What’s in a question? Parents’ question use in dyadic interactions and the relation to preschool-aged children’s math abilities

https://doi.org/10.1016/j.jecp.2021.105213Get rights and content

Highlights

  • The cognitive demand (CD) of questions relates to children’s early academic skills.

  • Parents’ total Qs do not relate to children’s math or language skills.

  • Parents’ high-CD Qs relate to children’s spatial skills and standardized math.

  • Parents’ high-CD Qs relate to children’s vocabulary skills.

Abstract

The cognitive complexity of adults’ questions, particularly during shared book reading, supports children’s developing language skills. Questions can be described as having low cognitive demand (CD; e.g., labeling, matching) or high-CD (e.g., comparing, predicting). Little is known about the relation between different types of parental questioning and children’s math abilities. The current study examined the quantity of low- and high-CD and domain-specific math questions that parents posed to their 4-year-old children in three structured activities and how the frequency of those questions relates to children’s concurrent math and language skills. Parent–child dyads (n = 121) were observed interacting with a picture book, grocery store toys, and a puzzle for about 5 min each, and children completed math and spatial assessments. Although the frequency with which parents asked questions did not relate to children’s outcomes, parents’ use of high-CD questions was associated with children’s spatial skills, standardized math scores, and vocabulary skills after controlling for parental utterances, child utterances, child age, and family socioeconomic status. However, domain-specific math questions were not related to any child outcomes above and beyond parents’ total questions. This study suggests that domain-general questions that vary in CD (low and high) are differentially related to children’s math and language abilities, which can inform the ways in which parents engage in early learning opportunities with their children.

Introduction

Young children learn through dynamic social interactions with others (e.g., Rogoff, 1990, Vygotsky, 1978). Individual differences in children’s cognitive abilities stem, in part, from variations in the quantity and quality of those interactions such as the types of conversations that adults and children have. For instance, the amount and diversity of home math activities and math talk, including conversations about math concepts between parents and children, is related to children’s math knowledge (e.g., Casey et al., 2018, Ramani et al., 2015, Thompson et al., 2017). Another important aspect of adult–child discussions is adults’ use of questions that encourage children to verbalize their current knowledge and learn new information (e.g., Tompkins, Bengochea, Nicol, & Justice, 2017) and thus have the potential to affect children’s cognitive development.

Although there is a consistent and growing body of literature on the role of questioning in children’s language and literacy skills, what remains relatively understudied is whether adults’ question use is associated with other cognitive abilities such as math skills. The current literature suggests that questioning benefits learning because it is an open form of communication that provides children with the opportunity to generate hypotheses and display mastery compared with, for example, direct instruction in which they might assume that the communicator’s intent is to teach the “whole truth” and leave them little to no room for making inferences (Yu, Landrum, Bonawitz, & Shafto, 2018). Moreover, questions can differ by cognitive complexity (i.e., the extent to which the question demands abstract or conceptual thought) and type (i.e., domain specificity), which may differentially engage children in challenging conversations and thus relate to children’s cognitive development in unique ways. For instance, questions of low cognitive demand (CD) focus on perceptible information (e.g., identifying, recalling) and allow children the opportunity to demonstrate the knowledge and practice skills they already have, whereas high-CD questions (e.g., predicting, explaining) invite them to think beyond perceptible information and challenge them to use their emergent language abilities. Adult questioning fosters children’s language and problem-solving skills, which are relevant to the development of mathematical thinking (e.g., Purpura & Ganley, 2014). For example, young children with greater language ability may be more capable of processing challenging input (e.g., “Why do you think this happened?” vs. “What color is this?”), which may require complex multistep reasoning similar to what they employ when responding to cognitively demanding math-related input (e.g., “How much money do I owe you if each corn is $2?” vs. “How many apples are there?”).

