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. Author manuscript; available in PMC: 2023 Jul 1.
Published in final edited form as: J Educ Psychol. 2021 Jul 29;114(5):1178–1191. doi: 10.1037/edu0000679

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

Alex M Silver 1, Leanne Elliott 1, Melissa E Libertus 1
PMCID: PMC9439076  NIHMSID: NIHMS1722852  PMID: 36061985

Abstract

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 (Mage = 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.

Keywords: math abilities, home numeracy, math talk, inhibitory control, early childhood

Introduction

How do children learn? Researchers and philosophers have argued over this question for hundreds, if not thousands, of years. Evidence in diverse areas of child development, ranging from emotion regulation (e.g., Flouri, Midouhas, & Joshi, 2014) to behavioral regulation (e.g., Kim & Kochanska, 2012) and from moral cognition (e.g., Kochanska, Aksan, Knaack, & Rhines, 2004) to language (e.g., Baroody & Diamond, 2012), suggests that only considering environmental factors does not fully explain children’s development in these domains. However, children’s own abilities alone cannot explain development in these domains either. Furthermore, simply including both child-level and environmental factors as predictors of development, such as controlling for child-level factors when examining the influence of environmental factors or vice versa, may not be sufficient. Instead, decades of work in these fields suggest that examining the dynamic interaction between child-level and environmental factors may provide more insight. Specifically, it is important to investigate how children’s abilities, interests, and attitudes influence their environments, how the environment adapts to meet children where they are, and how children’s skills change to better interact with their environment.

Recently, the Opportunity-Propensity framework has been used to explain children’s development in areas ranging from academics to social skills by examining the role of the opportunities they are provided to learn in their environment and children’s propensity to learn, as well as how antecedent factors like socioeconomic status relate to both opportunity and propensity (see Byrnes, 2020). Work under this theory has typically employed mediational path modeling, such that antecedent factors predict the opportunity and propensity factors that then independently relate to achievement. Importantly, this work has not typically examined interactions between children’s opportunity and propensity to learn directly. One recent study found that children’s executive functioning facilitates their learning from school math instruction, such that children with higher executive functioning benefit more from math lessons (Ribner, 2020). However, no work to date has examined whether children’s abilities lead to differential benefit from educational engagement in children prior to formal schooling in the home learning environment. Here, we fill this gap and specifically examine whether considering the interaction between environmental opportunities in the home and child-level propensities may help explain individual differences in three- to four-year-old children’s developing math skills.

Children’s early math skills are related to both later math achievement and educational attainment (Duncan et al., 2007), which in turn are related to career choice, employment and income, as well as health and financial decision-making (e.g., Agarwal & Mazumder, 2013; Currie & Thomas, 2001; Reyna & Brainerd, 2007; Trusty, Robinson, Plata, & Ng, 2000). These individual differences in math performance are present even by the beginning of formal education (Jordan, Kaplan, Nabors Olah, & Locuniak, 2006). Thus, understanding the factors related to this variability should be a crucial public health and educational priority.

Environmental Influences on Children’s Math Development

Over the past decade, numerous studies have examined how parents’ math talk, or discussion of math concepts, is related to children’s math performance. Past work indicates that parents’ math talk with their young children is often positively associated with both children’s current as well as their later math performance (Casey et al., 2018; Elliott, Braham, & Libertus, 2017; Gunderson & Levine, 2011; Levine, Suriyakham, Rowe, Huttenlocher, & Gunderson, 2010; Ramani, Rowe, Eason, & Leech, 2015; Susperreguy & Davis-Kean, 2016). Some recent experimental evidence suggests there may be a causal link between exposure to math talk and children’s math learning (Braham, Libertus, & McCrink, 2018; Gibson, Gunderson & Levine, 2020; Purpura, Napoli, Wehrspann, & Gold, 2016). Purpura and colleagues (2016) found that children who were exposed to quantitative and spatial language embedded within a storybook performed better than children in a business-as-usual control group. Meanwhile, Braham and colleagues (2018) found that prompting parents to engage in math talk with their children was associated with children’s increased attention to number outside of the parent-child interaction. Recently, Gibson and colleagues (2020) found that parents who read books specially designed with numerical content to their young children had children whose number knowledge improved compared to children whose parents read books without numerical content, with books focusing on small numbers being particularly helpful. These findings suggest that exposure to math language may directly improve children’s math performance. However, these types of interactions may not naturally occur at home and it is unknown how long the effects of these interventions may last. Thus, further work is needed to determine whether parents spontaneously provide the kind of rich mathematical language input that might be required to help children’s math learning.

Recent work has indicated that perhaps only certain types of math talk may be particularly beneficial for children. Specifically, math talk that involves counting and labeling present sets of objects is consistently related to preschool-aged children’s concurrent and later math performance (Casey et al., 2018; Gunderson & Levine, 2011; Ramani et al., 2015). Other work suggests that discussion of large numbers may be especially helpful, possibly because of children’s prior knowledge of smaller numbers, and particularly when combined with counting and labeling of set sizes (Elliott et al., 2017; Gunderson & Levine, 2011). Although the specific patterns of when and why math talk is most predictive of children’s math learning have yet to be fully uncovered, these findings suggest that these associations are likely more complex than many past studies have assumed.

In addition to measuring the amount of math talk, work examining environmental influences on children’s math learning has also looked at the types of activities that may promote math talk as well as more informal engagement with math concepts. Recent studies have examined the role of the home numeracy environment in children’s math development, particularly focusing on parental activities with their child in the home. Participating in more frequent math-related activities at home, such as measuring ingredients while cooking or playing board games with dice or spinners, has been found to be associated with better math performance in some studies (Blevins-Knabe & Musun-Miller, 1996; Huntsinger, Jose, & Luo, 2016; Kleemans, Peeters, Segers, & Verhoeven, 2012; LeFevre et al., 2009; Mutaf Yildiz, Sasanguie, De Smedt, & Reynvoet, 2018; Niklas & Schneider, 2013; Ramani et al., 2015). However, other work has failed to replicate this finding, and has found no significant relation between parent-child engagement in math activities and children’s math performance (DeFlorio & Beliakoff, 2014; Missall, Hojnoski, Caskie, & Repasky, 2014; Skwarchuk, 2009).

Several plausible explanations have been proposed to explain these inconsistent links between children’s math performance and the home numeracy environment. On the one hand, these mixed findings may be attributable to variations in the measurement of the home numeracy environment. Most measures of the home numeracy environment and math talk only address the frequency of math engagement, which does not capture the quality of the interactions that families are having around math (Elliott & Bachman, 2018). Similarly, most studies examining the home numeracy environment rely on self-report questionnaires that ask parents to identify how often they engage in listed math activities, which may suffer from incorrect parental recollections of activities, biases in over- or under-reporting activities, insufficient ways of capturing how parents may assimilate math into their daily routine outside of purposeful “math activities”, or incomplete lists of activities that do not encompass everything families do to engage in math. Alternatively, children at different ages and levels of knowledge may benefit more or less from particular types of engagement (see Thompson, Napoli, & Purpura, 2017), and commonly used math activity questionnaires may not capture these nuances.

One possibility that has not been explored is whether these inconsistencies in the extant literature are attributable to unmeasured, child-level factors that may moderate these associations. Specifically, we suggest a crucial factor that should be taken into consideration in this discussion of the home numeracy environment: children’s own propensity for learning math in this context. If children may differ in their ability to attend to and learn from the math input that they are exposed to, it stands to reason that some children may benefit more from math engagement than others. To date, however, past literature has only examined the main effects of environmental opportunities to learn math or child-level propensity factors that relate to math learning in the home. Here we consider the potential moderating role of child-level factors when considering the impact of parental math input. In particular, we present inhibitory control as a potential candidate that may moderate the effects of parental math input on children’s math achievement.

