Causal Effects of Parent Number Talk on Preschoolers' Number Knowledge

What the Science of Learning Teaches Us About Arithmetic Fluency

High-quality mathematics education not only improves life outcomes for individuals but also drives innovation and progress across society. But what exactly constitutes high-quality mathematics education? In this article, we contribute to this discussion by focusing on arithmetic fluency. The debate over how best to teach arithmetic has been long and fierce. Should we emphasize memorization techniques such as flashcards and timed drills or promote "thinking strategies" via play and authentic problem solving? Too often, recommendations for a "balanced" approach lack the depth and specificity needed to effectively guide educators or inform public understanding. Here, we draw on developmental cognitive science, particularly Sfard's process-object duality and Karmiloff-Smith's implicit-explicit knowledge continuum, to present memorization and thinking strategies not as opposing methods but as complementary forces. This framework enables us to offer specific recommendations for fostering arithmetic fluency based on the science of learning. We define arithmetic fluency, provide evidence on its importance, describe the cognitive structures and processes supporting it, and share evidence-based guidance for promoting it. Our recommendations include progress monitoring for early numeracy, providing explicit instruction to teach important strategies and concepts, implementing well-structured retrieval practice, introducing time-limited practice only after students demonstrate accuracy, and allocating sufficient time for discussion and cognitive reflection. By blending theory, evidence, and practical advice, we equip educators and policymakers with the knowledge needed to ensure all children have access to the opportunities needed to achieve arithmetic fluency.

Less is not always more: Rich and meaningful counting books lead to greater gains in number understanding than sparse counting books

Children vary widely in their number knowledge by the time they enter kindergarten, and this variation is related to their future academic success. Although talk about number predicts children's early understanding of foundational number concepts, we know little about whether interventions can increase this talk nor about the types of number talk that are most beneficial to children's number understanding. The current project examines whether embedding number talk in goal-based stories leads to more robust number learning than providing the same numeric input outside of this context. Parent-child dyads (N = 71; child age = 3 years) were randomly assigned within their preintervention cardinal number understanding levels to one of three conditions: rich counting books (narrative and pictures involving a number goal), sparse counting books (text and pictures that provide opportunities to count and label the same cardinalities as in the rich condition but with no narrative), or nonnumerical control books that involve labeling colors of objects. Children's number knowledge was measured at pretest and at 2 and 4 weeks into the intervention. Findings showed that children randomized to rich counting book condition showed significantly greater cardinal number knowledge and counting skill by the final testing session compared to children in the sparse counting book condition and the color control book condition, which did not significantly differ from each other. Results have implications for the types of number talk that most effectively support children's number learning in the home environment and for the design of interventions. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Impacts of number lines and circle visual displays on caregivers' fraction understanding

Playful fraction picture books, together with math instructional content called "back matter," may promote fraction learning, which is crucial because fractions are difficult and often disliked content. However, open questions remain regarding how different types of back matter may affect caregivers' ability to use fraction picture books as a teaching tool. The current study offers a novel investigation into how back matter affects caregivers' (N = 160) fraction understanding (i.e., equivalence and arithmetic) and subjective beliefs about math using a pretest/posttest design. We contrasted existing back matter text with research-informed back matter text crossed with either circle area or number line visual displays. Caregivers' performance improved from pretest to posttest in the Researcher-Generated + Circles condition (fraction equivalence) and in the Existing + Circles, Researcher-Generated + Circles, and Researcher-Generated + Number Lines conditions (fraction arithmetic). In addition, caregivers were aware of their learning; they predicted improvements in their fraction arithmetic performance over time. These findings suggest that brief interventions, such as back matter in children's picture books, may improve adults' fraction understanding.

