It’s more than just fun and games: Play-based mathematics activities for Head Start families

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Early Childhood Research Quarterly

It’s more than just fun and games: Play-based mathematics activities for Head Start families Geetha B. Ramani ∗ , Nicole R. Scalise Department of Human Development and Quantitative Methodology, University of Maryland, College Park, 3304 Benjamin Building, College Park, MD 20742, United States

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Article history: Received 17 November 2017 Received in revised form 16 July 2018 Accepted 18 July 2018 Available online xxx Keywords: Home numeracy environment Mathematical knowledge Head Start Math games Interventions

a b s t r a c t Discrepancies in early mathematical knowledge between children from different socioeconomic backgrounds have been found before the start of kindergarten. The early home environment is one context that can address these discrepancies. This study examined whether an informal mathematical activity that has been successful at promoting children’s numerical knowledge could be translated into a home activity for families from lower-income backgrounds. Families from Head Start programs (n = 39) were randomly assigned to play either a numerical magnitude comparison game or a shape and color matching game. Results showed that playing the numerical magnitude comparison game did not improve children’s numerical knowledge, although playing the shape and color matching game did improve children’s shape knowledge. However, parental reports of the frequency of game playing at home related to children’s learning from both games. Analyses of audio recordings of the families playing the games at home revealed there was wide variability in how parents assisted the children during the card game play. Results are discussed in terms of the benefits and challenges of mathematical interventions targeting the home context. © 2018 Elsevier Inc. All rights reserved.

1. Introduction The home environment plays an essential role in children’s early mathematical development. Children enter formal schooling with a wealth of foundational mathematical knowledge, such as verbal counting skills, identifying written numerals, and comparing the magnitudes of small numbers (Geary, 2006). Children’s experiences at home likely contribute to these early competencies. Indeed, there is growing empirical support that both the type of mathematical activities families engage in at home as well as the quality of mathematical input that children receive are strongly related to children’s early mathematical knowledge (Elliott, Braham, & Libertus, 2017; LeFevre, Polyzoi, Skwarchuk, Fast, & Sowinski, 2010; Levine, Suriyakham, Rowe, Huttenlocher, & Gunderson, 2010; Niklas & Schneider, 2014; Ramani, Rowe, Eason, & Leech, 2015; Skwarchuk, Sowinski, & LeFevre, 2014). However, income-based gaps in some areas of early mathematical knowledge have been found amongst preschoolers, with children from lowerincome backgrounds on average falling more than 7 months behind their same-age peers from middle- to higher-income backgrounds

(Ramani & Siegler, 2011; Starkey, Klein, & Wakeley, 2004). The early home environment is likely one source of this income-related gap, but also an important context where these discrepancies could be remediated. Providing lower-income families with mathematical activities could benefit the development of their children’s mathematical knowledge and enable them to start school with comparable foundational mathematical skills to their peers. The present study targeted the early home learning environment as a context to improve the mathematical achievement of low-income children. Specifically, we examined whether providing families from Head Start programs with informal mathematical card games to play at home can improve their children’s mathematical knowledge. Although there is strong correlational evidence of the importance of the early home environment for children’s mathematical achievement (e.g., Niklas & Schneider, 2014; Skwarchuk et al., 2014), little research has experimentally tested whether specific activities that families use at home influence children’s mathematical knowledge. These findings could help identify causal relations between the home environment and children’s mathematical knowledge, as well as potential tools to improve the mathematical achievement of children from lower-income families.

∗ Corresponding author. E-mail address: [email protected] (G.B. Ramani). https://doi.org/10.1016/j.ecresq.2018.07.011 0885-2006/© 2018 Elsevier Inc. All rights reserved.

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1.1. Mathematical activities and interactions in the early home environment Sociocultural perspective provides theoretical motivation for targeting the early home environment as a means to improve children’s mathematical knowledge. Theorists rooted in this approach posit that engaging in everyday, informal activities with adults can contribute to children’s knowledge by providing them with new information and supporting their skill development (Gauvain, 2001; Vygotsky, 1976). Parents can support children’s learning by guiding and assisting them during common and familiar activities (Rogoff, 1990). When applied to the development of mathematical understanding, informal activities and interactions with adults can provide children with extensive mathematical information in the home (LeFevre et al., 2009; Saxe, 2004). For example, parents can guide their children to make correct measurements when cooking together, count the number of forks needed for a family dinner, or identify the shapes of signs when driving in a car. Empirical research rooted in the sociocultural perspective has shown how engaging in number-related activities in the home is related to children’s mathematical knowledge. Mathematical activities can be formal, where the goal of the activity is for children to learn about numbers, such as engaging in number-related activity books and worksheets (Huntsinger, Jose, Larson, Balsink Krieg, & Shaligram, 2000; Skwarchuk, 2009). Alternatively, they can be informal activities, where the math content is embedded in play or games, such as playing board games and singing songs (BlevinsKnabe & Musun-Miller, 1996; Saxe, Guberman, & Gearhart, 1987). Both types of activities have been shown to be related to children’s mathematical knowledge. For example, the frequency with which parents from middle-class backgrounds reported engaging their kindergarten children in direct teaching activities at home, such as identifying numbers, counting, and performing simple calculations, predicted children’s mathematical fluency a year later (Manolitsis, Georgiou, & Tziraki, 2013). Informal number-related activities, such as games, are also related to children’s mathematical knowledge and may be more developmentally appropriate than formal activities for fostering mathematical development in young children. Games are engaging, enjoyable, and socially interactive, all characteristics which can provide an ideal context for learning (Hassinger-Das et al., 2017). Parent reports of engaging in informal activities at home provide support for this hypothesis. Specifically, LeFevre et al. (2009) found parents’ reports of engaging in activities involving numbers, including playing board games, were correlated with children’s numerical knowledge in areas related to quantity, place value, numeral identification, and arithmetic performance in kindergarten through second grade. Similarly, surveys from families from a range of socioeconomic backgrounds showed that playing board games at home was related to their preschool children’s counting abilities, as well as their knowledge of everyday numerical knowledge, such as birthdays and phone numbers (Benavides-Varela et al., 2016). Overall, there is substantial correlational evidence of the relations between engaging in numeracy-related activities at home and children’s concurrent and later mathematical knowledge. From a sociocultural perspective it is not only engaging in mathematical activities that is important for children’s learning, but also the quality of the interactions. Joint activities provide opportunities for parents to assist their child through a variety of scaffolding techniques, such as adapting an activity to a child’s abilities, asking a child questions, demonstrating strategies to complete the activity, providing guidance on how to complete an activity, and providing feedback on performance (Gauvain, 2001). However, few studies have examined these types of parent behaviors during mathematical games with preschoolers. In one study, Bjorklund, Hubertz, and Reubens (2004) observed that middle-class parents used var-