The Role of Inhibitory Control in Children’s Math Development

Decades of work on the development of numerical cognition suggest that math achievement in early childhood is related to many child-level factors, including general cognitive abilities from non-verbal logical reasoning skills and non-verbal IQ (e.g., Fuchs et al., 2005; Passolunghi, Cargnelutti, & Pastore, 2014), to literacy and verbal skills (e.g., Purpura, Hume, Sims, & Lonigan, 2011), and from working memory (e.g., Geary, Hoard, Byrd-Craven, & DeSoto, 2004) to general processing speed (e.g., Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007). Much research suggests that children’s executive functioning is also closely related to their math performance (see Espy et al., 2004). In particular, inhibitory control, or the ability to ignore distractions or inhibit a prepotent response, has consistently been found to be strongly related to children’s early math achievement (see Allan, Hume, Allan, Farrington, & Lonigan, 2014 for meta-analysis). Children with higher inhibitory control tend to perform better in math, even when controlling for general cognitive abilities, demographic factors, and other executive functioning skills (Espy et al., 2004).

Inhibition has been linked to a variety of math skills (see Cragg & Gilmore, 2014; Van Dooren & Inglis, 2015). Children’s inhibitory control is related to foundational math abilities, including approximation of quantities (Fuhs & McNeil, 2013; Gilmore et al., 2013), as well as counting, simple non-verbal arithmetic, and number recognition (Bull, Espy, & Wiebe, 2008). Additionally, inhibitory control is associated with performance in later school-based math skills, including arithmetic, number sequencing, and graphical representation of data (Bull et al., 2008; Gilmore et al., 2013). Previous work suggests that inhibition is particularly important for problem solving, strategy choice, and efficient allocation of cognitive resources (see Van Dooren & Inglis, 2015).

Children with higher inhibitory control are able to ignore distractions and pay closer attention, and thus, we suggest that this ability may help some children benefit more from parental math input. Children with better inhibition may be able to focus on their parents’ math input and learn more from it than children with lower inhibition, who may be more likely to get distracted or not notice the mathematical nature of their parents’ input. Although many past studies have examined main effects of inhibitory control and other executive functions on children’s math skills, to our knowledge no research has examined the potential moderating role that these domain-general factors may play in the association between parents’ math input and children’s math skills.

The Current Study

Here, we aim to investigate whether three- to four-year-old children’s inhibitory control may moderate the effect of parental math input, as measured through parental number talk or parental home math activities, on children’s math achievement. We first expect that parents who talk more about numbers with their children and parents who engage in more frequent math activities with their children will have children with better math performance. Additionally, based on prior work we expect that children with higher inhibitory control will perform better in math than their peers with lower inhibitory control. Critically, we hypothesize that children’s inhibitory control will moderate the effects of these parental influences on children’s math performance, such that children with higher inhibitory control will benefit more from high levels of parental math input than children with lower inhibitory control. To test the domain-specificity of these predicted effects, we also examine whether the interactions between inhibitory control and parent math input predict children’s vocabulary skills. Additionally, we test whether the effect of other types of parental input, specifically parents’ overall amount of talk and the frequency of their home literacy activities, on children’s math performance is moderated by children’s inhibitory control.

Finally, to test the specificity of our associations, we also control for a number of other potentially confounding parent- and child-level factors, such as parents’ overall talk, parents’ reported frequency of engaging in literacy activities with their child, parents’ math achievement, children’s general ability to follow task instructions in the inhibitory control task, children’s vocabulary, as well as children’s age and gender. By controlling for parents’ overall talk and frequency of engaging in literacy activities, we can ensure that any associations are truly due to parents’ math input, rather than parental engagement with their child more broadly. We also control for parents’ math achievement, to be sure that effects are not simply driven by parents’ own math abilities and level of comfort engaging in math with their child. Further, by controlling for children’s ability to follow task instructions in the inhibitory control task, we can ensure that it is truly children’s inhibitory control skills, and not broader cognitive abilities, that are implicated here. Similarly, we control for children’s expressive vocabulary to be sure that any effects found are specifically predictive of math performance, and not children’s general cognitive abilities. Finally, we control for children’s age and gender, to be sure that any relations found are not driven by potential differences in parents’ engagement with children of different ages or genders, as past work has indicated that parents may engage differently with children based on these demographic characteristics (e.g., Jacobs & Bleeker, 2004; Thompson et al., 2017).

Method

Participants

Participants were 123 preschool-aged children (59 girls) and one of their parents. Children ranged in age from 3 years 9 months to 4 years 0 months (child M age = 3 years 11 months, SD = 1 months). As these data were collected as part of a larger longitudinal study, we aimed to have a fairly narrow age range for data collection at this timepoint, to be able to appropriately compare children’s performance and to ensure that none of the children entered kindergarten before completing the study. Children were predominantly White, non-Hispanic (80%), while 10% were White, Hispanic/Latino, 3% were Black/African American, non-Hispanic, 2% were Asian, non-Hispanic and 5% were another race or multiple races. Parents were mostly mothers (95%) and were highly educated: 89% had earned a Bachelor’s degree or higher, with education level in the sample ranging from having completed high school to having completed a graduate degree. The majority of children (78%) attended some type of out-of-home childcare; however, children did not differ on critical measures based on their childcare status and this variable was not further addressed. An additional 39 children (20 girls) participated but were dropped from analyses due to incomplete or missing data. However, Little’s MCAR test indicated that there was not sufficient evidence to reject the null hypothesis that these data were missing completely at random, χ2(52, N = 162) = 48.12, p = .627, supporting our use of listwise deletion. Families were recruited from a mid-sized city in the United States through a combination of flyers, online postings, and mailings, and were compensated $8 per hour for their time. They were told the study was designed to study how parents support their children’s early learning but were not told that the study was specifically focused on math in an attempt to observe their naturalistic behavior. Prior to any data collection, parents provided written informed consent as approved by the local Institutional Review Board.

Procedure

Parents and children visited the lab four times in total over the span of six months. However, all data for the present study are derived from the first visit to the lab. During the two-hour visit, parents and children completed a short 10-minute naturalistic free play interaction. They were brought into a room containing a table covered in toys (including books, plastic food, a cash register, plastic utensils, plates and cups, trains and cars, blocks, paper and colored pencils, a toy boat, and puppets; see Figure 1 for a photograph of the set-up), and were instructed that they could play together however they wanted for ten minutes. Though they were not told that the study was specifically focused on math, nor instructed to engage in any particular way with the materials, some of the toys (i.e., blocks, trains/cars, plastic food, plates and cups, colored pencils) were in large sets that could be counted, and the cash register and blocks had numbers printed on them, which could encourage math talk. Parents and children then individually completed a number of activities and assessments. Children completed a standardized math assessment and a measure of inhibitory control. Parents completed a standardized math assessment and filled out questionnaires about their family’s demographic information, the frequency they engage in math and literacy activities with their child, as well as their child’s expressive vocabulary.

Figure 1.

Figure 1.

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Photograph of the material set-up for the 10-minute naturalistic free play interaction.

In addition to the measures of interest described in detail below, children also completed assessments measuring their non-symbolic numerical comparison ability and number knowledge. Parents also completed standardized assessments of their reading skills and an assessment measuring their non-symbolic numerical comparison ability. These activities were not of interest to the current study and are thus not further described here. More details regarding these other components of the full longitudinal study are described in studies addressing other research aims (Silver, Elliott, Imbeah & Libertus, 2020; Silver, Elliott & Libertus, 2021; Thippana, Elliott, Gehman, Libertus & Libertus, 2020).

Measures

Children’s Standardized Math Achievement

Children completed the Test of Early Mathematics Ability, 3rd edition (TEMA-3; Ginsburg & Baroody, 2003), a standardized math assessment that assesses numbering skills, number-comparison facility, numeral literacy, mastery of number facts, calculation skills, and understanding of concepts. The TEMA-3 was administered and scored by a trained experimenter. Raw TEMA-3 scores were used as the measure of children’s math abilities. The TEMA-3 demonstrates high consistency and reliability with Cronbach’s alpha of .94 and test-retest reliability of .82 (Ginsburg & Baroody, 2003).

