Children’s Spontaneous Focus on Number before and after Guided Parent-Child Interactions in a Children’s Museum

Abstract

Little is known about whether and how parents can foster their children’s spontaneous focus on number, an unprompted measure of attention to small numbers of objects that predicts later math achievement. In the current study, we asked fifty-four preschool-aged children and their parents to play together in a children’s museum exhibit using either a numerical prompt or a non-numerical prompt (control condition). Before and after playing with their parent, children completed assessments to measure individual differences in their tendency to spontaneously focus on number. After playing with their parent, children whose parents received the numerical prompt showed greater spontaneous focus on number compared to children whose parents received the control prompt. These findings suggest that when parents interact in an informal play setting with their children in ways that involve numerical content, it sharpens children’s later spontaneous attention to numerical information.

Young children vary in their tendency to notice exact quantities in their environment. At the grocery store, for example, one preschooler may point out that there are exactly four bananas in the bunch, while another may notice that all of the bananas are yellow. The frequency with which children focus their attention on the exact number of objects in a set, without guidance or prompting, has been termed spontaneous focus on number (SFON; Hannula & Lehtinen, 2005).

SFON is a valuable construct for predicting math achievement. SFON measured in preschool not only predicts children’s counting skills (Edens & Potter, 2013; Hannula & Lehtinen, 2005; Hannula, Rasanen, & Lehtinen, 2007), but also performance on an arithmetic assessment two years later (Hannula, Lepola, & Lehtinen, 2010) and on a standardized math achievement test seven years later (Hannula-Sormunen, Lehtinen, & Räsänen, 2015). Importantly, SFON does not predict later reading skills (Hannula-Sormunen et al., 2015; Hannula et al., 2010) and the relation between SFON and math achievement cannot be explained by children’s tendency to focus on a non-numerical dimension, i.e., focusing on spatial relations (Hannula et al., 2010). Together, these findings suggest that SFON is an important domain-specific factor underlying children’s math competence.

To quantify individual differences in children’s SFON, researchers have designed imitation tasks that ask children to copy an experimenter’s behavior (e.g., placing stamps on a picture of an animal or feeding berries to a toy parrot), and assess the extent to which children reproduce the same number of actions as the experimenter instead of focusing solely on the action (e.g., stamping or feeding) or other possible dimensions (e.g., color or shape of the stamp or berries) (Hannula & Lehtinen, 2005). Children’s scores on these types of SFON assessments are reasonably stable over a three-year span from the ages of four to six; children who exhibited low SFON in the first year of the study were also likely to do so in the third year (Hannula & Lehtinen, 2005). Because the SFON construct requires children’s attention to quantity to be spontaneous, meaning self-initiated and non-guided, the task materials and verbal instructions are carefully designed to avoid any cues that may explicitly guide the child’s attention towards number (Hannula et al., 2010). Further, the numbers of actions remain limited to small sets sizes so that children have the necessary enumeration skills to perform the task. When children with low SFON scores were explicitly guided to focus their attention on number they were able to perform the task, meaning their low SFON scores were not a result of insufficient math skills (Hannula & Lehtinen, 2005).

Can children’s SFON tendencies be increased? In a small quasi-experimental study, Hannula, Mattinen, and Lehtinen (2005) demonstrated that it is possible to enhance 3-year-olds SFON tendencies over a four-week period in daycare classrooms. They provided professional development training to educate teachers on the concept of SFON and gave children opportunities to direct their attention to small numbers of items in structured games (e.g., hiding toy ducks) and everyday situations in the classroom (e.g., cleaning up toys). Their results suggest that certain learning materials and types of social interactions from teachers can heighten children’s attention to numerical aspects of their environment over a month-long period. Thus, it seems that young children’s SFON is malleable in certain contexts, but we know little about how quickly enhancements in SFON can occur, or if they can occur outside of the classroom via adults without professional development training.