Assessing the association between parents' math talk and children's math performance: A preregistered meta-analysis

The home math environment has gained considerable attention as a potential cause of variation in children's math performance, and recent research has suggested positive associations between parents' math talk and children's mathematical performance. However, the extent to which associations reflect robust causal effects is difficult to test. In a preregistered meta-analysis, we assess the association between parents' math talk and children's math performance. Our initial search identified 24,291 potential articles. After screening, we identified 22 studies that were included in analyses (k = 280 effect sizes, n = 35,917 participants). A multilevel random effects meta-analysis was employed, finding that parents' math talk is significantly associated with children's math performance (b = 0.10, SE = 0.03, p = .002). We tested whether associations differ as a function of sample characteristics, observation context, observation length, type of math talk and math performance measured, and modeling approaches to math talk variable analysis. In addition, we tested whether associations are robust to the inclusion of strong baseline covariates and found that effects attenuated when children's domain-general and/or prior math abilities are included. We discuss plausible bounds of the effects of parents' math talk on children's mathematical performance to inform power analyses and experimental work on the impact of parents' math language on children's math learning.

Generalizability of the effectiveness of a preschool mathematics intervention for low-socioeconomic status Turkish children

A socioeconomic status (SES)-related achievement gap in mathematics emerges in children from many countries before school entry, persists in primary school, and imposes challenges for education systems worldwide. In response, the United Nations' sustainable development goals include universal access to quality preschool education to support universal numeracy. A generalizability study of the effectiveness of an early mathematics intervention was conducted for low-SES Turkish preschool children (33 boys, 27 girls; Mage = 4.32). Classrooms were randomly assigned to treatment (Pre-K Mathematics) or control conditions. Children's early mathematical knowledge was assessed by the Child Math Assessment. A statistically significant positive impact was found (ES = 1.32). This indicates some generalizability of the intervention and supports the feasibility of using early intervention to achieve UN goals.

Chinese parents' support of preschoolers' mathematical development

Research has documented the critical role played by the early home environment in children's mathematical development in Western contexts. Yet little is known about how Chinese parents support their preschoolers' development of math skills. The Chinese context is of particular interest because Chinese children outperform their Western counterparts in math, even early in development. The current study sought to fill this gap by examining a sample of 90 families of 4- and 5-year-olds from mainland China. Parental support-as measured by the frequency of parent-child engagement in home activities as well as parent number talk-and parents' role in children's numeracy skills were investigated. Results indicate wide variation among parents in both types of support. Frequency of engagement in formal numeracy activities, including counting objects and reading number story books, was related to children's knowledge of cardinality. A principal components analysis did not identify informal numeracy activities as a distinct home activity component, likely due to the infrequent occurrences of game-like numeracy activities among the Chinese families. Instead, a structured activity component emerged (e.g., playing musical instruments) and was positively related to children's arithmetic skills. Diversity, but not quantity, of parent number talk was related to children's symbolic magnitude understanding. The distinctive relationships between specific parental measures and child outcomes speak to the need for nuanced identification of home environment factors that are beneficial to particular math competencies. The findings also suggest cultural variations in the mechanisms that support children's mathematical development, highlighting the merits of investigating this topic in non-Western contexts.

The algorithmic origins of counting

The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take finite data and go far beyond what they directly observe or perceive. To illustrate, this paper then outlines a model which acquires a counting procedure using observations of sets and words, extending the proposal of Piantadosi et al. (2012). This new version of the model responds to several critiques of the original work and outlines an approach which is likely appropriate for acquiring further aspects of mathematics.

Investigating associations between parent engagement and toddlers' mathematics performance

Early mathematics skills relate to later mathematics achievement and educational attainment, which in turn predict career choice, income, health and financial decision-making. Critically, large differences exist among children in early mathematics performance, with parental mathematics engagement being a key predictor. However, most prior work has examined mothers' mathematics engagement with their preschool- and school-aged children. In this Registered Report, we tested concurrent associations between mothers' and fathers' engagement in mathematics activities with their 2- to 3-year-old toddlers and children's mathematics performance. Mothers and fathers did not differ in their engagement in mathematics activities, and both parents' mathematics engagement related to toddlers' mathematics skills. Fathers' mathematics engagement was associated with toddlers' number and mathematics language skills, but not their spatial skills. Mothers' mathematics engagement was only associated with toddlers' mathematics language skills. Critically, associations may be domain-specific, as parents' literacy engagement did not relate to measures of mathematics performance above their mathematics engagement. Mothers' and fathers' mathematics activities uniquely relate to toddlers' developing mathematics skills, and future work on the nuances of these associations is needed.

