Concurrent and longitudinal predictors of calculation skills in preschoolers

A longitudinal study of math skills in heritage bilingual children: profiles of strengths and weaknesses

Many children are exposed to a heritage language in the home context, and they learn mathematics in the school context in the societal language (Italian in the present study). More evidence is needed on how Heritage Bilinguals (HBs) perform in different subtypes of numeracy and mathematics skills in a longitudinal perspective. This longitudinal study aimed to analyze the mathematical skills of heritage bilingual children. 220 HBs (50.5% female, from different linguistic/ethnic groups, including Indo-Iranian, Arabic, Chinese, Romanian, Albanian and Slavic languages) and 440 monolinguals (46.8% female, mostly Italian) were followed from second to third grade (aged between 7 and 9 years). The following tasks were administered: dictation, symbolic comparison, number line, mental calculation, multiplication tables, approximate calculation, problem-solving and written calculations. The results showed an advantage for HBs in approximate calculation, but they underperformed in problem-solving, multiplication tables, and mental calculations. A profile analysis highlighted the percentages of children at risk for math impairment. The study provides a longitudinal profile of strengths and weaknesses in the mathematics profile of children with HBs, with developmental trajectories that vary according to verbal load. The discussion focuses on the role of verbal load in math tasks in the assessment of HBs, and implications for clinical and educational contexts.

Home Learning Environment and Screen Time Differentially Mediate the Relationship Between Socioeconomic Status and Preschoolers' Learning and Behavioural Profiles

Environmental variables related to the home context, including home literacy and numeracy, screen exposure and Socioeconomic Status (SES) are potential risks or protective factors for children's academic achievements and behaviour. The present multi-informant study aims to contribute to this issue by investigating SES's direct and indirect relationships in early learning (i.e., literacy, numeracy, and cognitive) and behavioural skills within a large sample of young children. One parent and one teacher for each of 1660 preschoolers filled out a questionnaire investigating SES, tablet and TV use, home learning activities, behavioural problems/strengths (parents' questionnaire), and children's learning skills and behaviour (teachers' questionnaire). Results of path analysis showed that tablet time and home learning environment mediate the effect of SES on early learning as assessed by teachers; as for the home learning environment, it was also a mediator of the relationship between SES and behavioural problems. Implications of these results for research in the field and educational policies are discussed.

Symbolic and non-symbolic predictors of number line task in Italian kindergarteners

The number line estimation task (NLE) is often used as a predictor for broader measures of mathematical achievement. In spite of its popularity, it is still not clear whether the task is based on symbolic or non-symbolic numerical competence. In particular, there is only a very limited amount of studies investigating the relationship between NLE performance and symbolic vs. non-symbolic math skills in children who have not yet begun formal schooling. This study investigates the strength of the association between NLE performance and symbolic and non-symbolic tasks in young kindergarteners. Ninety two 5-year-old children completed the NLE task (range 0-100) and a battery of early numerical competence tests including symbolic-lexical tasks, symbolic semantic tasks, and non-symbolic semantic tasks. The relationship between symbolic and non-symbolic early numerical competence and NLE performance was analyzed using a regression model based on the Bayesian Information Criterion (BIC). Results show that only symbolic semantic tasks are significant predictors of NLE performance. These results suggest that symbolic numerical knowledge is involved in number line processing among young children, whilst non-symbolic knowledge is not. This finding brings new data to the debate on the relationship between non-symbolic numeral knowledge and symbolic number processing and supports the evidence of a primary role of symbolic number processing already in young kindergarteners.

Home Literacy and Numeracy Interact and Mediate the Relationship Between Socio-Economic Status and Early Linguistic and Numeracy Skills in Preschoolers

This longitudinal study aimed at evaluating the relationships between socio-economic status (SES) and early literacy and numeracy skills, testing home literacy and home numeracy as mediators. It also investigated the interaction of home literacy and numeracy on early literacy and numeracy skills. The study involved 310 preschool children attending the second and the third year. Parents completed questionnaires on SES and home literacy and numeracy. In the first session, children were administered language measures and non-symbolic numeracy skills and, in the second wave, tasks of early literacy and symbolic numeracy skills. Structural equation models (SEMs) showed that SES was predictive of early language and literacy skills and non-symbolic numeracy skills. In addition, home literacy and home numeracy significantly mediated the relationships between SES and children’s skills. Finally, home literacy and home numeracy showed a significant negative interaction on symbolic numeracy skills. Implications for research and educational settings are discussed.

Home activities and cognitive skills in relation to early literacy and numeracy: testing a multifactorial model in preschoolers

The aim of the present study was to test environmental and cognitive variables as possible cross-domain predictors of early literacy and numeracy skills. One hundred forty-eight preschool children (mean age = 64.36 months ± 3.33) were enrolled in the study. The battery included a home literacy and home numeracy questionnaire, measures and phonological and visuo-spatial working memory, tasks tapping response inhibition, and predictors of literacy (vocabulary, phonological awareness, letter knowledge) and numeracy (magnitude comparison, number knowledge) skills. The structural equation model indicated that verbal working memory and, to a lesser extent, inhibition represented cross-domain predictors, whereas home numeracy activities and visuo-spatial working memory explained additional variance only for early numeracy skills. Implications for parents and educators are discussed.