In the current study, we examined whether and how parents can foster their children’s SFON through a single play session in the informal learning setting of a children’s museum. Children’s museums provide an ideal space for children to learn new information through playful social interactions with their parents and other children. Partnerships between cognitive development researchers and museums have been important for studying how children learn outside of the laboratory and classroom settings (see Callanan, 2012, for a review), and numerous studies have examined how parent-child interactions in museum settings can benefit children’s understanding of science and engineering concepts (for reviews see, Haden et al., 2016; Haden, 2010). In science exhibits, for example, parents play an important role in shaping their children’s learning experiences; children are more focused, explore more, and learn more when interacting with their parent compared to on their own (Crowley et al., 2001; Crowley & Galco, 2001; Puchner, Rapoport, & Gaskins, 2001). Yet, little research has examined how museum visits with parents can promote children’s learning in the mathematical domain. A central aim of this study is to determine what sorts of readily instituted, playful, prompts are efficacious at shifting how parents interact, to produce gains in a domain many parents traditionally find either uninteresting or anxiety-inducing (Cannon & Ginsburg, 2008; Evans, Fox, Cremaso, & McKinnon, 2004; Skwarchuk, 2009).

In the present study, we sought to examine whether children’s attention to numerical information – an important predictor of their math abilities – can be enhanced through guided parent-child interactions at a children’s museum. We provided parents with one of two prompts to guide their play with their preschool-aged children in a grocery store exhibit. One of the prompts guided parents to incorporate information about numbers (numerical prompt) while the other guided parents to incorporate information about healthy eating (non-numerical control prompt) into their grocery store play. Before and after playing with their parent, children completed pre- and post-test assessments to measure individual differences in their tendency to spontaneously focus on number. Based on the exploratory findings of Hannula, Mattinen, and Lehtinen (2005), we predict that parent-guided play involving numerical content will have a positive impact on children’s performance on the SFON post-test compared to children in the control condition.

Method

Participants

Seventy children were recruited with their parent at the Children’s Museum of Manhattan. This sample size was determined via a G*Power (Faul et al., 2007) analysis, with a predicted moderate effect size (estimated from Hannula et al., 2005), α=.05, power 1-β=.80. Parent-child dyads were excluded if they did not complete all tasks (n=7), were not fluent in English (n=4), interacted in the grocery store for less than 3 minutes (n=4) ¹, or if there was an experimenter error (n=1). The final sample included 54 children (26 females; 28 males) and their parents (45 mothers; 7 fathers)². The children’s ages ranged from 2.97 years to 5.27 years (M=4.14 years, SD=7.29 months). Nineteen parents completed a masters or doctoral degree, 25 graduated from college, six had some college education, one graduated from high school, one had some high school education, and two did not report their highest level of education.

Procedure

Prior to participation, all parents provided written consent for themselves and for their child, and children provided verbal assent. The procedure followed the protocol approved by the Barnard College Institutional Review Board (“Mathematical and Spatial Development Throughout the Lifespan”; 1617–0530-044C). All activities took place in or near the play grocery store section of the PlayWorks© exhibit. This section contained barrels of toy food, shopping baskets, and a check out lane with a cash register, scanner, and moving conveyor belt. Parents were told that we were interested in how they played with their children in the grocery store exhibit, and were randomly assigned to receive one of two small booklets of cards with prompts and information to guide their play. Both before and after the parent-guided play, children completed a Spontaneous Focusing on Number (SFON) assessment on a small rug next to the grocery store exhibit. Children received stickers after completing each task.

Measures

Parent-guided play.

