Age-related differences in the relation between the home numeracy environment and numeracy skills

1.1 The HNE

The HNE is increasingly recognized as an important predictor of children's early numeracy skills (Niklas & Schneider, 2013). In fact, evidence suggests that early home experiences may have a greater influence on educational attainment than the influence of socioeconomic status (Anders et al., 2012; Melhuish et al., 2008). HNE activities can be grouped into two categories: direct and indirect (LeFevre et al., 2009). Direct activities are explicitly mathematics-centered and are used by parents to help their children develop mathematics skills. For example, parent–child engagement in counting objects, practicing number names, and printing numbers are direct HNE practices. Indirect, or informal, HNE activities are tasks or play activities in which the aim is not explicitly to provide mathematics instruction, yet may incidentally engage children's mathematics skills (Missall, Hojnoski, Caskie, & Repasky, 2015). For example, cooking with a child is a task that may incidentally teach mathematical language (add more flour, crack two eggs; Sonnenschein et al., 2012).

1.2 Relations between the HNE and child performance

Despite evidence suggesting that the HNE is related to mathematics skills, findings overall have been mixed across different ages (LeFevre et al., 2009; Manolitsis, Georgiou, & Tziraki, 2013; Missall et al., 2015; Zippert & Ramani, 2016). Specifically, research on kindergarten-aged children often demonstrates a positive relation between the HNE and early mathematics skills (Blevins-Knabe & Musun-Miller, 1996; LeFevre et al., 2009; LeFevre, Polyzoi, Skwarchuk, Fast, & Sowinski, 2010; Niklas & Schneider, 2013), whereas findings for preschool-aged children have been more equivocal (Anders et al., 2012; Blevins-Knabe, Austin, Musun, Eddy, & Jones, 2000; Missall et al., 2015; Ramani, Rowe, Eason, & Leech, 2015; Skwarchuk, 2009). Though findings have been mixed across all age groups, they tend to be most inconsistent for younger preschool-aged children (i.e., 3 and 4-year-olds). The results of several studies of the HNE demonstrating this pattern are summarized in Table 1. Given that differences in children's numeracy skills are present as early as preschool entry (Starkey, Klein, & Wakeley, 2004), it is important to investigate inconsistencies in relations between the HNE and children's outcomes from an early age. Further, positive relations tend to be found primarily for direct numeracy activities but not indirect activities (LeFevre et al., 2010; Manolitsis et al., 2013; cf., LeFevre et al., 2009).

Findings of the relation between the HNE and mathematics skills in preschool have been more mixed than in kindergarten. Some studies on preschool-aged children have found a relation between the HNE and children's mathematics skills (e.g., Anders et al., 2012; Skwarchuk, 2009). For example, Anders et al. (2012) found that the quality of the home learning environment was strongly associated with numeracy skills in the first year of preschool. In contrast, some studies involving preschool-aged children have found mixed or nonsignificant relations between the HNE and mathematics skills. Ramani et al. (2015), for example, found that parent-reported teaching activities contributed to the prediction of children's foundational mathematics knowledge but not advanced numerical knowledge. Similarly, DeFlorio and Beliakoff (2015) found that some HNE activities were related to children's mathematics performance, but others were not related. Finally, other studies have found that the HNE is not related to mathematics skills (Missall et al., 2015). A potential explanation for these differences across age groups may be that researchers often utilize the same HNE questions for parents of children of various ages. Though the questions are appropriate in general, certain questions may be more appropriate or applicable to specific age groups. As such, it is important to understand how specific HNE questions differentially relate to children of different ages.

1.3 The current study

The mixed findings of the relation between the HNE and children's numeracy performance for preschool-aged children indicate a need to examine the HNE in relation to children's age. In this study, we seek to address the discrepancies in these findings by investigating the relation between the HNE and children's numeracy skills at the item level (i.e., specific parent–child practices rather than the HNE as a whole) in the context of developmental progression of numeracy skills. Specifically, we hypothesized that parents engage in more complex numeracy activities with older preschool children compared to younger children and that HNE activities would be differentially related to numeracy performance at different ages such that more basic HNE practices (e.g., counting and quantity comparison) would be related to younger preschool children's numeracy performance and more advanced practices (e.g., simple sums and numeral naming) would be related to older preschool children's numeracy performance. We examined these hypotheses by (a) comparing the frequency of HNE activities across age groups and (b) identifying the HNE activities that are correlated with numeracy performance for the different age groups (i.e., 3 and 4-year-olds).

