeconomic background exists. Using multivariate regression and discriminant analysis techniques, we calculated similarities and differences between groups by comparing these precursors. Significant differences were found between the Spanish and Chilean groups (p < .05); however, no differences were observed in non-symbolic comparison and receptive vocabulary. Possible reasons for the existence and extent of these differences are discussed in terms of socio-cultural and educational contexts.

How do socioeconomic attainment gaps in early mathematical ability arise?

Socioeconomic attainment gaps in mathematical ability are evident before children begin school, and widen over time. Little is known about why early attainment gaps emerge. Two cross-sectional correlational studies were conducted in 2018-2019 with socioeconomically diverse preschoolers, to explore four factors that might explain why attainment gaps arise: working memory, inhibitory control, verbal ability, and frequency of home mathematical activities (N = 304, 54% female; 84% White, 10% Asian, 1% black African, 1% Kurdish, 4% mixed ethnicity). Inhibitory control and verbal ability emerged as indirect factors in the relation between socioeconomic status and mathematical ability, but neither working memory nor home activities did. We discuss the implications this has for future research to understand, and work towards narrowing attainment gaps.

Visual perception and linguistic abilities, not quantitative knowledge, count in geometric knowledge of kindergarten children

Geometric knowledge is one of the important mathematical skills acquired by children at a young age and is a major area of future mathematical learning; however, there is no direct research on the factors influencing kindergarteners' early geometric knowledge. The pathways model to mathematics was modified to examine the cognitive mechanisms underlying geometric knowledge in Chinese kindergarten children aged 5-7 (n = 99). Quantitative knowledge, visual-spatial processing, and linguistic abilities were stepped into hierarchical multiple regression models. The results revealed that after age, sex, and nonverbal intelligence were statistically controlled, visual perception, phonological awareness, and rapid automatized naming in linguistic abilities significantly predicted the variation in geometric knowledge. For quantitative knowledge, neither dot comparison nor number comparison test could be a significant precursor of geometry skills. The findings indicate that visual perception and linguistic abilities, not quantitative knowledge, account for the geometric knowledge of kindergarten children.

The importance of spatial language for early numerical development in preschool: Going beyond verbal number skills

Recent evidence suggests that spatial language in preschool positively affects the development of verbal number skills, as indexed by aggregated performances on counting and number naming tasks. We firstly aimed to specify whether spatial language (the knowledge of locative prepositions) significantly relates to both of these measures. In addition, we assessed whether the predictive value of spatial language extends beyond verbal number skills to numerical subdomains without explicit verbal component, such as number writing, symbolic magnitude classifications, ordinal judgments and numerosity comparisons. To determine the unique contributions of spatial language to these numerical skills, we controlled in our regression analyses for intrinsic and extrinsic spatial abilities, phonological awareness as well as age, socioeconomic status and home language. With respect to verbal number skills, it appeared that spatial language uniquely predicted forward and backward counting but not number naming, which was significantly affected only by phonological awareness. Regarding numerical tasks that do not contain explicit verbal components, spatial language did not relate to number writing or numerosity comparisons. Conversely, it explained unique variance in symbolic magnitude classifications and was the only predictor of ordinal judgments. These findings thus highlight the importance of spatial language for early numerical development beyond verbal number skills and suggest that the knowledge of spatial terms is especially relevant for processing cardinal and ordinal relations between symbolic numbers. Promoting spatial language in preschool might thus be an interesting avenue for fostering the acquisition of these symbolic numerical skills prior to formal schooling.

Understanding the complexities of mathematical cognition: A multi-level framework

Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.

Associations and indirect effects between LEGO® construction and mathematics performance

There is a known association between LEGO® construction ability and mathematics achievement, yet the mechanisms which drive this association are largely unknown. This study investigated the spatial mechanisms underlying this association, and whether this differs for concrete versus digital construction. Between January 2020 and July 2021, children aged 7-9 years (N = 358, 189 female, ethnicity not recorded) completed spatial and mathematics tasks, and either a concrete or digital Lego construction task. Mediation analyses examining direct and indirect pathways (through spatial skills) between Lego construction ability and mathematics explained 8.4% to 26.6% of variance in mathematics scores. Exploratory moderated mediation analyses revealed that only the indirect path through mental rotation differed between Lego conditions. Findings are discussed in relation to theories of spatial-numerical associations and the potential of Lego training for mathematics improvement.

