Computational Play in Early Childhood: Integrating Analog and Digital Tools to Support Mathematical Learning and Computational Thinking

Abstract

Although play naturally embeds computational thinking (CT) and mathematical learning in early childhood education, designing developmentally appropriate learning activities that purposefully nurture and extend these competencies remains a challenge. This study investigates how young children engage with foundational mathematical and computational concepts through analog (DUPLO^®) and digital (Blue-Bot) tools in a play-responsive early childhood education workshop setting. The study adopts a qualitative workshop format aimed at promoting playful exploration and active experimentation, involving eleven 4–5-year-old children and their two teachers. Based on a sociocultural perspective, the findings highlight that mathematics is a human activity embedded in everyday playful practices. In particular, unplugged analog activities, embedded within an open-ended narrative framework, guided and structured the process. Based on these findings, we suggest “computational play” as a framework for developmentally appropriate integration of computational thinking (CT) and mathematics. This framework offers implications for educators seeking to support early CT and mathematical learning in playful, exploratory early childhood education (ECE) environments.

1. Introduction

Children naturally observe and engage with mathematical aspects of their environment from an early age, comparing quantities, recognizing patterns, navigating spatial relationships, and solving problems (e.g., Lüken, 2023; Inchaustegui & Alsina, 2020; Solem & Reikerås, 2017; Reikerås et al., 2012). Early mathematics provides a foundation for understanding the world and supports future academic success (Clements & Sarama, 2024; Masek et al., 2024). Play is central to this development, offering rich opportunities for mathematical engagement (Ginsburg, 2006). Computational thinking (CT) involves structured problem-solving strategies such as abstraction, pattern recognition, decomposition, algorithmic design, and evaluation (Selby & Woollard, 2013), and has gained attention in mathematics education (e.g., Weintrop et al., 2016; Bers et al., 2022). Aligned with the European Commission’s (2023) report, these strategies, when embedded in play, provide intuitive and engaging pathways for children to explore mathematical ideas, such as sequencing actions in games or designing repeating patterns with blocks (cf. Ginsburg, 2006). When CT strategies are embedded within playful learning experiences, they can create intuitive and engaging pathways for children to explore mathematical ideas. Playful contexts invite experimentation, problem-solving, and creativity, allowing children to approach mathematical concepts in ways that are meaningful and accessible. In this paper, we refer to computational play as the integration of mathematical and CT learning within a playful pedagogical framework that combines analog and digital technologies to support mathematical problem-solving. As a methodological approach, computational play enables educators to foster children’s conceptual understanding of mathematics while helping them identify meaningful connections between mathematics and computational thinking. Despite its potential to bridge these domains, relatively little research has explicitly focused on computational play as a distinct area of research. Addressing this gap holds both theoretical and practical value, particularly as playful computational frameworks may foster intuitive and creative engagement with mathematical concepts.

Given the growing emphasis on both mathematics and CT in early childhood education (ECE), this study investigates how young children engage in computational play using both analog and digital tools. It also examines how such play can foster meaningful mathematical learning. The study is guided by two research questions:

• How do children in ECE engage with and integrate early mathematical learning and computational thinking through playful frameworks?
• In what ways can computational play support different aspects of early mathematics in ECE workshop settings?

Grounded in a sociocultural perspective (Lave & Wenger, 1991; Säljö, 2005; Vygotsky, 1978), this study views learning as situated and mediated through cultural tools and social interaction. Playful settings, where children explore possibilities, test ideas, and engage in “what-if” scenarios, provide fertile ground for integrating computational thinking (CT) and mathematics (Meek, 1995). These environments allow children to interact with the physical properties of materials, which can support and extend their creative intentions (Brooks & Sjöberg, 2023). Such hands-on exploration can be facilitated through both analog and digital tools, each offering distinct and complementary affordances for learning (Brooks & Edstrand, 2023; Brooks et al., 2024). Within this context, CT and early mathematics are not introduced as separate domains but emerge through playful, situated activity, embedded in children’s social and material engagements.

2. Literature Review

This literature review examines recent research on the integration of mathematics and computational thinking (CT) in early childhood education. Particular attention is given to approaches that align with play-oriented pedagogies and combine digital and analog tools. The review also traces emerging perspectives that position CT as a creative, social, and embodied practice, laying the groundwork for the concept of computational play.

2.1. Integrating Computational Thinking and Mathematics in Early Childhood

Ye et al. (2023) underscore the increasing presence of Computational Thinking (CT) in primary mathematics education, emphasizing both unplugged and plugged tools. Their review promotes early, engaging exposure to core CT practices such as algorithms, debugging, and abstraction. Notably, they highlight connections between mathematical reasoning and CT, especially in geometry and number operations, though their focus remains on digital tools and outcome-based learning. Echoing this integration agenda, Rahmawati et al. (2024), however, focused on older learners, highlighting the reciprocal relationship between computational and mathematical thinking. Their work reinforces the idea that embedding this integration early, especially through developmentally appropriate and play-oriented contexts, may enhance children’s conceptual foundations and readiness for more advanced applications later in their education.