Parents were randomly assigned to receive either Budget prompt cards (n=27) or Healthy Eating prompt cards (n=27), and were asked to guide their child’s play in the grocery store for approximately five minutes using the cards (see Appendix for the full prompts). The Budget prompt cards told parents that fostering children’s early math skills is important. Parents were asked to help their child shop for food and plan a meal with a $20 budget. They were provided with pictures of each food group and their respective prices: Fruit ($2), Vegetables ($1), Grains ($1), Protein ($3), and Dairy ($2) (see Figure 1 for an example of a card). The Healthy Eating prompt cards told parents that establishing early healthy eating habits is important. Parents were asked to help their child shop for ingredients and plan a balanced meal that included all food groups. They were provided with pictures of each food group: Fruit, Vegetables, Grains, Protein, and Dairy (Figure 1). If after five minutes, the parent and child were still playing, the experimenter approached them to indicate that five minutes had passed but welcomed them to continuing playing if they were not finished.

Figure 1.

Examples of cards in the Budget prompt card packet and Healthy Eating card packet.

Parents and children were each given an audio recorder (Olympus VN-722PC) on a lanyard to record their speech during the interaction and were then left alone to play in the grocery store. The recordings of parents’ and children’s speech were later transcribed to quantify the total number of spoken utterances (continuous units of speech beginning and ending with a clear pause) and amount of number talk (total frequency of number word use, after Levine et al. (2010)) during guided play. Number talk scores from two parents and two children were removed as outliers as their scores were more than 2.5 standard deviations from the mean.

Spontaneous Focusing on Number (SFON) pre- and post-test.

Children’s spontaneous attention to number was assessed using SFON stamping tasks modeled after Hannula and Lehtinen (2005). All children in the final sample completed a Dinosaur Stamping Task and a Ladybug Stamping Task, one before the parent-child interaction in the grocery store exhibit (pre-test) and the other after the interaction (post-test). The order of the Dinosaur Stamping Task and Ladybug Stamping Task was counterbalanced across children. A total of three trials were administered in each task. The experimenter carefully avoided giving any feedback about the child’s performance or using any phrases that could suggest the task was about numbers or math.

In the Dinosaur Stamping Task (see Figure 2), the experimenter and child sat side-by-side in front of two copies of a dinosaur picture and two self-inking stampers (one yellow and one blue). The experimenter started by saying, “First, I’ll give my dinosaur spikes. Then, I’ll turn it over and I want you to make your dinosaur look like mine.” The experimenter picked up the blue stamper and placed two stamps, one at a time, on the dinosaur’s back. The experimenter then turned her picture over, gave both stampers to the child, and said, “Now make your dinosaur look like mine.” The procedure was repeated in the second trial with four yellow spikes on a novel dinosaur picture, and in the third trial with five spikes (three blue and two yellow) on a novel dinosaur picture. The Ladybug Stamping Task followed the same procedure and differed from the Dinosaur Stamping Task only in terms of the pictures, color of the stampers, and placement of the stamps. The number of stamps in each trial was identical to the Dinosaur Task: the experimenter made two purple spots in the first trial, four silver spots in the second trial, and five spots (three purple and two silver) in the third trial.

Figure 2.

Experimenter’s models in Trial 1, 2, and 3 of the Dinosaur Stamping Task

Children received points for each trial in which they made the same or close to the same number of stamps as the experimenter regardless of the location or color of the stamps. On a given trial, children received two points for producing the exact same number of total stamps, one point for producing a number of stamps that was one away from the exact number of total stamps, or zero points for producing a number of stamps two or more away from the exact number of total stamps. This scoring system resulted in a possible range of scores from 0–6 on each task³.

Results

Preliminary analyses and pre-test results

Parent-child dyads were randomly assigned to receive either Budget prompt cards or Healthy Eating prompt cards to guide their play in the grocery store. Independent samples t-tests confirmed that there were no differences in child age or parent education across the two groups (Table 1). Children had similar SFON scores at pre-test regardless of whether they completed the Dinosaur Stamping Task (M=3.76, SD=1.68) or Ladybug Stamping Task (M=3.8, SD=2.09), t(52)=.16, p=.875. Thus, SFON scores across the two task types were combined in further analyses.

Table 1.

Independent samples t-tests of mean differences in sample characteristics, duration of play, and amount of talk during play by the two conditions.