Talking About the Absent and the Abstract: Referential Communication in Language and Gesture

Human language permits us to call to mind objects, events, and ideas that we cannot witness directly, either because they are absent or because they have no physical form (e.g., people we have not met, concepts like justice). What enables language to transmit such knowledge? We propose that a referential link between words, referents, and mental representations of those referents is key. This link enables us to form, access, and modify mental representations even when the referents themselves are absent ("absent reference"). In this review we consider the developmental and evolutionary origins of absent reference, integrating previously disparate literatures on absent reference in language and gesture in very young humans and gesture in nonhuman primates. We first evaluate when and how infants acquire absent reference during the process of language acquisition. With this as a foundation, we consider the evidence for absent reference in gesture in infants and in nonhuman primates. Finally, having woven these literatures together, we highlight new lines of research that promise to sharpen our understanding of the development of reference and its role in learning about the absent and the abstract.

Preschool Children's Loose Parts Play and the Relationship to Cognitive Development: A Review of the Literature

Play is an integrative process, and the skills acquired in it-overcoming impulses, behavior control, exploration and discovery, problem-solving, reasoning, drawing conclusions, and attention to processes and outcomes are foundational cognitive structures that drive learning and motivation. Loose parts play is a prominent form of play that many scholars and educators explicitly endorse for cognitive development (e.g., divergent thinking, problem-solving). It is unique among play types because children can combine different play types and natural or manufactured materials in one occurrence. While educators and policymakers promote the benefits of loose parts play, no previous research has explored the direct relationship between preschool-age children's indoor loose parts play experiences and cognitive development. We address this gap by bringing together the relevant literature and synthesizing the empirical studies on common play types with loose parts, namely object and exploratory, symbolic and pretend, and constructive play. We also focus on studies that examine children's experiences through loose parts, highlighting the impact of different play types on learning through the reinforcement of cognitive skills, such as executive function, cognitive self-regulation, reasoning, and problem-solving. By examining the existing literature and synthesizing empirical evidence, we aim to deepen our understanding of the relationship between children's play with loose parts and its impact on cognitive development. Ultimately, pointing out the gaps in the literature that would add to the body of knowledge surrounding the benefits of play for cognitive development and inform educators, policymakers, and researchers about the significance of incorporating loose parts play into early childhood education.

The Role of Working Memory in Early Literacy and Numeracy Skills in Kindergarten and First Grade

The working memory system supports learning processes such as acquiring new information and the development of new skills. Working memory has been found to be related to both early literacy and early numeracy in kindergarten and to linguistic and mathematical academic skills at older ages, but the contribution of each of the memory components at these ages is not yet clear. The purpose of this study is to examine the unique connections among the various systems of WM, early literacy, and early numeracy using various assessment tests of simple WM and complex WM, as well as a variety of tasks in math and language skills administered to the same 250 children in kindergarten and 150 children in first grade. Consistent with the predictions, significant relations among all components of memory and mathematics and language knowledge at both ages were found, although these connections were differential for the different types of tasks and memory systems. The connection of complex WM was stronger in its contribution and more significant in first grade in both mathematics and language domains. Complex WM resources were more important in early literacy at kindergarten age, while simple WM seems to be important in early numeracy. The theoretical and educational implications of these results are discussed accordingly.