Addressing challenges with coding-based CT instruction, Wang et al. (2022) propose a non-programming, “plugged” approach to CT in primary mathematics. Their design-based study with 9–10-year-olds revealed that CT competencies, particularly decomposition, algorithmic thinking, and problem-solving, can be meaningfully cultivated through visually scaffolded, mathematically grounded micro-worlds. While their study focuses on slightly older children, the principles they propose, such as CT–math alignment and progressive task design, affirm that CT can be developed meaningfully without direct coding instruction. This broader interest in CT–math integration is also evident in recent literature reviews (Lv et al., 2023; Ye et al., 2023), which document a growing body of research across K–12 education. However, these reviews consistently note a lack of empirical studies in early childhood contexts. When such studies do exist, they typically focus on geometry and number operations and often involve robotic or visual coding tools. Within these, core CT dimensions such as decomposition, pattern recognition, and abstraction dominate, reflecting a continued emphasis on algorithmic thinking. This thematic convergence underscores a pressing need for early childhood research that addresses CT through more developmentally aligned pedagogies.

For example, Shumway et al. (2021) demonstrate how robotic toys can support early spatial reasoning and arithmetic, pointing to the potential of interactive technologies in bridging CT and mathematics among young learners. Their work connects well with the concept of digital making (Lv et al., 2023), which involves children creating tangible or digital artifacts and supports CT through creative and purposeful construction. Both studies illustrate the power of hands-on engagement for integrating CT into early mathematics learning. Further extending this line of inquiry, Nordby et al. (2024) explore how teachers employed Bee-Bot robots to support spatial reasoning in geometry tasks. While students benefitted from embodied interactions, such as programming Bee-Bot to move in geometric paths, the study also highlights pedagogical challenges. Specifically, the absence of a visual trace required auxiliary representations (e.g., arrows on paper), which introduced cognitive complexity for both students and teachers. These findings suggest that while tools like Bee-Bot hold promise, their value depends heavily on how they are contextualized within learning environments.

In sum, the literature suggests a shared recognition of the potential for CT–math integration in early education yet also reveals a gap in approaches that align with the developmental and pedagogical values of early childhood. Building on this foundation, the present study seeks to broaden the landscape by incorporating analog making and narrative-driven, embodied learning, thereby extending the range of CT-informed mathematics experiences available to young learners.

2.2. Towards Computational Play

The following section continues the literature review by tracing emerging perspectives that broaden traditional understandings of computational thinking in early childhood. While these perspectives resonate with the theoretical stance adopted in our study, the focus here remains on synthesizing existing contributions in order to situate the concept of computational play within current research. The theoretical implications of this framing will be developed further in the subsequent section.

As CT gains traction in educational policy and curriculum design, particularly in primary and secondary contexts, questions remain about its applicability in early childhood education. Core CT competencies such as problem-solving, abstraction, and algorithmic thinking are frequently framed within procedural, skill-based paradigms rooted in frameworks like those of Wing (2010), the CSTA (2017), and ISTE (2021). While influential, these models often assume a developmental readiness and disciplinary structure more suited to older learners. As Lee et al. (2022) and Brooks and Sjöberg (2023) argue, such frameworks may not adequately reflect the relational, embodied, and creative learning processes typical of early years education. In response, adjacent research fields such as making, tinkering, and digital fabrication (Blikstein, 2018; Peppler et al., 2016) emphasize creativity, material engagement, and peer collaboration as foundational to early CT. These approaches position CT not as a discrete subject but as a set of dispositions and practices nurtured through expressive, hands-on experiences. Such perspectives invite a broader, more nuanced understanding of what computational learning might look like in early childhood settings.

Within this evolving conceptual landscape, the notion of computational play has emerged as a unifying framework (Brooks & Edstrand, 2023; Brooks et al., 2024; Bertel & Fredskilde, 2021). Rather than viewing CT as a linear sequence of skills to be mastered, computational play situates computational and mathematical thinking within the narrative, social, and imaginative play practices that are central to young children’s learning. This framing does not dilute CT’s rigor; rather, it anchors it in the relational, multimodal, and exploratory processes through which children construct meaning. Empirical evidence supports this synthesis. Clements and Sarama (2024) emphasize the importance of carefully designed learning environments and resources in promoting mathematical thinking in young children. Their work highlights how guided play and embedded challenges can foster abstract reasoning through concrete interaction. Similarly, narrative-driven approaches and storytelling through play have been shown to facilitate creative problem-solving (Portsmore & Milto, 2018) and digital literacy (Fredskilde & Bertel, 2025). Complementing this, Lüken (2023) observed that children aged 1 to 6 naturally engage in visual patterning and repetition during free play, demonstrating foundational algebraic thinking as they invent, extend, and vary patterns. Similarly, Inchaustegui and Alsina (2020) document how pattern recognition, sequencing, and prediction can emerge organically in everyday play contexts, including storytelling and games.

Taken together, these studies illustrate that CT and mathematical competencies are not foreign to early childhood play but often embedded within it. However, the challenge remains to design environments and pedagogies that surface, extend, and support these competencies in intentional ways. The framework of computational play offers a compelling response to this challenge by providing a theoretically robust and developmentally sensitive way of integrating CT with early mathematics. The present work takes up this challenge by designing analog–digital learning environments that center children’s storytelling, physical construction, and exploratory engagement. Rather than simplifying CT to fit young learners, we explore how early childhood learning environments can be expanded to include CT through the dynamic and generative medium of play.

3. Theoretical Framework

This study draws on a sociocultural perspective, emphasizing the role of cultural tools and imagination in shaping mathematical learning within a playful setting (Vygotsky, 1978; Wertsch, 1998). Playful settings in early mathematics encompass both analog and digital tools, which act as mediational means (Wertsch, 2007; Säljö, 2019), fostering children’s imagination and mathematical reasoning through activities such as counting, comparing, and problem-solving. These tools provide access points (Edstrand, 2017; Giddens, 2002) to mathematical knowledge as well as enabling children to explore mathematics playfully. Central to this perspective is the idea that mathematics, as a sociocultural product, is embedded in human practices and interactions.