Although it is reasonable that questioning in the context of adult–child interactions may be associated with children’s math abilities, few studies have examined this relation. In addition, it is not clear whether connections between adult question use and children’s cognitive abilities are domain general or domain specific. Thus, in this study, we examined how the frequency and CD of parents’ question use relates to preschool-aged children’s math skills. Moreover, given the link between parental math talk and children’s math skills, we investigated whether parents’ domain-specific math questioning relates to children’s math abilities above and beyond overall questioning. Lastly, we aimed to replicate previous findings of the link between parents’ question use and children’s language skills as a validity check of our measures. It is possible that whereas domain-general questioning (i.e., all questions) supports both math and language skills, parents’ domain-specific math questioning may be uniquely associated with children’s math skills given that math questions are more likely than domain-general or total questions to promote mathematical thinking and the domain-specific relations between children’s vocabulary and math skills (e.g., Purpura & Reid, 2016).

Extant research demonstrates associations between parents’ and teachers’ question use and children’s vocabulary skills (Fletcher et al., 2008, Leech et al., 2013) as well as improvements in language skills (Blewitt et al., 2009, Leech et al., 2013, Rowe et al., 2017, Strouse et al., 2013, van Kleeck et al., 2006, Walsh & Rose, 2013), story comprehension (Strouse et al., 2013), story retelling and memory (Daubert et al., 2020, Kang et al., 2009), and exploratory and casual learning (Daubert et al., 2020, Yu et al., 2018). In contrast, studies of the associations between domain-general parental questions and children’s math achievement are scarce. Reynolds, Vernon-Feagans, Bratsch-Hines, Baker, and Family Life Key Project Investigators (2019) found that fathers’ average numbers of “wh-” questions (i.e., who, what, when, where, and why) during shared book viewing with their children at 6, 24, and 36 months of age were related to children’s math achievement in kindergarten. This relation held even after controlling for maternal language input and a variety of demographic variables such as socioeconomic status (SES) and home environment quality. The authors argued that these paternal questions parallel the type of “academic language” that children are exposed to during the first year of formal schooling, and thus they set the foundation for literacy and math achievement in kindergarten (Reynolds, E., Vernon-Feagans, L., Bratsch-Hines, M., Baker, C. E., & Family Life Key Project Investigators, 2019). Although this study did not examine child math achievement before formal schooling, we believe that parental questions at the preschool age may also be aligned with the language that researchers use to assess math skills (e.g., in math story problems). Children who are exposed to a greater quantity of questions may have more experience with the vocabulary and reasoning strategies required to respond to the assessment items. Thus, the frequency with which parents ask questions may be associated with children’s math performance.

Beyond the quantity of questions, researchers have examined the unique contributions of the cognitive complexity or demand of adult questions to children’s developing skills (Blank et al., 1978, Danis et al., 2000, De Temple and Snow, 2003; Rowe, Coker, & Pan, 2004; Zucker, Justice, Piasta, & Kaderavek, 2010). However, researchers vary in how they define levels of complexity (see Walsh & Hodge, 2016, for a review). Common question types include literal versus inferential, perceptual versus conceptual, low versus high demand, contextualized versus decontextualized, immediate versus nonimmediate, closed versus open, wh- questions, and dialogic questions (e.g., CROWD prompts, i.e., completion, recall, open-ended questions, wh- questions, and distancing; Whitehurst et al., 1994). Despite slight definitional differences, researchers tend to differentiate questions by the amount of abstract conceptual thought that is required of children to respond. Low-CD questions focus on identifying perceptually present, immediate, or concrete information within a text or scenario, whereas high-CD questions require respondents to go beyond presented information and make connections, summaries, explanations, and predictions. In addition, wh- questions and dialogic questions can be separated into categories of lower and higher order; dialogic reading moves from questions of low CD (e.g., “What is that?”; “What food did the animal eat?”) to questions of higher CD (e.g., “What do you think will happen next?”; “How is this animal different from that one?”). Moving forward, the terms low-CD questions and high-CD questions are used to refer to these two distinct orders of question complexity.