Children’s Inhibitory Control

Children’s inhibitory control was assessed using a modified Day-Night Stroop task (Gerstadt, Hong, & Diamond, 1994). In this assessment, children were shown images and instructed to say “day” when shown one image, and “night” when shown another image. Children completed an incongruent task (measuring their inhibition) and a control task. The incongruent task asked children to say “night” when shown a sun image, and “day” when shown a moon image, requiring children to inhibit their prepotent association response. The control task showed children images of either a checkerboard or a squiggle pattern and required children to form a new association between the images and the same words, without requiring inhibition of a prepotent response. This control task requires the same formation of a new association between a word and picture as in the incongruent task but does not require inhibition. By including children’s scores in the control task in models using the incongruent task, we can control for children’s ability to form a new association and use this association to follow a rule in the incongruent task, such that performance on the incongruent task should reflect only their ability to inhibit a prepotent response.

The order in which children were administered the incongruent and control tasks was counterbalanced across children. Performance did not differ depending on the order of task administration, χ2(26) = 14.13, p = .971. After the experimenter explained the task, children received 16 trials of the incongruent task and 16 trials of the control task, each of which had 8 trials of “day” and 8 trials of “night” correct responses. Children were not given any feedback after responding to a trial. In each trial, children could receive 0, 1 or 2 points for their response. Children received 2 points for every response that was correct on the first try, and 1 point for an incorrect response that they fixed spontaneously (though they were not instructed explicitly that they could correct their responses, occasionally children self-corrected and thus were given partial credit). Children received 0 points for any incorrect responses. Children’s scores for all incongruent task trials were averaged to create their incongruent task score, and their scores for all control task trials were averaged to create their control task score. Past work demonstrates that the Day-Night Stroop task is a reliable measure of young children’s interference control that is highly correlated with other measures of inhibition, with correlation coefficients as high as .79 (Montgomery & Koeltzow, 2010).

Parents’ Number Talk

Parent-child conversations during the 10-minute free play sessions were transcribed and coded for parent number talk during these interactions. Specifically, all parent and child speech was transcribed verbatim, and these transcripts were then searched in a word processor for instances of number words. Counts of parents’ use of number words were tallied for each interaction for each value between zero and ten (e.g., counts of how many times the parent said the word “five”), with coders only counting numerical instances of “one” (e.g., “Can I have one more plate?”) and not instances where “one” was used as a pronoun (e.g., “Can I have that one?”). Additionally, numbers larger than ten were collapsed into a single category and counted. In addition to explicit number words, we also coded for words that might elicit number talk (e.g., “count,” “number,” and “how many”) in the same manner, with each term searched in a word processor and the counts for each term tallied. This coding system was based on past work examining number talk, including both number words and elicitations (Elliott et al., 2017; Levine et al., 2010). However, in contrast to Levine and colleagues (2010) who only coded number words up to 10 and in light of the older age range of our child participants, we included all instances of number words, regardless of the size of the number. All transcripts were coded by a second, blind coder, and discrepancies in counts of any individual search terms were resolved by a third coder. Reliability was quite high; a third coder was needed for only 16.6% of transcripts. Descriptive statistics for parent usage of number words and elicitations are presented in Table 1. Total instances of number words (M = 13.02, SD = 12.39) and number elicitations (M = 4.09, SD = 4.12) were tallied; because these were quite skewed, the total instances of number words and number elicitations used by parents were combined to form a single measure of parent number talk (with a skewness of 1.83).

Table 1.

Descriptive statistics for parent number talk

Number Word M SD Min Max % of Parents Using at Least One Instance
Zero 0.15 0.51 0 4 11.38
One 3.81 3.45 0 15 85.37
Two 1.94 2.32 0 16 72.36
Three 1.01 1.64 0 12 46.34
Four 0.77 1.44 0 10 39.84
Five 1.46 2.35 0 14 49.59
Six 0.44 0.92 0 5 26.02
Seven 0.18 0.51 0 3 13.01
Eight 0.32 0.89 0 6 16.26
Nine 0.18 0.59 0 3 9.76
Ten 1.14 2.42 0 19 37.40
Greater than Ten 1.61 3.43 0 26 36.59
Number Elicitation M SD Min Max % of Parents Using at Least One Instance
Number 0.78 1.62 0 10 33.33
Count 0.46 1.09 0 6 21.95
Add 0.17 0.47 0 3 13.82
Subtract 0.01 0.09 0 1 0.81
Multiply 0 0 0 0 0
Divide 0.01 0.09 0 1 0.81
Sum 0 0 0 0 0
Take away 0 0 0 0 0
Plus 0.20 0.87 0 8 8.94
Minus 0.01 0.09 0 1 0.81
Times 0 0 0 0 0
How much 1.63 2.32 0 11 55.28
How many 0.85 1.37 0 7 40.65
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Parents’ Overall Talk

To control for individual differences in parental language use more generally, we also coded parents’ overall talk during these interactions. The total number of words that parents used was tallied from the same transcriptions used to code number talk in order to form a measure of parents’ overall word tokens. Including this control variable helped to ensure that the measure of parental number talk reflected math input specifically and not simply overall language input, as parents who talk more to their children may also be using more number words and elicitations in their interactions.

Home Math Activities

Parents reported the frequency of home math activities using the home activities questionnaire from LeFevre and colleagues (2009). Parents were asked to indicate how often in the past month they had participated in listed activities (e.g., “Identifying names of written numbers”) with their child on a scale from 0 (“Did not occur”) to 4 (“Almost daily”), and their responses for the 23 math-related items were averaged to create a total score. The scale showed good internal consistency in our sample, with Cronbach’s alpha of .80. Means and standard deviations for individual items are shown in Table 2.

Table 2.

Item-level descriptive statistics for parent-reported math and literacy activities

Math Items M SD
Using Number or Arithmetic Flashcards 0.46 0.93
Identifying Names of Written Numbers 2.78 1.22
Playing with Number Fridge Magnets 0.88 1.31
Counting Objects 3.80 0.47
Sorting Things by Size, Color, or Shape 2.87 1.10
Counting Down (10, 9, 8, 7,…) 1.88 1.33
Learning Simple Sums (e.g., 2 + 2 = 4) 1.42 1.25
Printing Numbers 1.22 1.21
Playing Store 2.08 1.33
Talking about Money when Shopping (e.g., "Which costs more?") 1.53 1.25
Measuring Ingredients when Cooking 1.98 1.17
Being Timed 1.16 1.42
Playing with Calculators 0.62 0.99
"Paint-By-Number" Activities 0.29 0.64
Building Lego or Construction Sets (Duplo, Megablocks, etc.) 3.07 1.00
"Connect-the-Dot" Activities 0.93 1.10
Playing with Blocks 2.95 1.07
Using Calendars and Dates 1.76 1.40
Having Your Child Wear a Watch 0.37 0.89
Using Number Activity Books 1.04 1.21
Reading Number Storybooks 1.88 1.28
Playing Board Games with Die or Spinner 1.69 1.17
Playing Card Games 1.25 1.18
Literacy Items M SD
Identifying Names of Written Alphabet Letters 3.55 0.77
Identifying Sounds of Alphabet Letters 3.09 1.02
Printing Letters 2.27 1.39
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Home Literacy Activities

To control for parents’ level of engagement in other educational activities at home with their child, we also measured the frequency of home literacy activities using the home activities questionnaire from LeFevre and colleagues (2009). Parents were asked to indicate how often in the past month they had participated in listed activities (e.g., “Identifying names of written alphabet letters”) with their child on a scale from 0 (“Did not occur”) to 4 (“Almost daily”), and their responses for the three literacy-related items were averaged to create a total score. This scale had acceptable internal consistency in our sample, with Cronbach’s alpha of .60. Means and standard deviations for individual items are shown in Table 2. As in the study where these items were originally used (LeFevre et al., 2009), literacy activities at home were included as a control variable, hence the lower number of items included in this composite compared to math activities, the key construct of interest. Nonetheless, including this control variable helped to ensure that the measure of parental math activities reflected math input specifically and not simply overall educational input, as parents using more math activities with their child may simply be engaging in more frequent activities with their children in general.

Parents’ Standardized Math Performance

Parental math performance was assessed using the Woodcock-Johnson Tests of Achievement III (WJ-III; Woodcock, McGrew, & Mather, 2001). Parents completed the Math Calculation subtest, which is untimed and asked them to solve as many problems as they could, including arithmetic, algebra and calculus. Then parents completed the Math Fluency subtest, a timed test where they were given simple arithmetic problems and instructed to complete as many problems as they could in three minutes. Parents’ scores on the Math Calculation and Math Fluency subtests were then used to compute a normed Math Calculation Skills Composite Score. The WJ-III is a standardized measure of achievement, with the Math Calculation Skills Composite Score showing excellent reliability with Cronbach’s alpha of .94 (Woodcock et al., 2001).

