Predictors of early numeracy: Is there a place for mistakes when learning about number?

It is one thing to be able to count and share items proficiently, but it is another thing to know how counting and sharing establish and identify quantity. The aim of the study was to identify which measures of numerical knowledge predict children's success on simple number problems, where counting and set equivalence are at issue. Seventy‐two 5‐year‐olds were given a battery of nine tasks on each of three sessions (at 3‐monthly intervals). Tasks measured procedural proficiency, conceptual understanding (using an error‐detection paradigm) and the ability to compare sets using number knowledge. Procedural skills remained fairly stable over the 6‐month period, and preceded children's ability to detect another's violations to those procedures. Regression analysis revealed that children who are sensitive to procedural errors in another's counting and sharing are more likely to recognize the significance of cardinal numbers for set comparisons. We suggest that although children's conceptual understanding of well‐rehearsed routines is often limited, conceptual insight might be achieved by setting tasks that require reflection rather than practice.     

Training counting skills and working memory in preschool

Previous studies have shown that early numeracy skills predict later mathematics learning and that they can be improved by training. Cognitive abilities, especially working memory (WM), play an important role in early numeracy, as well. Several studies have shown that working memory is related to early numeracy. So far, existing literature offers a good few examples of studies in which WM training has led to improvements in early numerical performance as well. In this study, we aim at investigating the effects of two different training conditions: (1) counting training; and (2) simultaneous training of WM and counting on five‐ to six‐year‐old preschoolers' (N = 61) counting skills. The results show that domain‐specific training in mathematical skills is more effective in improving early numerical performance than WM and counting training combined. Based on our results, preschool‐aged children do not seem to benefit from short period group training of WM skills. However, because of several intervening factors, one should not conclude that young children's WM training is ineffectual. Instead, future studies should be conducted to further investigate the issue.     

Relations between Preschool Children’s Fine Motor Skills and General Cognitive Abilities

ABSTRACT

An increasing number of findings suggest that cognition is grounded in sensorimotor experiences. Research suggests that fine motor skills (FMS) link to cognitive abilities. Existing studies, however, lack conceptual and methodological differentiation regarding FMS and little is known about the directional nature of links. In study 1, we measured three types of FMS, namely dexterity, grapho-motor skill, speed-dominated FMS in a sample of preschool children (n = 78) aged 4.42 years, and analyzed their links with nonverbal reasoning and general knowledge. Factor analyses verified the existence of these three distinct subsets of FMS. A unique link was found for dexterity and reasoning after controlling for age, attention and processing speed. In study 2, using a cross-lagged-panel design with two measurement points one year apart in preschool (n = 84), a cross-lagged link from four-year-old children’s dexterity to their reasoning skills at age five was demonstrated. Findings support the idea of FMS being involved in the development of cognitive abilities.     

Parents' Estimations of Preschoolers' Number Skills Relate to at‐Home Number‐Related Activity Engagement

According to Hunt's match hypothesis, the accuracy of parents' beliefs about their children's abilities can influence the nature of the early learning experiences they provide. The present study examined the accuracy of parents' beliefs about their preschoolers' number development and relations to parent‐reported frequency of engaging children in number related experiences at home. Parents reported engaging their preschoolers more frequently in conventional numeracy activities, (i.e. counting and identifying numbers) than advanced number‐related activities (e.g. arithmetic) at home, though the frequency of advanced activities increased with the development of children's advanced number skills. Parents were most uncertain about their children's advanced number skills, though they demonstrated an overall tendency to overestimate their children's abilities across number tasks. Increased rates of overestimation and decreased rates of underestimation were associated with increased incidences of advanced activity engagement at home. Thus, results suggest guiding parents to understand their own children's numerical understanding in a wide range of number domains could promote more advanced at‐home number‐related activity engagement. Copyright © 2016 John Wiley & Sons, Ltd.     