Exposure to low-CD questions allows children to practice existing skills and demonstrate current knowledge, whereas high-CD questions challenge them to use their emergent language skills and solve problems. Specifically, responses to high-CD questions require children to adopt higher levels of abstract thinking compared with low-CD questions. For instance, asking children about the color of an object, a common low-CD question posed by parents and teachers, generally requires a single word response. Similarly, asking children “how many” objects are present requires counting, which taps a basic number skill. In contrast, asking children about why or how a process works emphasizes cause-and-effect relations and sequencing or patterning. In the context of play with physical materials, this may encourage children to actively explore the materials, access their memory of the prior steps they took in a process, and practice producing a higher quantity and diversity of talk. Consequently, children become better communicators and are more likely to produce answers of greater complexity or detail than they would when responding to low-CD questions.

Given the impact of parents’ questioning on children’s verbal communication skills, it is possible that parents’ questioning (specifically high-CD questions) may support children’s math skills through their influence on children’s language skills, which are also associated with children’s math abilities (e.g., Zhang et al., 2017). Language acquisition, specifically vocabulary, involves making connections between words and people, objects, events, or concepts. A similar associative process is involved in the acquisition of the mathematical language that is necessary for understanding and responding to math assessments. For instance, when young children learn the meanings of number words, they develop an understanding that each number word corresponds to one specific quantity. When children transition to learning about relatively complex math concepts, such as arithmetic operations, they must understand how operations describe the relations between numbers (e.g., the word “add” refers to combining or summing the quantities of numbers). Parents’ questioning may encourage children to engage in the cognitive process of making connections between words and their meanings, which children can apply to their learning of math words and concepts. Parental questions may facilitate young children’s acquisition of math (and non-math) vocabulary, which contributes to children’s performance on math assessments, particularly if the tasks have a high language demand (e.g., the assessment questions are orally presented to children) and contain relatively challenging items (e.g., arithmetic or multistep problem solving).

Despite the dearth of studies examining adults’ questioning and its relation to children’s math skills, there are studies that have found that other aspects of adults’ verbal input, such as the complexity or abstractness of their speech, affect children’s math skills (e.g., Baker et al., 2015, Ribner et al., 2020). Baker et al. (2015) found that the complexity of fathers’ language input, as measured by the mean length of their utterances during shared book viewing with their 5-year-old children, was associated with children’s math skills during the spring of their kindergarten year. This relation held even after controlling for maternal language input, SES, race, parental age, and parental education. One possibility for this relation is that fathers’ use of complex utterances promoted children’s vocabulary and reasoning skills, which fostered more accurate responses on the math assessment. In other words, children who are accustomed to receiving more complex input engage in deeper reasoning and can better comprehend math word problems. Relatedly, Ribner et al. (2020) studied mothers’ distancing language, which requires cognitive abstraction and focuses on information beyond the perceptible or immediate context, paralleling our definition of high-CD input. Mothers were observed sharing a wordless picture book with their 5- and 6-year-old children, and mothers’ talk was coded for “distancing utterances.” The researchers found that high-CD language mediated the relation between maternal input and children’s math and language skills, providing further evidence of the importance of high-CD verbal input for children’s academic skill development. Thus, it is possible that parents’ high-CD questions, but not low-CD questions, are related to children’s math abilities. Aside from supporting children’s language abilities, frequent exposure to high-CD questions may contribute to children’s problem-solving skills. Children with higher problem-solving skills may have a greater capacity to apply their knowledge and strategies to answering math assessment items that require multiple steps or cover concepts with which they are less familiar. The current study will add to the existing literature on the role of parents’ questioning in children’s early competencies by examining how low- and high-CD questions are associated with children’s math skills.

Few studies have examined the ways in which math content is conveyed (e.g., through explanations or questions), and little is known about whether domain-specific math questions are related to children’s math skills. Given the domain-specific contributions of math-related input to children’s math skills, which are reviewed below, it is important to consider whether exposure to domain-specific questions (i.e., those addressing math content) relate to children’s abilities over and above domain-general questions. Many studies have demonstrated that the quantity of number and spatial talk that adults and children engage in is related to young children’s concurrent math abilities (e.g., Elliott et al., 2017, Levine et al., 2010, Pruden et al., 2011, Ramani et al., 2015) as well as their growth in math (e.g., Casey et al., 2018, Susperreguy and Davis-Kean, 2016). One possibility for these findings is that math-specific input from parents encourages children to focus on and learn about math concepts and/or learn the language necessary to express these concepts. Thus, children with better math language skills are likely to perform better on math assessments. Indeed, Purpura & Reid (2016) found that preschool-aged children’s number skills were positively related to their math vocabulary above and beyond their general vocabulary. The authors’ math language test measured children’s understanding of specific words related to quantity and spatial concepts that were considered typical in early mathematics, including “take away,” “more,” “below,” and “nearest.” Thus, the association between children’s math and language skills may be domain specific. In the context of parents’ question input, parents’ domain-specific math questions may benefit children’s math skills over and above all questioning given that math questions are more likely than general questions to promote mathematical thinking and learning.