2.1 Participants

One hundred and eighty-four preschool children from 16 preschool centers participated in this study. The study includes 71 three year olds (M age = 3.54, SD = 0.30) and 113 four year olds (M age = 4.43 and SD = 0.28). Participants were approximately representative of the local demographics (56.7% Caucasian, 6.7% African American, 12.2% Hispanic, 7.2% Asian, and 17.2% multiracial). Approximately half (52.7%) of the sample was female. Participants came from a range of socioeconomic status backgrounds as 21.2% of participating parents had a high school degree or less, 32.1% attended some college, and 46.7% had a college degree or higher.

2.2 Measures

2.3 Procedure

3.1 Differences in home numeracy activities at 3 and 4 years of age

3.1.2 Age-related differences in practices

As shown in Figure 1 and Table 2, parents of 4-year-olds engaged in HNE activities with their child more frequently than did parents of 3-year-olds for broad measures of both direct (p = .042, d = 0.31) and indirect activities (p = .011, d = 0.39). Among direct items, parents of 4-year-olds did the following with their child more frequently than the parents of 3-year-olds: printing numbers (p = .004, d = 0.61), using number activity books (p = .028, d = 0.33), and learning simple sums (p = .006, d = 0.42). Among the indirect items, parents of 4-year-olds did the following activities with their child more frequently than the parents of 3-year-olds: counting out money (p = .026, d = 0.34); sorting things by size, color, or shape (p = .037, d = 0.16); and talking about money while shopping (p = .008, d = 0.41).

Table 2. Frequency of HNE activities at different ages

	3-year-olds (n = 71)		4-year-olds (n = 113)
Task	M	SD	M	SD	p
Direct activities
Direct activities composite	2.02	0.81	2.29	0.92	.042
Counting objects	3.57	0.88	3.46	0.96	.440
Printing numbers	1.50	1.32	2.10	0.44	.004
Reading number storybooks	2.66	1.09	2.39	1.39	.162
Using number activity books	1.61	1.21	2.02	1.30	.028
Using the terms “more or less”	2.18	1.70	2.63	1.55	.061
Counting down	1.57	1.57	2.02	1.45	.052
Learning simple sums	1.04	1.24	1.58	1.33	.006
Identifying the names of written numbers	2.01	1.57	2.10	1.51	.710
Indirect activities
Indirect activities composite	1.36	0.76	1.67	0.84	.011
Using calendars and dates	1.49	1.41	1.85	1.53	.107
Measuring ingredients while cooking	1.32	1.31	1.59	1.35	.184
Playing board games with die or spinner	1.04	1.10	1.30	1.24	.140
Connect-the-dot activities	1.17	1.18	1.37	1.18	.272
Counting out money	1.04	1.20	1.47	1.33	.026
Making and sorting collections	1.84	1.39	2.01	1.45	.421
Playing store	1.47	1.40	1.86	1.40	.069
Playing card games	1.20	1.02	1.38	1.18	.289
Sorting things by size, color, shape	2.16	2.23	2.55	2.54	.037
Talking about money while shopping	1.01	1.18	1.53	1.36	.008

• N = 184. Home numeracy environment (HNE) scores are based on the following scale: 0 = never, 1 = one to three times per month, 2 = about once a month, 3 = two to five times per week, 4 = daily, and 5 = multiple times a day.

3.2 Relations between specific HNE activities and mathematics performance

As shown in Table 3, neither the broad measure of direct activities nor the broad measure of indirect activities were related to 3-year-olds' PENS-B scores. However, the broad measure of direct activities was related to 4-year-olds' PENS-B scores. For 3-year-olds, the direct activities of counting objects (r = .30, p = .025), using the terms “more or less” (r = .30, p = .024), and counting out money (r = −.37, p = .007) were correlated with PENS-B scores. However, when partial correlation analyses were conducted accounting for parental education (scored as a dichotomous variable of “less than a 2-year college degree” or “2-year college degree or higher”), the relation between these variables was no longer significant. For 4-year-olds, counting down (r = .20, p = .047), learning simple sums (r = .27, p = .006), and identifying names of written numbers (r = .26, p = .009) were positively correlated with PENS-B scores. The same items were significant when partial correlations accounting for parental education were calculated. Importantly, there were no HNE activities that were significantly correlated with PENS-B scores for both 3 and 4-year-olds.

4.1 Frequency of engagement in HNE activities

Overall, parent–child HNE engagement was quite low for both 3 and 4-year-olds. Ten of the 18 activities only occurred about once per month. Though parents of 4-year-olds engaged their children overall in more HNE activities than parents of 3-year-olds, these differences were not found for all HNE activities. Rather, these differences were found for specific activities that may be categorized as more complex, such as learning simple sums. This finding suggests that the greater amount of engagement in HNE activities with older children does not reflect an overall increase in HNE activities, but rather an adding on of more complex activities. In considering how the HNE influences children's numeracy development, researchers should consider the mathematical learning trajectory and where specific HNE activities fall on this trajectory.