Building on this, we draw on Bishop’s (1988) framework, which classifies mathematics into six fundamental activities: counting, locating, measuring, designing, playing, and explaining. These activities capture the ways in which mathematics is interwoven with everyday life. Importantly, young children naturally engage in these activities through their interactions with the world, using them to make sense of their surroundings (Solem & Reikerås, 2017). This highlights the importance of playful frameworks in fostering children’s engagement and mathematical exploration. Finally, this chapter outlines the key aspects of the playful framework used in this study, focusing especially on a sociocultural view of imagination (Vygotsky, 1978).

3.1. Mathematical Framing

Research indicates that long before starting school, children spontaneously explore and use mathematics, at least at its intuitive beginnings, and their mathematical understanding can be surprisingly complex and sophisticated (Seo & Ginsburg, 2004; Clements & Sarama, 2020). Two of Bishop’s (1988) mathematical activities are counting and measuring. Both are concerned with numbers but involve different cognitive processes and practical applications in mathematical reasoning. Counting focuses on discrete aspects of mathematics, such as determining quantities using whole numbers, whereas measuring deals with continuous aspects, involving the comparison of attributes like length, weight, or volume. Here, Bishop (1988) also refers to the practical skills and procedures that individuals or groups use in their daily lives. Further, Bishop (1988) distinguishes between two types of spatial structuring, referring to two kinds of geometric concepts: locating and designing, both of which are crucial for mathematical learning. Locating focuses on the topographical aspects of the environment, such as position and spatial relationships, whereas designing involves the conceptualization of objects, leading to the foundational understanding of shape and form. Bishop’s (1988) emphasis on the sociocultural aspects of mathematics is particularly evident in the last two activities: playing and explaining. He argues that these activities are primarily concerned with connecting individuals to their social environment, rather than their physical surroundings. Playing involves engaging with social procedures and rules of performance while fostering imagination, what Bishop refers to as exploring “what if” scenarios. Explaining focuses on cognitive processes, including exploring and conceptualizing the environment, and sharing these conceptualizations with others. Bishop’s activities, as they are translated to an ECE context (Solem & Reikerås, 2001, 2017), have a central position in working with mathematics in the Nordic ECEs, since these categories are much in line with the sociocultural view on learning in Nordic ECEs. In this study, we explore how these six mathematical activities relate to computational play, focusing particularly on introducing early mathematics in early childhood education.

3.2. Playful Framing

The present study examines children’s engagement with computational and mathematical ideas through a playful framing that attends to both social and material dimensions of learning. This framework draws on the notion of play-responsiveness, which emphasizes the interplay between children’s activities, the tools and materials available, and the social contexts in which interactions unfold (Goodyear & Carvalho, 2013). It offers a holistic, yet open-ended, lens for exploring how young learners make sense of complex concepts through embodied, imaginative, and collaborative activity. Play, as a concept, is dynamic and multifaceted. Vygotsky (1978) positioned imaginative play as a critical context for development, describing it as a zone of proximal development where children explore the world and their own capacities. Aligned with Bishop (1988), Vygotsky (1930/2004) underlines that children, through imagination, not only engage with “what is”, but begin to inquire into “what if”; expanding their understanding of both the real and the possible. This imaginative dimension is particularly relevant to early mathematical and computational thinking. For example, through patterning, sequencing, spatial reasoning, and problem-solving, children often engage in foundational mathematical ideas during play. Cremin et al. (2013) demonstrate how narrative and storytelling can serve as powerful vehicles for such learning, inviting children into shared imaginative spaces where mathematical and computational exploration are naturally embedded. In these contexts, designing a path for a robot or telling a story with programmable elements may simultaneously develop children’s sense of number, direction, shape, and sequence (Fredskilde & Bertel, 2025).

Sutton-Smith (1997) describes play as inherently open-ended, flexible, and adaptive, qualities that also characterize productive mathematical and computational inquiry. Pellegrini et al. (2007) similarly underscore how play supports innovation and responsiveness to changing environments. These qualities become especially relevant in today’s digital landscape, where coding toys, interactive platforms, and programmable objects are reshaping how play unfolds. To support learning in such contexts, it becomes crucial to design play-responsive digital–analog environments—spaces where analog materials (e.g., blocks, paper, LEGO^®) and digital tools (e.g., programmable robots, tablets) co-exist in ways that stimulate creativity, reasoning, and collaboration.

Play-responsiveness has been explored in ECE research with a focus on adult–child interaction and the co-construction of meaning through dialogue and shared activity (Pramling et al., 2019; Wallerstedt & Pramling, 2023). The present study builds on this tradition but extends it by emphasizing open-ended design features that allow for the integration of computational and mathematical experiences within children’s self-directed play. Previous work (e.g., Brooks & Edstrand, 2023; Granone & Reikerås, 2024; Bertel & Fredskilde, 2021) suggests that when environments are designed to be open-ended and multimodal, they support the emergence of both imaginative exploration and mathematical reasoning. Mattelmäki et al. (2011, p. 79) define open-ended environments as those that “allow and inspire new individual interpretations for various participants”. Studies such as Bartholomew and Strimmel (2017) have shown that learners respond positively to design challenges, particularly valuing the opportunity for creative problem-solving. When analog and digital resources are integrated, such activities create opportunities for children to develop ideas, engage in coding, and collaborate within playful learning contexts. Central to this is the role of mediating tools, which act as “access points” to knowledge (Edstrand, 2017; Giddens, 2002), supporting both exploration and meaning-making in play-responsive settings.

