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.     

Subitizing or counting as possible screening variables for learning disabilities in mathematics education or learning?

This paper aims to highlight the significance of a particular aspect of magnitude processing, namely counting and subitizing or the rapid enumeration of small sets of items, for learning. Emphasis is laid on the historical roots and the conceptual framework as well as on studies on pre-verbal and school-age children. Evidence of the potential value of this research for the assessment of children at risk of mathematical learning disabilities, is presented. Inherent to its nature, subitizing relies on rapid, preverbal analogue magnitude comparisons being triggered. We will highlight the differences with counting, and the implications of shortcomings in counting and subitizing in children with mathematical learning disabilities for the automaticity of number magnitude processing. Furthermore we especially look in this paper at the varying assessment paradigms which are used in research with different age groups, something which has received insufficient attention in the past. Finally, we outline the challenges for future research on mathematical learning disabilities.     

Gender differences in both tails of the distribution of numerical competencies in preschool children

Gender differences in mathematical achievement have been examined in a wide range of age groups but only a few studies addressed this issue in preschool children. We compared preschool girls (n?=?570) and boys (n?=?524) from Germany with regard to numerical competencies. Differences in overall group means and the frequency of representation at low, middle, or high levels of performance were explored for girls and boys. Analysis of overall group means revealed that boys showed a better performance than girls (d?=?.32). The analysis of frequencies showed differences in both tails but not in the middle of the distribution of numerical competencies. While boys were more often found at higher levels of performance, girls were found to be overrepresented in the low-ability end of the distribution. These findings demonstrate that gender differences in mathematical achievement can emerge before school entry and stress the importance of further research looking for gender divides in mathematical achievement in preschool children from different countries as well as possible underlying factors.     

Improving Preschoolers’ Numerical Abilities by Enhancing the Home Numeracy Environment

Research Findings: Young children develop numeracy competencies during interactions with more knowledgeable others. Such interactions typically occur in the home numeracy environment (HNE). In this study a nonintensive intervention procedure was developed to improve both the HNE and numerical competencies. All parents of 113 Australian children (age 4 years, 5 months, on average at the beginning of the study) were invited to participate in a 2-part intervention that included attending 1 group meeting at which information regarding the HNE was provided and participating in an additional individual session that introduced them to the principles of counting. The HNE and children’s numerical competencies were assessed before and after the intervention. Participating and nonparticipating families did not differ on any of the study variables at the beginning of the study, yet not only did the intervention group significantly improve their HNE, but children in this group also showed significantly greater numerical competency development compared with the nonparticipating group. Practice or Policy: Results indicate that less intensive interventions can have effects on the HNE and children’s numerical competencies. Consequently, even on small budgets interventions should be undertaken.     

Home learning environment and development of child competencies from kindergarten until the end of elementary school

Literacy and mathematical competencies are essential for a successful school career and precursors of these abilities develop in kindergarten. In addition to children’s early cognitive abilities, family characteristics such as the socioeconomic status and the home learning environment (HLE) are predictors of early child competencies. However, few studies outside the US and the UK have analyzed long-term effects of the early HLE on child development, simultaneously considering various explanatory factors. In this longitudinal study, data of 920 German children were obtained in kindergarten some 18 months before school entry (child mean age: 4;10). At this point, precursors of reading, spelling and mathematics were assessed. In addition, parents were asked to complete surveys on family characteristics. Child assessments were repeated with standardized measures of mathematical and literacy abilities at the end of Grade 1 and in the middle of Grade 4 (child mean age: 9;9), the final grade in German elementary schools. In Grade 4, teachers were also asked to provide their recommendation for children’s secondary school track (“Hauptschule” for lowest secondary school track, “Realschule”, or “Gymnasium” as highest secondary school track). HLE was not only a good predictor of early abilities, but also directly predicted competencies at the end of elementary school when precursors, former academic achievement and child and family characteristics were controlled for. In addition, children living in more favorable HLEs were more likely to be recommended for higher secondary school tracks by their teachers.     

Executive Function Skills,Early Mathematics,and Vocabulary in Head Start Preschool Children

Research Findings: The contribution of 3 executive function skills (shifting, inhibitory control, and working memory) and their relation to early mathematical skills was investigated with preschoolers attending 6 Head Start centers. Ninety-two children ranging in age from 3 years, 1 month, to 4 years, 11 months, who were native English or Spanish speakers were assessed for these executive function skills as well as their receptive vocabulary skills and early mathematical abilities using the Child Math Assessment (Starkey, Klein, & Wakeley, 2004), which captures an array of skills across 4 domains. Hierarchal regression analyses revealed that inhibitory control and working memory made unique contributions to children’s early mathematical abilities in the domains of numeracy, arithmetic, spatial/geometric reasoning, and patterning/logical relations after we controlled for age, receptive vocabulary, and previous Head Start experience. Furthermore, receptive vocabulary also accounted for significant variance in children’s early mathematical abilities above and beyond executive function skills. No group differences emerged between English-only and dual language learners on the fit of the regression models. Practice or Policy: These findings extend previous research highlighting the interface of executive function skills and mathematical learning in early childhood with further evidence to support this relationship beyond early numeracy and counting using a broad measure of critical early math skills. In addition, the intricate role of language in the development of early mathematical competence is considered. Implications of these findings for scaffolding executive function skills and vocabulary within prekindergarten math curricula are discussed, with particular consideration for children from low socioeconomic backgrounds.     