	Budget Condition	Healthy Eating Condition
	(n = 27)	(n = 27)	t	df	p
Child age (days)	1488	1533	.75	52	.454
Parent education	4.31	4.00	1.3	50	.194
Length of guided play	5min 33sec	5min 25sec	.39	52	.700
Parent total utterances during guided play	81.52	86.59	.80	52	.430
Child total utterances during guided play	38.70	38.40	.06	52	.951
Parent number words during guided play	27.40	1.33	−8.84	50	<.001
Child number words during guided play	14.96	.70	−5.86	50	<.001

Note. Parents rated their highest level of education on a 5-point scale (1 = some high school, 2 = high school diploma/GED, 3 = some college, 4 = Bachelor’s degree, 5 = Master’s/Doctoral degree).

Children’s SFON scores at pre-test ranged from 0 to 6 (M=3.8, SD=1.87) and were entered into an analysis of covariance (ANCOVA) with condition (Budget, Healthy Eating) as a between-subjects variable, and controlling for child age. Importantly, children assigned to the Budget and Healthy Eating condition scored similarly on the SFON pre-test (3.97 vs. 3.62, respectively), controlling for their age, F(1,51)=.56, p=.455, η²=.01 (see Figure 3). Further, age was a significant covariate in the model, with older children scoring higher on the SFON pre-test, F(1,51)=11.87, p=.001, ${\eta }_p^2=.19$.

Figure 3.

Effect of parent-guided play condition on children’s SFON scores at pre-test and post-test. Error bars represent +/− one standard error.

As Table 1 indicates, there were no significant differences in average duration of grocery store play, amount of parent talk, and amount of child talk across the Budget and Healthy Eating conditions suggesting the prompts led to similar levels of engagement among parents and their children. Parents in the Budget condition used significantly more number words (M=27.4, SD=15.22, range: 3–61) than parents in the Healthy Eating condition (M=1.33, SD=1.73, range: 0–6), suggesting that parents in the Budget condition did adhere to the instructions provided to them in the prompt. Across conditions, high levels of parent number talk were correlated with high levels of child number talk, r(50)=.74, p < .001. Children in the Budget condition also used significantly more number words (M=14.96, SD=12.60, range: 0–40) than children in the Healthy Eating condition (M=.70, SD=1.14, range: 0–4).

Effect of parent-guided play condition on children’s SFON

Children’s SFON scores at post-test ranged from 0 to 6 (M=3.81, SD=1.65). An ANCOVA on children’s post-test SFON scores, controlling for child age, indicated a main effect of condition, F(1,51)=4.22, p=.045, ${\eta }_p^2=.08$, with children in the Budget condition scoring higher on SFON compared to children in the Healthy Eating condition after the parent-guided play (see Figure 3). This small-to-moderate effect size, found for a brief 5-minute intervention, is in accord with the moderate effect size after a weeks-long intervention found by Hannula et al. (2005). Further, age was a significant covariate in the model, with older children scoring higher on the SFON post-test, F(1,51)=13.81, p=.001, ${\eta }_p^2=.21$. To examine if there were differential effects by age, we added an interaction between condition (Budget vs. Healthy Eating) and child age into the model, but this interaction was not significant. This indicates that SFON malleability, for this study at least, does not change much between 3 and 5 years of age.

When the duration of play was included in the model predicting children’s SFON post-test scores, there was no significant main effect of duration of play, F(1,49)=.82, p=.369, η²=.02, nor was there an interaction between condition (Budget vs. Healthy Eating) and duration of play, F(1,49)=1.48, p=.229, η²=.03, indicating that children who played for longer did not have greater scores on the SFON assessment afterwards.

Finally, children’s SFON scores at post-test were entered into an ANCOVA that additionally controlled for children’s SFON scores at pre-test, as well as child age. In this model, the main effect of condition was weakened, but remained marginally significant, F(1,50)=3.57, p=.065, η²=.07.