4.2 Relations between HNE activities and mathematics performance

The composite measure of the direct HNE practices was related to PENS-B scores of 4-year-olds but not of 3-year-olds. This relation may be due to the greater frequency of engagement in complex direct activities for 4-year-olds compared with 3-year-olds. Indirect activities, as a whole, were not related to PENS-B scores of either age group, a finding that is consistent with previous research (LeFevre et al., 2010; Manolitsis et al., 2013). It is possible that indirect activities were not related to PENS-B scores (at either the composite or individual level) because they occurred so infrequently, rarely more than about once per week. Further, the lack of relation may be because parents did not take advantage of the opportunity that indirect activities present for mathematically-focused dialogue but focused instead on different aspects of the activities (e.g., cultural relevance; Vandermaas-Peeler, Nelson, & Bumpass, 2007). Further research is needed to examine differences in parent–child practices related to quantity and quality of practices and how that distinction relates to improving children's mathematical performance.

As expected, different types of individual HNE activities were associated with PENS-B scores for the different age groups. Specifically, more basic activities were correlated with PENS-B scores of 3-year-olds (though this relation was attenuated after controlling for parental education) and more complex activities were correlated with PENS-B scores of 4-year-olds. These findings indicate that parent–child numeracy activities are not consistently associated with numeracy performance across the preschool years. It may be that correlates “advance” along the learning trajectory of preschoolers as children advance in their ability levels. Importantly, none of the same HNE practices were correlated with numeracy outcomes of both 3 and 4-year-olds. This differential relation suggests that there is significant development in mathematical competencies within a year, an idea that is consistent with results of previous studies (Arnold et al., 2002; Clements & Sarama, 2007; NMAP, 2008; Siegler & Ramani, 2008). However, it must be noted that when parental education was accounted for in the relation between HNE items and numeracy skills, no items were significantly related to numeracy performance for 3-year-olds, but the same items were still related for 4-year-olds. This finding suggests that the relation may be driven by parental education, where children from families with higher parental education may engage in more mathematical activities than children from families with lower parental education, particularly at younger ages.

Given the prior mixed findings on the relation between the HNE and mathematics performance in preschool, it may be that the items did not align specifically with the age or developmental level of children in some of the samples. In contrast, more commonly practiced activities may be those that align with the age or ability level of older preschool and kindergarten age children. This alignment may explain why there is more consistency in relations with older children. Note that three of the most commonly practiced items for 4-year-olds were the ones that were significantly related to mathematics performance. Ultimately, it may be necessary to design HNE measures that vary by age so as to evaluate the most relevant practices for a child's age and expected ability level.

4.3 Limitations

A few limitations of this study should be noted. First, the study is correlational in nature and the two age groups were assessed concurrently, rather than assessing the same participants at 3 and 4 years of age. As such, causal claims cannot be made about the effect of HNE practices on mathematics performance. Second, this study used caregiver report to assess the HNE. Although caregiver report is often used to measure the home environment, research that uses diary methods or recordings of parent–child interactions may help to provide a better assessment of the frequency, and particularly the quality, with which parents engage in different activities in the home. In addition, caregiver report may be subject to reporter bias. Third, the list of HNE practices was limited. Additional HNE practices, such as identifying which of two numbers is larger, and a more detailed breakdown of included practices should also be examined in future research. As the items used in this study were broadly defined, definite conclusions cannot be drawn regarding whether an item should be regarded as basic or complex and whether or not these more narrowly specified items would be related to performance at different ages. For example, the current item “counting objects” could be modified to be “counting small quantities of objects (five objects or fewer)” and “counting larger quantities of objects (more than five objects).” Finally, the PENS-B assesses children's general numeracy abilities. Though understanding the relations between specific aspects of the HNE and children's broad numeracy skills is useful, future research should include assessments of children's specific numeracy outcomes. For example, it is important to understand the relation between the frequency of parents working with children to identify written numerals and children's numeral identification skills.

4.4 Implications and future directions

The findings indicate that further research on the HNE may benefit from utilizing different HNE activities to assess children of different ages. Though questionnaires that are widely used to assess the HNE (e.g., the measure utilized in the LeFevre et al. 2010 study) are appropriate for certain age groups, they may not be appropriate to understand the HNE of all children. When HNE activities are being used as predictors of numeracy performance, they should account for the changes in children's mathematical abilities across the given time. Further research is needed to determine which specific HNE practices are not only the strongest correlates, but also the strongest predictors of numeracy performance at each age. Selecting age-appropriate HNE practices may enable research in this area to more accurately reflect the relations between parent–child mathematics engagement and children's numeracy performance across the developmental spectrum.