In addition, differences in the content of adult math input, which may vary by cognitive complexity, are uniquely predictive of child math achievement. For instance, Casey et al. (2018) examined the maternal support of numerical concepts, such as counting and arithmetic, in 3-year-old children during play with a cash register, dress-up clothes, and building blocks. The researchers identified numerical concepts along a continuum from least developmentally complex to most complex, and the frequency of maternal linguistic support for such concepts was coded as follows: (1) identifying numerals, (2) one-to-one counting, (3) labeling sets, and (4) operations. Children’s math achievement at 4.5 and 6 and 7 years of age was measured using the Applied Problems subtest of the Woodcock–Johnson (WJ) Tests of Achievement (Woodcock & Johnson, 1989), which requires children to analyze and solve mathematical problems presented pictorially and orally. Maternal talk about labeling sets of objects significantly predicted children’s later math achievement even after controlling for other forms of numerical support (i.e., less complex talk about identifying numerals and counting). Similarly, Elliott et al. (2017) found that mothers’ talk about numbers greater than 10, not mothers’ overall number talk, was associated with 5- and 6-year-old children’s formal math ability. These studies suggest that although math talk is important to children’s math development, more cognitively demanding input about developmentally complex math concepts (e.g., talk about large numbers or labeling sets) may be more appropriate for or beneficial to children at particular ages or skill levels than low cognitively demanding input (e.g., talk about small numbers or identifying numerals).

Given the nuance regarding how math input may support children’s math skills, it is possible that low- and high-CD domain-specific math questioning may be differentially associated with children’s math skills. For instance, the frequency of parents’ low-CD math questions (e.g., “How many …?”) may relate to children’s cardinal number knowledge more strongly than arithmetic or problem-solving skills. In contrast, parents’ high-CD math questions (e.g., “How do you know who has more?”; “How many more …?”) may relate to children’s ability to solve complex or multistep math problems. These questions may encourage children to engage in metacognitive activities, such as reflecting on their strategy use and monitoring their own abilities, which are likely used when children complete math assessments that require them to problem solve.

Two studies have specifically examined adults’ domain-specific question use in relation to children’s math skills. First, Daubert and Ramani (2019) investigated changes in 3- to 5-year-olds’ math skills after playing a linear number board game with an experimenter. Children who interacted with an experimenter who asked math questions (e.g., “How many spaces …?”) improved more on subsequent arithmetic and magnitude comparison tasks than children who received math statements (e.g., “You are two spaces ahead”) and general positive encouragement (e.g., “Let’s hope you get a good spin!”). Second, Uscianowski, Almeda, and Ginsburg (2018) examined parents’ use of questions during hypothetical book reading with their children. The researchers presented participants recruited online with visual storybook pages and asked them to indicate questions that they would ask their children to help them learn about characters, numbers, or shapes. In addition, parents reported their children’s abilities in the domains of reading, numbers, and shapes by responding to the question, “Compared with 10 children of the same age as your child, your child would be better than [how many] of them with reading comprehension/numbers/shapes, such as describing what just happened in the story/ counting a group of objects/naming and recognizing different shapes?” Parents’ high-CD questions about number (e.g., “If two animals walk away, how many animals would we have left?”) versus low-CD questions (e.g., “What number do you see?”) during hypothetical shared book reading were positively related to their children’s counting ability, whereas no significant associations were found for parents’ language about shapes. These studies suggest that exposure to domain-specific math questions may benefit children’s acquisition of math knowledge. We expand on the work reviewed above by investigating the domain-specific and domain-general relations between parental questioning and children’s math skills before formal schooling.