Cognitive skills in mathematical problem solving in Grade 3

Background. Research on the relationship between cognitive skills and mathematical problem solving is usually conducted on adults or on participants with acquired deficits associated with brain injury (e.g. Cipolotti, 1995 ; Cohen, Dehaene, & Verstichel, 1994 ; McCloskey, 1992 ). Aims. In these studies we wanted to make a contribution to the field of children's mathematical problem solving. The first aim of this study was to investigate whether mathematical problem solving in children is merely determined by semantic elaboration, as hypothesized in some of the models of adult processing (semantic hypothesis). In addition, we aimed to investigate whether there is a continuum from very good to very poor mathematical problem solving among children with mathematical learning disabilities showing immature cognitive skills (maturational lag hypothesis). Sample. The participants were 376 third graders and 107 second graders. Method. The internal structure of the data was analysed with a principal components analysis. In addition, two MANOVA were conducted to compare children with learning disabilities or problems with age‐matched and performance‐matched subjects. Results. Two components, a semantic and a non‐semantic one, were needed to account for an adequate fit of the dataset. In addition, children with mathematical learning disabilities had less‐developed cognitive skills compared with peers without learning disabilities, but they did not differ from younger children on seven of the nine cognitive skills. Conclusions. This study highlighted that children's mathematical problem solving is not determined by one general component. The picture is more complex, since two mathematics components were found. In addition, although our findings point in the direction of the maturational lag hypothesis it may be important to assess the different cognitive skills and especially assess the number system knowledge, since it seems below average in children with mathematical learning disabilities, compared with the knowledge of younger children with comparable skills in mathematics.     

Numeracy skills in young children as predictors of mathematical competence

As mathematical competence is linked to educational success, professional achievement, and even a country's economic growth, researchers have been interested in early predictors for quite some time. Although there have been numerous studies on domain-specific numerical abilities predicting later mathematical competence in preschool children, research in toddlers is scarce, especially regarding additional influential aspects, such as domain-general cognitive abilities and the children's social background. Using a large-scale dataset, the present study examined predictive effects of numeracy skills in 17-month-olds for later mathematical achievement. We found small, positive effects, even when controlling for child-related variables (i.e., age and sex) and the children's social background (i.e., maternal education and household language). Additionally, we compared results with a domain-general categorization task and found no distinct effect on mathematical competence. The present results are discussed with regard to the specificities of the dataset, as well as implications for future studies on predictors of mathematical competence.     

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.     

Working memory and fine motor skills predict early numeracy performance of children with cerebral palsy

Early numeracy is an important precursor for arithmetic performance, academic proficiency, and work success. Besides their apparent motor difficulties, children with cerebral palsy (CP) often show additional cognitive disturbances. In this study, we examine whether working memory, non-verbal intelligence, linguistic skills, counting and fine motor skills are positively related to the early numeracy performance of 6-year-old children with CP. A total of 56 children (M = 6.0, SD = 0.61, 37 boys) from Dutch special education schools participated in this cross-sectional study. Of the total group, 81% of the children have the spastic type of CP (33% unilateral and 66% bilateral), 9% have been diagnosed as having diskinetic CP, 8% have been diagnosed as having spastic and diskinetic CP and 2% have been diagnosed as having a combination of diskinetic and atactic CP. The children completed standardized tests assessing early numeracy performance, working memory, non-verbal intelligence, sentence understanding and fine motor skills. In addition, an experimental task was administered to examine their basic counting performance. Structural equation modeling showed that working memory and fine motor skills were significantly related to the early numeracy performance of the children (β = .79 and p < .001, β = .41 and p < .001, respectively). Furthermore, counting was a mediating variable between working memory and early numeracy (β = .57, p < .001). Together, these findings highlight the importance of working memory for early numeracy performance in children with CP and they warrant further research into the efficacy of intervention programs aimed at working memory training.     