4. Materials and Methods

This paper presents a study involving children aged 4–5, centered on workshop activities designed to explore how they engage with mathematics through computational play, robotics, and traditional creative materials such as LEGO^®. The study is part of a larger research project on early childhood education and computational play.

The study employs a qualitative workshop-based methodology designed to encourage children’s playful exploration and experimentation. Such an approach has seen growing application across various research domains (Storvang et al., 2018). The workshop format is closely linked to the notion of participation and is frequently used in contexts where creative, domain-relevant problem-solving and active learning are central (Ødegaard et al., 2023; Brooks et al., 2023; Ørngreen & Levinsen, 2017). In this study, the workshop was deliberately structured to align with both the children’s interests and the overarching research questions. Central to the workshop design was the creation of an environment that fostered active engagement and participant agency. To support this, a variety of tools were incorporated to stimulate the children’s involvement and foster a sense of inspiration and ownership (Schei & Ødegaard, 2017). As Ørngreen and Levinsen (2017) argue, effective workshops are designed to meet predefined yet flexible aims.

In what follows, we describe the materials and procedures used in the study, detail our data collection process, address ethical considerations, and outline our analytical framework.

4.1. Participants and Context

The study involved eleven children (seven girls and four boys), all aged 4–5, and their two educators from a neighborhood kindergarten in northern Denmark. This kindergarten was selected due to its close proximity to the workshop facility and the educators’ familiarity with the organizing university, particularly its play-responsive pedagogical approach. The participants had limited prior experience with digital technologies. Facilitated by two university staff members, the 75 min workshop took place in a child-friendly, playful space adapted from a conference facility, designed to encourage exploration, experimentation, and hands-on engagement with a variety of tools. Neither the children nor the educators had prior experience with the robotic technology used to explore mathematical concepts. The educators’ role was to assist and support the children during the activities, while the facilitators were responsible for initiating and guiding each session.

4.2. Materials

The workshop was structured around a narrative titled Escape from the Zoo, in which children helped animals escape by completing a series of tasks. Each child used LEGO^® DUPLO^® bricks to build an animal based on their choice of a visual template and then transported it to an island using a Blue-Bot1 robot (Figure 1a). All children had individual access to LEGO^® DUPLO^® materials. The Blue-Bot robot was unfamiliar to all participants. The activities were designed to promote computational play and support early mathematical learning. Children worked in six pairs of, each on a grid-based mat aligned with the Blue-Bot’s movement patterns (Figure 1b). In each pair, two children worked together, except in one case where a child completed the activities in close collaboration with an educator. The materials and tools formed the basis for the subsequent workshop procedures, which are described in the next section.

4.3. Procedure

The workshop was structured into four phases, each serving a distinct purpose: (1) Setting the scene, (2) Exploration, (3) Design and making, and (4) Sharing and co-imagining. While these phases were intended to unfold sequentially, time constraints allowed for some flexibility, enabling participants to move between phases as needed. The children’s educators played an active role throughout, supporting the facilitators and encouraging the children’s participation. The workshop design was anchored in a narrative scenario (Escape from the Zoo) introduced at the outset, featuring characters and a clear goal to guide the children’s engagement.

Table 1. Overview of the different phases of the workshop design.

Phase	Purpose	Main Activities	Learning Focus
Setting the Scene	Introduce narrative and context	Storytelling, character introduction	Narrative framing, imagination. Introduction to pre-mathematical spatial concepts such as over, under, between, and around
Exploring	Familiarize with robots and the environment	Hands-on testing, group discussion	Logical sequencing, basic problem-solving
Designing and Making	Create artefacts linked to narrative	Building fruits and habitats, basic coding	Algorithmic thinking, spatial reasoning
Sharing and Co-imagining	Reflect, share, and extend ideas	Group reflection, idea sharing, symbolic return	Critical thinking, collaboration, abstraction

provides a condensed overview of the four workshop phases, including their goals, core activities, and intended learning outcomes. These were later adapted in response to the children’s engagement, as illustrated in the paragraph that follows Table 1 overview.

The four-phase structure was supported by a range of playful, hands-on tasks that helped bridge the narrative with early mathematical and computational learning. The following examples illustrate how this unfolded in practice: To illustrate how the workshop combined playful engagement with learning goals, each phase included structured yet open-ended tasks. In Setting the Scene, facilitators introduced the Escape from the Zoo narrative using story cards, animal figures, and LEGO^® DUPLO^®, inviting children to guess which animals needed help and how they might escape. During Exploration, children experimented with Blue-Bot movements, discovering how sequences of directional commands could create paths, such as a square or backwards. In the Design and Making phase, children engaged in imaginative play with the DUPLO^® figures and robots, creating stories and characters and imitating animal sounds, demonstrating imaginative thinking tied to color, shape, and function. As children programmed robots to deliver these fruits, they practiced counting steps, estimating distances, and debugging simple code. In Sharing and Co-imagining, children reflected on their creations, proposed new stories (e.g., a girl imagined that a table is a cloud) and used language to describe actions while reinforcing collaborative and reflective thinking.