Based on the gaps in the extant literature reviewed above, additional work is needed to further delineate the role of questions, both domain general and domain specific, for children’s math abilities. Specifically, although exposure to parental questions, including domain-specific math questions, related to children’s math abilities (Daubert and Ramani, 2019, Reynolds et al., 2019), it is unknown whether questions that vary in complexity (i.e., low and high CD) are differentially associated with children’s math skills. In addition, although one study found that parents’ self-reported question use about number related to counting skill (Uscianowski et al., 2018), the researchers relied on mono-method data sources, whereby parents reported on their question use in a hypothetical situation and estimated their children’s abilities. Parent reports of their children’s math skills are generally inaccurate (e.g., Zippert & Ramani, 2017), and parents’ indications of behavior in an online survey might not reflect their actual behaviors when interacting with their children. Observational studies of parent–child interactions to explore the complexity of parents’ questioning and direct assessments of children’s math skills have the potential to strengthen the ecological validity of these findings.

The current study addressed these research gaps by exploring the relation between children’s math abilities and the CD (low and high) and type (domain general and domain specific) of parent questions with children during three structured observational tasks. We also comparatively examined children’s language skills to demonstrate that whereas domain-general questioning may support both math and language skills, domain-specific math questioning may uniquely relate to math skills. Although domain-specific math questions vary in complexity and have the potential to relate to different domains of children’s math skills as reviewed above, the frequency of high-CD math questions in our sample was relatively low. Given that more than half of our parents (n = 76) never asked a high-CD domain-specific math question, we summed parents’ low- and high-CD math questions for our analyses. In addition, our analyses controlled for the total number of parental utterances, child utterances, child age, and SES, which relate to our cognitive outcomes of interest (e.g., Cristofaro & Tamis-LeMonda, 2011). Thus, we sought to address the following four research questions (RQs):

  • RQ1: Does the frequency with which parents ask questions relate to children’s math outcomes?

  • RQ2: Does the frequency with which parents ask low- and high-CD questions relate to children’s math abilities?

  • RQ3: Does the frequency with which parents’ ask domain-specific math questions relate to children’s math skills above and beyond the total number of questions?

  • RQ4: Does the frequency with which parents ask questions (i.e., total, low- and high-CD, and domain-specific math) relate to children’s language skills?

Given recent work on parental questioning, the complexity of parents’ overall language input, and contributions to children’s school readiness skills (e.g., Ribner et al., 2020), it was hypothesized that parents’ overall questioning and high-CD questioning are related to children’s concurrent math and language skills. Moreover, it was predicted that parents’ use of domain-specific math questions would be positively associated with children’s concurrent math abilities but not language abilities over and above parents’ total questioning.

Method

Our data are derived from a study examining how parents promote early learning in 4-year-old children. The original sample comprised 178 parent–child dyads, but 48 families were excluded from the current analyses due to insufficient video data as a result of equipment failures (e.g., camera battery power loss; n = 2), failure to complete any tasks relevant to our research questions (structured observations; child assessments due to experimenter error, child fatigue, or disinterest; parent questionnaire; n = 44), and the presence of additional family members interacting with the child during the entirety of the structured observations (n = 2). In addition, 9 dyads were statistically significant outliers in analyses (based on dfbetas; see details below) and thus were excluded. The final sample included in this report consisted of 121 parent–child dyads (Mchild age = 53.52 months, SD = 3.48, range = 48–59.88; 54% male). Families were recruited from a large mid-Atlantic metropolitan area of the United States through the distribution of flyers in the community and in-person contact between the study team and potential participants at preschools and daycare centers. Parents and children were mostly tested in their own homes but also occasionally in our lab or in preschool and daycare centers (see below), and the majority of caregivers were mothers (n = 114). The race/ethnicity of the caregivers was 82.31% White, 12.31% Black or African American, and 3.85% Asian or Pacific Islander (1.54% did not report this information). Caregivers reported having less than a bachelor’s degree (17.69%), a bachelor’s degree (36.15%), or more than a bachelor’s degree (46.15%), and they completed an average of 16.35 years of education (SD = 1.97, range = 11–18). The mean yearly household income that parents reported was $107,791.72 (SD = $78,303.36, Med = $95,000). Welch’s t tests and chi-square tests were used to compare the excluded group with the final sample on the reported demographic variables. The two groups did not significantly differ across these characteristics.