Predictors of Children's Early Numeracy: Environmental Variables, Intergenerational Pathways, and Children's Cognitive, Linguistic, and Non-symbolic Number Skills

Early numeracy skills in preschool years have been found to be related to a variety of different factors, including Approximate Number System (ANS) skills, children's cognitive and linguistic skills, and environmental variables such as home numeracy activities. The present study aimed to analyze the differential role of environmental variables, intergenerational patterns, children's cognitive and linguistic skills, and their ANS in supporting early math skills. The sample included 64 children in their last year of kindergarten and one parent of each child. Children were administered a battery of cognitive and linguistic tasks, and a non-symbolic comparison task as a measure of ANS. Parents were administered similar tasks assessing cognitive skills, math skills, and ANS skills (estimation and non-symbolic comparison), together with a questionnaire on home numeracy. Results showed that home numeracy predicted children's early math skills better than a number of parent and child variables. Considering children's skills, their ability in the non-symbolic magnitude comparison task was the strongest predictor of early math skills. Results reinforce the importance of the role of home numeracy activities and children's ANS skills above that of parents' math skills.

The contribution of attentional processes to calculation skills in second and third grade in a typically developing sample

Attention is an important, multifaceted cognitive domain that includes many key cognitive processes involved in learning. This study aimed to identify the predictive links between different components of attentional skills and core calculation skills development, using two standardized measures assessing calculation (AC-MT 6–11) and attention skills (CAS) in a sample of 143 typically developing children of age range from 7.6 years to 9.4 years. The results showed that in 2nd grade, selective visuo-spatial attention emerged as an important predictor in the written calculation task, while the ability to inhibit distracting information seemed to better predict accuracy in oral calculation. In 3rd grade, visuo-spatial components of attention emerged as no longer predictive, whereas planning and active visuo-spatial attention abilities emerged as predictive of accuracy in the oral calculation task. These results confirm previous findings about the contribution that attentional skills may have in calculation skills development, supporting evidence for progressive automation attentional components over time.

Quality of Explanation as an Indicator of Fraction Magnitude Understanding

Students' explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 fourth-grade students at risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of students' explanations of those comparisons, as well as the relation between those measures and scores on a criterion test: released fraction items from the National Assessment of Educational Progress. We also considered the extent to which reasoning and language contribute to the prediction. Results indicated a significant moderate correlation between accuracy and explanation quality. Commonality analyses indicated that explanation quality accounts for little variance in National Assessment of Educational Progress scores beyond what is accounted for by traditional measures of magnitude understanding. Implications for instruction and assessment are discussed.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5-6 and 7-8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Time processing impairments in preschoolers at risk of developing difficulties in mathematics

The occurrence of time processing problems in individuals with Development Dyscalculia (DD) has favored the view of a general magnitude system devoted to both numerical and temporal information. Yet, this scenario has been partially challenged by studies indicating that time difficulties can be attributed to poor calculation or counting skills, which can support reasoning on time in school-aged children and adults. Here, we tackle this debate by exploring the performance of young children before they fully develop the symbolic number system. Preschoolers at risk of developing DD were compared with typically developing children in a series of tasks investigating time processing and in their 'sense of time', evaluated by parents and teachers. Results yielded a poorer performance in time reproduction of 5-second intervals and in time discrimination, as well as a weaker 'sense of time', in children at risk of DD. These findings provide evidence of a common magnitude system that would be responsible for deficits in both numerical and temporal domains, already at early stages of life.

Early Literacy and Numeracy Skills in Bilingual Minority Children: Toward a Relative Independence of Linguistic and Numerical Processing

Many studies have suggested that the concept of "number" is relatively independent from linguistic skills, although an increasing number of studies suggest that language abilities may play a pivotal role in the development of arithmetic skills. The condition of bilingualism can offer a unique perspective into the role of linguistic competence in numerical development. The present study was aimed at evaluating the relationship between language skills and early numeracy through a multilevel investigation in monolingual and bilingual minority children attending preschool. The sample included 156 preschool children. Of these, 77 were bilingual minority children (mean age = 58.27 ± 5.90), and 79 were monolinguals (mean age = 58.45 ± 6.03). The study focused on three levels of analysis: group differences in language and number skills, concurrent linguistic predictors of early numeracy and, finally, profile analysis of linguistic skills in children with impaired vs. adequate numeracy skills. The results showed that, apart from the expected differences in linguistic measures, bilinguals differed from monolinguals in numerical skills with a verbal component, such as semantic knowledge of digits, but they did not differ in a pure non-verbal component such as quantity comparison. The multigroup structural equation model indicated that letter knowledge was a significant predictor of the verbal component of numeracy for both groups. Phonological awareness was a significant predictor of numeracy skills only in the monolingual group. Profile analysis showed that children with a selective weakness in the non-verbal component of numeracy had fully adequate verbal skills. Results from the present study suggest that only some specific components of language competence predict numerical processing, although linguistic proficiency may not be a prerequisite for developing adequate early numeracy skills.