Increases in the verbal and fluid cognitive abilities of disadvantaged children attending preschool in the Netherlands

The current longitudinal study examined the development of general cognitive abilities of 4–6-year-old children of low-income, ethnic-minority families in preschool over two and a half years by determining the changes in general, and in verbal and fluid cognitive abilities, relative to age norms, using an intelligence test. The results revealed significant increases over time, relative to age norms, in full scale and in both verbal and fluid intelligence test scores of disadvantaged children, with medium effect sizes. These gains in measured intelligence were moderated by children's home language and age. Children who gained most also profited most from their increased abilities with respect to emergent school skills. Gains in verbal intelligence predicted emergent school vocabulary, but gains in fluid intelligence did not. Overall, gains in fluid intelligence predicted emergent math skills, and gains in verbal intelligence predicted emergent math skills only among older children.     

The rule counts! Acquisition of mathematical competencies with a number board game

The study evaluates the linear number board game 100 House. Taking into account Krajewski's (2003, 2013) development model of mathematical competencies, this game supports the development of mathematical competencies in 6-year-old children. The board game design is based on the American cognitive alignment framework approach and aims to enhance the number board game Race to Space (Laski & Siegler, 2014). German 6-year-old children (N = 48) received four game-playing sessions, either counting on from their current position on the board game (count-on condition) or counting their steps from one (count-from-1 condition). In a pretest, posttest, and follow-up session, children's mathematical performance was assessed. The results show that playing the game led to stable improvements, especially in mathematical competencies of the first and second level of the underlying development model. Children in the count-on condition displayed a greater benefit. Supporting mathematical competencies by playing number board games is discussed.     

Maternal Math Talk in the Home and Math Skills in Preschool Children

Research Findings: The current study analyzed the relation between the amount of mathematical input that preschool children hear (i.e., math talk) from their mothers in their homes and their early math ability a year later. Forty mother–child dyads recorded their naturalistic exchanges in their homes using an enhanced audio-recording device (the Language ENvironment Analysis System). Results from a sample of naturalistic interactions during mealtimes indicated that all mothers involved their children in a variety of math exchanges, although there were differences in the amount of math input that children received. Moreover, being exposed to more instances of math talk was positively related to children’s early mathematical ability a year after the recordings, even after we controlled for maternal education, self-regulation, and recorded minutes. Practice or Policy: These findings improve the understanding of how mothers use math with their preschool children in naturalistic contexts, providing some insight for parents into how to foster children’s math skills through verbal input in their normal routines. Moreover, these findings inform kindergarten teachers and practitioners about the math input that children receive at home, which may encourage them to adapt their practice by considering the home environment.     

Sources of Individual Differences in Children's Understanding of Fractions

Longitudinal associations of domain‐general and numerical competencies with individual differences in children's understanding of fractions were investigated. Children (n = 163) were assessed at 6 years of age on domain‐general (nonverbal reasoning, language, attentive behavior, executive control, visual‐spatial memory) and numerical (number knowledge) competencies; at 7 years on whole‐number arithmetic computations and number line estimation; and at 10 years on fraction concepts. Mediation analyses controlling for general mathematics ability and general academic ability revealed that numerical and mathematical competencies were direct predictors of fraction concepts, whereas domain‐general competencies supported the acquisition of fraction concepts via whole‐number arithmetic computations or number line estimation. Results indicate multiple pathways to fraction competence.     

Scaffolding Narrative Skills: A Meta-Analysis of Instruction in Early Childhood Settings

Research Findings: Children’s ability to tell stories and to understand the stories of others typically emerges in early childhood, supported by primary caregivers and educators. This article reviews instruction designed to foster children’s narrative skills in preschool and kindergarten settings and examines the effects using meta-analysis. The review covers more than 3 decades (1980–2013) of experimental research (k = 15 studies, 28 effects). The findings showed that verbal scaffolding, alone or in combination with other strategies, was the predominant teaching approach. The meta-analysis revealed average effects (weighted for sample size) for narrative expression (.50) and a slightly larger effect for comprehension (.58). These effects were unrelated to the duration of instruction. However, when verbal strategies were combined with nonverbal ones, such as engaging children in enacting stories or in telling stories with props, the effects for expression increased (i.e., children’s storytelling improved more from pretest to posttest). Practice or Policy: The review indicates promising strategies for supporting narrative skills. Furthermore, the studies identified can serve as a resource for practitioners by suggesting diverse kinds of verbal scaffolds, complementary nonverbal approaches, and storybooks that have been used effectively to foster narrative competencies among young children.     

