Toddler home math environment: Triangulating multi-method assessments in a U.S. Sample

Introduction

Current research has documented the home math environment (HME) of preschoolers and kindergarteners. Very few studies, however, have explored the number and spatial activities in which parents engage with children during their toddler years.

Methods

This study examined the HME of 157 toddlers using several methodologies, including surveys, time diaries, and observations of math talk. Further, it examined correlations within and across data sources to identify areas of convergence and triangulation, and correlated HME measures with measures of toddlers' number and spatial skills.

Results

Findings showed that, in general, uses of different types of math activities, including both number and spatial, were intercorrelated within method. Across methods, there was high intercorrelation between the frequency of math activities reported on parent surveys and the diversity of types of math activities endorsed in time diary interviews. Parent math talk gleaned from semi-structured interviews functioned as a separate aspect of the HME; different types of math talk shared few intercorrelations with engagement in math activities as reported in either surveys or time diaries. Finally, several HME measures positively correlated with toddlers' math skills.

Discussion

Given extant research demonstrating that both math activities and math talk predict children's math skills, our results stress the need for multimethod studies that differentiate among these HME opportunities.

Time spent playing predicts early reading and math skills through associations with self-regulation

Children's play time has declined in recent decades, which could negatively impact early self-regulation-a vital component of school readiness. To date, studies have not fully explored how the time spent playing relates to children's self-regulatory skills, and in turn, their early reading and math competencies. Using data from time diaries and direct assessments of self-regulation, prereading, and math skills, this study examined how minutes spent playing at home predict these skills in a sample of 128 children followed from age four to five. Additionally, it considered whether self-regulation explained links between play time and prereading and math. Results showed that the time spent playing positively related to children's self-regulation. Moreover, through its association with self-regulation, play time had indirect effects on prereading and math skills measured one year later. Results suggest that fostering opportunities for play time during the preschool years may help to boost school readiness skills.

Self-regulation in toddlers and the emergence of pre-academic disparities

A growing body of research has examined how children's self-regulation during early and middle childhood mediates SES disparities in academic achievement. Evidence suggests that these self-regulation skills begin developing even earlier, during the toddler years, but more work is needed examining how different measures of self-regulation relate to key constructs such as socioeconomic status (SES) and toddlers' pre-academic skills. In this online study, we examine multiple approaches to measuring self-regulation using confirmatory factor analyses and assess the extent to which self-regulatory skills help explain SES differences in early math and language skills among a sample of 158 two- and three-year-old children. Self-regulation was assessed through a battery of parent- and examiner-ratings. Children's counting, cardinality, and vocabulary skills were measured online through direct assessments and parent surveys. Two self-regulation factors emerged representing parent-reported and observational measures, and only observational measures of self-regulation mediated associations between SES and children's math and language skills. Parent-reported self-regulation was not uniquely related to SES or children's pre-academic skills, underscoring the need for careful consideration of how self-regulation is measured among toddlers when examining its associations with pre-academic skills.

Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

The relationship between executive functions (EF) and academic achievement is well-established, but leveraging this insight to improve educational outcomes remains elusive. Here, we propose a framework for relating the role of specific EF on specific precursor skills that support later academic learning. Starting from the premise that executive functions contribute to general math skills both directly - supporting the execution of problem solving strategies - and indirectly - supporting the acquisition of precursor mathematical content, we hypothesize that the contribution of domain-general EF capacities to precursor skills that support later learning can help explain relations between EF and overall math skills. We test this hypothesis by examining whether the contribution of inhibitory control on general math knowledge can be explained by inhibition's contribution to processing rational number pairs that conflict with individual's prior whole number knowledge. In 97 college students (79 female, age = 20.58 years), we collected three measures of EF: working memory (backwards spatial span), inhibition (color-word Stroop) and cognitive flexibility (task switching), and timed and untimed standardized measures of math achievement. Our target precursor skill was a decimals comparison task where correct responses were inconsistent with prior whole number knowledge (e.g., 0.27 vs. 0.9). Participants performed worse on these trials relative to the consistent decimals pairs (e.g., 0.2 vs. 0.87). Individual differences in the Stroop task predicted performance on inconsistent decimal comparisons, which in turn predicted general math achievement. With respect to relating inhibitory control to math achievement, Stroop performance was an independent predictor of achievement after accounting for age, working memory and cognitive flexibility, but decimal performance mediated this relationship. Finally, we found inconsistent decimals performance mediated the relationship of inhibition with rational number performance, but not other advanced mathematical concepts. These results pinpoint the specific contribution of inhibitory control to rational number understanding, and more broadly are consistent with the hypothesis that acquisition of foundational mathematical content can explain the relationships between executive functions and academic outcomes, making them promising targets for intervention.

