The study centers on what researchers call early math precursors, a framework developed by Hynes-Berry, Chen, and Abel that identifies four foundational pre-mathematical skills: attributes, comparison, change, and pattern. Attributes involve noticing the properties of objects, such as color, size, texture, and quantity. Comparison encompasses recognizing similarities and differences. Change refers to joining, separating, and altering objects and quantities. Pattern captures sequences, regularities, and routines. Because these precursors precede formal numeracy, they are considered critical stepping stones toward later quantification, arithmetic, and mathematical reasoning.

The stakes are considerable. Longitudinal research has shown that early numeracy skills trigger snowballing effects, compounding children’s mathematical knowledge across elementary and middle school grades and even supporting socio-emotional development and literacy. A 2025 longitudinal meta-analysis in the Journal of Educational Psychology confirmed the strong predictive power of early numeracy for later mathematics achievement. Yet despite this evidence, most research on early math has focused on preschoolers, leaving a significant gap in understanding what mathematical support looks like for infants and toddlers, particularly in the informal environments where very young children actually spend their time.

To address this gap, Campana and Kociubuk conducted a qualitative descriptive study using naturalistic observations of six video-recorded storytimes at different branches of a large urban public library system. The recordings captured six library educators, 63 children aged zero to three, and 61 caregivers, including both the formal storytime programs and the open play sessions before and after. The researchers applied a deductive coding schema based on the four early math precursors, supplemented by inductive coding of the methods, strategies, and resources educators used. Intercoder reliability was strong, with a Krippendorff’s alpha of 0.802, and the team reinforced trustworthiness through prolonged engagement, data triangulation across branches and educators, and investigator triangulation.

The findings were striking in their breadth. All four early math precursors appeared across every one of the six storytimes, and nearly all of the subcodes within each precursor were observed at least once per session. Attribute and comparison were the most frequently observed, with comparison subcodes appearing an average of 60 times per storytime and attribute subcodes an average of 57 times. The most common specific elements were physical attributes, temporal and spatial attributes, and similarities comparisons. Pattern was the least observed broad precursor, averaging 32 appearances, a result the authors note aligns with prior research finding that patterns are present but not prominent in early math curricula, possibly because educators receive limited professional development on pattern content for very young children.

The researchers identified five broad methods through which the precursors emerged: reading books, singing songs, chanting rhymes, talking during introductions and transitions, and free play. In one reading example, an educator sharing the book Ten Little Fingers, Two Small Hands prompted caregivers to hold up fingers, count aloud, and wiggle hands, weaving together attribute vocabulary, quantity demonstration, comparison of hands and fingers, and the number sequence from one to ten. In a singing activity about falling autumn leaves, children handled leaf manipulatives while exploring size, color, quantity, and spatial location, taking two leaves from a basket one by one, and letting the leaves fall to the ground, engaging all four precursors in a single song.

Chanting rhymes proved especially rich in attribute vocabulary. In one recurring chant, an educator led children and caregivers through saying goodbye quickly, slowly, high, low, quietly, and loudly, using exaggerated gestures and vocal variation to reinforce opposites and physical concepts while the routine structure of opening and closing each session with the same chant reinforced pattern recognition. Even transitions between activities carried mathematical weight: when an educator introduced the song Go In and Out the Window, the spatial opposites in the lyrics, the ordered steps, and the promise of repeating the song weekly all supported attributes, comparison, and patterns. During free play, caregivers naturally extended the precursors, asking children to count train cars, name colors, explain that green means go and red means stop, or negotiate that holding one more toy meant putting one down, while a baby chasing a programmable Bee-Bot robot demonstrated change through tracking movement and altering her environment by moving blocks from its path.

Two strategies ran through every method: the use of math-related vocabulary and embodied learning, in which physical movements and sensory experiences anchor abstract concepts. The researchers interpreted their findings through Jerome Bruner’s Three Modes of Representation and Lev Vygotsky’s Zone of Proximal Development. Bruner described how children progress from enactive representation, learning through motor responses and manipulation in the first year of life, to iconic representation through images during ages one to six, and finally to symbolic representation through abstract language around age seven. Storytime practices, from finger counting to leaf waving to toy manipulation, aligned squarely with the enactive and iconic modes appropriate for babies and toddlers, while math vocabulary, though symbolic, was consistently paired with concrete representations. Vygotsky’s theory illuminated the adults’ role: educators and caregivers scaffolded experiences children could not access independently, operating within each child’s zone of proximal development.

The caregiver dimension carries particular practical significance. Research indicates that many parents feel anxious or insecure about mathematics, and the quality of adult support has an outsized impact on children’s later mathematical success. By modeling precursor-rich interactions during storytimes, library educators may be training caregivers to replicate these scaffolds at home, multiplying the impact far beyond the library walls. The authors argue that early childhood organizations should treat the four precursors as a valuable framework, train educators in their use, encourage more intentional pairing of math vocabulary with embodied learning and manipulatives, and use family engagement efforts to build caregiver confidence in supporting early math.

The study does have limitations, including its small sample of six storytimes from a single library system, the absence of demographic and developmental data on participants, and reliance on video recordings that may have missed some behaviors. Future research, the authors suggest, should examine how the precursors appear in daycare classrooms, museums, and other settings, and test whether precursor training interventions improve educator knowledge and behavior. Still, the message for parents and educators is clear: the building blocks of mathematics are not found only in flashcards and counting drills. They are in the rhythm of a chant, the colors of autumn leaves, the clatter of toy trains, and the wiggling of ten little fingers, moments that a well-designed storytime delivers by the dozen.

Subject of Research: Early math precursors in public library storytimes for babies and toddlers

Article Title: Building a Strong Math Foundation: Supporting Early Math Precursors for Babies and Toddlers

Article References: Campana, K., & Kociubuk, J. (2026). Building a Strong Math Foundation: Supporting Early Math Precursors for Babies and Toddlers. Early Childhood Education Journal. https://doi.org/10.1007/s10643-026-02351-0

Image Credits: AI Generated

DOI: 10.1007/s10643-026-02351-0

Keywords: early math precursors, babies and toddlers, public library storytimes, early childhood education, math vocabulary, embodied learning, Zone of Proximal Development, Bruner modes of representation, caregivers, informal learning environments, Building, Strong