Exploring the role of "in the moment" and global caregiver and child factors in caregiver questioning during shared book viewing

Questions of high (vs. low) cognitive demand (CD), which encourage children to engage in abstract or critical thinking (e.g., problem solve, reason about cause-and-effect relations, make inferences), may drive relations between children's language exposure and early skills. The present study adopted a micro-analytic approach to examine caregivers' high-CD questioning with their preschool-aged children while viewing a wordless picture book (n = 121) and "in the moment" (e.g., interaction time, child responses) and global factors (e.g., caregiver education). The probability of caregivers' high-CD questioning increased with interaction time and caregiver education. Post-hoc exploratory analyses revealed that the relation between children's responses and caregivers' high-CD questioning depended on caregivers' perceptions of children's vocabulary skills. Specifically, the probability of caregivers' subsequent high-CD questioning was greater if their child did not respond previously and if caregivers perceived them to have high vocabulary skills. In contrast, caregivers' questioning remained relatively constant for responsive children across different vocabulary skills. Thus, caregivers may employ certain types of input during brief, informal learning interactions with their children by considering their own and their child's propensities and micro-level changes that occur during their conversations.

Features in children's counting books that lead dyads to both count and label sets during shared book reading

This study examined how book features influence talk during shared book reading. We used data from a study in which parent-child dyads (n = 157; child's M_age  = 43.99 months; 88 girls, 69 boys; 91.72% of parents self-reported as white) were randomly assigned to read two number books. The focus was comparison talk (i.e., talk in which dyads count a set and also label its total), as this type of talk has been shown to promote children's understanding of cardinality. Replicating previous findings, dyads produced relatively low levels of comparison talk. However, book features influenced the talk. Books containing a greater number of numerical representations (e.g., number word, numeral, and non-symbolic set) and a greater word count elicited more comparison talk.

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.

With a little help from our pediatrician: An intervention to promote mathematics-related home activities through regular well-child visits

Introduction

Children's involvement in mathematics-related activities in the home environment is associated with the development of their early numeracy over the preschool years. Intervention studies to promote parents' awareness and provision of mathematics-related home activities are however scant. In this study we developed and tested the effectiveness of a non-intensive intervention program delivered by community pediatricians to promote mathematics-related activities in the home environment.

Methods

Parents of 204 Italian children were invited to report on the frequency of mathematics-related home activities when children attended the first preschool year (3 years, 8 months of age on average) and, subsequently, the third preschool year (5 years, 6 months of age on average). At both waves, children were also assessed on their early numeracy. In occasion of the routine well-child visit at age 5, parents who were randomly allocated to the intervention condition (vs. a business-as-usual control condition) received guidance on age-appropriate home mathematics-related practices to sustain children's numerical development.

Results

Results revealed that parents in the intervention group improved their provision of home mathematics-related activities at the post-intervention assessment (relative to baseline) to a greater extent than parents in the control condition. No effect was observed on children's early numeracy.

Discussion

Overall, results are promising in suggesting that community pediatricians may be a resource to promote home mathematics-related activities though non-intensive low-cost interventions.

Verbal counting and the timing of number acquisition in an indigenous Amazonian group

Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words.

Environmental influences on mathematics performance in early childhood

Math skills relate to lifelong career, health, and financial outcomes. Individuals' own cognitive abilities predict math performance and there is growing recognition that environmental influences including differences in culture and variability in math engagement also impact math skills. In this Review, we summarize evidence indicating that differences between languages, exposure to math-focused language, socioeconomic status, attitudes and beliefs about math, and engagement with math activities influence young children's math performance. These influences play out at the community and individual level. However, research on the role of these environmental influences for foundational number skills, including understanding of number words, is limited. Future research is needed to understand individual differences in the development of early emerging math skills such as number word skills, examining to what extent different types of environmental input are necessary and how children's cognitive abilities shape the impact of environmental input.

