Beyond Deficit Narratives: Family Math Practices and Early Numeracy Development Across Socioeconomic Contexts

Abstract

While home literacy practices have been extensively documented in developmental psychology and education literature, equivalent attention to the home mathematics environment—often termed "family math"—has only recently gained momentum. Historically, research examining early numeracy development across varying socioeconomic status (SES) has been dominated by deficit narratives, which frequently characterize under-resourced households as mathematically impoverished. This mixed-methods comparative study challenges these assumptions by examining mathematical interactions during everyday activities, such as cooking, shopping, and playing games, across families from diverse socioeconomic and ethnic backgrounds. Drawing on a sample of 412 families with preschool-aged children (ages 4–5), we utilized parental surveys, standardized early numeracy assessments, and a subsample of video-recorded naturalistic observations ( n = 60) to capture the frequency, quality, and nature of family math engagement. Quantitative analyses reveal that while SES and parental math attitudes significantly predict children's baseline early numeracy, the frequency of informal, everyday mathematical practices serves as a powerful mediator. Qualitative thematic analysis of observational data documents rich, complex mathematical engagement in low-SES and working-class communities, often embedded in survival and caregiving tasks rather than formalized pedagogical activities. By highlighting these culturally embedded "funds of knowledge," this study reframes family engagement in mathematics education, arguing for asset-based pedagogical frameworks that recognize and leverage the diverse ways families already engage in mathematical thinking.

Introduction

The foundation of mathematical cognition is laid long before children enter formal schooling. Early numeracy skills—encompassing counting, cardinality, spatial reasoning, and pattern recognition—are robust predictors of not only later mathematics achievement but also overall academic success and high school graduation rates (Duncan et al., 2007; Watts et al., 2014). Consequently, understanding the environments that foster these foundational skills has become a critical imperative in the social sciences and behavioral studies. The home learning environment is widely recognized as a primary engine of cognitive development; however, the literature has historically exhibited a pronounced asymmetry. While shared book reading and home literacy practices are universally championed and deeply researched, the equivalent domain of "family math" has remained comparatively underexplored until the last decade (Blevins-Knabe, 2016; Hornburg et al., 2021).

As the field of mathematics education expands its focus to the home learning environment, a problematic trend has emerged. Studies frequently highlight a "mathematics gap" at kindergarten entry, correlating lower socioeconomic status (SES) with depressed early numeracy scores (Clements & Sarama, 2007). In attempting to explain this gap, researchers and policymakers have often relied, implicitly or explicitly, on deficit narratives. These narratives suggest that low-SES parents, often from marginalized ethnic backgrounds, lack the knowledge, resources, or motivation to engage their children in mathematical thinking (García & Weiss, 2017). Such perspectives fail to account for the culturally specific, informal ways in which mathematics is practiced in everyday life.

The present study seeks to disrupt these deficit-oriented frameworks by systematically investigating family math practices across diverse socioeconomic contexts. We posit that mathematical engagement is ubiquitous but manifests differently depending on a family's cultural background, economic realities, and parental math attitudes. By examining everyday activities—specifically cooking, grocery shopping, and board games—we aim to document the rich mathematical interactions that occur in under-resourced communities. In doing so, this research addresses the following questions:

1. How do the frequency and type of family math practices vary across different socioeconomic and ethnic groups?
2. To what extent do parental math attitudes (e.g., math anxiety, beliefs about math importance) moderate the relationship between SES and family math engagement?
3. How do informal, everyday mathematical practices mediate the relationship between socioeconomic status and children's early numeracy development?
4. What qualitative forms do these mathematical interactions take in naturalistic, everyday settings across diverse households?

Literature Review

The Home Mathematics Environment and Early Numeracy

The home mathematics environment (HME) comprises the resources, activities, and interactions provided by caregivers that support children's mathematical development (Skwarchuk et al., 2014). Research typically bifurcates the HME into formal and informal practices. Formal practices are explicit, pedagogical activities intended to teach math, such as using flashcards or practicing counting to 100. Informal practices, conversely, are everyday activities where math is incidental but integral, such as measuring ingredients for a recipe, discussing the shapes of street signs, or keeping score in a game (LeFevre et al., 2009).

Recent empirical work suggests that while formal practices are easily quantifiable, informal practices may be equally, if not more, influential in developing a child's conceptual understanding of mathematics. Ramani and Siegler (2008) demonstrated that playing linear numerical board games significantly improves the numerical magnitude knowledge of children from low-income backgrounds. Similarly, Vandermaas-Peeler et al. (2012) found that incorporating math into cooking activities enhances children's understanding of fractions, measurement, and estimation. Despite these findings, the measurement of the HME in large-scale surveys often biases toward formal, school-like activities, inadvertently obscuring the informal math happening in diverse households.