ious types of guidance while playing a board game with their preschoolers over the course of several weeks. Parents adapted the type of guidance they provided based on their children’s use of arithmetic and counting strategies while playing the game. Parents used more cognitive directives, such as modeling, instructing, and re-representing the problem to make it more familiar, when their children used less sophisticated strategies. Parents from both middle- and lower-income backgrounds use a variety of guidance while playing number board games with their preschoolers, such as providing physical and verbal hints and prompting after children make errors. Children often perform the numeracy-related activities during the game more accurately when guidance is provided (Vandermaas-Peeler, Ferretti, & Loving, 2012; Vandermaas-Peeler & Pittard, 2014). Together, these studies suggest that parents provide more assistance when their children need it, but adapt their feedback as children’s game play improves. Empirical work suggests that increasing mathematical activities in the home environment may be beneficial particularly for families from lower-income backgrounds. Analyses of four nationally representative samples over a 25-year period showed that the gap in the frequency with which parents report engaging in activities related to teaching letters and numbers has significantly increased between lower- and middle-income families over time (Kalil, Ziol-Guest, Ryan, & Markowitz, 2016). However, there is also large variation among lower-income families in the frequency with which they engage in mathematical activities at home (Ramani et al., 2015; Saxe et al., 1987). Similar to middle-income families, this variation is related to children’s numerical knowledge. Amongst families whose children attend Head Start, parents’ reports of playing games at home, specifically board games, card games, and computer games, correlated with their children’s counting and cardinality understanding (Ramani et al., 2015). Despite this correlational evidence, there is limited experimental research that has examined how children’s home environment can be used to improve their mathematical knowledge, especially among families from lower-income backgrounds. One study found that providing parents of preschoolers with minimal information about mathematical concepts, in the form of counting principles and a number-related dice game, improved the frequency with which they reported engaging in mathematical activities at home as well as their children’ counting skills compared to families who did not receive the information (Niklas, Cohrssen, & Taylor, 2016). In another study with first grade children, middle-class families were provided with iPads and asked to play either a math-related app or a reading-related app. Each of the apps required parents to read passages and answer either math- or reading-related questions. The more often families used the math-related app, the higher children’s mathematics achievement was at the end of the school year, controlling for their achievement at the beginning of the school year (Berkowitz et al., 2015). Together, these studies suggest that the home environment could be an ideal context for promoting low-income children’s mathematical knowledge. 1.2. Benefits of playing card games for children’s mathematical knowledge In designing a game for Head Start families to play at home, we integrated the sociocultural perspective with a theory of mathematical development. According to the Integrated Theory of Numerical Development (Siegler, 2016; Siegler, Thompson, & Schneider, 2011), numerical development involves an increased understanding of the magnitudes across a range of numbers that expands across the lifespan. From birth, humans are sensitive to large differences in non-symbolic numerical magnitudes, also considered as an intuitive understanding of quantities. Non-symbolic magnitude representations, also known as the Approximate Num-

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ber System (ANS; Libertus, Feigenson, & Halberda, 2011), are typically measured by assessing the precision with which two sets of items can be discriminated (Halberda & Feigenson, 2008). During the toddler and preschool years, numerical magnitude development involves refining non-symbolic representations and adopting symbolic representations of small whole numbers (Siegler, 2016). Symbolic representations include attaching meaning to number words (e.g., one, two three) and written numerical symbols (e.g., 1, 2, 3). Both symbolic and non-symbolic magnitude understanding have been linked to broader mathematics performance (e.g., Inglis, Attridge, Batchelor, & Gilmore, 2011; Kolkman, Kroesbergen, & Leseman, 2013; Libertus, Feigenson, & Halberda, 2013; Sasanguie, Göbel, Moll, Smets, & Reynvoet, 2013). The integrated theory of numerical development suggests that activities that support children’s magnitude knowledge of both symbolic and non-symbolic numbers may benefit their later math performance. Since young children may be more competent at discriminating between non-symbolic magnitudes, having both non-symbolic and symbolic representations available simultaneously could help them to make judgments about the magnitudes of symbolic numbers. That is, having redundant cues about the magnitudes of numbers could be helpful to young children as their symbolic magnitude representations are emerging (Siegler & Booth, 2004). One type of activity that seems ideal for building young children’s numerical knowledge is playing numerical card games, since cards include cues that link symbolic and non-symbolic magnitude representations. Recent empirical work provides support for this hypothesis. Preschool children from Head Start programs were randomly assigned to play one of two numerical card games with an experimenter for four 15-min sessions (Scalise, Daubert, & Ramani, 2017). In the magnitude comparison game, similar to the card game War, children had to identify which number on two cards was larger and the player with the larger card took the pair. In the other card game, a numerical matching game similar to the game Memory, children took turns with the experimenter turning over pairs of facedown cards to try to find a match. The player who found the most pairs won. Both games involved playing with the same numerical cards, and accordingly, children in both conditions improved their counting and numerical identification skills. However, only playing the numerical magnitude comparison game improved children’s symbolic numerical magnitude knowledge and eliminated the performance gap in that area that had previously existed between the Head Start participants and middle-income participants. These findings suggest that brief experience playing a numerical magnitude comparison card game with an adult can make a significant improvement in Head Start children’s magnitude skills. 1.3. The current study The current study extends previous research by providing mathematical card games to families in Head Start to use as a tool to support their child’s mathematical development at home. This study fills a critical gap in the play-based, early mathematics intervention literature. Previous research that has used games to promote children’s numerical knowledge typically relies on trained researchers to implement the intervention activities (e.g., Laski & Siegler, 2014; Ramani & Siegler, 2008; Scalise et al., 2017; Whyte & Bull, 2008), which limits our understanding of using the games in different contexts. Only one known experimental study to date has provided Head Start families with mathematical activities to play at home. Families were randomly assigned to receive one of two commercially available board games: either the number-based board game Chutes and Ladders, or the color-based board game Candyland (Sonnenschein, Metzger, Dowling, Gay, & Simons, 2016). Parents were asked to