The sample was small and the study limited to a single workshop, both representing methodological constraints. Designed as an exploratory qualitative investigation, the study aimed to gain in-depth insights into participants’ experiences rather than produce generalisable results. To strengthen the data’s reliability and depth, six researchers acted as observers, systematically documenting the workshop. This approach enabled the collection of rich, situated data that can inform future research and design iterations.

4.4. Data Collection

Data collection involved a combination of video recordings, photographs, and written observational notes captured during pair-based activities. Each of the six workstations was outfitted with a video camera that continuously recorded the children’s interactions as they engaged with the assigned tasks. Six researchers participated in the data collection process, each observing approximately one to two groups and documenting children’s actions and interactions throughout the workshop. Supplementary photographs were also taken periodically to capture key moments across the various activities.

The use of video recordings provided valuable insights into how children engaged with both analog and digital materials to convey meaning. These multimodal interactions, featuring gestures, facial expressions, gaze, movement, and manipulation of objects, are particularly characteristic of early childhood learning and play (Flewitt, 2016). The visual data enabled a close examination of children’s activity across multiple modes, offering a deeper understanding of their meaning-making processes. For example, in the domain of mathematics, observers noted children counting aloud as they programmed the robot’s steps, identifying and extending patterns in the grid layout, and using spatial language such as “next to,” “in front of,” or “turn right.” In relation to computational play, documented examples included children engaging in imaginative coding scenarios, such as pretending the robot was “getting lost” or “asking for help”, as well as instances where they debugged their code by testing, adjusting, and re-testing command sequences. Observers also recorded how the play-responsive setting encouraged children to take initiative, pose hypotheses (“What if we turn it twice?”), and co-construct solutions with peers or facilitators.

4.5. Ethical Considerations

The study adhered to established research ethics principles, including transparency, thorough documentation, and the safeguarding of all participants’ privacy and well-being throughout the research process (Danish Ministry of Higher Education and Research, 2014; GDPR, 2016). Prior to data collection, both educators and parents received detailed written information about the study’s purpose and procedures. Parental consent was obtained through signed forms that also granted permission to use video and photographic material for research dissemination.

Ethical considerations were further grounded in the United Nations Convention on the Rights of the Child (UNCRC, 1989), ensuring the child participants’ rights to information, agency, and protection. The children were introduced to the study in an age-appropriate manner, including the aim of the workshop, the types of activities involved, and how video recordings would be used. The cameras were physically shown to the children, and they were explicitly informed that participation was voluntary and could be withdrawn at any time without needing to provide a reason. Children were encouraged to communicate any discomfort to their teachers or the researchers. Verbal consent was obtained from all children and was treated as ongoing and negotiable throughout the entire workshop session.

4.6. Analysis

The analysis combined an inductive thematic approach (Braun & Clarke, 2006) with a deductive lens drawing on Bishop’s (1988) mathematical activities and computational thinking to refine the emerging themes. Selected video recordings and photographs were reviewed to identify and transcribe key episodes, focusing on both verbal and non-verbal interactions. The children’s conversations, originally in Danish, were translated into English for analysis. Guided by Braun and Clarke’s (2006) framework, the process involved the following steps:

• Transcription: Video and photographic data were initially tagged according to emerging patterns. Selected episodes were transcribed and reviewed by the research team to assess their relevance;
• Coding: During transcription, all researchers annotated the data with preliminary codes, highlighting recurring dialogues, notable interactions, and interesting quotes. These annotations served as a foundation for later coding;
• Theme Development: Codes were organized into tentative themes through an iterative process using physical mind maps. This step gradually distilled the data into overarching themes, such as children’s engagement with mathematical concepts, play responsiveness, and interactions with both digital (Blue-Bots) and analog (DUPLO^®) materials. The focus was on capturing children’s actions, emotions, and motivations during computational play;
• Review and Refinement: Themes were refined by revisiting and re-watching the video material. Relevant clips and quotes were grouped according to observed practices, such as spatial reasoning and peer collaboration. This allowed for deeper interpretation of how children engaged with mathematical ideas (e.g., counting, locating, designing, explaining) through play-responsive coding activities;
• Finalization: The final analysis resulted in four key themes, supported by selected episodes and illustrative quotes.

Alongside the inductive thematic analysis, we used a deductive lens based on Bishop’s (1988) mathematical activities and CT, allowing us to refine the themes while linking them to established theoretical concepts.

To support the analysis, observation notes were incorporated, with each observer anonymized using numerical identifiers. Photographs used in the article were extracted from the video recordings. This analytical process moved from broad, common-sense interpretations to detailed, situated practices and, ultimately, to thematic and theoretical insights. This approach aimed to capture the complexity of children’s play and the contextual factors shaping their engagement with computational and mathematical concepts. To enhance validity, the themes were cross-checked across multiple data types and discussed among the research team to ensure consistency and minimize potential bias.

The following section presents the four themes that emerged from the analysis, offering insights into how children’s computational and mathematical understanding unfolded during the workshop.

5. Results

This article explored the dynamics of a play-responsive workshop in which children engage in tasks designed to support their emerging computational and mathematical understanding. The findings examined how children connect with and empathize with the narrative Escape from the Zoo (see Section 4.2), and how they begin to integrate computational and mathematical concepts into their play activities. Drawing on observation notes and video recordings, the analysis is illustrated with selected quotes and images.

The results are presented under four themes:

• Children’s interpretation and adaptation of tasks;
• Children’s engagement with unplugged and plugged tools;
• Fostering mathematical learning through playful design tasks;
• Collaborative construction and spatial reasoning in play.