Children’s Vocabulary

To ensure that the measure of children’s math achievement reflected math ability specifically, and not simply children’s cognitive abilities in general, we included a measure of children’s expressive vocabulary. Children’s vocabulary was assessed using the Developmental Vocabulary Assessment for Parents, a parent-report measure of children’s language development (DVAP; Libertus, Odic, Feigenson, & Halberda, 2015). Parents were asked to read through a representative list of 212 words derived from the Peabody Picture Vocabulary Test, 4th edition (Dunn & Dunn, 2007), and check off any words that they had heard their child say. Children’s scores were calculated as the total number of words that parents reported their children to have used. This questionnaire has been validated as an alternative to a time-intensive, experimenter-administered test of vocabulary. The DVAP shows high concurrent validity and is highly correlated with other measures of children’s vocabulary ability, including the Peabody Picture Vocabulary Test (with a coefficient of .69) and the MacArthur-Bates Communicative Development Inventories (with a coefficient of .79; Libertus et al., 2015).

Analysis Plan

To examine the independent and potentially interacting contributions of parents’ math input and children’s inhibitory control on children’s math achievement, we estimated a series of hierarchical linear regression models, first examining parental number talk during the parent-child interactions and then math activities as measured through the home activities questionnaire as measures of math input. We first regressed children’s math achievement scores in the TEMA-3 on parents’ number talk and children’s inhibitory control performance on the Day-Night Stroop incongruent task, controlling for children’s performance on the Day-Night Stroop control task, parents’ overall talk, parents’ math achievement, children’s vocabulary, as well as children’s age and gender. We then added an interaction term between parents’ number talk and children’s inhibitory control performance on the Day-Night Stroop incongruent task to that basic model to evaluate whether children’s inhibitory control moderates the effect of parental number talk on children’s math achievement.

To ensure the robustness and specificity of any potential effects, we planned to run a series of models in the event of a significant interaction between parents’ number talk and children’s inhibitory control performance predicting children’s math achievement. To determine whether the interaction is specific to number talk, or may be due to parental talk with their child more generally, we planned to regress children’s math achievement on parents’ overall talk and children’s inhibitory control, and their interaction. To determine whether the interaction is specific to predicting children’s math performance, rather than their cognitive abilities more generally, we planned to regress children’s vocabulary on parents’ number talk, children’s inhibitory control, and their interaction.

Second, we ran similar models with parental report about the frequency of math activities as the measure of math input. To this end, we regressed children’s math achievement as measured by performance on the TEMA-3 on parents’ frequency of engaging in math activities with their child and children’s inhibitory control performance on the Day-Night Stroop incongruent task, controlling for children’s performance on the Day-Night Stroop control task, parents’ frequency of engaging in literacy activities with their child, parents’ math achievement, children’s vocabulary, and children’s age and gender. Finally, we added an interaction term between parents’ home math activities and children’s inhibitory control performance on the Day-Night Stroop incongruent task to that base model to examine whether children’s inhibitory control moderates the effect of parental math activities on children’s math achievement.

Again, to ensure the robustness and specificity of any potential effects, we planned to run a series of models in the event of a significant interaction between parents’ math activities and children’s inhibitory control performance predicting children’s math achievement. To determine whether the interaction is specific to math activities, or may be due to parents’ educational engagement with their child more generally, we planned to regress children’s math achievement on parents’ literacy activities and children’s inhibitory control, and their interaction. To determine whether the interaction is specific to predicting children’s math performance, rather than their cognitive abilities more generally, we planned to regress children’s vocabulary on parents’ math activities, children’s inhibitory control, and their interaction.

Results

Descriptive statistics and correlations are shown in Table 3. Notably, parents’ number talk and their math activities at home were significantly yet only moderately correlated, justifying the analytic decision to model child X environment interactions with each type of parental math input separately. We saw considerable variability in parents’ number talk during the 10-minute naturalistic free play interaction, ranging from 0 instances of number talk to 89 instances of number talk, with an average of approximately 17 instances of number talk. Parents used on average about 13 number words and 4 number elicitations. Only one parent did not use any number talk; all other parents used at least one instance of number talk during the interaction with their child. The bivariate correlation between parent number talk and children’s math achievement was not statistically significant, r = .04, nor was the correlation between parent number words and children’s math, r = .05, or parent number elicitations and children’s math, r = −.01. Additionally, parents’ engagement in math activities varied quite a bit, with parents on average reporting engaging in math activities with their child between a few times a month and about once a week (M = 1.65; range from 0.73 to 2.96). The correlation between parents’ math activities and children’s math achievement was marginally significant, r = .17.

Table 3.

Descriptive statistics and bivariate correlations for all study variables, N = 123

Variable 1 2 3 4 5 6 7 8 9
1. Child Math Achievement 1
2. Day-Night Stroop: Incongruent .30*** 1
3. Day-Night Stroop: Control .16† .30*** 1
4. Number Talk .04 −.06 .09 1
5. Overall Talk .10 −.06 −.04 .18* 1
6. Math Activities .17† −.04 −.03 .21* .11 1
7. Literacy Activities .26** .05 −.09 .05 .04 .46*** 1
8. Parent Math Achievement .12 .11 −.08 .02 −.02 −.14 −.03 1
9. Child Vocabulary −.02 .03 .04 .01 .14 .21* −.00 −.05 1
M 10.76 1.29 1.50 17.12 833.00 1.65 2.98 105.20 96.75
SD 5.53 .56 .48 15.56 237.08 .51 .80 13.39 26.91
Min 0 0 0 0 248.00 .73 .67 79.00 32.00
Max 27.00 2.00 2.00 89.00 1459.00 2.96 4.00 136.00 165.00
Open in a new tab
†

p < .10

*

p < .05

**

p < .01

***

p < .001

Children’s math achievement was first regressed on parents’ number talk and children’s inhibitory control, controlling for children’s performance on the Day-Night Stroop control task, parents’ overall talk, parents’ math achievement, children’s vocabulary, children’s age and children’s gender. This model was statistically significant overall, F(8,114) = 2.03, p = .049, and explained 12.5% of the variance in children’s math achievement. As shown in Table 4 (Model 1) and replicating previous work, children’s inhibitory control was significantly related to their math achievement, as a 1 standard deviation increase in children’s inhibitory control was associated with a 0.27 standard deviation increase in their math achievement score, a small to medium effect size with Cohen’s f2 = .07. However, parents’ number talk was not significantly related to children’s math achievement. We then added the interaction term between parental use of number talk and children’s inhibitory control to this model, which was statistically significant overall, F(9,113) = 2.33, p = .019 (Table 4, Model 2). This interaction was significant with a small to medium effect size with Cohen’s f2 = .04, and resulted in an additional 3.2% of variance explained in children’s math achievement, a significant increase from the first model, ΔF(1,113) = 4.26, p = .041. A plot of this interaction is shown in Figure 2. Although the number talk variable was highly skewed, as reported in the methods, residuals from this model showed no evidence of skew (skewness = 0.30), suggesting that the regression assumption was not violated in this model. Simple slopes analyses suggested that, at high levels of children’s inhibitory control (1 SD above the mean), there was a marginally significant association between children’s math performance and parents’ number talk, B = 0.10, 95% CI [−0.01, 0.20], p = .076, whereas at low levels of inhibitory control (1 SD below the mean), there was no significant association between children’s math performance and parent number talk, B = −0.06, 95% CI [−0.16, 0.03], p = .163.

Table 4.