‘Infinity Means it Goes on Forever’: Siblings' Informal Teaching of Mathematics

Sibling‐directed teaching of mathematical topics during naturalistic home interactions was investigated in 39 middle‐class sibling dyads at two time points. At time 1 (T1), siblings were 2 and 4 years of age, and at time 2 (T2), siblings were 4 and 6 years of age. Intentional sequences of sibling‐directed mathematical teaching were coded for (i) topics (e.g., number), (ii) contexts (e.g., play with materials/toys), and (iii) type of knowledge (conceptual and procedural). Siblings engaged in teaching number, geometry, and measurement at T1 and demonstrated preliminary evidence of teaching of grouping, relations, and operations at T2. Regarding context, at T1, mathematical teaching occurred most frequently during play with materials/toys, while at T2, games with rules were prominent. Teaching of conceptual or procedural knowledge varied over time and by topic and context. Findings are discussed in light of recent work on understanding children's mathematical knowledge as it develops in the informal family context. Copyright © 2015 John Wiley & Sons, Ltd.     

Math Intervention For Latino Parents and Kindergarteners Based on Food Routines

Family food routines are important contexts through which children develop math knowledge and skills. The Food For Thought (FFT) program teaches Latino parents strategies to develop their kindergarten children's math abilities during family food routines such as grocery shopping and cooking. We examined whether attendance to FFT was related to children's math outcomes at post-test (right after program completion). Sixty-eight low-income Latino parents and their kindergarten children (M?=?71 months) participated in the four-week program taking place in schools. Children's math skills (counting, numeral recognition and cardinal understanding) were assessed at pre- and post-test. The association between parents' attendance to FFT meetings and children′s math outcomes at post-test depended on children's initial levels of math skills (i.e., math skills at pre-test). Children with lower initial math skills whose parents attended more FFT meetings had more advanced math outcomes at post-test, than children with lower initial math skills whose parents attended fewer FFT meetings. The effect size of this interaction was moderate, d?=?0.46. Limitations and future directions of this early math intervention targeting Latino families are discussed.     

Racing dragons and remembering aliens: Benefits of playing number and working memory games on kindergartners' numerical knowledge

Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet‐based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten‐age children. We hypothesized that playing a number‐based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; M_age = 71.87 months) were randomly assigned to either play a number‐based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain‐specific and domain‐general skills can benefit a broad range of kindergarten‐aged children.     

What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual counts. On incorrect counts, the frog violated the word-object correspondence principle. On unusual counts, the frog violated a conventional but inessential feature of counting, for example, starting in the middle of the array of objects. Procedural knowledge was assessed using speed and accuracy in counting objects. The patterns of change for procedural knowledge and conceptual knowledge were different. Counting speed and accuracy (procedural knowledge) improved with grade. In contrast, there was a curvilinear relation between conceptual knowledge and grade that was further moderated by children's numeration skills (as measured by a standardized test); the most skilled children gradually increased their acceptance of unusual counts over grade, whereas the least skilled children decreased their acceptance of these counts. These results have implications for studying conceptual and procedural knowledge about mathematics.     

Relationship between fine/gross motor skills and language and math development in Colombian Caribbean children: A study in Barranquilla

Literature suggests that motor skills are associated with other areas of development or domains, such as language and math, especially at early ages. These results are mainly based on studies developed in medium-to-high sociocultural contexts. Thus, this study was conducted in a medium-to-low-income area. The aim was to know the 4–5 years old children's motor development (both fine and gross motor skills), and its relation to language and mathematical development. A total of 219 Colombian Caribbean children (105 boys and 114 girls) aged 4 and 5 years participated in this study. Results revealed higher motor skills among girls, although differences by gender were not notable. Positive and significant correlations were found between motor skills and language and mathematical skills, although most of the correlations were weak or moderate. Also, it was observed that fine motor skills were less related to language or mathematical development in comparison with gross motor skills, especially among boys. These results suggest that among Colombian Caribbean children gross motor skills could have a higher influence on the development and acquisition of some language and mathematical skills in comparison with fine motor skills.     