Parents and children were observed engaging in three structured observational tasks: (a) shared picture book viewing, (b) a magnet board puzzle activity, and (c) pretend grocery shopping. Dyads were given approximately 5 min to complete each activity and were given more time (no more than an additional 3 min) if needed to complete each task. In the book task, parent–child dyads were asked to look at a wordless picture book together that was specifically created by the research team and that had the potential to elicit conversations about numbers and spatial relations. In the puzzle task, dyads were presented with magnet shapes and were asked to construct an image of an animal using these shapes based on a model. In the grocery shopping task, dyads were given a set of developmentally appropriate toys, including pretend food items and a cash register, and were instructed to play with the toys as they normally would. The majority of these interactions took place in participants’ homes, and 3 dyads engaged in these activities in a quiet room in our lab. Each task was video-recorded and transcribed by trained research assistants in our lab.

For each transcription, occurrences of parent questions were extracted by searching for question marks (total questions) and then those questions were coded as either low- or high-CD questions based on previous work (e.g., Blank et al., 1978, Uscianowski et al., 2018, van Kleeck et al., 2006). Low-CD questions relate to perceptually present or immediate information and require a response low in CD such as labeling, locating, identifying, recalling information, counting, or completing sentences (e.g., “What color is that?”). High-CD questions require the respondent to think beyond perceptually present information and a response higher in CD such as predicting, summarizing, comparing, unifying a sequence of events, problem solving, or explaining (e.g., “Why do you think that happened?”). Few questions occurring in low frequency and unrelated to the task, such as “Can I go to the bathroom?”, were coded as “other” and were not included in our analyses. See Table 1 for a full description of question categories and examples from each task. To control for the amount of language input from parents and children, we counted the total number of parental and child utterances in each task. An utterance refers to speech by an individual speaker that is bounded by a speaker transition, a grammatical closure (i.e., a terminal punctuation mark such as a period or question mark), or a pause of more than 2 s (Pan, Rowe, Spier, & Tamis-LeMonda, 2004).

Furthermore, each question was coded to indicate whether it contained math-related content. Questions were coded as being domain-specific if they included at least one word pertaining to math concepts, including identifying numerals, counting, labeling sets, ordinal relations, patterns, and arithmetic, as well as abstract concepts, such as dates and time. These categories were chosen based on a combination of coding schemes in the existing math talk literature (e.g., Braham, 2020, Casey et al., 2018, Ramani et al., 2015, Simpson and Linder, 2016). Questions containing number words were not coded as domain specific if they were not specific to a math concept. For instance, the question “How are these two pieces different?” is not a domain-specific question because it does not require a math-related response. In addition, the question’s interpretation would remain the same if the word “two” were omitted. In contrast, the question “Can you point to the number two?” is a domain-specific question because it involves identifying a numeral.

Each task was coded for the frequency of different categories of questioning (i.e., CD and domain specificity) by two research assistants, and at least 20% of the transcriptions per task were double-coded. Every coded transcription was reviewed to compare the exact questions coded, and pairs of coders were considered to be in agreement only if the codes and particular questions matched. Disagreements were discussed between the pair of coders and the first author, who made the final decision regarding codes. Moreover, 20% of the transcriptions were double-coded for the number of domain-specific math questions, and disagreements were discussed between coders and the first author before final decisions were made. To assess the degree of agreement between each pair of coders in identifying the frequency, CD, and type of parents’ questions, kappa (κ) statistics were calculated for categorizing questions as low-CD questions (.88), high-CD questions (.88), and domain-specific math questions (.95). The total numbers of parental utterances, child utterances, parent questions, parent low-CD questions, parent high-CD questions, and parent domain-specific questions were summed across the three tasks for analyses.