Audio-Corsi: a novel system to evaluate audio-spatial memory skills

Spatial memory (SM) is a multimodal representation of the external world, which different sensory inputs can mediate. It is essential in accomplishing everyday activities and strongly correlates with sleep processes. However, despite valuable knowledge of the spatial mechanisms in the visual modality, the multi-sensory aspects of SM have yet to be thoroughly investigated due to a lack of proper technologies.This work presents a novel acoustic system built around 3D audio spatial technology. Our goal was to examine if an afternoon nap can improve memory performance, measured through the acoustic version of the Corsi Block Tapping Task (CBTT), named Audio-Corsi. We tested five adults over two days. During one of the two days (Wake), participants performed the Audio-Corsi before (Pre) and after (Post) a wake resting period; while the other day (Sleep), participants performed the Audio-Corsi before (Pre) and after (Post) a nap. Day orders were randomized. We calculated the memory span for the Pre and Post session in both the Wake and Sleep days. Preliminary results show a significant difference in the memory span between the Wake and Sleep days. Specifically, memory span decreased between the pre-and post-test during the wake day. The opposite trend was found for the sleep day. Results indicate that SM can be improved by sleeping also in the acoustic modality other than the visual one.Clinical Relevance- The technology and procedure we designed and developed could be suitable in clinical and experimental settings to study high-level cognitive skills in the auditory sensory modality and their relationship with sleep, especially when vision is absent or distorted (i.e. blindness).

Spatial-Numerical Magnitude Estimation Mediates Early Sex Differences in the Use of Advanced Arithmetic Strategies

An accumulating body of literature points to a link between spatial reasoning and mathematics learning. The present study contributes to this line of research by investigating sex differences both in spatial representations of magnitude and in the use of arithmetic strategies, as well as the relation between the two. To test the hypothesis that sex differences in spatial-numerical magnitude knowledge mediate sex differences in the use of advanced strategies (retrieval and decomposition), two studies were conducted. Study 1 included 96 US first graders (53% girls); Study 2 included 210 Russian first graders (49% girls). All participants completed a number line estimation task (a spatially based measure of numerical magnitude knowledge) and an arithmetic strategy task (a measure of strategy choice). The studies showed parallel results: boys produced more accurate numerical magnitude estimates on the number line estimation task and used advanced strategies more frequently on the arithmetic task. Critically, both studies provide support for the mediation hypothesis (although there were some differences in the pattern obtained for the two strategies). The results are discussed in the context of broader research about the relation between spatial and mathematical skills.

Proportional Reasoning Deficit in Dyslexia

Dyslexia has been linked to an altered perception of metrical structures in language, but no study to date has explored the link between reading impairments and other forms of metrical thinking (e.g., proportional reasoning). In the present study, we assessed proportional reasoning in 16 dyslexic children and 16 age-matched controls from 7 to 10 years of age in order to investigate whether dyslexia might be also linked to an altered form of metrical thinking. We found that dyslexic children are less accurate in performing judgments about proportionality compared to typical peers and that reading accuracy correlates with proportional reasoning abilities for 7-8-year-old children. Overall, these findings suggest that a link exists between reading and proportional reasoning abilities. We might speculate that fostering reasoning based on the meter can facilitate reading because it permits the segmentation of words in syllables and that dyslexia can be identified early with alternative non-reading tasks such as the proportional reasoning task used in this work.

Early rapid naming longitudinally predicts shared variance in reading and arithmetic fluency

A number of cognitive factors have been suggested to underlie development in reading and arithmetic skills. Although the two domains are strongly linked, only a few studies have investigated the processes that are shared between them during the early school years. Rapid automatized naming (RAN) has been identified as a strong predictor of a common fluency factor in reading and arithmetic. In the current study with 232 Norwegian children, we examined how RAN in preschool and Grade 1 relates to the shared and nonshared variance in arithmetic fluency and reading fluency in Grade 3. Furthermore, we examined whether related processing skills (phoneme awareness, working memory, speed of processing, and symbol knowledge) can account for the relationship between RAN and shared fluency-or if they predict variance that is unique to each domain. Our results show that RAN in both preschool and Grade 1 is a strong predictor of shared variance between reading fluency and arithmetic fluency measured several years later, whereas other predictors mainly relate to the nonshared parts of variance in the fluency outcomes. That is, control variables with the theoretical potential to explain some of RAN's relation to the overlap between reading and arithmetic fluency do not in fact account for this relationship. Our findings provide a starting point for future investigations of the mechanisms of rapid naming.