Self‐regulated learning of basic arithmetic skills: A longitudinal study

Background. Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students’ strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other important aspects in self‐regulated learning. Aim. The main purpose of this study was to examine relations between young primary school children's basic mathematical skills and their use of math strategies, their metacognitive competence and motivational beliefs, and to investigate how students with basic mathematics skills at various levels differ in respect to the different self‐regulation components. Sample. The participants were comprised of 27 Year 2 students, all from the same class. Method. The data were collected in three stages (autumn Year 2, spring Year 2, and autumn Year 3). The children's arithmetic skills were measured by age relevant tests, while strategy use, metacognitive competence, and motivational beliefs were assessed through individual interviews. The participants were divided into three performance groups; very good students, good students, and not‐so‐good students. Results. Analyses revealed that young primary school children at different levels of basic mathematics skill may differ in several important aspects of self‐regulated learning. Analyses revealed that a good performance in addition and subtraction was related not only to the children's use of advanced mathematics strategies, but also to domain‐specific metacognitive competence, ability attribution for success, effort attribution for failure, and high perceived self‐efficacy when using specific strategies. Conclusions. The results indicate that instructional efforts to facilitate self‐regulated learning of basic arithmetic skills should address cognitive, metacognitive, and motivational aspects of self‐regulation. This is particularly important for low‐performing students.     

Longitudinal associations between children's understanding of emotions and theory of mind

Theory of mind competence and knowledge of emotions were studied longitudinally in a sample of preschoolers aged 3 (n=263) and 4 (n=244) years. Children were assessed using standard measures of theory of mind and emotion knowledge. Three competing hypotheses were tested regarding the developmental associations between children's theory of mind abilities and their knowledge of emotions. First, that an understanding of emotion develops early and informs children's understanding of others’ thinking. Alternatively, having a basic theory of mind may help children learn about emotions. Third, that the two domains are separate aspects of children's social cognitive skills such that each area develops independently. Results of hierarchical regressions supported the first hypothesis that early emotion understanding predicts later theory-of-mind performance, and not the reverse.     

Reconsidering Advertising Literacy as a Defense Against Advertising Effects

It is widely assumed that advertising literacy makes children less susceptible to advertising effects. However, empirical research does not provide convincing evidence for this view. In this article, we explain why advertising literacy as it is currently defined (i.e., conceptual knowledge of advertising) is not effective in reducing children's advertising susceptibility. Specifically, based on recent insights on children's advertising processing, we argue that due to the affect-based nature of contemporary advertising, children primarily process advertising under conditions of low elaboration and, consequently, are unlikely to use their advertising knowledge as a critical defense. Moreover, literature on cognitive development suggests that children's ability to use advertising knowledge as a defense will be further limited by their immature executive functioning and emotion regulation abilities. Therefore, we argue that the current conceptualization of advertising literacy needs to be extended with two dimensions: advertising literacy performance, which takes into account the actual use of conceptual advertising knowledge, and attitudinal advertising literacy, which includes low-effort, attitudinal mechanisms that can function as a defense under conditions of low elaboration. We conclude our article with specific directions for future research and implications for the ongoing societal and political debate about children and advertising.     