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play the game at home at least three times a week for five weeks with their children. Researchers found children in both conditions improved their counting and numeral identification abilities. Poststudy interviews revealed that not all families were playing the game as instructed. Parents also reported that it would have been beneficial to train the children to play the game in the classroom and incentivize the game play to increase children’s enthusiasm and motivation. In a second study, Sonnenschein and colleagues indeed found that providing both parents and children with training on how to play the board game and stickers as an after-game incentive for children was more successful in improving children’s numerical magnitude knowledge than not providing training or incentives. This suggests that having children be active participants in the game play training may be critical for games to be successful at home. The present study contributes to the limited research in the area of mathematical home interventions. The first goal of the study was to examine the effectiveness of play-based mathematical activities, specifically card games, for families from low-income backgrounds. Based on previous findings (Scalise et al., 2017), we hypothesized that playing a numerical magnitude comparison card game would promote children’s numerical knowledge, specifically their counting, numeral identification, and numerical magnitude knowledge. We also hypothesized that playing this game would promote children’s cardinality knowledge because during the game children practice counting and labeling the set sizes on the cards. The current study also included an active non-numerical card game condition. The previous study with card games used a numerical card game as a control (Scalise et al., 2017). Including a non-numerical control game allows for teasing apart the improvements in children’s numerical skills that can be attributed to practice with the numerical game, as opposed to other mathrelated experiences at school and at home during the same period. Specifically, children in the control group played a shape and color matching game that required players to match a target card on either the shape or color, similar to the game Uno. Given that the nature of the game involved children labeling shape names, we also hypothesized that playing the shape and color matching game would improve children’s shape knowledge. All of the families in both conditions received training on how to play the game and sticker incentives to give to children. The second goal of the study was to examine the frequency of families’ card game playing at home. Specifically, we examined parents’ reports of how much time they spent playing the game. Previous research has found that the amount of time spent playing math games is related to children’s mathematical achievement (Berkowitz et al., 2015). However, given the limited number of studies that have tracked how much families play a game provided to them, this goal was exploratory, but extends our knowledge of how families use the game. Relations between game playing time and children’s learning gains were also examined. We also were interested in the quality of the game play. Therefore, the third goal was to analyze how parents support their children during game play. We were interested in whether parents were playing the game as designed and responding to the cues in the game. Specifically, we examined the frequency with which families were using number words as well as shape and color words during the games. We were also interested in the kinds of guidance that parents were providing to the children. There is limited research on how parents scaffold their children while playing informal math games. Although parents were trained on the rules of the games, their game play likely varies more than that of an experimenter following a script. This variation in parental guidance as well as the number words and shape and color words used during the game could relate to their children’s learning from the game.

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2. Methods 2.1. Participants Forty-three Head Start preschoolers and one parent/guardian per child were enrolled in the study. Four children not included in the analyses because three of the families had two children participate in the study; one child from each of the families was chosen at random to include in the analyses. Another child’s family was unable to meet an experimenter to receive the game materials. The final sample included 39 children (56% female) and one parent/guardian per child (85% female), ranging in age from 3 years, 7 months to 5 years, 7 months (M = 4 years, 7 months; SD = 0.72 years). Among the child participants 54% were African American or Black; 10% were Asian or Pacific Islander; 8% were Caucasian; 13% were biracial; and 15% did not report their race. Twenty-six percent of child participants were Hispanic or Latino. Head Start is a federally funded preschool program for families living at or below the poverty line, which was an annual household income of $24,300 or less for a family of four during the year these data were collected. Participants were recruited from two Head Start locations: 19 participants were recruited from a mid-Atlantic state and 20 participants were recruited from a Pacific northwestern state. 2.2. Procedure Child participants met one-on-one with a trained experimenter for a 15-min pretest assessment, which included five measures of numerical knowledge and two measures of shape knowledge. After the pretest assessment, children and their parent/guardian (subsequently referred to as parents) were randomly assigned to one of two intervention conditions: a numerical magnitude comparison game (n = 22) or a shape and color matching game (n = 17). The random assignment was stratified by gender and the child’s classroom within the Head Start center. Roughly equal numbers of children from each site were assigned to the two conditions. The enrolled parent was provided with their intervention materials and briefly taught how to play the game by an experimenter. Parents were provided a packet of materials that included a deck of cards in a box, instructions, recording log, stickers, and an audio recorder. The instructions on how to play the game were provided in detail including diagrams of game play in the packet of materials, as well as brief instructions in the box of cards. Both the verbal and written instructions given were adapted from how an experimenter played the game with children in the previous study (Scalise et al., 2017). Families were asked to play the assigned intervention game twice a week for 15-min at home across six weeks, for a total of three hours. They were also asked to audio record themselves while they played the game and complete a written log of the dates and times that they played. Parents received instructions on how to use the audio recorder both in person from an experimenter and in writing as a part of the study materials that they took home. Parents received weekly reminders to play the game via text message, email, or a paper slip sent home with their child. At the end of the six weeks, children were administered the same numerical and shape knowledge measures individually. After children completed their posttest assessment, parents met the experimenters to provide the audio recorders and written tracking logs, and receive the card game for the other intervention condition. Families received $50 for participating in the study and returning the audio recorder. 2.3. Measures of mathematical knowledge Prior to families playing the games and at the end of the six weeks, children were administered identical pretest and posttest

assessments with seven tasks from two areas of mathematical knowledge: numerical knowledge and shape knowledge. All children were presented the tasks in the same order: verbal counting, numeral identification, symbolic magnitude comparison, cardinality, number line estimation, shape naming, and shape finding. 2.3.1. Numerical knowledge measures Five measures of children’s numerical knowledge were administered. 2.3.1.1. Verbal counting. Children were asked to count out loud, starting from one (adapted from Ramani & Siegler, 2008). They were stopped by the experimenter when they made a counting error or reached 25 correctly. The dependent measure was the highest number counted to without errors divided by the highest possible score (i.e., 25). 2.3.1.2. Numerical identification. Children were presented with 10 cards in random order, each with an Arabic numeral from 1 to 10, and asked to identify the numeral (Ramani & Siegler, 2008). The dependent measure was the percentage of numerals correctly labeled. 2.3.1.3. Symbolic magnitude comparison. Children were asked to compare 20 pairs of symbolic numerals ranging from 1 to 9 presented in a paper booklet (Ramani & Siegler, 2008). After two practice trials with experimenter feedback, participants were shown 18 test pairs of numbers in the booklet and asked to indicate which number is larger. The test pairs were read aloud by the experimenter without accuracy feedback. Each number was counterbalanced for side of presentation (i.e., 3|8, 8|3). The ratio between pairs ranged from 1.1 (e.g., 8|9) to 9.0 (e.g., 9|1). The dependent measure was the percentage of correct comparisons. 2.3.1.4. Number line estimation. Children were administered a 0–10 number line estimation task that has been previously used with children in Head Start programs (Ramani & Siegler, 2008; Siegler & Ramani, 2008). Children were shown 20 cm lines on a tablet computer, with a 0 labeled at the left end and 10 labeled at the right end, and asked to make a mark on the line where a target number would go. After practice making marks on an example trial, children were administered 18 trials with numbers ranging from 1 to 9. All nine numbers from 1 to 9 were presented once before any number was presented twice; the order of the nine numbers were random both times. On each trial, the experimenter identified the number at the top and then asked, “If this is where 0 goes (pointing) and this is where 10 goes (pointing), where does N go?” The dependent variable was the accuracy of children’s estimates, measured by percentage of absolute error (PAE), which is computed using the formula: PAE = (|estimate − estimated quantity|/scale of estimates) × 100. Lower scores would indicate higher accuracy, therefore, we reversed this score to ease interpretability. Pretest data was missing for one participant and was imputed with the pretest mean across conditions. 2.3.1.5. Cardinality. One measure of cardinality knowledge was administered. Specifically, children were given 15 plastic tokens and asked to give some of the tokens back to the experimenter (Give-N task, adapted from Sarnecka & Lee, 2009). The experimenter first asked the child for a number of tokens (e.g., “Can you give me one token?”), then waited until the child provided at least one token and asked if it was the number requested (e.g., “Is this one token?”). If the child said no, the experimenter asked again for the target number, allowing the child to make any corrections they chose. If the child said yes, regardless of their accuracy, the experimenter moved on to the next trial. Children were asked for 1, 2, 3, 4, 5, 6,

