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

The paper provocatively challenges the prevalent metaphor of ‘ecosystems’—a term that has long captured the interdependent relationships among formal institutions, informal learning environments, and industry partners in STEM education. While ecosystems emphasize interconnectedness and shared growth, the authors argue that this framing overlooks the nuanced, competitive, and transactional realities emerging within the educational landscape. By proposing the concept of “STEM learning markets,” they invite stakeholders to reconsider the distribution of resources, power asymmetries, and motivations that shape contemporary STEM learning provision.

This paradigm shift is significant because it acknowledges the growing influence of market logics in education, where choice, competition, and consumer demand increasingly dictate the availability and quality of learning opportunities. Unlike ecosystems, which evoke harmony and mutual benefit, markets foreground issues of access, equity, and commodification. As formal institutions such as schools and universities navigate partnerships and overlaps with informal providers—ranging from science museums and coding bootcamps to online platforms—their interplay becomes less about symbiosis and more about negotiation and strategic positioning.

Central to the authors’ argument is the recognition that formal and informal STEM learning are not naturally or inherently complementary sectors but are instead interwoven within complex relational frameworks shaped by institutional goals, funding mechanisms, and learner expectations. This perspective compels educators, policymakers, and researchers to critically assess how power dynamics influence who benefits from STEM education and who remains marginalized. In so doing, it uncovers hidden barriers embedded within current provision models that may hinder inclusive access to STEM opportunities.

Moreover, the marketplace analogy offers a compelling framework to understand the multiplicity of actors involved in STEM learning provision, each bringing distinctive resources, expertise, and agendas. For instance, nonprofit organizations may emphasize mission-driven engagement and outreach, whereas private companies might prioritize product-market fit and brand visibility. Governments and educational authorities often find themselves negotiating the tensions between public good imperatives and economic competitiveness. The resulting interplay is far from harmonious, calling for nuanced governance mechanisms and accountability structures to align diverse stakeholder interests.

Importantly, the study highlights that framing STEM education as a market does not advocate for unregulated privatization or consumerism. Rather, it foregrounds the need for critical awareness about the consequences of market logics and calls for deliberate policymaking that can harness the benefits of flexible learning modalities without exacerbating disparities. This balance is especially crucial as informal learning spaces rapidly evolve through digital technologies, expanding the marketplace while simultaneously risking a fracturing of coherent STEM education pathways.

From a theoretical standpoint, Archer and colleagues draw on interdisciplinary approaches, integrating insights from education sociology, market studies, and learning sciences to craft their conceptual model. This multidisciplinary synthesis enriches the discourse by moving beyond simplistic binaries of formal/informal and public/private sectors, instead presenting a textured analysis of how learning provision unfolds in practice. Their framework allows for a granular examination of factors such as reputation economies, certification values, and the role of narratives in shaping learner engagement within diverse STEM contexts.

The conceptual reframing also has profound implications for research methodologies in STEM education. It encourages scholars to adopt mixed methods approaches capable of capturing the transactional nature of learning interactions, provider strategies, and learner experiences across settings. Tracking how learners navigate multiple STEM provision options requires attention to temporal dimensions and spatial dynamics, as opportunities may be dispersed, unevenly distributed, or temporally bounded. Market-based thinking prompts new questions about learner agency and the strategic use of informal spaces as “commercially” influenced environments.

On a practical level, the model invites educational leaders to rethink collaboration strategies, resource allocation, and impact measurement within STEM provision networks. Recognizing the competitive elements at play suggests that fostering genuine partnerships calls for transparent communication, shared goals, and equitable governance that go beyond surface-level coordination. It challenges providers to consider how their offerings are positioned within a broader market and how they can co-create value with learners and communities.

Further complicating the picture is the role of technology in reshaping STEM markets. Digital platforms have lowered traditional barriers to entry, enabling new providers to emerge while disrupting established ones. This democratization introduces both opportunities and risks: it broadens access but may also introduce information asymmetries and quality concerns. Market conceptualization sensitizes us to issues of consumer protection, branding, and the reputational capital of informal STEM providers in virtual and physical realms.

In light of increasing global attention to workforce development and STEM equity, the market metaphor also sheds light on policy tensions. Governments seek to stimulate participation and skill acquisition to compete in a knowledge economy, but must guard against deepening systemic inequities due to uneven market access. Accordingly, policy interventions need to be attuned to how subsidies, accreditation, and regulatory frameworks can shape the configurations of STEM learning markets, mitigating detrimental effects of commodification while promoting innovation.