Fine motor skills enhance lexical processing of embodied vocabulary: A test of the nimble-hands,nimble-minds hypothesis

Research suggests that fine motor skills (FMS) are linked to aspects of cognitive development in children. Additionally, lexical processing advantages exist for words implying a high body–object interaction (BOI), with initial findings indicating that such words in turn link to children’s FMS—for which we propose and evaluate four competing hypotheses. First, a maturational account argues that any links between FMS and lexical processing should not exist once developmental variables are controlled for. Second, functionalism posits that any link between FMS and lexical processing arises due to environmental interactions. Third, the semantic richness hypothesis argues that sensorimotor input improves lexical processing, but predicts no links between FMS and lexical processing. A fourth account, the nimble-hands, nimble minds (NHNM) hypothesis, proposes that having greater FMS improves lexical processing for high-BOI words. In two experiments, the response latencies of preschool children (n?=?90, n?=?76, ages?=?5;1) to 45 lexical items encompassing high-BOI, low-BOI, and less imageable words were measured, alongside measures of FMS, reasoning, and general receptive/expressive vocabulary. High-BOI words appeared to show unique links to FMS, which remained after accounting for low-BOI and less imageable words, general vocabulary, reasoning, and chronological age. Although further work is needed, the findings provide initial support for the NHNM hypothesis.     

Attaching meaning to the number words: contributions of the object tracking and approximate number systems

Children's understanding of the quantities represented by number words (i.e., cardinality) is a surprisingly protracted but foundational step in their learning of formal mathematics. The development of cardinal knowledge is related to one or two core, inherent systems – the approximate number system (ANS) and the object tracking system (OTS) – but whether these systems act alone, in concert, or antagonistically is debated. Longitudinal assessments of 198 preschool children on OTS, ANS, and cardinality tasks enabled testing of two single‐mechanism (ANS‐only and OTS‐only) and two dual‐mechanism models, controlling for intelligence, executive functions, preliteracy skills, and demographic factors. Measures of both OTS and ANS predicted cardinal knowledge in concert early in the school year, inconsistent with single‐mechanism models. The ANS but not the OTS predicted cardinal knowledge later in the school year as well the acquisition of the cardinal principle, a critical shift in cardinal understanding. The results support a Merge model, whereby both systems initially contribute to children's early mapping of number words to cardinal value, but the role of the OTS diminishes over time while that of the ANS continues to support cardinal knowledge as children come to understand the counting principles.     

TV as storyteller: How exposure to television narratives impacts at‐risk preschoolers' story knowledge and narrative skills

Educational media serve as informal educators within the home by supplementing young children's development. Substantial evidence documents the contributions of educational television to preschoolers' acquisition of a variety of skills; however, television's natural capacity as storyteller and the role it plays in preschoolers' early literacy development has been largely overlooked. This study examined the effects of viewing different TV program types on 311 at‐risk preschoolers' story knowledge and narrative skills. Children were assigned to one of 4 viewing conditions (i.e. watching up to 40 episodes of a particular program type): no viewing; expository; embedded narrative; or traditional narrative. Story knowledge scores were higher for those viewing either narrative type. In contrast, viewing specific narrative types differentially affected the component skills of narrative competence. Story retelling and identification of explicit story events were higher after repeat viewing of embedded narratives while generating implicit story content was higher after repeat viewing of traditional narratives.     

Additive and synergistic relations of early mother–child and caregiver–child interactions and socioeconomic outcomes in adulthood

Prior theoretical and empirical studies have linked the first 3 years of children's life with later life outcomes. One primary explanation is the critical role these experiences play in children's early brain development (including their early language and cognitive abilities) and subsequent schooling achievement. The current study is a registered report with two complementary research objectives: (1) examine to what extent stimulating and responsive interactions with mothers and nonparental caregivers during the first 3 years of life show additive or synergistic associations with key socioeconomic outcomes in adulthood (i.e., educational attainment, salary, and employment status), and (2) examine to what extent academic skills (i.e., mathematics, vocabulary, and literacy) during childhood and adolescence mediate these associations. The sample included 1364 individuals from a birth cohort study who were followed until age 26. Mother–child interactions had positive associations with educational attainment and negative associations with full-time employment, though no synergistic associations were found for the socioeconomic outcomes. In addition, the indirect effects of mother–child interactions on educational attainment through mathematics were strongest for children with less stimulating and responsive caregiver–child interactions. Potential implications of these findings for developmental theory are discussed.