Parents’ number talk and children’s inhibitory control predicting children’s math achievement

Model 1 Model 2
Variable B (S.E.) β B (S.E.) β
Number Talk 0.01 (0.03) .01 0.02 (0.03) .04
Day-Night Stroop: Incongruent 2.68** (0.92) .27** 2.84** (0.91) .29**
 Number Talk x Day-Night Stroop: Incongruent - - 0.14* (0.07) .19*
Day-Night Stroop: Control 1.08 (1.09) .09 0.83 (1.08) .07
Overall Talk 0.00 (0.00) .13 0.00 (0.00) .14
Parent Math Achievement 0.04 (0.04) .10 0.03 (0.04) .07
Child Vocabulary −0.01 (0.02) −.05 −0.01 (0.02) −.06
Child Age −0.20 (7.92) −.00 −−2.78 (7.90) −.03
Child is Male 0.65 (0.98) .06 0.19 (0.99) .02
Constant 10.46*** (0.70) - 10.77*** (0.71) -
F-statistic F(8, 114) = 2.03* F(9, 113) = 2.34*
R 2 .12 .16
Open in a new tab
*

p < .05

**

p < .01

***

p < .001

Figure 2.

Figure 2.

Open in a new tab

Interaction between parents’ number talk and children’s inhibitory control predicting children’s math achievement. Note: low child inhibitory control and low parent number talk are at 1 SD below the respective means, and high child inhibitory control and high parent number talk are at 1 SD above the respective means.

We next examined the robustness of this interaction and its domain-specificity, by examining whether the same results would be found for parents’ overall talk to their child, or whether this interaction was specific to math input. We regressed children’s math achievement on parents’ overall talk and children’s inhibitory control, the interaction between parents’ overall talk and children’s inhibitory control, controlling for parents’ number talk, children’s performance on the Day-Night Stroop control task, parents’ math achievement, children’s expressive vocabulary, children’s age, and children’s gender. This model was only marginally significant overall, F(9,113) = 1.89, p = .061, and explained 13.1% of the variance in children’s math achievement, as shown in Table 5. Notably, the interaction between parents’ overall talk and children’s inhibitory control was not significant, β = .08, p = .372.

Table 5.

Parents’ overall talk and children’s inhibitory control predicting children’s math achievement

Variable B (S.E.) β
Overall Talk 0.00 (0.00) .14
Day-Night Stroop: Incongruent 2.62** (0.93) .27**
 Overall Talk x Day-Night Stroop: Incongruent 0.00 (0.00) .08
Day-Night Stroop: Control 1.03 (1.09) .09
Number Talk 0.01 (0.03) .02
Parent Math Achievement 0.04 (0.04) .09
Child Vocabulary −0.01 (0.02) −.05
Child Age −1.06 (7.99) −.02
Child is Male 0.68 (0.98) .06
Constant 10.47*** (0.70) -
F-statistic F(9, 113) = 1.89
R 2 .06
Open in a new tab
**

p < .01

***

p < .001

We further checked for the domain-specificity of our results by examining whether the interaction between parents’ number talk and children’s inhibitory control was uniquely related to children’s math performance or whether this interaction predicted their cognitive abilities more generally. To this end, we regressed children’s vocabulary on parents’ number talk, children’s inhibitory control, the interaction between number talk and inhibitory control, and controlling for children’s performance on the Day-Night Stroop control task, parents’ math achievement, children’s math achievement, children’s age, and children’s gender. This model was not statistically significant, F(9,113) = 0.56, p = .830, and explained only 4.2% of the variance in children’s vocabulary, as shown in Table 6. The interaction between parents’ number talk and children’s inhibitory control was not statistically significant, β = .05, p = .652.

Table 6.

Parents’ number talk and children’s inhibitory control predicting children’s vocabulary

Variable B (S.E.) β
Number Talk −0.03 (0.17) −.01
Day-Night Stroop: Incongruent 2.74 (4.93) .06
 Number Talk x Day-Night Stroop: Incongruent 0.17 (0.37) .05
Day-Night Stroop: Control 2.63 (5.59) .05
Overall Talk 0.02 (0.01) .16
Parent Math Achievement −0.12 (0.19) −.06
Child Math Achievement −0.31 (0.49) −.06
Child Age −23.20 (40.95) −.05
Child is Male 5.15 (5.10) .10
Constant 97.61*** (6.40) -
F-statistic F(9, 113) = 0.56
R 2 .04
Open in a new tab
***

p < .001

We then examined the relation between home math activities and children’s inhibitory control in predicting children’s math achievement. We regressed children’s math achievement on home math activities and children’s inhibitory control, controlling for the same set of covariates listed above, except that parents’ overall talk was replaced by parents’ report of the frequency of home literacy activities. This model was significant overall, F(8,114) = 3.40, p = .002, and explained 19.3% of the variance in children’s math achievement. As shown in Table 7 (Model 1), children’s inhibitory control was significantly related to children’s math achievement, as a 1 standard deviation increase in children’s inhibitory control was associated with a 0.24 standard deviation increase in children’s math achievement, a small to medium effect size with Cohen’s f2 = .07. However, home math activities were not significantly related to children’s math achievement. We then added the interaction between home math activities and children’s inhibitory control to this model, which was statistically significant overall, F(9,113) = 3.09, p = .002 (Table 7, Model 2). This interaction term was not statistically significant, however, and resulted in only an additional 0.4% of variance explained in children’s math achievement, which was not a significant increase from the base model, ΔF(1,113) = 0.63, p = .430. A plot of this non-significant interaction is shown in Figure 3. As the interaction between home math activities and children’s inhibitory control failed to reach conventional statistical significance, we did not perform either of the planned robustness checks.

Table 7.

Parents’ math activities and children’s inhibitory control predicting children’s math achievement

Model 1 Model 2
Variable B (S.E.) β B (S.E.) β
Math Activities 1.19 (1.09) .11 1.34 (1.11) .12
Day-Night Stroop: Incongruent 2.43** (0.89) .25** 2.43** (0.89) .25**
 Math Activities x Day-Night Stroop: Incongruent - - 1.46 (1.60) .08
Day-Night Stroop: Control 1.35 (1.04) .12 1.36 (1.04) .12
Literacy Activities 1.57* (0.69) .23* 1.46* (0.69) .22*
Parent Math Achievement 0.05 (0.04) .13 0.05 (0.04) .13
Child Vocabulary −0.01 (0.02) −.05 −0.01 (0.02) −.05
Child Age 4.16 (7.67) .05 3.65 (7.69) .04
Child is Male 0.76 (0.96) .07 0.76 (0.96) .07
Constant 10.29*** (0.69) - 10.31*** (0.70) -
F-statistic F(8, 114) = 3.32** F(9, 113) = 3.04**
R 2 .19 .19
Open in a new tab
*

p < .05

**

p < .01

***

p < .001

Figure 3.

Figure 3.

Open in a new tab

Non-significant interaction between parents’ math activities and children’s inhibitory control predicting children’s math achievement. Note: low child inhibitory control and low parent math activity are at 1 SD below the respective means, and high child inhibitory control and high parent math activity are at 1 SD above the respective means.

Discussion

Math achievement has been suggested as an important determinant of long-term outcomes (Duncan et al., 2007). Past work exploring predictors of early individual differences in math achievement suggest that children’s general cognitive abilities (e.g., Allan et al., 2014) as well as environmental factors play a role in shaping early math learning (e.g., LeFevre et al., 2009). Although recent work has stressed the importance of considering both child-level propensity factors and environmental opportunity factors when studying math achievement (see Byrnes, 2020), far less attention has been paid to the interaction between these predictors. Here, we find that children’s domain-general propensity to attend to relevant input and inhibit distractions moderates the link between opportunities to engage in math in the early home environment and children’s math achievement. Extending past research, we see that opportunities and propensities interact to shape children’s performance rather than independently predicting math achievement.

Predictors of Children’s Math Performance

Replicating a robust literature, we found that children’s inhibitory control was consistently related to their math performance. These results add to a considerable number of studies and meta-analyses indicating the relation between inhibition and early math performance (see Allan et al., 2014 for meta-analysis). However, surprisingly, and in contrast to some previous work (e.g., Purpura et al., 2011), children’s vocabulary was not associated with their math performance. This may be due to variations in the measurement approaches utilized to assess these skills. Specifically, children’s expressive vocabulary was reported via parent questionnaire, whereas other child measures, including children’s math performance and inhibitory control, were directly assessed via experimenter-administered tasks. Despite these methodological differences, it is important to note that parent reports of expressive vocabulary as measured through the DVAP tend to be highly correlated with children’s performance in experimenter-administered vocabulary tests (Libertus et al., 2015).