Socioeconomic Status and the Deficit Narrative

Socioeconomic status is a pervasive variable in developmental research, consistently correlating with academic outcomes. In mathematics education, the disparity in early numeracy skills between children from low- and high-SES backgrounds is well-documented (Starkey et al., 2004). The dominant interpretation of this gap has historically leaned on a deficit model, which attributes lower achievement to a lack of cognitive stimulation and parental involvement in low-SES homes.

However, sociocultural theorists argue that this perspective is fundamentally flawed because it measures all families against a white, middle-class, school-centric standard of parenting (Moll et al., 1992). Moll's concept of "funds of knowledge" posits that working-class and minority households possess historically accumulated and culturally developed bodies of knowledge and skills essential for household functioning and well-being. When viewed through this asset-based lens, activities such as budgeting limited financial resources, navigating public transit schedules, and altering recipes based on available ingredients are recognized as highly complex mathematical tasks. The failure of traditional assessments to capture these practices perpetuates the myth of the mathematically impoverished low-SES home.

Parental Math Attitudes and Anxiety

A critical factor influencing family engagement in mathematics is the parent's own relationship with the subject. Mathematics anxiety—a feeling of tension and fear that interferes with math performance—is highly prevalent among adults (Maloney & Beilock, 2012). Parents with high math anxiety are less likely to engage in math-related activities with their children and, when they do, may inadvertently transfer their anxiety, particularly when assisting with formal homework (Maloney et al., 2015).

Importantly, parental math attitudes intersect with SES. Adults from marginalized educational backgrounds may have experienced punitive or exclusionary math instruction, leading to higher rates of math anxiety and a belief that math is an innate ability rather than a developable skill (Boaler, 2016). Understanding how these attitudes shape the choice between formal and informal math practices is essential for developing effective family engagement interventions.

Methodology

Research Design

This study employed an explanatory sequential mixed-methods design (Creswell & Plano Clark, 2017). Phase 1 consisted of a large-scale quantitative survey and child assessment to identify broad patterns linking SES, parental attitudes, family math practices, and early numeracy. Phase 2 involved qualitative, naturalistic video observations of a purposively selected subsample to deeply explore the nature of mathematical interactions during everyday activities.

Participants

Participants for Phase 1 included 412 parent-child dyads recruited from preschools, community centers, and pediatric clinics across three distinct geographic regions in the United States (urban, suburban, and rural). Children (48% female) ranged in age from 48 to 71 months ( M = 58.2, SD = 6.4). The sample was intentionally stratified to ensure socioeconomic and ethnic diversity.

Socioeconomic status was calculated using a composite index of household income, parental education, and occupational prestige. Based on this index, families were categorized into three tiers: Low-SES (34%), Middle-SES (38%), and High-SES (28%). The racial/ethnic composition of the sample was 41% White, 28% Hispanic/Latino, 21% Black/African American, and 10% Asian/Pacific Islander.

For Phase 2, a subsample of 60 families was purposively selected from the Phase 1 cohort. We selected 20 families from each SES tier, ensuring a mix of high and low reported math anxiety within each group, to participate in the observational component.

Measures

Early Numeracy Assessment

Children's early numeracy was assessed using the Woodcock-Johnson IV (WJ-IV) Applied Problems and Quantitative Concepts subtests (Schrank et al., 2014). These standardized measures assess counting, cardinality, simple addition and subtraction, and understanding of mathematical vocabulary. Raw scores were converted to W-scores for analysis, providing an equal-interval metric suitable for modeling growth and comparing across ages.

Parental Survey: The Home Mathematics Environment Questionnaire

Parents completed a modified version of the Home Numeracy Questionnaire (Skwarchuk et al., 2014). The survey assessed:

• Formal Math Practices: Frequency of explicit teaching activities (e.g., "How often do you use flashcards with your child?"). Rated on a 5-point Likert scale (1 = never, 5 = daily).
• Informal Math Practices: Frequency of embedding math in daily tasks (e.g., "How often do you involve your child in measuring ingredients while cooking?").
• Parental Math Anxiety: Measured using the Abbreviated Math Anxiety Scale (AMAS; Hopko et al., 2003), adapted for parenting contexts.
• Beliefs about Math: Assessing the belief in the importance of early math versus early literacy.

Observational Coding Scheme

For Phase 2, families were provided with wearable action cameras and asked to record themselves engaging in three standard activities over a two-week period: (1) preparing a meal together, (2) a grocery shopping trip (or unpacking groceries), and (3) playing a board or card game.

Video data were transcribed and coded using the Math Talk Classification Scheme (adapted from Levine et al., 2010). Utterances were coded into categories including Number Talk (counting, labeling set sizes), Spatial Talk (shapes, dimensions, spatial relations), Measurement/Magnitude (more/less, heavy/light, fractions), and Operations (addition, subtraction). We also coded for the Initiator (parent vs. child) and the Context (pedagogical vs. pragmatic).