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8, and 10 items. If the child provided a correct response, the experimenter next asked them for N + 1 tokens. If the child provided an incorrect response for any trial greater than one, the experimenter then asked them for N-1 in the next trial. The task ended when the child reached 10 items correctly, or had given at least two correct responses for N and two incorrect responses for N +1 (e.g., responded correctly twice for three tokens, and incorrectly twice for four tokens). The dependent measure was the highest number for which a correct response was provided. 2.3.2. Shape knowledge measures Children were administered two assessments of shape knowledge designed for this study, adapted from the early geometry skill recommendations from the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM) (NAEYC & NCTM, 2010). 2.3.3. Shape naming Children were shown five cards with different shapes (circle, square, rectangle, triangle, pentagon) and asked to name each shape. The dependent measure was the percentage of shapes correctly named. 2.3.4. Shape finding Children were shown a computer-generated picture of a playground park and were asked to find different shapes within the scene. Children were asked to show the experimenter any circles they saw (sun, balloons), squares (hopscotch squares, birthday present), rectangles (swing seat, table), triangles (sun rays, kite), and pentagons (climbing rock, birthday present). The dependent measure was the percentage of hidden shapes correctly identified. 2.4. Mathematical card games 2.4.1. Magnitude comparison card game Families were provided with a deck of 40 cards of a standard size numbered 1–10 with both red Arabic numerals and red dots representing the quantity (Fig. 1a; Scalise et al., 2017). In this game, called Top It, Take It, parents were instructed to shuffle and divide the deck evenly between them and their child, then have both players turn over their top card, identify the number, and say which number was more. Parents were also asked to help their child identify the correct numeral by counting the dots on the card. The player with the card of greater magnitude took both cards. After all of the cards had been played at the end of the game, both players counted the cards they took to see who had more. The player who had more cards was the winner. 2.4.2. Shape and color matching card game In this game, called Match It, families were provided with a deck of 40 cards with different colored backgrounds (red, yellow, green, blue) and different shapes (circle, square, rectangle, triangle, pentagon; Fig. 1b). Parents were instructed to shuffle and give themselves and their child five face-up cards. The remaining cards were placed face-down in the center, with one additional card placed face-up as the target card. Players took turns saying the shape and color of the target card (e.g., a blue pentagon), then selecting a card that matched the target card in shape or color from their face-up cards. If a player had a matching card, they placed it in the center on top of the target card and it was the next player’s turn. If a player did not have a matching card they drew a new card from the remaining pile of cards, played the new card if they could, or added the new card to their face-up cards if they could not play it. The first player to use all of their face-up cards was the winner.

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2.4.3. Measures of parent guidance and talk Of the 39 families enrolled in the study, one audio recording from each of 34 families was transcribed. Seven of these families played the games in a language other than English (six in Spanish and one in Mandarin). These files were transcribed and translated into English by native speakers of that language. Audio recordings are missing for five of the families because one family did not return the audio recorder, three of the families had less than 30 s of audio, and one family played the games in a relatively rare dialect (Tigrinya), which we were unable to translate. One audio recording from the first time families played the game was transcribed because one-third of families (n = 11) did not have a second audio recording that occurred more than one week later with the same adult speaker leading the interaction, limiting the conclusions that could be drawn from comparing interactions over time. Recordings were transcribed using the CHAT conventions of the Child Language Data Exchange System (CHILDES, MacWhinney, 2000). Transcriptions were conducted at the utterance level, which is a phrase of words that is preceded and followed by a pause in speech, changes in conversational turns, or changes in intonation patterns. A second reliable transcriber verified each transcript. Children played the games with a range of advanced partners at home, including fathers, mothers, grandparents, and older siblings. Transcripts were searched for shape, color, and number words said by the children and the advanced partners. Since the word “one” can be used numerically (e.g., “one card”) or non-numerically (e.g., “hand me that one over there”), only instances in which the word one was used numerically were included in the overall number of words (Levine et al., 2010). Since the total amount of words that speakers used varied, we created proportions for the shape and color words and number words by dividing by the total number of words used by the speakers (e.g., tokens). Each transcript was also coded for the type of guidance provided by advanced partners (e.g., prompt, prompt after error, affirmation, disaffirmation, provide answer, cognitive directive; adapted from Bjorklund et al., 2004). Definitions and examples are presented in Table 1. Each utterance of an advanced partner was given a single code; utterances that did not involve guidance, but were related to game were coded as other game-related talk. One master coder (second author) coded all of the transcripts. Twenty percent of the transcripts were coded independently by a second trained coder, with a Cohen’s kappa of .81. Proportions for each category with the total number of the speaker’s utterances during the interaction were created. 3. Results We first present the descriptive statistics followed by the effects of condition across the mathematical knowledge measures. The next sections include correlations between children’s performance on the mathematical knowledge measures, parents’ report of their game playing time at home, and families’ talk and guidance while playing the games. 3.1. Preliminary and descriptive analyses Given the related nature of the mathematical knowledge measures, we first conducted multivariate analyses of the measures followed by univariate analyses. We report Pillai’s Trace as an Fstatistic and partial eta squared as the effect size. 3.1.1. Site differences To test whether there were differences in children’s initial knowledge between the two sites (mid-Atlantic state and Pacific northwestern state), a MANOVA was first conducted on the

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Fig. 1. Mathematical card games: (a) numerical magnitude comparison game, Top it, take it; (b) shape and color matching game, Match it.

Table 1 Coding scheme of parents’ guidance during the card game play. Code

Definition

Example

Prompt

Parent suggesting child provide an answer or response without any specific strategy.

“What shape do you have?” “Show me the highest number.”

Prompt after error

Parent prompt (suggesting child answer) following child error.

“Does that match?”

Affirmation

Parent demonstrates agreement to child’s answer or response. Includes restating a child’s correct answer.

“That’s right!” “Good job.”

Disaffirmation

Parent corrects child’s response or provides a definitive negative response indicating a child’s error.

“No, that’s not right.”

Provide answer

Parent provides child with correct answer or spontaneously produces the answer without the child saying anything.