Effect of parents’ number talk on children’s SFON

Across conditions, parent number talk was positively associated with children’s SFON scores at post-test at marginal significance, r(49)=.254, p=.072. Parents who used number words more frequently while playing in the grocery store tended to have children who focused more on number during the SFON task afterwards. Parents’ number talk was not associated with children’s SFON scores at pre-test, r(49)=.17, p=.246, and there was no association between children’s number talk and their SFON score at pre-test, r(49)=.07, p=.624, or at post-test, r(49)=.16, p=.272.

Discussion

The present study was designed to experimentally test whether young children’s spontaneous focus on number (SFON) could be increased through a single 5-minute session of targeted parent-guided play in a children’s museum. The hypothesis, that parent-guided play specifically involving numerical content would have a positive impact on children’s performance on the SFON post-test compared to children in the control condition, was supported, though the effect weakened when additionally controlling for children’s SFON pre-test scores.

The results of our study suggest that engaging with numerical content in the context of play may increase children’s attention to numerical information. The children in our study were randomly assigned to one of two parent-guided play conditions in the museum’s mock grocery store. We found no differences in children’s SFON before parent-guided play. In contrast, after parent-guided play children in the Budget condition demonstrated higher SFON on the post-test compared to children in the Healthy Eating condition. When controlling for pre-test scores, the effect was marginally significant. This likely is due to the fact that - although we were successful at crafting a SFON task that had middling scores - there ultimately were more children at ceiling (n=12) than floor (n=4). This results in more children having only downward movement possible from pre- to post-test than upward movement, which dampened the effect of condition when implementing a pre-test to post-test analysis, instead of a simple effect of condition on later SFON. A critical step forward in this line of work will be to replicate and extend this finding using more sensitive measures of SFON to better capture changes in children’s performance over time.

What may have been the mechanism that led to differences between our conditions in children’s post-test SFON scores? One theory is engagement by the parents; perhaps parents in the Budget condition were more verbally expressive and this increased overall interest and performance. However, the Budget and Healthy Eating prompts led to similar levels of verbal engagement among parents and their children. Thus, the differences in children’s SFON scores are potentially due to the content of the instructions provided by the parents, and not children’s overall engagement or motivation. This altered content could be either verbal, or non-verbal. Verbally, parents in the Budget condition used more number content in their speech compared to parents in the Healthy Eating condition, as indicated by differences in their frequency of number word use. Previous research studies demonstrate that parents’ and teachers’ use of number words while talking to children at home or in the classroom is positively related to growth in children’s math knowledge over time (Boonen, Kolkman, & Kroesbergen, 2011; Gunderson & Levine, 2011; Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006; Levine, Suriyakham, Rowe, Huttenlocher, & Gunderson, 2010). Here, our findings suggest that parents’ number talk was one factor leading to improvement, as it marginally related to SFON scores at post-test. The fact that this effect was marginal suggests it was only partially responsible for the significant overall effect of condition. The intervention may have also influenced other, non-verbal, aspects of the interaction, such as dyadic joint attention to small sets, or gestures to a set with the cardinal label applied. Studying how parents can go beyond language to create a mathematically conducive environment is a promising avenue for future work in this field.

This study adds critical new insight into SFON, which is generally viewed as an indicator of children’s sensitivity to opportunities to use their number knowledge (Hannula & Lehtinen, 2005). Children who focus more on numbers in their environment are thought to receive more practice with numerical information, in turn boosting their mathematical abilities (Hannula-Sormunen et al., 2015; Hannula et al., 2010, 2007). If practice using numerical information is key, it is important to examine how we can promote SFON in order to impact the developmental trajectory of children’s math skills. Until now, there was only one study that empirically investigated how to enhance children’s SFON (Hannula et al., 2005). As discussed in the introduction, Hannula and colleagues (2005) gave preschool teachers professional development training and weekly guidance over a month-long period on how to provide their students with opportunities to direct their attention to small numbers of items in the classroom. Children in these classrooms developed more SFON tendencies over the month compared to children in control classrooms who had their typical instruction. Our study substantially extends the findings of Hannula and colleagues (2005) in a number of ways. First, with a larger sample our study used random assignment to compare children in the experimental group to an active control condition. Second, our study took place outside of the classroom and is the first to examine if children’s SFON can be enhanced through guided play with parents without professional development training. Third, our findings suggest that SFON enhancement effects could occur quickly, after just five minutes.