Parental math input is not uniformly beneficial for young children: The moderating role of inhibitory control

Recent work has stressed the importance of considering child-level propensities and environmental opportunities when studying early math achievement; however, few studies investigate the interaction between these factors. This study examined whether children's inhibitory control moderates the association between parental math input and children's math performance. Parental math input via number talk and parent-reported frequencies of math activities were measured in 123 children (M age = 3.9 years) and one of their parents. High levels of parent number talk were associated with higher math achievement among children with higher inhibitory control. This association was not seen in children with lower inhibitory control, for children's vocabulary as the outcome measure, or for parents' overall talk or parent-reported math activities as the opportunity measures. Thus, children may differentially benefit from parental math input depending on their cognitive abilities and this association is specific to parental number talk and children's math abilities.

The Effects of Language Instruction on Math Development

How does language shape mathematical development? In this article, we consider this question by reviewing findings from cross-sectional and longitudinal research. In this literature, we find that differences in the structures of languages and individual variation in language ability are associated with mathematical performance in both obvious and unexpected ways. We then consider the causal nature of these relations, with a focus on experimental studies that have tested the effects of language instruction on mathematical outcomes. Findings from this work show that certain forms of language instruction meaningfully improve performance in several mathematical domains, providing strong evidence of a linguistic pathway in mathematical development. However, much additional research is needed to understand how language instruction may be integrated optimally into math education. We conclude with recommendations for research.

Socioeconomic Variations in the Frequency of Parent Number Talk: A Meta-Analysis

Using data from 12 studies, we meta-analyze correlations between parent number talk during interactions with their young children (mean sample age ranging from 22 to 79 months) and two aspects of family socioeconomics, parent education, and family income. Potential variations in correlation sizes as a function of study characteristics were explored. Statistically significant positive correlations were found between the amount of number talk in parent-child interactions and both parent education and family income (i.e., r = 0.12 for education and 0.14 for income). Exploratory moderator analyses provided some preliminary evidence that child age, as well as the average level of and variability in socioeconomic status, may moderate effect sizes. The implications of these findings are discussed with special attention to interpreting the practical importance of the effect sizes in light of family strengths and debate surrounding "word gaps".

Nurturing the Mathematical Brain: Home Numeracy Practices Are Associated With Children's Neural Responses to Arabic Numerals

Disparities in home numeracy environments contribute to variations in children's mathematical skills. However, the neural mechanisms underlying the relation between home numeracy experiences and mathematical learning are unknown. Here, parents of 66 eight-year-olds completed a questionnaire assessing the frequency of home numeracy practices. Neural adaptation to the repetition of Arabic numerals and words was measured in children using functional MRI (n = 50) to assess how sensitive the brain is to the presentation of numerical and nonnumerical information. Disparities in home numeracy practices were related to differences in digit (but not word) processing in a region of the left intraparietal sulcus (IPS) that was also related to children's arithmetic fluency. Furthermore, digit-related processing in the IPS influenced the relation between home numeracy practices and arithmetic fluency. Results were consistent with a model hypothesizing that home numeracy practices may affect children's mathematical skills by modulating the IPS response to symbolic numerical information.

Predicting children's emerging understanding of numbers

How do children construct a concept of natural numbers? Past research addressing this question has mainly focused on understanding how children come to acquire the cardinality principle. However, at that point children already understand the first number words and have a rudimentary natural number concept in place. The question therefore remains; what gets children's number learning off the ground? We therefore, based on previous empirical and theoretical work, tested which factors predict the first stages of children's natural number understanding. We assessed if children's expressive vocabulary, visuospatial working memory, and ANS (Approximate number system) acuity at 18 months of age could predict their natural number knowledge at 2.5 years of age. We found that early expressive vocabulary and visuospatial working memory were important for later number knowledge. The results of the current study add to a growing body of literature showing the importance of language in children's learning about numbers.

A strengths-based, culturally responsive family intervention improves Latino kindergarteners' vocabulary and approaches to learning

Food routines are an ecocultural asset of Latino families. This cluster-randomized trial with 248 children (M_age  = 67 months; 50% girls; 13 schools) investigated the impact of a 4-week family program designed to capitalize on food routines in improving Latino kindergarteners' outcomes in the United States. There were moderate-to-large impacts on child vocabulary (especially food-related) at end-of-treatment and the 5-month follow-up, and suggestive evidence of moderate impacts on approaches to learning (ATL; including ATL math) and executive function at the 5-month follow-up (d = .38-.95). There were no statistically significant impacts on children's math or literacy skills. A strengths-based, culturally responsive family intervention that is integrated into Latino family life can improve the skills needed to succeed in school.