“That’s a pentagon.”

Parent guides the child’s thinking about the game play, by: –Modeling game play or a strategy for child to imitate

“Count the dots on your card.”

Cognitive directives

“What shape and color is that card? Do you have a card with that same color or shape?” “So you played an 8 and I played a 2, and 8 is more than 2.”

–Suggesting a specific strategy to use –Re-representing a question in a way that is more familiar to the child Game-related other talk

Parent talk about other aspects of the game play, like setting up the cards or picking up certain cards.

“Shuffle the deck.” “Who’s turn is it?” “Flip a card over.”

Note: Coding scheme was adapted from Bjorklund et al. (2004).

measures of mathematical knowledge with the site as the betweensubjects factor. The main effect for site was not significant, F(7, 31) = 1.81, p = .12, Áp 2 = .29 However, the children recruited from the Pacific northwest site were significantly older than the children recruited from the mid-Atlantic site, 59 months versus 51 months, t(37) = 3.94, p < .001, d = 1.27. Age was also correlated with several of the mathematical knowledge measures at pretest (see Table A1 in Supplementary materials). Thus, age was controlled in the analyses testing for condition differences.

3.1.2. Parents’ report of game playing Eighty-six percent of the families completed at least part of the recording logs (n = 20 magnitude comparison game; n = 16 shape and color game). One family only reported the time played. There was large variation in the amount of time and number of games that families reported playing during the six weeks of the study. For the magnitude comparison game, parents reported playing on average a total of 213 min (SD = 225; range = 13–1035 mins) and a total of 23 games (SD = 12; range = 1–42 games). The correlation between the total number of minutes playing the game and number of games was significant, r(19) = .56, p = .01. Parents reported

playing the shape and color game on average a total of 185 min (SD = 91; range = 32–430 mins) and a total of 45 games (SD = 28; range = 10–96 games). The total number of minutes playing the game and number of games was not correlated, r(16) = .33, p = .22. This suggests there was more variability in the amount of time it took families to play each round of the shape and color game. There was no significant difference between the two conditions in the total amount of time the families reported playing the game (M = 213 vs. 185 mins), t(34) = 0.47, p = .64, d = 0.16. Families reported playing the shape and color game more than families reported playing the magnitude comparison game, on average 45 versus 23 games, t(33) = 3.09, p = .004, d = 1.02. This difference was expected because one magnitude comparison game took approximately twice as long to play as one shape and color matching game.

3.1.3. Parent support and talk during game play Of the 34 audio recordings included in the analyses, 50% (n = 17) of the game playing interactions involved 2 people, 29% (n = 10) of them involved 3 people, and 15% (n = 5) involved 4 people. Because families varied in the number of advanced partners playing with

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Table 2 Descriptive data for the transfer measures as a function of group. Pretest

Posttest

Pretest vs. posttest

Mean

SD

Min

Max

Mean

SD

Min

Max

r

Cohen’s d

Numerical magnitude comparison card game (n = 22) Numerical knowledge measures Verbal counting (% correct) Numeral identification (% correct) Symbolic magnitude comparison (% correct) Number line estimation (Reversed % Absolute Error) Cardinality (highest number correct)

58.00 79.60 74.73 72.57 5.50

24.18 28.00 28.00 9.04 3.11

8.00 0.00 33.00 56.00 1.00

100.00 100.00 100.00 86.00 10.00

70.18 83.20 78.28 72.13 7.17

21.05 16.44 19.39 8.424 3.24

40.00 50.00 39.00 53.00 2.00

100.00 100.00 100.00 84.00 10.00

.62** .53* .75*** .56** .57**

0.62 0.17 0.21 −0.05 0.36

Shape measures Shape naming (% correct) Shape finding (% correct)

63.00 46.40

19.80 22.79

20.00 10.00

100.00 90.00

63.60 50.20

21.94 25.82

0.00 0.00

100.00 90.00

.81*** .66**

0.05 0.19

Shape and color game (n = 17) Numerical knowledge measures Verbal counting (% correct) Numeral identification (% correct) Symbolic magnitude comparison (% correct) Number line estimation (reversed % absolute error) Cardinality (highest number correct)

53.88 62.90 67.97 74.80 4.58

32.03 38.20 20.02 8.43 3.18

4.00 0.00 33.00 58.00 1.00

100.00 100.00 100.00 91.00 10.00

60.24 71.80 75.49 74.55 6.00

26.78 30.26 21.88 8.72 3.82

8.00 20.00 39.00 55.00 1.00

100.00 100.00 100.00 90.00 10.00

.68** .95*** .77*** .40 .72**

0.27 0.82 0.53 −0.03 0.38

Shape measures Shape naming (% correct) Shape finding (% correct)

60.00 51.20

25.50 18.33

0.00 20.00

100.00 90.00

81.20 61.80

25.95 23.78

0.00 20.00

100.00 100.00

.72** .63**

1.10 0.59

Note: r = re-test reliability (Pearson correlation). * p < .05. ** p < .01. *** p <.001.

the children (e.g., mother, father, older siblings), we created a composite of the family members’ guidance of the game play for the correlational analyses. However, the majority of transcripts involved guidance from at least one parent/guardian, therefore we subsequently refer to players providing guidance as parents.

3.2.2. Shape measures The MANCOVA showed there was a significant interaction between session and condition, F(2, 35) = 9.35, p = .001, Áp 2 = .35. There were no main effects of session, F(2, 35) = 3.06, p = .06, Áp 2 = .15, condition, F(2, 35) = 0.64, p = .54, Áp 2 = .04, or age, F(2, 36) = 3.00, p = .06, Áp 2 = .15.

3.2. Main analyses

3.2.2.1. Shape naming. The ANCOVA revealed a significant main effect of session, F(1, 36) = 5.81, p = .02, Áp 2 = .14, and a session and condition interaction, F(1, 36) = 18.45, p < .001, Áp 2 = .34. There was no main effect for condition, F(1, 36) = 1.19, p = .28, Áp 2 = .03, or age, F(1, 36) = 0.12, p = .73, Áp 2 = .00. After controlling for age, children’s performance on the shape naming task improved from pretest to posttest for children who played the shape and color game (adjusted Ms = 60% to 82%, t(16) = 5.84, p = .01, d = 0.94), but not for children who played the magnitude comparison game, (63% to 63%, t(21) = 1.00, p = .98, d = 0.01).