From Non-symbolic to Symbolic Proportions and Back: A Cuisenaire Rod Proportional Reasoning Intervention Enhances Continuous Proportional Reasoning Skills

The persistent educational challenges that fractions pose call for developing novel instructional methods to better prepare students for fraction learning. Here, we examined the effects of a 24-session, Cuisenaire rod intervention on a building block for symbolic fraction knowledge, continuous and discrete non-symbolic proportional reasoning, in children who have yet to receive fraction instruction. Participants were 34 second-graders who attended the intervention (intervention group) and 15 children who did not participate in any sessions (control group). As attendance at the intervention sessions was irregular (median = 15.6 sessions, range = 1-24), we specifically examined the effect of the number of sessions completed on their non-symbolic proportional reasoning. Our results showed that children who attended a larger number of sessions increased their ability to compare non-symbolic continuous proportions. However, contrary to our expectations, they also decreased their ability to compare misleading discretized proportions. In contrast, children in the Control group did not show any change in their performance. These results provide further evidence on the malleability of non-symbolic continuous proportional reasoning and highlight the rigidity of counting knowledge interference on discrete proportional reasoning.

Children's discrete proportional reasoning is related to inhibitory control and enhanced by priming continuous representations

Children can successfully compare continuous proportions as early as 4 years of age, yet they struggle to compare discrete proportions at least to 10 years of age, especially when the discrete information is misleading. This study examined whether inhibitory control contributes to individual differences in discrete proportional reasoning and whether reasoning could be enhanced by priming continuous information. A total of 49 second-graders completed two tasks. In the Hearts and Flowers (H&F) task, a measure of inhibition, children pressed on either the corresponding or opposite side, depending on the identity of the displayed figure. In the Spinners task, a measure of proportional reasoning, children chose the spinner with the proportionally larger red area across continuous and two discrete formats. In the discrete adjacent format, the continuous stimuli were segmented into sections, which could be compatible with the proportional information or misleading; the discrete mixed format interspersed the colored sections from the discrete adjacent conditions. Finally, two priming groups were formed. Children who saw the continuous format immediately before the discrete adjacent format formed the continuous priming group (n = 26). Children who saw the discrete mixed format immediately before the discrete adjacent format formed the discrete priming group (n = 23). Our results showed that children who performed better on the H&F task also had better performance on the discrete counting misleading trials. Furthermore, children in the continuous priming group outperformed children in the discrete priming group, specifically in contexts where discrete information was misleading. These results suggest that children's proportional reasoning may be improved by fostering continuous representations of discrete stimuli and by enhancing inhibitory control skills.

Neural Effects of Gender and Age Interact in Reading

There has been an enduring fascination with the possibility of gender differences in the brain basis of language, yet the evidence has been largely equivocal. Evidence does exist, however, for women being at greater risk than men for developing psychomotor slowing and even Alzheimer disease with advancing age, although this may in part at least be due to women living longer. We examined whether gender, age, or their interaction influenced language-related or more general processes in reading. Reading consists of elements related to language, such as the processing of word sound patterns (phonology) and meanings (semantics), along with the lead-in processes of visual perception and orthographic (visual word form) processing that are specific to reading. To test for any influence of gender and age on either semantic processing or orthography-phonology mapping, we tested for an interaction of these factors on differences between meaningful words and meaningless but pronounceable non-words. We also tested for effects of gender and age on how the number of letters in a word modulates neural activity for reading. This lead-in process presumably relates most to orthography. Behaviorally, reading accuracy declined with age for both men and women, but the decline was steeper for men. Neurally, interactions between gender and age were found exclusively in medial orbitofrontal cortex (mOFC). These factors influenced the word-non-word contrast, but not the parametric effect of number of letters. Men showed increasing activation with age for non-words compared to words. Women showed only slightly decreasing activation with age for novel letter strings. Overall, we found interactive effects of gender and age in the mOFC on the left primarily for novel letter strings, but no such interaction for a contrast that emphasized visual form processing. Thus the interaction of gender with age in the mOFC may relate most to orthography-phonology conversion for unfamiliar letter strings. More generally, this suggests that efforts to investigate effects of gender on language-related tasks may benefit from taking into account age and the type of cognitive process being highlighted.