5.1. Children’s Interpretation and Adaptation of Computational and Mathematical Tasks

Observations and video recordings reveal that the children were engaged with and empathetic toward the Escape from the Zoo narrative. As part of the activity, the children “travelled” to their islands by taking a short flight across the room. During this flight, they engaged with mathematical concepts such as over the table, under the table, around the chair, and between two chairs. This activity was facilitated by the workshop facilitators, who guided the children on the journey. The children participated by making airplane sounds like “whroom” and by verbally identifying concepts such as “over” and “under.” They also navigated around the room through locating activities, identifying objects such as tables and chairs before eventually arriving at the islands where the Blue-Bots were stationed.

On the way to the islands, one facilitator dropped a suitcase containing the animals’ packed lunches (made of DUPLO^®). Upon arriving at the islands, the children discovered the Blue-Bot and began exploring it. They tested the buttons and quickly figured out how to move the robot forward, engaging with it intuitively. After a short period of exploration, they were given a new task: retrieve the lunchboxes with fruits that were lost during the journey. The children collected DUPLO^® bricks in four colors, yellow, green, red, and blue, each representing a type of fruit. By grouping the bricks by color, the children engaged in a counting activity that reflected early numeracy skills such as sorting, classifying, and connecting numbers to physical quantities. A wagon was attached to the back of the Blue-Bot to transport the fruit (see Figure 2). The children then attempted to program the Blue-Bot to collect each fruit and load it onto the wagon.

At this point, it became clear that the children needed more guidance from the facilitators:

“I know one trick, and that is that you press the cross [on the Blue-Bot] to delete [what you have done previously] otherwise it remembers the old code.”

(Facilitator 1, personal communication, 7 November 2023.)

The children quickly adopted this advice, pressing the cross button when entering new commands. For example, two girls drove their Blue-Bot to their island and responded as follows:

Girl1. No, we press the cross.

Girl2: Now we are here

Girl1. We are here

Girl2: We must get our fruit off

(Group of two girls, personal communication, 7 November 2023.)

Now on the island, the girls began placing DUPLO^® bricks by hand onto the designated colored areas on the mat. When the facilitator asked if they wanted to program the Blue-Bot to move the fruits to the marked fields, the girls instead placed the fruits back on the wagon. This is an example of a task that was not clearly communicated, as the girls did not understand that they were expected to program the Blue-Bot to distribute the fruits. It also illustrates verbal explanation during Blue-Bot programming, explaining why certain steps, such as pressing the cross button, were necessary, and indicating when they had “landed” on the island, highlighting the role of explanation in the activity.

The children’s interactions with both the bricks and Blue-Bot illustrated key elements of plugged and unplugged computational thinking (CT), such as abstraction (e.g., building simplified representations of the children’s chosen animals or using a colored brick to represent a particular fruit), sequencing (e.g., when programming the Blue-Bot, children worked out that the robot needed a specific sequence of directional commands, such as “forward, forward, turn right”, in order to reach the desired square on the grid mat) problem-solving (e.g., when the Blue-Bot did not reach the intended square, children discussed and adjusted their commands, trying alternative routes to solve the challenge of navigating the grid), and algorithmic thinking (e.g., children began to break down a larger task, such as moving the Blue-Bot in a certain direction, into smaller steps, creating a clear algorithm of directional commands to achieve the same result). Initially, they engaged through trial and error, pressing buttons to observe movement, an essential component of computational play, where learning occurs through hands-on interaction with digital or analog tools. Across the six groups, children approached tasks in different ways and often needed guidance from educators or facilitators to successfully navigate Blue-Bot around the mat. For example, one group programmed the Blue-Bot to move forward but manually turned it by hand, demonstrating problem-solving skills:

Facilitator 2: Do you remember what to do with the robot?

Boy1: Yes

Facilitator 2: Can you try to turn it around?

Boy 2: How do you do that? [They try to reach the blue spot on the mat.]

Facilitator 2: Can you get to the red one? [Straightens the mat to align it.]

Boy 1: [Moves the Blue-Bot diagonally and then programs it to move forward again.]

(Group of two boys, personal communication, 7 November 2023.)

As shown in Figure 3, using the grid-based mat, the children engaged in spatial reasoning by turning the Blue-Bot diagonally and guiding it toward specific targets. This exchange illustrates how trial-and-error exploration helped children develop control over Blue-Bot’s movements. Their skills were still emerging, often requiring facilitator support to refine their understanding of sequencing and directional commands, foundational elements of CT.

While collaborating with the facilitator, the boys demonstrated the ability to program Blue-Bot to turn 90 degrees and move forward. In doing so, they worked on spatial localization, navigating relationships between direction and rotation on the mat. When asked to program Blue-Bot to move around colored squares, the boys successfully directed the robot forward but also adjusted its movement manually when they encountered difficulty. They remained engaged and were able to guide the robot around the colored areas on the mat.

This scenario highlights the diverse strategies children employed when programming Blue-Bot. Some groups moved the robot by hand, while others attempted full programming but intervened manually when stuck. This reflects the open-ended nature of play, where children are encouraged to experiment and solve problems in their own ways. Facilitators and educators respected these varied approaches, supporting children in accordance with their developmental levels.

This flexibility is further illustrated when one group programmed their robot to interact with another group’s robot, prompting the second group to program theirs to respond and move toward the first group’s island. This kind of peer interaction added a new layer of social collaboration and playful engagement.