To test our first set of hypotheses, we investigated the differences of the two card game conditions (magnitude comparison and shape and color game) on low-income preschoolers’ mathematical knowledge. We conducted two doubly multivariate repeated measures analyses with child age at pretest as a covariate (MANCOVAs) to examine the effects of participant condition and session. The first 2 (condition: magnitude comparison or shape and color game) × 2 (session: pretest or posttest) repeated measures MANCOVA was conducted on the numerical outcome measures (counting, numeral identification, symbolic magnitude comparison, number line estimation, and cardinality). The second MANCOVA was conducted on the shape outcome measures (shape naming and shape finding). Table 2 reports the unadjusted means and standard deviations for each task. We report Pillai’s Trace as an F-statistic and partial eta squared as the effect size. In case of a significant group effect, we calculated univariate ANCOVAs and conducted planned comparisons with paired samples t-tests using the means and standard errors adjusted for child age in order to examine improvements by condition.

3.2.1. Numerical knowledge measures The MANCOVA revealed no main effects of session, F(5, 32) = 0.25, p = .94, Áp 2 = .04; condition, F(5, 32) = 0.91, p = .48, Áp 2 = .13; and a nonsignificant interaction between session and condition, F(5, 32) = 0.23, p = .95, Áp 2 = .04. There was a significant effect of age, F(5, 32) = 7.54, p < .001, Áp 2 = .54, whereby older children were more accurate across condition and session on measures of numerical knowledge.

3.2.2.2. Shape finding. There were no main effects of session, F(1, 36) = 0.47, p = .50, Áp 2 = .01, condition, F(1, 36) = 0.92, p = .34, Áp 2 = .03, age, F(1, 36) = 2.88, p = .11, Áp 2 = .02; and a nonsignificant interaction between session and condition, F(1, 36) = 0.83, p = .37, Áp 2 = .04. 3.3. Correlations between game play reports and gains on mathematical knowledge We next examined whether parents’ reports of playing the games related to children’s age and learning in the two conditions. Specifically, we investigated whether parents’ reports of the total time playing the game and the overall number of games played correlated with children’s age and their gain scores (posttest − pretest) for each of the outcome measures. We conducted Pearson correlations separately by condition since the number of games varied between them. As shown in Table 3, for the magnitude comparison game the amount of time playing correlated with children’s improvements on the mathematical measures. Specifically, families’ reports of

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Table 3 Correlations between parents’ reports on game playing logs and children’s gain scores on the mathematical knowledge measures.

Age Verbal counting Numeral identification Symbolic magnitude Number line Cardinality Shape naming Shape finding * **

Numerical magnitude comparison game

Shape and color game

Number of minutes

Number of games

Number of minutes

Number of games

−.41 .25 −.28 .49* .45* −.08 .13 −.07

−.55* .16 −.20 .17 −.05 −.14 .05 −.06

.18 .25 .28 .37 .22 .28 .32 .75**

.32 .63** .09 .20 .20 .12 −.23 .33

p < .05. p < .01.

time playing the game correlated with children’s gains on the numerical magnitude comparison task, r(20) = .49, p = .029, and on the number line estimation task, r(20) = .45, p = .047. There were no other significant correlations between reports of time playing the game and the outcome measures. Children’s age was only negatively correlated with the overall number of games that families reported playing, r(20) = .55, p = .016. The overall number of games that families reported playing was not related to children’s gains on the mathematical measures. For children who played the shape and color game, the total number of minutes families reported playing the game was only correlated with gain scores on the shape finding task, r(16) = .75, p = .001. The overall number of times that families reported playing the shape and color game only correlated with children’s gain scores on the verbal counting task, r(16) = .63, p = .009. There were no other significant correlations for the shape and color condition. 3.4. Correlations between game play talk and gains on mathematical knowledge We analyzed the talk from the initial time families played the game (see Table 4). As would be expected, both parents and children who played the magnitude comparison game used a greater proportion of number words than those playing the shape and color card game (parents: t(32) = 3.18, p < .01, d = 1.12; children: t(32) = 5.68, p < .001, d = 2.01). Similarly, both parents and children who played the shape and color game used more shape and color words than those who played the magnitude comparison card game (parents: t(32) = 8.07, p < .001, d = 2.85; children: t(32) = 5.85, p < .001, d = 2.07). There was a wide range in the amount of scaffolding that the parents provided during game play. Parents produced on average a total of 243 utterances (SD = 134) during the interactions, with a range of 46–719 utterances. Across the two conditions, the amount of parents’ talk coded as providing guidance (all guidance codes not including other-game related talk) was on average 68 utterances (SD = 35), with a range from 12 to 150 utterances. The average proportion of parents’ guidance utterances to total utterances was 30% (SD = 10%) with a range of 12% and 48%. There were no differences between the two conditions in the proportion of guidance utterances between the magnitude comparison game and shape games, (M = 29% and 31%, t(32) = 1.22, p = .23, d = 0.43). We also correlated the number, shape and color words, and the guidance measures from the transcripts with children’s gain scores on the mathematical knowledge measures separately by condition (Table 5). For the numerical magnitude comparison game, there were no significant correlations between the parents’ or children’s talk and gains on the mathematical measures. For the shape and color game, child’s age was negatively correlated with parents’ use of affirmations, r(17) = .56, p = .023. For the talk measures, parents’ use of number words and cognitive directives as a form of guid-

ance was positively related to gains on verbal counting, r(17) = .68, p = .003, and r(17) = .50, p = .048, respectively. However, parents’ use of prompts was negatively correlated with gains on verbal counting, r(17) = −.61, p = .012. Parents’ use of disaffirmations was related to children’s gains on the shape naming task, r(17) = 0.49, p = 0.05. 4. Discussion The goal of the present study was to examine whether providing families from low-income backgrounds with mathematical card games would improve children’s numerical and shape knowledge. In this section, the findings are discussed in relation to the benefits of providing families with mathematical activities to play at home as well as the challenges and implications of home-based interventions for improving children’s mathematical skills. 4.1. Using card games as a home-based mathematical intervention The results showed providing families from Head Start programs with mathematical card games improved some aspects of their children’s mathematical knowledge. As hypothesized, having children play the shape and color matching card game at home improved their shape knowledge. Specifically, providing families with a game that included naming and matching different shapes improved children’s ability to name shapes. This suggests that card games can be used to help children learn mathematical information beyond just numbers, including important early geometry skills (NAEYC & NCTM, 2010). Contrary to our hypotheses, playing the numerical magnitude card game did not significantly improve children’s performance on the numerical knowledge measures relative to playing the shape and color game. Although the numerical magnitude comparison game was previously successful in improving Head Start children’s numerical magnitude knowledge when played with a researcher (Scalise et al., 2017), similar improvements were not found when the game was provided to families. Other research has found that extending successful classroom activities can have varying results when taken to the home environment (Sonnenschein et al., 2016). It is possible that improvements to children’s numerical knowledge were not found because the training provided to the families was not sufficient. Families were only given a brief training prior to the start of the study, while more specific training on the games could have led to stronger effects. Although the fidelity of implementation was not formally evaluated in this study, there is some evidence that families varied their game play from the given instructions. For example, families who played the shape and color game used number words although this was not explicitly included in the instructions. Previous research suggests that with sufficient training, non-researchers can implement intervention protocols with fidelity. When paraprofessionals from Head Start