Here, we did not find significant direct associations between parent math input, as measured through math talk and math activities, and children’s math performance. The previous literature regarding these relations is mixed, with some studies finding positive relations between parents’ input and children’s performance (e.g., Levine et al., 2010; Ramani et al., 2015; Susperreguy & Davis-Kean, 2016; LeFevre et al., 2009), and others failing to detect a link (e.g., DeFlorio & Beliakoff, 2014; Missall et al., 2014; Skwarchuk, 2009). These inconsistencies in the extant literature led us to investigate whether child factors interact with parent input to predict children’s performance, such that perhaps these positive associations between engagement and performance are only seen for some children. As such, we tested whether children’s inhibitory control might moderate the association between parental engagement and children’s math performance.

Interactions between Math Talk and Inhibitory Control

As hypothesized, we detected a significant interaction between exposure to math input, at least through parental number talk, and children’s inhibitory control. Specifically, we found that for children with lower inhibitory control, parental number talk was not associated with children’s math performance. However, for children with higher inhibitory control, parental number talk predicted math performance, as higher parental number talk was associated with better math performance. Critically, neither the bivariate correlation nor the main effect between number talk and children’s achievement reached conventional statistical significance levels, underscoring the necessity of accounting for variability across children. In other words, had we not examined this interaction with inhibitory control, we would have concluded that number talk was unrelated to math performance in this sample, when in fact this association was only true for children with higher inhibitory control (but not detectable in the main effects analyses). These findings qualify past research that has documented positive associations between parental math talk and children’s math achievement and suggest that these associations may only be seen (or at least may be strongest) among children with higher inhibitory control.

Importantly, we found that the association between parental number talk and children’s inhibitory control and math performance was domain-specific to math. In the follow-up robustness checks, we saw that the interaction between parents’ talk and children’s inhibitory control was specific to talk about numbers, as the interaction between parents’ overall talk and children’s inhibitory control did not predict children’s math achievement. Similarly, we found that the interaction between parents’ number talk and children’s inhibitory control did not predict children’s vocabulary. Thus, this interaction appears to be specific to parental math input, rather than overall parental input, and children’s math performance, rather than children’s cognitive abilities more broadly.

Parental math talk may encompass discussion of a wide range of math concepts, yet by focusing only on number talk and collapsing it into a single measure, we may overlook important nuances in the nature of these interactions. For example, inhibitory control may be particularly beneficial for some types of math talk more than others, such that the size of this interaction varies across domains of math talk. One possibility is that more complex math talk, such as conversations about measurement or patterns, may require more inhibitory control for children to attend to and learn from, whereas discussion of more foundational math concepts such as labeling set sizes may be beneficial regardless of children’s inhibition. Some previous work suggests that particular types of math talk are more strongly related to children’s learning at different ages (e.g., Casey et al., 2018; Elliott et al., 2017; Gunderson & Levine, 2011), and likewise, as children learn and are exposed to more challenging math concepts, the types of math input that require children’s inhibitory control may vary as well. Future work may examine whether different math concepts require differing contributions of inhibitory control for children of different ages.

Additionally, it is important to consider the direction of these relations. Theoretically, we assume that parental math talk in the context of higher inhibitory control leads to increased math performance. Alternatively, children with higher math performance may seek out or encourage environments that are more supportive of math, subsequently leading their parents to talk more about math. Some previous work supports our assumption that math talk would promote children’s math learning: interventions that increase the amount of math talk children are exposed to result in better math performance, compared to control groups (see Braham et al., 2018; Gibson et al., 2020; Purpura et al., 2016). Future research is needed to test whether this interaction is also causal in nature, such that children with higher inhibitory control may be more responsive to experimental manipulations in math talk. In addition, future work is needed to examine whether training children’s inhibitory control may yield improvements in math depending on the amount of math talk that children experience.

Null Associations with Home Math Activities

In contrast to some previous work (e.g., LeFevre et al., 2009), we did not find any significant relations between home math activities and children’s math performance, either when examining main effects or children with high or low levels of inhibitory control. Though bivariate correlations between home math activities and children’s math achievement were positive and marginally significant, no significant association was observed when controlling for covariates. Additionally, inhibitory control did not moderate this null main effect, such that the frequency of math activities was unrelated to children’s math achievement across children with high and low inhibitory control.

Why might number talk but not math activities interact with inhibitory control to predict math skills? Math activities may require less inhibition and instead require some other, unmeasured child-level propensity in order to be beneficial for children’s math learning. One possibility is that math activities may require more interest on the part of the child, sustained attention and memory to follow directions or remain engaged in the activity, or perhaps more math knowledge to benefit from the engagement.

Finally, it is important to consider that math engagement in the two contexts in this study were also measured quite differently. Although it is possible that math activities truly do not relate to math skills, and regardless of children’s inhibitory control, these differences could be attributed to methodological problems associated with self-report measures. Specifically, math activity questionnaires may not list all of the ways that parents and children engage in math naturally and can be subject to biases (see Elliott & Bachman, 2018).

In contrast to the null associations with home math activities, here we did observe a significant relation between home literacy activities and children’s math achievement. Parents who reported engaging in more frequent literacy activities had children who performed better in math, even when controlling for other covariates and including the frequency of home math activities in analyses. This perhaps somewhat surprising finding may have a few explanations. First, it is important to consider the scale used to measure activities in this study: while the home activities questionnaire asked parents to report the frequency of engagement in 23 different math activities, the questionnaire included only three literacy activities and showed only acceptable reliability. On the other hand, even with the limited number of literacy items measured, it might be that more frequent literacy activities truly do relate to children’s math achievement. Some previous work has found that engagement in math activities is associated with both children’s early literacy and math skills and suggests there may be cross-domain relations between home engagement in math and literacy and children’s achievement in those domains (Huntsinger et al., 2016; Napoli & Purpura, 2018).

Limitations, Conclusions and Future Directions

Our sample was composed primarily of White, educated mothers and their children who came into the lab for testing, and this sample bias may have been exacerbated by the use of listwise deletion as a technique for handling missing data. As such, our findings may not extend to other populations in other contexts. Much work has found that family socioeconomic status predicts children’s math performance (e.g., Jordan & Levine, 2009), and it is important to determine whether these same relations between parental math input and children’s inhibitory control predict math achievement in children whose parents may not have as much education or resources as those in the present study. Further, here we examined concurrent associations, thus we cannot draw causal conclusions. Longitudinal analyses will be needed to examine how these relations change over time, and experimental work in particular is needed to determine whether children with differing levels of inhibitory control benefit differently from math talk manipulations.

Finally, here we examined only one age range, and it is likely that these associations may change with age. Specifically, as children enter school, parents may become less important as the role of teachers increases, and parental influences may be less predictive of children’s performance. Relatedly, the way that inhibitory control helps children learn from math exposure may vary by context. It may be that inhibitory control operates differently with direct instruction compared to play as measured here (e.g., Bachman et al., 2018). Additionally, it is possible, and perhaps likely, that different child-level propensities for learning are important for benefitting from different types of math input at different ages. In particular, children’s prior knowledge as a propensity factor may be related to the benefits they receive from math input of different kinds. As children acquire more math knowledge, they may benefit from different types of math input. Perhaps in early childhood we see that math talk is particularly helpful, whereas as children get older, other types of input are more predictive. Future work should consider the influence of children’s age and knowledge on the benefit they receive from parental math input.

Our results suggest novel implications for future work, particularly work aimed at developing interventions for improving children’s math achievement. It may be that interventions should be tailored particularly to children’s propensity levels. Instead of simply encouraging all parents to talk more about math with their child, interventions should consider children’s inhibitory control and ability to benefit from the input. Finding ways to encourage discussion of math that does not require excessively taxing children’s executive functioning resources may be particularly beneficial for some children, whereas others may not require that kind of scaffolding. Alternatively, for children with low inhibitory control, it may be beneficial to train children’s inhibitory control skills in conjunction with encouraging parents to engage in more math talk.