5.2. Children’s Engagement with Unplugged and Plugged Tools

Observations showed that children were more engaged with the analog elements of the workshop, particularly working with DUPLO^®, than with the Blue-Bot. This is notable given the growing emphasis on digital skills and computational thinking (CT) in ECE education. These findings challenge assumptions that children naturally prefer digital tools and offer valuable insight into their learning preferences, engagement processes, and the importance of scaffolding when working with both analog and digital resources. Across observations and video data, children consistently chose to interact with DUPLO^®.

One girl takes her figure to the mat and builds with DUPLO^® bricks. Her group member attaches the wagon to the robot and programs it to pick up the DUPLO^® (fruit). The girl continues playing with her DUPLO^® figure, putting two figures together. She is not paying attention to Blue-Bot, her friend calls her, but she is completely focused on her building.

(Note, 6, personal communication, 7 November 2023.)

This example illustrates that the girl preferred to continue her current activity rather than transition to the next task.

Another case involved a boy who repeatedly built crocodiles, the animal he initially created in the first task. When he saw an opportunity, he located the template and built another. Later, when instructed to use six DUPLO^® bricks to design a new animal and create a template, he once again chose to build a crocodile. Repeating this process thus involved pattern recognition and (unplugged) algorithmic thinking, aligning with the mathematical activity of designing.

The following note illustrates how some children engaged deeply with DUPLO^®, often preferring it over Blue-Bot:

A couple of girls start constructing their characters from drawings and leave the instructions they have been given to do a bit of what they want instead; they start building/creating/playing. The children often prefer creating with DUPLO^®. In some groups, children do not care about the robot; they build/play with DUPLO^®.

(Note, 1, personal communication, 7 November 2023.)

In the workshop, DUPLO^® also supported counting, pattern recognition, and grouping. Children manipulated blocks of varying sizes and colors to count and sort by size, shape, or color. When stacking two or six blocks, the children explored mathematical ideas through “telling” and play, expressing mathematics in their own intuitive way. These activities also fostered algorithmic thinking by requiring children to plan steps, select blocks, and decide how to assemble them, essentially creating their own instructions.

This is further illustrated in the following note:

Children are instructed to pick up a specific number of LEGO^® fruits in different colors (e.g., two yellow, two blue, two red, two green). To accomplish this task, children must count to ensure they collect the correct number of bricks in each color.

(Note, 4, personal communication, 7 November 2023.)

Grouping by color or stacking to create figures engaged the children in foundational mathematical operations, such as using quantifiers to determine “how many”—and understanding number relationships by combining blocks into patterns or structures. As stated in Observation note 4, the children also programmed Blue-Bot to move in specific sequences and directions to complete tasks, requiring them to plan and understand how the robot responded to commands.

5.3. Fostering Mathematical Learning Through Playful Design Tasks

In the first task of the workshop, children were instructed to build an animal from DUPLO^® using a template, allowing them to follow a set of steps and develop their algorithmic thinking. The children showed strong interest in examining and using the template, as illustrated in the following observation:

A boy concentrates and builds according to a drawing. Using the drawing, the educator compares what he built. The boy dismantles and rebuilds. The educator points to the drawing and shows how the blocks can be combined to follow the drawing.

(Note, 2, personal communication, 7 November 2023.)

In this observation note, the boy refers to the 1:1 DUPLO template (Figure 4b) as a guide to build his animal figure (Figure 4a). He aimed to replicate the model as closely as possible and required educator assistance to complete the task.

Building DUPLO^® structures based on templates fosters algorithmic thinking by visually breaking down the steps needed to achieve a desired outcome. This structured method helped children deconstruct complex tasks into manageable sequences. Following the drawings encouraged pattern recognition, logical sequencing, and attention to detail, skills central to both mathematical and computational thinking. While designing, children also played with geometric properties such as symmetry and proportion. This approach scaffolded their ability to visualize and recreate complex shapes, bridging abstract design and hands-on construction.

Templates served as effective tools for guiding children through design processes while reinforcing algorithmic thinking. A counting activity was subtly embedded in the template task, as children count blocks and arrange them in logical sequences. This supported early arithmetic development and introduced concepts of pattern and number relationships. In the example, the boy also engaged in measurement by building his crocodile in a 1:1 ratio with the template, developing fine motor skills, counting, measuring, and problem-solving abilities.

The next task is to draw a recipe for the animal they have made. There is a paper with squares and blocks in different colors. The girl puts her animal on the drawing and takes the crayon and fills in the squares. The boy has made a lion with red blocks at the bottom and starts filling in the squares.

(Note, 4, personal communication, 7 November 2023.)

Activities involving a 1:1 ratio facilitated children’s grasp of concepts of scale and proportion. This supported the development of spatial awareness by making abstract ideas, such as size relationships, tangible. Playing hands-on with scale also supported children in translating abstract mathematical ideas into concrete actions. When designing animals or drawing recipes, practical mathematical understanding was evident in the children’s use of measurement, ratio, and pattern recognition. These tasks demonstrate how foundational mathematical concepts naturally emerge through playful, hands-on engagement with DUPLO^®.

5.4. Collaborative Construction and Spatial Reasoning in Play

The final task in the workshop asked children to build a house for Blue-Bot using a 2D drawing as a guide to construct a 3D structure. This activity offered creative freedom while promoting collaboration, as children worked together and rotated roles within their groups. Figure 5a illustrates a completed 3D house created from a 1:1 template (Figure 5b). The child applied creative problem-solving to the house template by selecting different colors of DUPLO^® bricks and widening the structure to accommodate the Blue-Bot robot, demonstrating an integration of imaginative thinking and spatial reasoning.