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Table 4 Descriptive statistics of the family talk during the game play. Numerical magnitude comparison game (n = 20)

Shape and color matching card game (n = 14)

Mean

SD

Min

Max

Mean

SD

Min

Max

Number and shape and color talk Child’s number talk Child’s shape and color talk Parents’ number talk Parents’ shape and color talk

36 0 9 0

15 0 5 0

11 0 2 0

70 0 19 0

10 16 4 6

10 11 4 3

0 1 1 1

32 40 15 12

Guidance codes Prompt Prompt after error Affirmation Disaffirmation Provide answer Cognitive directives Other game-related talk

21 2 11 2 0 15 34

10 2 6 2 0 10 12

4 0 3 0 0 1 10

44 1 20 8 2 38 57

15 1 8 2 1 19 39

9 1 5 4 1 10 9

0 0 0 0 0 2 23

28 3 19 16 5 41 56

Note: Number words and shape and color words are percentages of total number of words. Guidance utterances are percentages of total number of utterances. Parents’ talk is a composite of all family members providing a guiding role during the game.

Table 5 Correlations between talk during game playing and gains on the mathematical knowledge.

Numerical magnitude comparison game Age Verbal counting Numeral identification Symbolic magnitude Number line Cardinality Shape naming Shape finding Shape and color game Age Verbal counting Numeral identification Symbolic magnitude Number line Cardinality Shape naming Shape finding

Child number Child shape and color

Parent number Parent shape and color

Prompt Prompt after error

Affirmation Disaffirmation Provide answer Cognitive directive

−.06 −.13 −.04

– – –

−.01 −.04 .27

−.05 .30 −.09

−.05 .17 −.30

−.37 −.12 −.07

−.25 .17 −.29

−0.36 0.26 −0.08

−0.13 0.32 0.07

−0.01 0.16 0.07

.19

–

−.32

−.11

.10

.18

.25

0.03

0.27

−0.05

.18 .11 .26 −.05

– – – –

−.24 −.13 −.19 −.10

−.05 .27 −.04 −.37

.12 .29 .38 −.27

.10 .04 .14 −.13

.11 .25 .18 −.44

−0.03 −0.02 −0.12 −0.42

0.06 −0.06 042 −0.07

−0.34 −0.06 −0.25 −0.21

.17 .46 .24

−.27 −.23 −.24

.03 .68** .16

.21 .03 .19

−.17 −.61* .24

−.04 −.38 .14

−.56* −.35 −.32

−0.47 −0.05 0.35

−0.07 −0.31 0.38

0.20 0.50* 0.04

.10

−.23

.14

−.23

−.29

.06

−.46

−0.32

0.21

0.14

.07 −.23 .12 −.29

−.18 .02 .05 −.16

.21 −.03 .19 .27

−.39 .10 .20 .02

−.27 −.08 .15 .06

−.05 −.16 .10 −.32

−.06 −.04 −.13 −.23

−0.09 −0.35 0.50+ −0.19

−0.08 −0.06 0.18 0.35

0.16 −0.09 −0.21 −0.17

Note: Children did not use any shape and color words when playing the numerical magnitude comparison game. + p = .05. * p < .05. ** p < .01.

classrooms were trained to play a board game with their students, they were successfully able to implement it with small groups (Ramani, Siegler, & Hitti, 2012). Specifically, teachers were provided with a manual, watched a demonstration video of an experimenter playing the game with a child, and were monitored by researchers during their first time guiding the game play. It could be important for future research to include training with a video demonstration and an opportunity to check in with a trained researcher. The fidelity of the families playing the game could also be monitored to see how it relates to their children’s learning. 4.2. Variations in game play experiences for families The parents’ logs of game playing and the talk from the first time families played the game suggest that children’s experiences playing the games at home varied widely. Across both conditions,

there was large variation in the amount of time and the overall number of games that parents reported playing at home. One family reported playing the game once, whereas another reported playing the game 96 times over the six weeks of the study. The variation in the time spent playing the games seems to have an important role in children’s learning. Specifically, the amount of time parents reported playing the magnitude comparison game was related to children’s improvements on both the symbolic magnitude comparison task and the number line estimation task. Improvements on the symbolic numerical magnitude comparison task found in a previous study when children played the game with experimenter was the motivation for the present study to provide the game to families (Scalise et al., 2017). However, this previous study did not include a number line estimation task, which is a more distal measure of numerical magnitude knowledge. In the present study, the relations between playing the magnitude comparison

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card game and the number line estimation task suggest that playing a card game that involves comparing numerical magnitudes could improve children’s broader knowledge of numerical magnitude, although the amount of time spent playing the game at home is a critical contributor to learning from it. The time parents reported playing the shape and color game was related to children’s improvements on the shape finding task, but not on the shape naming task. Similar to the magnitude knowledge measures, the shape naming task is a more direct measure of the practice children received while playing the game, whereas the shape finding task is a more distal measure. The shape finding task may also be a more difficult measure because there is a visual search component to the task requiring children to attend to the shapes in the larger scene, which can make it challenging for young children (Hommel, Li, & Li, 2004). It seems as though playing the shape and color game can improve children’s shape naming abilities, however, as with the magnitude comparison game, the amount of time families play the game is important for improving children’s shape finding skills. Across the conditions, the correlations suggest that greater engagement with the card games is important, consistent with other home-based mathematical interventions (Berkowitz et al., 2015). Although families were provided with weekly reminders via their preferred method of communication of either text messages, emails, or paper reminders, ensuring that families engage with the materials for the recommended amount of time is difficult. In addition to the playing logs, parents were asked to audio record the game playing sessions. Although all families did not record all of the sessions, it provided additional insight into their game play. Collecting multiple measures of what happens at home can help build a more accurate representation of families’ game playing experiences. Overall, examining the frequency with which families engage with the provided materials is important for understanding the role of dosage in the effectiveness of the home-based interventions. Understanding the quality of the interactions while playing the games is also important. When examining family members’ talk during game play for their use of the types of words relevant to the card game content, there was a range in the amount of shape and color words used during the shape and color game and number words used during the magnitude comparison game. Interestingly, even families who played the shape and color game used number words, and this number talk was related to improvements in children’s verbal counting. Aspects of parents’ guidance were also related to children’s improvements on counting. It is possible that families were using numbers when discussing shapes with their children (e.g., triangles have three sides), which helped them to improve their counting skills. This also can explain the unexpected relations between the number of games families played the shape and color game and improvements on counting. Together, the correlations from parents’ talk and the number of games played suggest that parents were going beyond just labeling the shapes by their name, but also using numbers to describe them. However, there were no relations between parents’ guidance and gains on the numerical knowledge measures for the numerical magnitude game, and minimal relations for gains on the shape measures for the families who played the shape and color game. This was surprising given the parents used a variety of guidance techniques, such as prompting and directing children’s attention during the games. It may be that understanding how parents’ scaffolding changes over time is more important than examining their initial game play, consistent with sociocultural theory and previous empirical work (Bjorklund et al., 2004). Although it was not possible to examine changes over time in the current study due to the limited number of recordings received, future research that examines guidance across multiple sessions could provide insight