Our findings suggest that it may be important to take into account individual differences between children that may influence the benefit they receive from parental math input. More generally, these results add to our understanding of the role of interactions between the environment and children’s abilities in early childhood, showing that children’s own general cognitive abilities may shape the benefit they receive from environmental input. This work opens possibilities for asking whether other child-level propensities influence the benefit children receive from other kinds of early academic engagement and the role that these interactions play for individual differences in children’s academic achievement.

Educational Impact and Implications Statement.

Parents who engage in more frequent math activities and talk more about math with their young children tend to have children who show better math skills, but there are mixed results and not every study has replicated this effect. We suggest that these inconsistencies may be due to child factors that help some children benefit more than others from their parents’ math input. Specifically, we find that high levels of parents’ math input are only related to better math performance when their 3- to 4-year-old children are better at ignoring distractions and focusing on relevant information. This suggests that not all children benefit equally from parent math input, and so interventions promoting math input at home must also consider children’s skills and characteristics rather than simply addressing parents’ behaviors.

Acknowledgements

This work was supported by the National Science Foundation under grant DUE1534830 to MEL, by the James S. McDonnell Foundation Scholar Award to MEL, and by the National Institutes of Health under grant T32GM081760 to AMS. We thank Abigail Haslinger, Jamie Patronick, Chelsea MacNeil, Amy Veasey, Erinn Hanner, Lauren Krawczyk and the research assistants in the Kids’ Thinking Lab for help with data collection and data entry. We especially thank the families who participated.