There are some limitations of our study that should be addressed in future research. First, we do not know how long the effects of our short parent-guided play sessions last. It would be interesting to replicate this study with a delayed post-test design and to test whether parents differ in subsequent interactions with their children in the same or other contexts without being prompted. Second, the experimenter was not blind to condition due to limited personnel. Although the experimenter carefully followed a pre-determined script for each child, future research is needed to replicate this effect using experimenters who are blind to condition when administering the SFON tasks. Third, while SFON has been linked to children’s more formal math abilities in other studies (such as counting and arithmetic; Edens & Potter, 2013; Hannula & Lehtinen, 2005; Hannula, Lepola, & Lehtinen, 2010), it is not yet understood why SFON predicts such skills. We were unable to directly assess children’s math abilities in our sample due to the time and testing space constraints of our study. An important direction for future research will be to examine whether interventions that increase SFON ultimately lead to improvements in formal math skills. Finally, although a power analysis was run to establish the correct sample size, it was based on a study done in a more formal learning context (a preschool). The more distracting and less controlled context of a children’s museum exhibit led to more participants excluded from the analyses and lower-than-predicted power. This also limited the power for subsequent, exploratory analyses and the ability to answer new questions with the available data. Going forward, researchers working in museums may find it helpful to consider a more conservative power analysis. While informal contexts provide valuable information regarding naturalistic parent-child interactions, they often result in briefer tasks and subsequently more variable performance than the previous work done in schools.

Overall, these findings emphasize the value of creating learning situations that incorporate numbers into play. Museums want caregivers to notice the learning value in play; however, many parents find it difficult to describe what and how children learn by playing in a museum (Letourneau, Meisner, Neuwirth, & Sobel, 2017). This calls for museums to clearly communicate how play contributes to different aspects of children’s learning, and for signage and materials that are evidence-based and realistically implemented (such as the ones used here). Here, our instructions to parents created learning experiences that incorporated rich numerical content and led to differences in children’s SFON. Studies such as this can assist children’s museum educators in crafting materials for effective, play-based learning that may boost children’s openness and attentiveness to math concepts, which may ultimately lead towards a pathway of increased practice with numbers and improvements in math performance.

Appendix

Budget Condition Script

Did You Know?

The preschool years are an important time for developing early math skills. Children can develop early math skills through play and listening to their parents use number words during interactions. Giving preschoolers a solid foundation in early math is critical for their future academic success. Giving children the responsibility of helping you make a shopping list and plan family meals is a great way to help them uncover math in everyday life.

Try This:

Pretend you are planning a meal for you and your child with a $20 budget. Have your child pretend to go grocery shopping to find all of the ingredients. Talk to your preschooler about how much items cost and how much money you have left. Make sure your meal does not cost more than $20.

Healthy Eating Condition Script

Did You Know?

The preschool years are an important time for developing healthy eating habits for life. Getting the right amount of nutrients is critical to healthy brain development and body growth in children. Fruits, vegetable, grains, protein, and dairy provide the nutrients that their bodies need. Giving children the responsibility of helping you make a shopping list and plan family meals is a great way to teach them about healthy eating habits.

Try This:

Pretend you are planning a meal for you and your child. Have your child pretend to go grocery shopping to find all of the ingredients. Talk to your preschooler about healthy food choices and a balanced diet. Make sure your meal includes all of the food groups.