into how changes in parents’ behaviors relate to children’s learning from the games. It is important to consider potential contributors to the variation in the frequency with which families played the games as well as the quality of their interactions. Children’s age was one contributor; it was correlated with the number of times families played the magnitude comparison game and parents’ use of affirmations while playing the shape and color game. Families may have played the magnitude comparison game more often with their younger children because they believed they had more room to improve the numerical skills or because younger children were more interested in playing the game than the older children. These are important factors when considering the target age for home mathematical activities. Another contributor could have been the number of people who played the game. The instructions did not specify that the game play was to be exclusive between the enrolled parent and child because we did not want to limit families’ opportunities to use the games at home. As a result, some children played with one parent, some played with multiple adults guiding the game play, and some played with younger siblings. When additional family members are involved, it can qualitatively change interactions. For example, when middle-class families were observed playing a board game with their preschooler and an older sibling, parents were more likely to use their turn to teach their preschoolers about numbers and adjust their scaffolding than when playing alone with their preschooler (Benigno & Ellis, 2004). Although additional family members can lead to variation in children’s experiences, providing materials that can include multiple family members may make activities more feasible to incorporate into daily lives. 4.3. Limitations and future research There are several limitations of the current study that should be considered. First, we acknowledge that the study included a relatively small sample size that limited our ability to detect smaller effects and only allowed us to detect larger effects. In particular, it is possible that the relatively high performance of children in the numerical magnitude condition on the numerical outcome measures at the beginning of the study limited their room for improvement. However, the findings provide insight into adapting successful mathematical activities played with an experimenter for use in the home context. Several benefits were found for providing families with the card games, and several barriers were identified that could be addressed in future research, such as providing families with more in-depth training. Similarly, the fact that game play was not uniform across families limits our interpretation of the findings, as families varied in the number of players in each game and the total exposure to the card games. However, this type of variation should be expected if families are to incorporate the game into their daily lives. Finally, information about families’ attitudes and experiences were not collected; therefore, it is difficult to know whether families felt the games were worthwhile or enjoyable. It is possible that there may have been differences in children’s motivation and attention to the games that varied by condition. Future research that collects such measures could help identify whether these are factors that contribute to variations in game playing experiences. 5. Conclusions Overall, the study adds to a growing body of research on the importance of the early home environment for children’s mathematical development, specifically for children from lower-income families whose numerical knowledge tends to trail behind that of children from higher-income backgrounds. Providing families with

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mathematical card games can be one way to promote children’s early mathematical knowledge, however, the amount of time that families spend playing the game is critical for improving children’s mathematical skills. The results provide experimental evidence to supplement the growing body of correlational work on how mathematical activities in the early home environment can improve children’s early mathematical knowledge. Encouraging families to use mathematical activities may be one way to promote the mathematical knowledge of children from low-income backgrounds, and lay a strong foundation for their later success in mathematics. Funding This work was supported by the Heising-Simons Foundation [2017-248] awarded to Geetha B. Ramani and the National Science Foundation [DGE 1322106] awarded to Nicole R. Scalise. Acknowledgements We would like to give special thanks to Zeno for their incredible collaboration in this research. We would also like to thank the families who participated in this research, as well as Myles Arrington, Mary DePascale, and Thierry Jean-Pharuns for their assistance with the transcription and coding associated with the study. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ecresq.2018.07. 011. References Benavides-Varela, S., Butterworth, B., Burgio, F., Arcara, G., Lucangeli, D., & Semenza, C. (2016). Numerical activities and information learned at home link to the exact numeracy skills in 5–6 years-old children. Frontiers in Psychology, 7, 94. http://dx.doi.org/10.3389/fpsyg.2016.00094 Benigno, J. P., & Ellis, S. (2004). Two is greater than three: Effects of older siblings on parental support of preschoolers’ counting in middle-income families. Early Childhood Research Quarterly, 19(1), 4–20. http://dx.doi.org/10.1016/j.ecresq. 2004.01.006 Berkowitz, T., Schaeffer, M. W., Maloney, E. A., Peterson, L., Gregor, C., Levine, S. C., et al. (2015). Math at home adds up to achievement in school. Science, 350(6257), 196–198. http://dx.doi.org/10.1126/science.aac7427 Bjorklund, D. F., Hubertz, M. J., & Reubens, A. C. (2004). Young children’s arithmetic strategies in social context: How parents contribute to children’s strategy development while playing games. International Journal of Behavioral Development, 28(4), 347–357. http://dx.doi.org/10.1080/01650250444000027 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 & Parenting, 5, 35–45. http://dx.doi.org/10.1002/(SICI)10990917(199603)5:1<35::AID-EDP113>3.0.CO;2-0 Elliott, L. E., Braham, E. J., & Libertus, M. E. (2017). Understanding sources of individual variability in parents’ number talk with (young) children. Journal of Experimental Child Psychology, 159, 1–15. http://dx.doi.org/10.1016/j.jecp.2017. 01.011 Gauvain, M. (2001). The social context of cognitive development. New York, NY: Guilford Press. Geary, D. C. (2006). Development of mathematical understanding. In D. Kuhn, R. S. Siegler, W. Damon, & R. M. Lerner (Eds.), Handbook of child psychology. Cognition, perception, and language (Vol. 2) (pp. 777–810). Hoboken, NJ: John Wiley. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457–1465. http://dx.doi.org/10. 1037/a0012682 Hassinger-Das, B., Toub, T. S., Zosh, J. M., Michnick, J., Golinkoff, R., & Hirsh-Pasek, K. (2017). More an just fun: A place for games in playful learning/Más que diversión: El lugar de los juegos reglados en el aprendizaje lúdico. Journal for the Study of Education and Development/Infancia y Aprendizaje, 1–28. http://dx. doi.org/10.1080/02103702.2017.1292684 Hommel, B., Li, K. Z., & Li, S. C. (2004). Visual search across the life span. Developmental Psychology, 40(4), 545–558. http://dx.doi.org/10.1037/00121649.40.4.545 Huntsinger, C. S., Jose, P. E., Larson, S. L., Balsink Krieg, D., & Shaligram, C. (2000). Mathematics, vocabulary, and reading development in Chinese American and

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Please cite this article in press as: Ramani, G. B., & Scalise, N.R. It’s more than just fun and games: Play-based mathematics activities for Head Start families. Early Childhood Research Quarterly (2018), https://doi.org/10.1016/j.ecresq.2018.07.011