Intergenerational associations of the approximate number system in toddlers and their parents

Intergenerational transmission of brain structure and function in humans: a narrative review of designs, methods, and findings

Children often show cognitive and affective traits that are similar to their parents. Although this indicates a transmission of phenotypes from parents to children, little is known about the neural underpinnings of that transmission. Here, we provide a general overview of neuroimaging studies that explore the similarity between parents and children in terms of brain structure and function. We notably discuss the aims, designs, and methods of these so-called intergenerational neuroimaging studies, focusing on two main designs: the parent-child design and the multigenerational design. For each design, we also summarize the major findings, identify the sources of variability between studies, and highlight some limitations and future directions. We argue that the lack of consensus in defining the parent-child transmission of brain structure and function leads to measurement heterogeneity, which is a challenge for future studies. Additionally, multigenerational studies often use measures of family resemblance to estimate the proportion of variance attributed to genetic versus environmental factors, though this estimate is likely inflated given the frequent lack of control for shared environment. Nonetheless, intergenerational neuroimaging studies may still have both clinical and theoretical relevance, not because they currently inform about the etiology of neuromarkers, but rather because they may help identify neuromarkers and test hypotheses about neuromarkers coming from more standard neuroimaging designs.

Exploring effects of an early math intervention: The importance of parent-child interaction

We explore whether training parents' math skills or playing number games improves children's mathematical skills. Participants were 162 parent-child dyads; 88.3% were white and children (79 female) were 4 years (M = 46.88 months). Dyads were assigned to a number game, shape game, parent-only approximate number system training, parent-only general trivia, or a no-training control condition and asked to play twice weekly for 8 weeks. Children in the number game condition gained over 15% SD on an assessment of mathematical skill than did those in the no-training control. After 8 additional weeks without training, effects diminished; however, children of parents in the ANS condition underperformed those in the no-treatment control, which was partially explained by changes in the home numeracy environment.

Associations Between Children’s Numeracy Competencies, Mothers’ and Fathers’ Mathematical Beliefs, and Numeracy Activities at Home

Children’s numeracy competencies are not only relevant for their academic achievement, but also later in life. The development of early numeracy competencies is influenced by children’s learning environment. Here, the home numeracy environment (HNE) and parent’s own beliefs about mathematics play an important role for children’s numeracy competencies. However, only a few studies explicitly tested these associations separately for mothers and fathers. In our study, we assessed mothers’ and fathers’ mathematical gender stereotypes, self-efficacy and their beliefs on the importance of mathematical activities at home, and tested their associations with parents’ numeracy activities and children’s numeracy competencies in a sample of N = 160 children (n = 80 girls) with an average age of M = 59.15 months (SD = 4.05). Both, fathers and mothers regarded boys as being more competent in mathematics than girls. Fathers when compared to mothers reported a greater mathematical self-efficacy. Further, only mothers’ self-efficacy was associated with the frequency of numeracy activities with the study child. In contrast, only fathers’ beliefs on the importance of mathematics was associated with their numeracy activities which, in turn, predicted children’s numeracy competencies. However, the non-invariant constructs and varying results lead to the question whether a revision of existing scales assessing parental beliefs and home numeracy activities is needed to investigate differences of mothers and fathers and their potential associations with children’s numeracy outcomes.

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.

Measuring Emerging Number Knowledge in Toddlers

Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers (N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss.

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 intergenerational transmission of mathematics achievement in middle childhood: A prospective adoption design

The present study uses a parent-offspring adoption design to examine the dual roles of heritable and environmental influences on children's mathematics achievement. Linked sets (N = 195) of adopted children, adoptive parents, and birth parents each completed a measure of mathematics fluency (i.e., simple computational operations). Birth parent mathematics achievement and adoptive father mathematics achievement positively correlated with child achievement scores at age 7, whereas adoptive mother and adopted child mathematics achievement scores were not significantly associated with one another. Additionally, findings demonstrated no significant effects of gene-environment interactions on child mathematics achievement at age 7. These results indicate that both heritable and rearing environmental factors contribute to children's mathematics achievement and identify unique influences of the paternal rearing environment on mathematics achievement in middle childhood.

Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics

The ability to intuitively and quickly compare the number of items in collections without counting is thought to rely on the Approximate Number System (ANS). To assess individual differences in the precision of peoples' ANS representations, researchers often use non-symbolic number comparison tasks in which participants quickly choose the numerically larger of two arrays of dots. However, some researchers debate whether this task actually measures the ability to discriminate approximate numbers or instead measures the ability to discriminate other continuous magnitude dimensions that are often confounded with number (e.g., the total surface area of the dots or the convex hull of the dot arrays). In this study, we used hierarchical linear models (HLMs) to predict 132 adults' accuracy on each trial of a non-symbolic number comparison task from a comprehensive set of trial-level characteristics (including numerosity ratio, surface area, convex hull, and temporal and spatial variations in presentation format) and participant-level controls (including cognitive abilities such as visual-short term memory, working memory, and math ability) in order to gain a more nuanced understanding of how individuals complete this task. Our results indicate that certain trial-level characteristics of the dot arrays contribute to our ability to compare numerosities, yet numerosity ratio, the critical marker of the ANS, remains a highly significant predictor of accuracy above and beyond trial-level characteristics and across individuals with varying levels of math ability and domain-general cognitive abilities.