The home numeracy environment and children's math skills: The moderating role of parents' math anxiety

Evidence suggests that parents' math anxiety moderates the association between parents' help in mathematics homework and first graders' mathematics skills. Understanding whether similar associations are evident in younger children, in regard to the home numeracy environment (HNE) is essential, given that early math skills are strong predictors of later academic outcomes, and children's skills prior to kindergarten are fostered principally by their parents. Thus, the purpose of this study was to examine the association and interaction between the HNE and parents' math anxiety related to preschool children's numeracy performance. Participants were 121 parent-child dyads. Results from hierarchical multiple regression models demonstrated that parents' math anxiety and the HNE, included as separate predictors of children's math skills, were not statistically significant. However, the interaction between HNE and parents' math anxiety was statistically significant, such that the positive association between HNE and children's numeracy skills emerged when parents felt less anxious about math. These findings highlight the importance of accounting for parents' math anxiety when exploring the home influences on children's numeracy skills.

A language compatibility effect in fraction processing

A language compatibility effect occurs when there is a match between what a language provides and what a mathematical task demands. Here, we investigated whether such an effect exists for fraction processing in English, which names the numerator first, versus Korean, which names the denominator first. We developed two new tasks: a fraction span task where participants view and then recall four fractions and a fraction identification task where they view one fraction and then another and judge whether the two fractions are the same or not. We generally found that English speakers were advantaged when the numerator drove task performance and Korean speakers were advantaged when the denominator was critical. These findings, particularly from the fraction identification task, were inconsistent with the attentional focus hypothesis, which proposes that the serialisation bias of a language guides which fraction component is attended to first. Rather, they were better explained by the verbal encoding hypothesis, which states that a necessary condition for observing language compatibility effects may be that the fraction components must be encoded in verbal working memory and rehearsed there.

Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence

Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the "Groupitizing" ability in 1209 third to eighth graders (mean age at first timepoint = 10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures the ability to use grouping cues to access the exact value of a set. Groupitizing improves each year from late childhood to early adolescence (d = 3.29), is a central predictor of math achievement (beta weight = .30), is linked to conceptual processes in mathematics (minimum d = 0.69), and helps explain the dynamic between the ongoing development of non-symbolic number concepts, systemic educational inequities in school associated with SES, and mathematics achievement (minimum beta weight = .11) in ways that explicit symbolic measures may miss.

The effect of implementation intentions on event-, time-, and activity-based prospective memory in typically developing children

Prospective memory (PM) refers to the ability to remember and complete planned tasks in the future, which relies on working memory (WM) for encoding and maintaining the intention. Implementation intention is a useful strategy for improving PM function in adults. Yet the effect of implementation intentions in children, and whether factors such as age, gender, and WM capacity could modulate its effect remains unclear. In this study, we examined the effect of implementation intentions on PM in 154 children at 7–11 years of age. The standard group received standard instructions on PM task, whereas the implementation intention group received additional PM instruction, which comprised the “if . . . then . . .” format and guided visual imagery of the PM scenario. Participants completed the computer-based PM tasks (tapping into focal event-, time-, and activity-based PM) and the WM tests. The results showed that the two groups exhibited similar focal event-, time-, and activity-based PM performance. Although age and gender did not modulate the effect of implementation intentions on PM, WM capacity moderated the implementation intention effect on time-based PM. Specifically, higher WM capacity predicted higher implementation intention benefit. These findings suggest that children with higher WM capacity may have higher chance to benefit from the implementation intention strategy.

With a little help from our pediatrician: An intervention to promote mathematics-related home activities through regular well-child visits

Introduction

Children's involvement in mathematics-related activities in the home environment is associated with the development of their early numeracy over the preschool years. Intervention studies to promote parents' awareness and provision of mathematics-related home activities are however scant. In this study we developed and tested the effectiveness of a non-intensive intervention program delivered by community pediatricians to promote mathematics-related activities in the home environment.