Data Analysis Strategy

Quantitative data were analyzed using R (Version 4.1.2). To examine the mediating role of informal math practices between SES and early numeracy, we employed structural equation modeling (SEM). The primary relationship can be expressed through the following multiple regression equation, which formed the basis of our path analysis:

Where Y _i represents the early numeracy W-score for child i , and the predictors represent the composite scores for socioeconomic status, parental math attitudes, and the frequency of formal and informal practices. To test for moderation by parental math attitudes, we introduced an interaction term:

Qualitative video data were analyzed using reflexive thematic analysis (Braun & Clarke, 2019). Two independent coders reviewed the transcripts, achieving an inter-rater reliability (Cohen's Kappa) of .84. Discrepancies were resolved through consensus meetings.

Results

Quantitative Findings

Descriptive Statistics and Correlations

Preliminary analyses revealed significant variations in the types of practices favored by different SES groups. High-SES families reported significantly higher frequencies of formal math practices ( M = 4.12, SD = 0.8) compared to Low-SES families ( M = 2.85, SD = 1.1), t (254) = 10.45, p < .001. However, the gap narrowed considerably regarding informal practices. Low-SES families reported robust engagement in informal math practices ( M = 3.65, SD = 0.9), particularly those related to household management and commerce.

Parental math anxiety was negatively correlated with formal math practices ( r = -.42, p < .01) but showed no significant correlation with informal practices ( r = -.08, p = .12). This suggests that parents with high math anxiety may avoid explicit math teaching but still naturally engage in mathematical thinking during everyday tasks.

Note. *p < .05, **p < .01, ***p < .001.

Mediation and Moderation Analysis

As shown in Table 1, the inclusion of formal and informal practices in Model 2 significantly reduced the direct effect of SES on early numeracy (from β = .38 to β = .22), indicating partial mediation. Notably, informal math practices emerged as a stronger predictor of early numeracy (β = .35) than formal practices (β = .28).

In Model 3, the interaction term between SES and Informal Practices was significant and negative (β = -.18, p < .05). Simple slopes analysis revealed that informal math practices had a stronger positive impact on early numeracy for children in low-SES households compared to high-SES households. This suggests that when low-SES families engage frequently in informal math, it acts as a powerful compensatory mechanism, effectively bridging the numeracy gap.

Qualitative Findings: Mathematics in the Mundane

The video observational data provided profound insights into how mathematics is operationalized in diverse households. Contrary to deficit narratives, low-SES and working-class families demonstrated highly complex mathematical environments. However, the context and purpose of the math talk differed significantly from high-SES households. We identified three primary themes: Pragmatic vs. Pedagogical Math, The Mathematics of Survival, and Spatial Reasoning in Play.

Theme 1: Pragmatic vs. Pedagogical Math

In high-SES households, math talk was frequently pedagogical—parents asked known-answer questions to test the child's knowledge. For example, while cooking, a high-SES mother might ask, "Look at these three apples. If I take one away, how many are left?" The math was overlaid onto the activity.

In contrast, in low-SES households, math talk was overwhelmingly pragmatic; the math was required to complete the task. The questions posed to children were genuine inquiries where the parent needed the child's cognitive assistance.

"We only have one cup of rice left, but we need to feed five people tonight. If we add these two cans of beans, will the pot be full enough? Look at the line on the pot. Tell me when the water hits the number 4." (Low-SES Mother, Cooking Observation)

This pragmatic engagement required children to engage in estimation, volume comprehension, and proportional reasoning, driven by authentic necessity rather than artificial testing.

Theme 2: The Mathematics of Survival and Budgeting

The grocery shopping observations revealed stark differences in mathematical engagement. High-SES families often focused on categorization (e.g., "Are tomatoes fruits or vegetables?") or simple counting ("Can you put six apples in the bag?").

For several low-SES families, the grocery store was a site of intense, high-stakes mathematical calculation involving budgeting, price comparison, and arithmetic. Children were frequently enlisted as co-calculators. In one observation, a father and his 5-year-old son navigated a strict $40 budget:

Father: "Okay, we have 40 dollars. The diapers are 15. How much does that leave us?"
Child: [Using fingers] "Ten... twenty... thirty... forty. Take away ten, take away five. Twenty-five!"
Father: "Right. Now, if we buy the big milk for 4 dollars, can we still get the chicken for 12?"

This interaction demonstrates advanced subtraction and working memory skills being scaffolded in a real-world context. The deficit perspective would likely miss this interaction entirely if it only surveyed parents on how often they use math workbooks.

Theme 3: Spatial Reasoning in Play

During the game observations, families across all SES tiers engaged in rich spatial and numerical talk. However, cultural variations emerged in the types of games played. While middle- and high-SES families frequently played commercial board games (e.g., Chutes and Ladders, which linearly supports number line estimation), several Hispanic/Latino families in our sample played Lotería or dominoes.