Footnotes

Conflict of Interest Statement

No potential conflict of interest is reported by the authors.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Agarwal S, & Mazumder B (2013). Cognitive Abilities and Household Financial Decision Making. American Economic Journal: Applied Economics, 5(1), 193–207. doi: 10.1257/app.5.1.193 [DOI] [Google Scholar]
  2. Allan NP, Hume LE, Allan DM, Farrington AL, & Lonigan CJ (2014). Relations between inhibitory control and the development of academic skills in preschool and kindergarten: a meta-analysis. Dev Psychol, 50(10), 2368–2379. doi: 10.1037/a0037493 [DOI] [PubMed] [Google Scholar]
  3. Bachman HJ, Degol JL, Elliott L, Scharphorn L, El Nokali NE, & Palmer KM (2018). Preschool Math Exposure in Private Center-Based Care and Low-SES Children’s Math Development. Early Education and Development, 29(3), 417–434. doi: 10.1080/10409289.2017.1406245 [DOI] [Google Scholar]
  4. Baroody AE, & Diamond KE (2012). Links Among Home Literacy Environment, Literacy Interest, and Emergent Literacy Skills in Preschoolers At Risk for Reading Difficulties. Topics in Early Childhood Special Education, 32(2), 78–87. doi: 10.1177/0271121410392803 [DOI] [Google Scholar]
  5. Blevins-Knabe B, & Musun-Miller L (1996). Number Use at Home by Children and Their Parents and Its Relationship to Early Mathematical Performance. Early Development and Parenting, 5(1), 35–45. doi: [DOI] [Google Scholar]
  6. Braham EJ, Libertus ME, & McCrink K (2018). Children's spontaneous focus on number before and after guided parent-child interactions in a children's museum. Dev Psychol, 54(8), 1492–1498. doi: 10.1037/dev0000534 [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Bull R, Espy KA, & Wiebe SA (2008). Short-term memory, working memory, and executive functioning in preschoolers: longitudinal predictors of mathematical achievement at age 7 years. Dev Neuropsychol, 33(3), 205–228. doi: 10.1080/87565640801982312 [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Byrnes JP (2020). The potential utility of an opportunity-propensity framework for understanding individual and group differences in developmental outcomes: A retrospective progress report. Developmental Review, 56. doi: 10.1016/j.dr.2020.100911 [DOI] [Google Scholar]
  9. Casey BM, Lombardi CM, Thomson D, Nguyen HN, Paz M, Theriault CA, & Dearing E (2018). Maternal Support of Children's Early Numerical Concept Learning Predicts Preschool and First-Grade Math Achievement. Child Dev, 89(1), 156–173. doi: 10.1111/cdev.12676 [DOI] [PubMed] [Google Scholar]
  10. Cragg L, & Gilmore C (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3(2), 63–68. doi: 10.1016/j.tine.2013.12.001 [DOI] [Google Scholar]
  11. Currie J, & Thomas D (2001). Early Test Scores, Socioeconomic Status and Future Outcomes. Research in Labor Economics, 20, 103–132. doi: 10.3386/w6943 [DOI] [Google Scholar]
  12. DeFlorio L, & Beliakoff A (2014). Socioeconomic Status and Preschoolers' Mathematical Knowledge: The Contribution of Home Activities and Parent Beliefs. Early Education and Development, 26(3), 319–341. doi: 10.1080/10409289.2015.968239 [DOI] [Google Scholar]
  13. Duncan GJ, Dowsett CJ, Claessens A, Magnuson K, Huston AC, Klebanov P, … Japel C (2007). School readiness and later achievement. Dev Psychol, 43(6), 1428–1446. doi: 10.1037/0012-1649.43.6.1428 [DOI] [PubMed] [Google Scholar]
  14. Elliott L, & Bachman HJ (2018). How Do Parents Foster Young Children's Math Skills? Child Development Perspectives, 12(1), 16–21. doi: 10.1111/cdep.12249 [DOI] [Google Scholar]
  15. Elliott L, Braham EJ, & Libertus ME (2017). Understanding sources of individual variability in parents' number talk with young children. J Exp Child Psychol, 159, 1–15. doi: 10.1016/j.jecp.2017.01.011 [DOI] [PubMed] [Google Scholar]
  16. Espy KA, McDiarmid MM, Cwik MF, Stalets MM, Hamby A, & Senn TE (2004). The contribution of executive functions to emergent mathematic skills in preschool children. Dev Neuropsychol, 26(1), 465–486. doi: 10.1207/s15326942dn2601_6 [DOI] [PubMed] [Google Scholar]
  17. Flouri E, Midouhas E, & Joshi H (2014). Family poverty and trajectories of children's emotional and behavioural problems: the moderating roles of self-regulation and verbal cognitive ability. J Abnorm Child Psychol, 42(6), 1043–1056. doi: 10.1007/s10802-013-9848-3 [DOI] [PubMed] [Google Scholar]
  18. Fuchs L, Compton DL, Fuchs D, Paulsen K, Bryant JD, & Hamlett CL (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97(3), 493. doi: 10.1037/0022-0663.97.3.493 [DOI] [Google Scholar]
  19. Fuhs MW, & McNeil NM (2013). ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control. Dev Sci, 16(1), 136–148. doi: 10.1111/desc.12013 [DOI] [PubMed] [Google Scholar]
  20. Geary DC, Hoard MK, Byrd-Craven J, & DeSoto MC (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. J Exp Child Psychol, 88(2), 121–151. doi: 10.1016/j.jecp.2004.03.002 [DOI] [PubMed] [Google Scholar]
  21. Geary DC, Hoard MK, Byrd-Craven J, Nugent L, & Numtee C (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Dev, 78(4), 1343–1359. doi: 10.1111/j.1467-8624.2007.01069.x [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Gerstadt CL, Hong YJ, & Diamond A (1994). The relationship between cognition and action: Performance of children 3 1/2-7 years old on a Stroop-like day-night test. Cognition, 53(2), 129–153. [DOI] [PubMed] [Google Scholar]
  23. Gibson DJ, Gunderson EA, & Levine SC (2020). Causal Effects of Parent Number Talk on Preschoolers’ Number Knowledge. Child Development. doi: 10.1111/cdev.13423 [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Gilmore C, Attridge N, Clayton S, Cragg L, Johnson S, Marlow N, … Inglis M (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS One, 8(6), e67374. doi: 10.1371/journal.pone.0067374 [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Ginsburg HP, & Baroody AJ (2003). TEMA-3: Test of Early Mathematics Ability-Third Edition. [Google Scholar]
  26. Gunderson EA, & Levine SC (2011). Some types of parent number talk count more than others: relations between parents' input and children's cardinal-number knowledge. Dev Sci, 14(5), 1021–1032. doi: 10.1111/j.1467-7687.2011.01050.x [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Huntsinger CS, Jose PE, & Luo Z (2016). Parental facilitation of early mathematics and reading skills and knowledge through encouragement of home-based activities. Early Childhood Research Quarterly, 37, 1–15. doi: 10.1016/j.ecresq.2016.02.005 [DOI] [Google Scholar]
  28. Jacobs JE, & Bleeker MM (2004). Girls' and Boys' Developing Interests in Math and Science: Do Parents Matter?. New directions for child and adolescent development, 106, 5–21. [DOI] [PubMed] [Google Scholar]
  29. Jordan NC, Kaplan D, Nabors Olah L, & Locuniak MN (2006). Number sense growth in kindergarten: a longitudinal investigation of children at risk for mathematics difficulties. Child Dev, 77(1), 153–175. doi: 10.1111/j.1467-8624.2006.00862.x [DOI] [PubMed] [Google Scholar]
  30. Jordan NC, & Levine SC (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Dev Disabil Res Rev, 15(1), 60–68. doi: 10.1002/ddrr.46 [DOI] [PubMed] [Google Scholar]
  31. Kim S, & Kochanska G (2012). Child temperament moderates effects of parent-child mutuality on self-regulation: a relationship-based path for emotionally negative infants. Child Dev, 83(4), 1275–1289. doi: 10.1111/j.1467-8624.2012.01778.x [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Kleemans T, Peeters M, Segers E, & Verhoeven L (2012). Child and home predictors of early numeracy skills in kindergarten. Early Childhood Research Quarterly, 27(3), 471–477. doi: 10.1016/j.ecresq.2011.12.004 [DOI] [Google Scholar]
  33. Kochanska G, Aksan N, Knaack A, & Rhines HM (2004). Maternal parenting and children's conscience: early security as moderator. Child Dev, 75(4), 1229–1242. doi: 10.1111/j.1467-8624.2004.00735.x [DOI] [PubMed] [Google Scholar]
  34. LeFevre J-A, Skwarchuk S-L, Smith-Chant BL, Fast L, Kamawar D, & Bisanz J (2009). Home numeracy experiences and children’s math performance in the early school years. Canadian Journal of Behavioural Science/Revue canadienne des sciences du comportement, 41(2), 55–66. doi: 10.1037/a0014532 [DOI] [Google Scholar]
  35. Levine SC, Suriyakham LW, Rowe ML, Huttenlocher J, & Gunderson EA (2010). What counts in the development of young children's number knowledge? Dev Psychol, 46(5), 1309–1319. doi: 10.1037/a0019671 [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Libertus ME, Odic D, Feigenson L, & Halberda J (2015). A Developmental Vocabulary Assessment for Parents (DVAP): Validating Parental Report of Vocabulary Size in 2- to 7-Year-Old Children. Journal of Cognition and Development, 16(3), 442–454. doi: 10.1080/15248372.2013.835312 [DOI] [Google Scholar]
  37. Missall K, Hojnoski RL, Caskie GIL, & Repasky P (2014). Home Numeracy Environments of Preschoolers: Examining Relations Among Mathematical Activities, Parent Mathematical Beliefs, and Early Mathematical Skills. Early Education and Development, 26(3), 356–376. doi: 10.1080/10409289.2015.968243 [DOI] [Google Scholar]
  38. Montgomery DE, & Koeltzow TE (2010). A review of the day–night task: The Stroop paradigm and interference control in young children. Developmental Review, 30(3), 308–330. doi: 10.1016/j.dr.2010.07.001 [DOI] [Google Scholar]
  39. Mutaf Yildiz B, Sasanguie D, De Smedt B, & Reynvoet B (2018). Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners. Front Psychol, 9, 340. doi: 10.3389/fpsyg.2018.00340 [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Napoli AR, & Purpura DJ (2018). The home literacy and numeracy environment in preschool: Cross-domain relations of parent-child practices and child outcomes. J Exp Child Psychol, 166, 581–603. doi: 10.1016/j.jecp.2017.10.002 [DOI] [PubMed] [Google Scholar]
  41. Niklas F, & Schneider W (2013). Casting the die before the die is cast: the importance of the home numeracy environment for preschool children. European Journal of Psychology of Education, 29(3), 327–345. doi: 10.1007/s10212-013-0201-6 [DOI] [Google Scholar]
  42. Passolunghi MC, Cargnelutti E, & Pastore M (2014). The contribution of general cognitive abilities and approximate number system to early mathematics. Br J Educ Psychol, 84(Pt 4), 631–649. doi: 10.1111/bjep.12054 [DOI] [PubMed] [Google Scholar]
  43. Purpura DJ, Hume LE, Sims DM, & Lonigan CJ (2011). Early literacy and early numeracy: the value of including early literacy skills in the prediction of numeracy development. J Exp Child Psychol, 110(4), 647–658. doi: 10.1016/j.jecp.2011.07.004 [DOI] [PubMed] [Google Scholar]
  44. Purpura DJ, Napoli AR, Wehrspann EA, & Gold ZS (2016). Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention. Journal of Research on Educational Effectiveness, 10(1), 116–137. doi: 10.1080/19345747.2016.1204639 [DOI] [Google Scholar]
  45. Ramani GB, Rowe ML, Eason SH, & Leech KA (2015). Math talk during informal learning activities in Head Start families. Cognitive Development, 35, 15–33. doi: 10.1016/j.cogdev.2014.11.002 [DOI] [Google Scholar]
  46. Reyna VF, & Brainerd CJ (2007). The importance of mathematics in health and human judgment: Numeracy, risk communication, and medical decision making. Learning and Individual Differences, 17(2), 147–159. doi: 10.1016/j.lindif.2007.03.010 [DOI] [Google Scholar]
  47. Ribner AD (2020). Executive function facilitates learning from math instruction in kindergarten: Evidence from the ECLS-K. Learning and Instruction, 65, 101251. doi: 10.1016/j.learninstruc.2019.101251 [DOI] [Google Scholar]
  48. Silver AM, Elliott L, Imbeah A, & Libertus ME (2020). Understanding the unique contributions of home numeracy, inhibitory control, the approximate number system, and spontaneous focusing on number for children’s math abilities. Mathematical Thinking and Learning, 1–16. [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Silver AM, Elliott L, & Libertus ME (2021). When beliefs matter most: Examining children’s math achievement in the context of parental math anxiety. Journal of Experimental Child Psychology, 201, 104992. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Skwarchuk S-L (2009). How Do Parents Support Preschoolers’ Numeracy Learning Experiences at Home? Early Childhood Education Journal, 37(3), 189–197. doi: 10.1007/s10643-009-0340-1 [DOI] [Google Scholar]
  51. Susperreguy MI, & Davis-Kean PE (2016). Maternal Math Talk in the Home and Math Skills in Preschool Children. Early Education and Development, 27(6), 841–857. doi: 10.1080/10409289.2016.1148480 [DOI] [Google Scholar]
  52. Thippana J, Elliott L, Gehman S, Libertus K, & Libertus ME (2020). Parents’ use of number talk with young children: Comparing methods, family factors, activity contexts, and relations to math skills. Early Childhood Research Quarterly, 53, 249–259. [Google Scholar]
  53. Thompson RJ, Napoli AR, & Purpura DJ (2017). Age-related differences in the relation between the home numeracy environment and numeracy skills. Infant and Child Development, 26(5). doi: 10.1002/icd.2019 [DOI] [Google Scholar]
  54. Trusty J, Robinson CR, Plata M, & Ng K-M (2000). Effects of Gender, Socioeconomic Status, and Early Academic Performance on Postsecondary Educational Choice. Journal of Counseling & Development, 78(4), 463–472. doi: 10.1002/j.1556-6676.2000.tb01930.x [DOI] [Google Scholar]
  55. Van Dooren W, & Inglis M (2015). Inhibitory control in mathematical thinking, learning and problem solving: a survey. Zdm, 47(5), 713–721. doi: 10.1007/s11858-015-0715-2 [DOI] [Google Scholar]
  56. Woodcock RW, McGrew KS, & Mather N (2001). Woodcock-Johnson III tests of achievement. [Google Scholar]

Associated Data

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Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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