Parent math anxiety predicts early number talk

Differences in children's math knowledge emerge as early as the start of kindergarten, and persist throughout schooling. Previous research implicates the importance of early parent number talk in the development of math competency. Yet we understand little about the factors that relate to variation in early parent number talk. The current study examined the relation of parent math anxiety and family socioeconomic status (SES) to parent number talk with children under the age of three (n = 36 dyads). For the first time, we show preliminary evidence that parent math anxiety (MA) predicts the amount of number talk children hear at home, beyond differences accounted for by SES. We also found a significant SES by parent MA interaction such that parent MA was predictive of higher-SES parents' number talk but not that of lower-SES parents. Furthermore, we found that these relations were specific to parents' cardinal number talk (but not counting), which has been shown to be particularly important in children's math development.

Brief Interventions Influence the Quantity and Quality of Caregiver-Child Conversations in an Everyday Context

Reading and arithmetic are difficult cognitive feats for children to master and youth from low-income communities are often less “school ready” in terms of letter and number recognition skills (Lee and Burkam, 2002). One way to prepare children for school is by encouraging caregivers to engage children in conversations about academically-relevant concepts by using numbers, recognizing shapes, and naming colors (Levine et al., 2010; Fisher et al., 2013). Previous research shows that caregiver-child conversations about these topics rarely take place in everyday contexts (Hassinger-Das et al., 2018), but interventions designed to encourage such conversations, like displaying signs in a grocery store, have resulted in significant increases in caregiver-child conversations (Ridge et al., 2015; Hanner et al., 2019). We investigated whether a similar brief intervention could change caregiver-child conversations in an everyday context. We observed 212 families in a volunteer-run facility where people who are food-insecure can select food from available donations. Volunteers greet all the clients as they pass through the aisles, offer food, and restock the shelves as needed. About 25% of the clients have children with them and our data consist of observations of the caregiver-child conversations with 2- to 10-year-old children. Half of the observation days consisted of a baseline condition in which the quantity and quality of caregiver-child conversation was observed as the client went through aisles where no signs were displayed, and volunteers merely greeted the clients. The other half of the observation days consisted of a brief intervention where signs were displayed (signs-up condition), where, volunteers greeted the clients and pointed out that there were signs displayed to entertain the children if they were interested. In addition, there was a within-subject manipulation for the intervention condition where each family interacted with two different categories of signs. Half of the signs had academically-relevant content and the other half had non-academically-relevant content. The results demonstrate that the brief intervention used in the signs-up condition increases the quantity of conversation between a caregiver and child. In addition, signs with academically-relevant content increases the quality of the conversation. These findings provide further evidence that brief interventions in an everyday context can change the caregiver-child conversation. Specifically, signs with academically-relevant content may promote school readiness.

Facilitating young children's numeracy talk in play: The role of parent prompts

Previous research has demonstrated the contribution of parents' number language to children's own engagement with numbers and later mathematical achievement. Although there is evidence that both the quantity and complexity of parent number talk contribute to children's math learning, it is unclear whether different forms of parents' number talk-statements versus prompts-offer unique contributions to how children engage in math. We examined parent number talk among 50 dyads of parents and 2- to 4-year-olds during pretend play, coding parents' provisions of informative number statements and prompts inviting children to engage in number talk. The total amount (tokens) and diversity (types) of children's number words were analyzed separately. Parents' number utterances, particularly prompts about number, were infrequent. Both parents' number statements and their prompts were uniquely related to children's number word tokens. Only prompts were associated with children's number word types. Follow-up analyses indicated that prompts were associated with lengthier parent-child conversations about number than parent statements and that children used larger number words when responding to parent prompts than when they themselves initiated number talk. These findings highlight the importance of parents' prompts for enhancing the quality of parent-child math exchanges by providing opportunities for children to advance their current use of numerical language. Consequently, parents' use of number-related prompts may play an important role in children's early math engagement.