The paper’s contribution is timely, given the accelerating demand for STEM competencies across industries and the growing diversity of learner pathways. As education systems globally grapple with how best to integrate informal STEM learning with formal curricula, understanding the market dynamics at play becomes indispensable. By foregrounding the transactional and relational complexity of STEM provision, Archer and colleagues provide a robust analytical tool that can guide future research, policy, and practice toward more equitable and effective STEM learning.

Ultimately, this reimagining from ecosystems to markets marks a paradigm shift with profound consequences. It encourages us to interrogate the assumptions underpinning STEM education narratives, scrutinize the structural forces driving provision, and consider the implications for learners who navigate increasingly complex educational terrains. Far from merely academic, this critical conceptualization beckons stakeholders to actively shape STEM infrastructures that respond to contemporary realities while striving to uphold principles of inclusion, quality, and societal benefit.

As the STEM education landscape continues to evolve, embracing nuanced frameworks like the market metaphor will be vital for fostering sustainable innovation and widening participation. Archer, Freedman, Nag Chowdhuri, and their team have laid the groundwork for this intellectual and practical endeavor, opening new avenues for inquiry and action in the pursuit of vibrant, responsive, and just STEM learning environments.

Subject of Research:
Critical conceptualization of the relationships between formal and informal STEM learning provision, shifting from the metaphor of ecosystems to that of learning markets.

Article Title:
From STEM learning ecosystems to STEM learning markets: critically conceptualising relationships between formal and informal STEM learning provision.

Article References:
Archer, L., Freedman, E., Nag Chowdhuri, M. et al. From STEM learning ecosystems to STEM learning markets: critically conceptualising relationships between formal and informal STEM learning provision. IJ STEM Ed 12, 22 (2025). https://doi.org/10.1186/s40594-025-00544-4

Image Credits: AI Generated

DOI: https://doi.org/10.1186/s40594-025-00544-4

Facebook, a dominant social media platform with billions of active users worldwide, presents an opportunity to harness its interactive nature for educational gains. Jin’s study meticulously examines how embedding Facebook-based writing tasks within EFL instruction can foster an environment markedly different from traditional classroom settings. Unlike conventional writing exercises that often feel detached and pressured, Facebook introduces an informal yet authentic digital space that amplifies student engagement and motivation. This shift undermines the historically rigid paradigms of writing instruction by leveraging the familiarity and immediacy that social networks provide.

Central to the study’s findings is the observed improvement in several critical facets of writing proficiency. Participants exposed to Facebook-mediated activities showed significant gains in content development, structural coherence, textual cohesion, and lexical variety. These metrics collectively point to a more comprehensive and sophisticated command of written English. The social media interface encourages iterative feedback and peer collaboration, prompting learners to refine their outputs through dynamic exchanges rather than static submissions. Such real-time interaction simulates authentic communication scenarios where language use is socially negotiated and continuously reshaped.

Perhaps even more compelling than the linguistic improvements is the discernible reduction in writing-related anxiety among participants. Traditional language classrooms can be formidable arenas where fear of error and negative evaluation stifle student expression. The informal tone and user-friendly design of Facebook diminish this apprehensi0n, creating a psychologically safe zone conducive to risk-taking and experimentation in writing. Students reported feeling less scrutinized and more willing to express their ideas freely, reinforcing the notion that lowering affective filters is as essential as mastering grammar or vocabulary in language acquisition.

The collaborative potential embedded within social media platforms constitutes another vital dimension highlighted by the research. Facebook’s infrastructure facilitates peer-to-peer interaction, fostering communal learning and knowledge co-construction. Through commenting, sharing, and reacting to each other’s posts, learners engage in dialogic processes that enrich their understanding and expose them to diverse linguistic inputs. This interactive model departs from traditional teacher-centered paradigms by positioning learners as active agents, collaboratively shaping their writing development.

However, despite the study’s illuminating conclusions, its scope is tempered by certain methodological constraints. The research sample hails from a single university, raising questions about the broader applicability of the results. Geographic and demographic homogeneity limit how widely we can generalize these findings across varied cultural and educational contexts. Moreover, the relatively modest participant pool calls for caution in interpreting the statistical robustness of the improvements documented. Subsequent studies employing larger, more diversified samples could fortify the empirical evidence base and unpack nuanced patterns of social media’s educational efficacy.