Mathematical language and mathematical abilities in preschool: A systematic literature review

It is well established that early general language during preschool is critical for children's mathematical abilities. In an attempt to further characterize this association between language and mathematics, an increasing number of studies show that one specific type of language, namely mathematical language or the key linguistic concepts that are required for performing mathematical activities, is even more critical to children's mathematical abilities. The purpose of this systematic review is to summarize the evidence on mathematical language and mathematical abilities. We focus on preschool children as nearly all of the existing work has been done at this age. We first explain how mathematical language has been defined across studies, and report how it has been evaluated in studies in preschool. Next, we present the results of our systematic review. Following the PRISMA guidelines and after a critical appraisal, we ended with a set of 18 papers that were all of sufficient methodological quality. In these studies, mathematical language was defined as terms that are about numbers and operations on numbers (e.g., nine), but also included linguistic terms that do not directly refer to numbers, yet are important to understand mathematical concepts (i.e., quantitative and spatial terms such as fewest and middle, respectively). Some of these studies evaluated children's performance on mathematical language tasks, while others evaluated the mathematical language input provided to the child by their (educational) environment (teachers/parents/interventionists). Mathematical language correlated positively with children's mathematical abilities, concurrently and longitudinally. It also directly affected children's mathematical abilities, as was shown by intervention studies. We discuss potential directions for future research and highlight implications for education, arguing for more support for teachers and parents to improve the use of mathematical language in the classroom and in home settings.     

The Transition from Early Child Care to Preschool: Emerging Toddler Skills and Readiness for Group-Based Learning

Research Findings: National policy today is on the brink of defining preschool experiences as essential for children’s academic success. Indeed, many children’s classroom experience begins as they transition from infant/toddler care to a preschool classroom. This study examined developmentally relevant skill domains among 36-month-olds (effortful control, social engagement, and language abilities) and tested their organization in a latent factor model of skills hypothesized to promote classroom adaptation. Assessments of low-income children interacting with a parent and examiner from the Early Head Start Research and Evaluation Project were utilized (n = 1,814). The data included observations of mother–child interactions during semistructured activities at home and child behavior assessments. Results indicated that the interrelated structure of children’s skills was best defined in a 2-factor, latent variable model: effortful control and social communication. These learning skills were related to but separate from general cognitive ability. Practice or Policy: Home-visiting programs for infants and toddlers are expected to promote children’s school readiness, yet little research has focused on the skills that facilitate children’s transition to the large-group learning environment at age 3. Implications of this model for early prevention efforts and early childhood teacher training to promote children’s readiness for group-based learning are discussed.     

Socioeconomic Status and Preschoolers' Mathematical Knowledge: The Contribution of Home Activities and Parent Beliefs

Research Findings: Children from families of lower socioeconomic status (SES) enter kindergarten with less developed mathematical knowledge compared to children from middle SES families. This discrepancy is present at age 3 years and likely stems from differences in the home learning environment. This study reports SES-related differences both in the quantity and quality of mathematical support children receive in the home and in parent beliefs about early mathematical development and then compares both with children's performance on a comprehensive mathematics assessment. Participants included 90 children in their 1st year of preschool (2 years before kindergarten entry) and 88 children in their prekindergarten year (the year just prior to kindergarten entry). Both cohorts were balanced for SES and gender. The results suggested minimal SES-related variation in mathematical support received in either cohort but clear SES differences in parents’ beliefs about early mathematical development. Middle SES parents of children in both cohorts held higher expectations in terms of skills they expected children to possess by age 5, as well as a more accurate understanding of which skills are within the developmental range of most children by age 5. These differences accounted for unique variance in children's scores on the mathematics assessment. Practice or Policy: Implications are discussed.     

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study

Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation.     