Methods

Parents of 204 Italian children were invited to report on the frequency of mathematics-related home activities when children attended the first preschool year (3 years, 8 months of age on average) and, subsequently, the third preschool year (5 years, 6 months of age on average). At both waves, children were also assessed on their early numeracy. In occasion of the routine well-child visit at age 5, parents who were randomly allocated to the intervention condition (vs. a business-as-usual control condition) received guidance on age-appropriate home mathematics-related practices to sustain children's numerical development.

Results

Results revealed that parents in the intervention group improved their provision of home mathematics-related activities at the post-intervention assessment (relative to baseline) to a greater extent than parents in the control condition. No effect was observed on children's early numeracy.

Discussion

Overall, results are promising in suggesting that community pediatricians may be a resource to promote home mathematics-related activities though non-intensive low-cost interventions.

Elementary math in elementary school: the effect of interference on learning the multiplication table

Memorizing the multiplication table is a major challenge for elementary school students: there are many facts to memorize, and they are often similar to each other, which creates interference in memory. Here, we examined whether learning would improve if the degree of interference is reduced, and which memory processes are responsible for this improvement. In a series of 16 short training sessions over 4 weeks, first-grade children learned 16 multiplication facts-4 facts per week. In 2 weeks the facts were dissimilar from each other (low interference), and in 2 control weeks the facts were similar (high interference). Learning in the low-similarity, low-interference weeks was better than in the high-similarity weeks. Critically, this similarity effect originated in the specific learning context, i.e., the grouping of facts to weeks, and could not be explained as an intrinsic advantage of certain facts over others. Moreover, the interference arose from the similarity between facts in a given week, not from the similarity to previously learned facts. Similarity affected long-term memory-its effect persisted 7 weeks after training has ended; and it operated on long-term memory directly, not via the mediation of working memory. Pedagogically, the effectiveness of the low-interference training method, which is dramatically different from currently used pedagogical methods, may pave the way to enhancing how we teach the multiplication table in school.

The differential relationship between visual and spatial working memory in children's mathematics performance

BACKGROUND

Previous research suggests that visuospatial working memory (WM) is a unique predictor of mathematics. However, evidence from neuropsychology and cognitive studies suggests dissociations between visual and spatial WM.

PROCEDURE

We examined the differential relationships between visual and spatial WM with mathematics using a new task that 1) utilized the same paradigm across visual and spatial tasks and 2) required executive WM.

MAIN FINDINGS

We found that our new spatial WM task related to mathematics scores while visual WM did not. Spatial WM related to mathematics scores for fourth-graders and not second graders, consistent with previous findings on the relationship between spatial skills and mathematics as mathematics becomes more complex. No relationship was found between spatial WM and reading scores at either grade level.

CONCLUSIONS

Our results highlight the dynamic relationship between WM components and mathematics over the elementary school years and suggest that spatial WM is a unique predictor of mathematics starting from middle childhood.

Phonological Processing, Visuospatial Skills, and Pattern Understanding in Chinese Developmental Dyscalculia

A number of previous studies have identified cognitive deficits in developmental dyscalculia (DD). Yet, most of these studies were in alphabetic languages, whereas few of them examined Chinese DD. Here, we conducted a study aiming to determine the cognitive factors associated with DD in Chinese children. Five candidate cognitive factors of DD-phonological retrieval, phonological awareness, visual-spatial attention, spatial thinking, and pattern understanding-were examined in the present study. A total of 904 Chinese children ages 8 to 11 years participated in this study. From the sample, 97 children were identified with DD through tests of arithmetic ability, and 93 age- and IQ-matched typically developing children were selected as controls. Logistic regression analysis revealed that phonological retrieval, pattern understanding, visual-spatial attention, and phonological awareness significantly predicted DD, whereas spatial thinking failed to do so. Results of logistic relative weights analysis showed that all five factors explained statistically significant amounts of variance in arithmetic scores. Phonological retrieval had the most influence on DD, followed by pattern understanding, visual-spatial attention, phonological awareness, and spatial thinking. These findings have important clinical implications for diagnosis and intervention of Chinese DD.