Children’s number and spatial skills were assessed in one session. The majority of the sessions occurred in a quiet room in participants’ homes (n = 109) immediately after the observational tasks on the same day, at children’s preschool or daycare center on a later day (n = 9), or in the lab (n = 3). Given the relatively low number of children who completed tasks in preschools or the lab, we used Welch’s t tests to compare child assessment scores between sessions that occurred in homes versus the other two locations and found no significant differences.

Participants completed the Give-N task (Wynn, 1992) and a counting task designed to assess their number skills. In the Give-N task, children were presented with a set of plastic counters (fish) and two bear puppets, and they were asked to help each bear count by giving it the right number of fish to eat. The puppets were presented individually for 6 trials each, and the range of fish to give each puppet was 1 to 6 in random order. After each trial, the experimenter checked whether children gave the correct number (e.g., “Is that three?”). The dependent measure was the percentage of correct responses. The Give-N task has been found to be highly reliable. Children who are considered a specific N-knower are given the same classification in a titrated version of the task (weighted κ = .87; Marchand & Barner, 2020). In the counting task, children were asked to count out loud to show the experimenter how high they could count. If children stopped after reaching a certain number, they were prompted to continue (e.g., “What comes next?”). Once children made one mistake or reached 100, they were stopped. The dependent measure was the highest number that children could count to without making any mistakes. A composite score of children’s number knowledge was computed by averaging the z scores of the Give-N and counting tasks.

Participants completed three assessments that tapped into their knowledge of patterns and geometry. In the patterning assessment (Cronbach’s α = .83; Rittle-Johnson, Zippert, & Boice, 2018), children were asked to indicate the next object in an arrangement (2 trials), find the missing object in the middle of a pattern (3 trials), complete a pattern by indicating the next four objects (3 trials), and create the same kind of pattern that was presented to them using different objects (2 trials). No feedback was given, and the dependent measure was the percentage of correct responses. In the geometric sensitivity task (Dehaene, Izard, Pica, & Spelke, 2006), children were presented with 12 trials of picture sets, each containing six different images. In each picture set, five of the six images represented a geometric property (e.g., of distance or angles) that was not present in the last image, and children were asked to identify the image that did not fit. Children completed 3 practice trials with feedback that explained the correct response (e.g., “See, this one is straight and the others are curved. See, this one is curved and this one is curved … so this one doesn’t go”). No feedback was given in the test trials, and the dependent measure was the percentage of correct responses. In the Children’s Mental Transformation Task (CMTT; Levine, Huttenlocher, Taylor, & Langrock, 1999), participants were presented with 16 trials, each containing two shapes that undergo a rotation or translation to create one of four picture options. No feedback was given on any item, and the dependent measure was the percentage of correct responses. A composite score of children’s spatial skills was computed by averaging the z scores of these three tasks.

Children completed the WJ- III Applied Problems subtest (r = .93; Woodcock, McGrew, & Mather, 2001), which measured their ability to analyze and solve math problems. The problems became progressively more difficult, from initial items requiring the application of basic number concepts, such as counting, to items requiring arithmetic and knowledge of units, such as currency and temperature. The standardized score on this subtest with an expected mean of 100 and a standard deviation of 15 was z scored for analyses.

Children’s expressive vocabulary was measured using the Developmental Vocabulary Assessment for Parents (DVAP; Libertus, Odic, Feigenson, & Halberda, 2015), which contains 212 nouns, verbs, and adjectives ranging in difficulty (e.g., “girl,” “jumping,” “hazardous”). Parents were instructed to indicate which of the listed words they had heard their children say, including words that their children might have used as a different part of speech or with a different pronunciation (e.g., “sleep” or “sreep” instead of “sleeping”). In addition, parents were instructed to refrain from asking their children whether they knew the words. Parents completed this questionnaire on a paper copy or electronic format. The words were derived from Form A of the Peabody Picture Vocabulary Test (PPVT-4; Dunn & Dunn, 2007), an experimenter-administered vocabulary assessment. Past work has demonstrated that scores on the DVAP highly correlate with children’s PPVT-4 performance and that the DVAP is a valid indicator of children’s expressive vocabulary (Libertus et al., 2015). The dependent measure was the total number of words indicated.