Dominoes, in particular, elicited high volumes of subitizing (instantly recognizing the number of objects without counting) and pattern recognition.

"You see the blank and the three? You need a three to match. Where is a three? No, don't count the dots, just look at the shape of the dots. A triangle of dots is three." (Middle-SES Grandfather, Game Observation)

These cultural artifacts serve as powerful, culturally sustaining tools for early numeracy development that are often excluded from traditional definitions of the home learning environment.

Discussion

The findings of this study offer a critical re-evaluation of the home mathematics environment, directly challenging the deficit narratives that have long permeated social science research regarding low-SES families. By integrating quantitative modeling with rich, naturalistic observations, we demonstrate that mathematical engagement is not the exclusive domain of affluent, highly educated households. Rather, mathematics is a ubiquitous human activity that adapts to the economic and cultural realities of the family unit.

Dismantling the Deficit Narrative

Our quantitative results confirm previous literature showing a baseline gap in early numeracy scores correlated with SES (Clements & Sarama, 2007). However, the mediation analysis reveals a more nuanced story. The frequency of formal math practices—those most closely resembling schoolwork—is heavily skewed toward high-SES households. If researchers only measure formal practices, low-SES families inevitably appear deficient.

When we expand our lens to include informal, everyday math practices, a different reality emerges. Low-SES families engage in these practices at high rates, and crucially, our moderation analysis (Figure 2) shows that these informal practices have a disproportionately positive impact on the numeracy skills of low-SES children. This aligns with Moll et al.'s (1992) "funds of knowledge" framework. The mathematical knowledge embedded in working-class households—budgeting, resource allocation, spatial navigation—is robust and cognitively demanding. The deficit lies not in the families, but in the narrow, school-centric metrics researchers use to evaluate them.

The Power of Pragmatic Mathematics

The qualitative data highlight a vital distinction between pedagogical and pragmatic math talk. In high-SES homes, math is often treated as a discrete subject to be practiced. In low-SES homes, math is frequently a tool for survival and household management. This pragmatic math is inherently meaningful. When a child helps calculate whether the family has enough money for groceries, the mathematical operations are grounded in immediate, tangible consequences.

Vygotskian sociocultural theory posits that cognitive development is deeply embedded in social interactions and cultural tools (Vygotsky, 1978). The authentic, goal-directed nature of pragmatic math may provide a stronger scaffold for conceptual understanding than abstract, pedagogical questioning. It requires children to engage in mathematical modeling—applying math to solve real-world problems—which is a core competency in advanced mathematics education.

Parental Math Anxiety and Engagement

Our findings regarding parental math anxiety offer important implications for family engagement strategies. Math anxiety negatively predicted the use of formal math practices but did not deter parents from engaging in informal math. This suggests that parents who feel intimidated by "school math" still feel competent navigating the math required for daily life.

Interventions that send home math worksheets or flashcards may inadvertently trigger parental math anxiety, leading to avoidance or the transmission of negative attitudes to the child (Maloney et al., 2015). Conversely, interventions that validate and encourage the math already happening in the kitchen, the grocery store, or during family game night can empower parents. By reframing everyday tasks as valuable mathematical learning opportunities, educators can build parental self-efficacy.

Limitations and Future Directions

While this study provides robust insights, several limitations must be acknowledged. First, the observational data, though naturalistic, are subject to the Hawthorne effect; families may have altered their behavior because they knew they were being recorded. Second, our sample, while diverse, may not capture the experiences of the most profoundly marginalized populations, such as families experiencing acute homelessness, where the cognitive load of survival may impact interaction patterns differently.

Future research should employ longitudinal designs to track how these early informal practices translate into formal mathematical achievement in elementary school and beyond. Additionally, there is a pressing need to develop culturally responsive early numeracy assessments that can capture the specific mathematical competencies children develop through informal, pragmatic family practices.

Conclusion

The development of early numeracy is a complex, socially situated process that extends far beyond the walls of the classroom and the boundaries of formal educational materials. This study provides compelling evidence that families across all socioeconomic strata are actively engaged in fostering their children's mathematical development. By shifting our focus from what under-resourced families lack to what they possess , we uncover a rich tapestry of everyday mathematical practices—from the precise measurements of family recipes to the complex arithmetic of grocery budgeting.

For educators, policymakers, and researchers in the social sciences, the implications are clear. We must abandon deficit-oriented frameworks that pathologize low-SES and minority families. Instead, we must adopt asset-based approaches that recognize, validate, and build upon the diverse "funds of knowledge" present in every community. True equity in mathematics education will not be achieved by forcing all families to adopt middle-class, school-centric practices, but by bridging the gap between the rich, informal mathematics of the home and the formal mathematics of the school.

References