Another caveat involves self-selection bias. Students opting into the study may have inherently been more technologically inclined or possessed positive predispositions toward social media use, skewing the outcomes. Their prior experience with digital platforms, particularly Facebook, might have facilitated smoother engagement, thereby amplifying benefits that less tech-savvy peers could struggle to access. This preexisting comfort level with online tools introduces variability in intervention effectiveness, underscoring the need for differentiated approaches sensitive to learners’ digital literacy.

Further practical considerations emerge from the global variability in platform accessibility. Facebook is inaccessible in certain countries subjected to network restrictions or regulatory barriers. This limitation poses a significant challenge to adopting uniform social media strategies in language education worldwide. Jin advocates for investigative efforts into alternative local or region-specific social networking services that could replicate Facebook’s pedagogical advantages within restricted environments. Such adaptive strategies would ensure equitable access to innovative digital learning opportunities.

The study’s implications extend beyond EFL writing classrooms by inviting reflection on the evolving role of technology in education. The integration of social media into formal curricula exemplifies the blurring lines between social interaction and academic learning, demanding educators rethink conventional instructional models. It signals a move toward embracing platforms already embedded in students’ daily lives, capitalizing on their intrinsic motivational power to enrich intellectual engagement.

Technically, incorporating Facebook-based writing tasks entails careful curriculum design. Educators must scaffold activities to utilize the platform’s unique affordances effectively, ensuring alignment with learning objectives. For instance, structuring peer feedback sessions, moderating discussions to maintain academic rigor, and designing prompts that evoke critical thinking necessitate pedagogical expertise tailored to online social environments. Moreover, concerns about digital distractions and potential privacy issues require thoughtful management to safeguard educational integrity and learner wellbeing.

The cognitive mechanisms underpinning the observed enhancements merit further exploration. Social media’s multimodal nature—combining text, visuals, and immediate communication—might stimulate diverse cognitive pathways, thereby reinforcing language acquisition. Additionally, the social presence afforded by platforms like Facebook can engender a sense of belonging and accountability, motivating sustained engagement. Understanding these psychological and neurological dimensions could inform more refined interventions to optimize learning outcomes.

The study’s timing is pivotal, situated within a broader global trend accelerated by the COVID-19 pandemic, which thrust online learning to the forefront. Educators grappling with remote instruction have sought innovative methods to preserve interactivity and student motivation. Jin’s research contributes empirical support for social media as a viable channel to bridge physical separation while maintaining dynamic educational exchanges, reinforcing its relevance in contemporary discourse on digital pedagogy.

Envisioning the future trajectory of this research field raises exciting possibilities. Cross-platform comparisons could identify differential impacts of various social media tools, tailoring approaches to distinct learner populations. Investigations extending beyond writing to oral skills, reading comprehension, and even intercultural competence might reveal holistic benefits of social media integration. Further, longitudinal studies tracking sustained proficiency and anxiety levels would illuminate the durability of these educational effects over time.

The intersection of technology, psychology, and language education epitomized in Jin’s work underscores the multidisciplinary nature of contemporary pedagogical innovation. It calls for collaboration among linguists, educators, cognitive scientists, and technologists to harness digital platforms intelligently and ethically. Together, such efforts promise to reshape language learning landscapes, transforming them into vibrant, socially rich, and learner-centered arenas.

In sum, this seminal investigation offers robust evidence that Facebook, far from being a mere social diversion, is a potent instrument to enhance L2 writing skills and alleviate anxiety. It champions an educational paradigm where technology and human interaction converge to nurture linguistic competence and confidence. As digital natives populate classrooms worldwide, integrating familiar social media into instruction may well define the next frontier of language education, cultivating empowered, engaged, and resilient learners.

Subject of Research: Integration of social media platforms, specifically Facebook, into second language (L2) writing instruction to improve writing proficiency and reduce writing-related anxiety in English as a Foreign Language (EFL) learners.

Article Title: Writing in the digital age: understanding the relationship between social media use and college students’ writing skills and anxiety.

Article References:
Jin, S. Writing in the digital age: understanding the relationship between social media use and college students’ writing skills and anxiety. Humanit Soc Sci Commun 12, 1048 (2025). https://doi.org/10.1057/s41599-025-05443-1

Image Credits: AI Generated