Early number word learning: Associations with domain-general and domain-specific quantitative abilities

Cardinal number knowledge-understanding “two” refers to sets of two entities-is a critical piece of knowledge that predicts later mathematics achievement. Recent studies have shown that domain-general and domain-specific skills can influence children’s cardinal number learning. However, there has not yet been research investigating the influence of domain-specific quantifier knowledge on children’s cardinal number learning. The present study aimed to investigate the influence of domain-general and domain-specific skills on Mandarin Chinese-speaking children’s cardinal number learning after controlling for a number of family background factors. Particular interest was paid to the question whether domain-specific quantifier knowledge was associated with cardinal number development. Specifically, we investigated 2–5-year-old Mandarin Chinese-speaking children’s understanding of cardinal number words as well as their general language, intelligence, approximate number system (ANS) acuity, and knowledge of quantifiers. Children’s age, gender, parental education, and family income were also assessed and used as covariates. We found that domain-general abilities, including general language and intelligence, did not account for significant additional variance of cardinal number knowledge after controlling for the aforementioned covariates. We also found that domain-specific quantifier knowledge did not account for significant additional variance of cardinal number knowledge, whereas domain-specific ANS acuity accounted for significant additional variance of cardinal number knowledge, after controlling for the aforementioned covariates. In sum, the results suggest that domain-specific numerical skills seem to be more important for children’s development of cardinal number words than the more proximal domain-general abilities such as language abilities and intelligence. The results also highlight the significance of ANS acuity on children’s cardinal number word development.

Walking another pathway: The inclusion of patterning in the pathways to mathematics model

According to the Pathways to Mathematics model [LeFevre et al. (2010), Child Development, Vol. 81, pp. 1753-1767], children's cognitive skills in three domains-linguistic, attentional, and quantitative-predict concurrent and future mathematics achievement. We extended this model to include an additional cognitive skill, patterning, as measured by a non-numeric repeating patterning task. Chilean children who attended schools of low or high socioeconomic status (N = 98; 54% girls) completed cognitive measures in kindergarten (M_age = 71 months) and numeracy and mathematics outcomes 1 year later in Grade 1. Patterning and the original three pathways were correlated with the outcomes. Using Bayesian regressions, after including the original pathways and mother's education, we found that patterning skills predicted additional variability in applied problem solving and arithmetic fluency, but not number ordering, in Grade 1. Similarly, patterning skills were included in the best model for applied problem solving and arithmetic fluency, but not for number ordering, in Grade 1. In accord with the hypotheses of the original Pathways to Mathematics model, patterning varied in its unique and relative contributions to later mathematical performance, depending on the demands of the tasks. We conclude that patterning is a useful addition to the Pathways to Mathematics model, providing further insights into the range of cognitive precursors that are related to children's mathematical development.

Children's knowledge of superordinate words predicts subsequent inductive reasoning

Children's early language knowledge-typically assessed using standardized word comprehension tests or through parental reports-has been positively linked to a variety of later outcomes, from reasoning tests to academic performance to income and health. To better understand the mechanisms behind these links, we examined whether knowledge of certain "seed words"-words with high inductive potential-is positively associated with inductive reasoning. This hypothesis stems from prior work on the effects of language on categorization suggesting that certain words may be important for helping people to deploy categorical hypotheses. Using a longitudinal design, we assessed 36 2- to 4-year-old children's knowledge of 333 words of varying levels of generality (e.g., toy vs. pinwheel, number vs. five). We predicted that adjusting for overall vocabulary, knowledge of more general words (e.g., toy, number) would predict children's performance on inductive reasoning tasks administered 6 months later (i.e., a subset of the Stanford-Binet Intelligence Scales for Early Childhood-Fifth Edition [SB-5] and Woodcock-Johnson Tests of Cognitive Abilities [WJ] concept formation tasks). This prediction was confirmed for one of the measures of inductive reasoning (i.e., the SB-5 but not the WJ) and notably for the task considered to be less reliant on language. Although our experimental design demonstrates only a correlational relationship between seed word knowledge and inductive reasoning ability, our results are consistent with the possibility that early knowledge of certain seed words facilitates performance on putatively nonverbal reasoning tasks.