Concurrent and longitudinal predictors of calculation skills in preschoolers

Early calculation abilities in preschoolers are predictive of mathematics achievement in subsequent grades (e.g., Jordan et al. 2009). Two studies were conducted to evaluate concurrent and longitudinal predictors of early calculation skills. In the first study, 102 preschoolers (57.8 % female; mean age?=?60.57?±?8.66 months) were given vocabulary, language comprehension, and verbal working memory tasks and a test battery that evaluated components of early number competence (quantity comparison, counting, number line, size seriation, semantic knowledge of digits, visual-spatial memory). The children were also asked to complete early calculation tasks, including addition and subtraction calculations. The results of this task constituted the dependent variable. The results showed that vocabulary, size seriation, and visual-spatial memory were significant concurrent predictors of early calculation competence. In the second study, 43 children completed the early number competence battery at time 1 (53.5 % female; mean age?=?59.30?±?3.46 months) and the linguistic and early calculation tasks at time 2, about 10 months later (mean age?=?69.43?±?3.31 months). The analysis of the longitudinal predictors of early calculation showed significant effects for counting and size seriation. The implications for preschool assessment and intervention are discussed.     

Subtypes of mathematical learning disability and their antecedents: A cognitive diagnostic approach

Using cognitive diagnostic modeling (CDM), this study identified subtypes of mathematics learning disability (MLD) based on children's numerical skills and examined the language and spatial precursors of these subtypes. Participants were 99 MLD children and 420 low achievers identified from 1839 Finnish children (966 boys) who were followed from preschool (age 6) to fourth grade (2007–2011). Five subtypes were identified: the arithmetic fluency deficit only subtype, the counting deficit subtype, the pervasive deficit subtype, the symbolic deficit subtype, and the counting and concept deficit subtype. Different subtypes depended on different constellations of language and spatial deficits. Findings highlight the effectiveness of CDM in identifying MLD subtypes and underscore the importance of understanding the specific deficits and antecedents of the subtypes.     

Numerical competence in young children and in children with mathematics learning disabilities

A longitudinal study was conducted on 82 children to investigate, firstly the numerical competence of young children and the predictive value of (pre)-numerical tests in kindergarten, and, secondly, whether children's knowledge of the numerical system and representation of the number size is related to their computation and logical knowledge and to their counting skills. In an additional cross-sectional study on 30 children with a clinical diagnosis of mathematical learning disability (MLD) of 8,5 years, age- and ability-matched with 2 × 30 children the same parameters of numerical competence were assessed. The longitudinal data showed individual differences in numerosity, as well as the relationship between a delay in arithmetics in grade l and problems on numerosity in kindergarten. In the cross-sectional results some evidence was found for the independence of numerical abilities in MLD-children. About 13% of them had still severe pre-numerical processing deficits (in number sequence production, cardinality skills and logical knowledge) in grade 3. About 67% had severe difficulties in executing calculation procedures and a lack of conceptual knowledge. A feature of 87% of the MLD-children was severe translation deficits, with a significantly worse knowledge of number words compared with the knowledge of Arab numerals. Finally a severe deficit in subitizing was found to be present in 33% of the MLD children. On a group level the processing deficits were linked to understanding numerosity, since the ability-matched younger children and the MLD-children had the same pre-numerical and numerical profile. Implications for the assessment of mathematical disabilities and the value of TEDI-MATH® as an instrument in this process are discussed.     

幼儿手指心象与感数发展及其相关研究

研究目的:探讨中国幼儿手指图式心理表征和感数发展的特点、年龄差异以及二者之间的相关性.研究方法:采用画手的投射测验和感数实验两种方法,在画手任务中年龄与不同画手指标为自变量,画手成绩为因变量;在感数实验设计中,年龄与不同数量类型为自变量,感数成绩为因变量.研究结论:(1)四五岁的幼儿在手指心象基本上能区分出手指与手掌,对于手指数量也有了较好的把握,但对不同手指相对大小和具体位置的表征还欠精确.(2)幼儿手指心象加工精确性存在显著的年龄差异,即五岁幼儿明显优于四岁幼儿.(3)当数目在3以内时,数量大小对感数成绩的影响差异不显著;当数目大于3时,数量大小对感数成绩的影响差异显著;总体上数量大小对感数成绩影响差异显著.(4)年龄对感数成绩的影响差异显著,即五岁幼儿感数成绩显著高于四岁幼儿.(5)幼儿的手指心象加工的准确性与感数成绩的高低存在显著的正相关,且前者对后者具有显著的预测作用.     

Preschool Verbal and Nonverbal Ability Mediate the Association Between Socioeconomic Status and School Performance

We compared the extent to which the long-term influence of family socioeconomic status (SES) on children's school performance from age 7 through 16 years was mediated by their preschool verbal and nonverbal ability. In 661 British children, who completed 17 researcher-administered ability tests at age 4.5 years, SES correlated more strongly with verbal than nonverbal ability (.39 vs. .26). Verbal ability mediated about half of the association between SES and school performance at age 7, while nonverbal ability accounted for a third of the link. Only SES, but not verbal or nonverbal ability, was associated with changes in school performance from age 7 to 16. We found that SES-related differences in school performance are only partly transmitted through children's preschool verbal abilities.