Parents completed electronic questionnaires in Qualtrics after the home visit. They provided their children’s gender and birth date, and age in months was calculated at the first assessment. Parents also reported on background characteristics, including educational attainment and household income. Parent education was converted to a continuous variable representing years of completed education (less than a high school diploma or GED [general equivalency diploma] = 11 years, high school diploma = 12 years, some college but no degree = 13 years, associate’s degree = 14 years, bachelor’s degree = 16 years, graduate degree = 18 years). An SES composite was created by averaging the standardized education and income variables.

To address RQ1, linear regression analyses were used to determine the relation between the frequency with which parents asked questions and children’s math outcomes. Model 1 contained total parent questions, parent utterances, child utterances, child age, and SES as predictors of child-level outcomes; number skills, spatial skills, and standardized math scores were dependent variables in individual models. To address RQ2 and build on previous work by specifying how the CD of parents’ questions may differentially relate to children’s skills, similar regression analyses were used to determine the association between the frequency of parents’ low- and high-CD questioning and children’s math outcomes after controlling for total parental utterances, child age, child utterances, and SES. Model 2 included the same three child outcomes as the dependent variables. To address RQ3, the same regression analyses were used to determine whether the frequency of parents’ domain-specific math questioning relates to children’s math outcomes after controlling for parents’ total questions, child age, child utterances, and SES (Model 3). Given the low occurrence of high-CD domain-specific math questions across participants (63% of parents asked no high-CD math questions), we used the total number of math questions in Model 3. To answer RQ4 and replicate previous work, we ran the same models for RQs 1 to 3 relating parents’ questioning to children’s expressive language skills.

We included parent utterances, child age, child utterances, and SES as our covariates of interest because of their potential relations to the amount of parental input that children may receive and our child outcomes. For instance, older children may receive more complex questions and may perform better on the math assessments compared with younger children. In addition, children who verbally contribute to conversations with their parents may receive more questions overall than children who speak less. The extent to which children converse may act as a signal to parents that they are capable of responding, or more likely to respond, to the input that they receive, which may motivate parents to question more frequently. Finally, past work has shown that there are SES disparities in the amount and diversity of domain-general parental language input (e.g., Schwab & Lew-Williams, 2016) and math-specific parental language input (e.g., Levine et al., 2010). Thus, we included SES as an additional covariate.

Models were first run with all available observations (n = 130), and then regression diagnostics were used to identify potentially influential points. Specifically, dfbetas were used to assess the degree to which particular data points influenced the regression estimates of our primary variables of interest (e.g., total parent questions). Outliers with relatively large influence were excluded from our analyses. In some cases, different outliers were identified for different models; we excluded all influential data points to keep a consistent sample across models. A total of 9 outliers were excluded (i.e., our final sample consisted of 121 observations).

Section snippets

Results

We observed substantial variability in the amount of parents’ question use when interacting with their children. Parents produced 105 to 597 total utterances (M = 277.71, SD = 71.01) across the three activities, with an average of 91.82 questions (SD = 35.66, range = 0–178). Children produced 54 to 440 total utterances (M = 159.76, SD = 57.02) across the three tasks. Parents produced more low-CD questions (M = 78.87, SD = 30.62) than high-CD questions (M = 12.95, SD = 10.18) overall, and the

Discussion

The current study explored the relation between the CD and type of questions parents use with children in dyadic interactions and children’s math and language skills. Specifically, we were interested in the complexity of parents’ questioning (low and high CD) and the relation to children’s math abilities because few studies have examined this. Although the frequency with which parents asked questions was not associated with any of our child outcomes, the CD of their questions differentially

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We thank our project team members for all their assistance with data collection and coding, Scott Fraundorf for his contributions to our statistical analyses, the generous support of the community partners that served as testing and recruitment sites, and the participating families who made our work possible. Primary funding for this project was provided by a grant from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD; 1 R01 HD093689-01A1) to Heather J.

Data availability

Data are available upon request from the corresponding author.

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