This task encouraged children to design creatively and collaborate effectively. They alternated roles by gathering materials, constructing, and adjusting designs together. The following observation illustrates this dynamic:

The girl sits by the template while the boy collects bricks. After a while, they switch, and the girl collects bricks. They drive the robot into the building; the girl moves the structure around the robot. The boy constructs another building. The children build a wall and place it behind the robot, but it falls. They rebuild it. The boy adds a staircase, but it is too high. The girl suggests a change, and they collaborate by respecting each other’s contributions and offering suggestions when stuck.

(Note, 3, personal communication, 7 November 2023.)

This collaborative problem-solving process highlights key aspects of mathematical understanding and computational thinking (CT), as well as negotiation, collaborative decision-making and co-creation.

Constructing a 3D house from a 2D template required children to use spatial reasoning. They had to visualize how flat shapes could become a 3D structure, developing their understanding of geometry, height, balance, and dimensions. For example, when adding a staircase or rebuilding a fallen wall, the children used trial and error, driving the robot into the structure to test its stability and negotiating changes when needed. These actions reflect CT practices related to evaluation like debugging and iteration, where children test and revise their solutions in response to outcomes. The task also aligns with the mathematical category of “designing”, as children merged creativity with practical problem-solving, adapting designs and exploring relationships between structural elements.

Collaboration encouraged children to express ideas, justify decisions, and respond to peer feedback. When the staircase proved too tall, the group discussed alternatives, listened to each other, and adjusted their design accordingly. Logical reasoning emerged as they analyzed structural failures and proposed modifications, such as repositioning walls or redesigning components.

Using the 2D template, children translated abstract representations into concrete actions. Aligning their work with the visual guide supported symbolic thinking and spatial mapping. This way, an “explaining” activity is evident in how children communicated their reasoning and refined their designs iteratively. By arranging bricks to match the 2D layout, they engaged with direction, depth, and alignment, strengthening spatial reasoning. Rebuilding collapsed structures further deepened their understanding of proportion and structural integrity, illustrating a “locating” activity.

The children were also engaged in playful exploration by testing their constructions by driving the robot into them, and imagination by adding creative features like staircases. This playful approach encouraged experimentation and learning through trial and error.

Overall, the house-building task integrated a combination of mathematical activities, i.e., designing, explaining, locating, and playing, within a collaborative and exploratory environment. Through social interaction, creative problem-solving, and hands-on experimentation, children engaged with both computational concepts such as deconstruction, debugging and iteration as well as mathematical concepts such as spatial reasoning, geometry, and sequencing. This example underscores the value of combining structured tasks with open-ended play to foster both mathematical and computational understanding as well as social development through computational play.

6. Discussion

This study set out to investigate how young children encounter and develop mathematical ideas within play-responsive environments that integrate both analog and digital tools. The findings indicate that when learning activities are designed to be multimodal, narrative-driven (Portsmore & Milto, 2018; Cremin et al., 2013), and open-ended (Mattelmäki et al., 2011; Bartholomew & Strimmel, 2017), children can engage with and begin to appropriate core mathematical and computational ideas in ways that reflect their agency and imagination (Meek, 1995). Rather than following rigid sequences of skills, the environments studied supported play caraterized by openness, flexibility, and adaptability (Sutton-Smith, 1997; Pellegrini et al., 2007). For example, the design offered multiple entry points and allowed for diverse interpretations, illustrating the potential of what we term computational play (Bertel & Fredskilde, 2021; Brooks & Edstrand, 2023; Brooks et al., 2024). A central insight is that mathematics and computational thinking (CT) are not external bodies of knowledge to be introduced but are already implicitly present in children’s play (Clements & Sarama, 2020). This resonates with sociocultural views that position learning as situated and mediated by cultural tools (Vygotsky, 1978; Wertsch, 2007), and with Bishop’s (1988) contention that mathematics is a human activity embedded in everyday practices. In the present study, children engaged in counting, measuring, designing, and explaining through both analog construction and digital programming tasks, often simultaneously. For example, when designing a bridge or telling a robot where to go, children demonstrated mathematical reasoning and algorithmic thinking. They broke navigation tasks into smaller directional steps to guide the robot (algorithmic thinking) and collaborated to adjust commands when the robot failed to reach its target (problem-solving), closely mirroring the real-world functions of these disciplines (Peppler et al., 2016; Shumway et al., 2021). These observations highlight how integrating mathematics and CT within a playful, computational play framework can make abstract concepts tangible, meaningful, and developmentally appropriate (Weintrop et al., 2016; Bers et al., 2022; European Commission, 2023).

From a developmental perspective, this approach aligns with findings from Clements and Sarama (2024), who emphasize the importance of structured play environments in promoting abstract reasoning through concrete interaction. The inclusion of open-ended materials (Bartholomew & Strimmel, 2017) such as DUPLO^® bricks and narrative prompts (Cremin et al., 2013) created opportunities for visual patterning and spatial structuring, which research has shown are foundational to early algebraic and geometric thinking (Lüken, 2023; Inchaustegui & Alsina, 2020). These findings echo Seo and Ginsburg’s (2004) observations that children engage in complex mathematical reasoning long before formal schooling, provided the environment affords such activity. They also resonate with Portsmore and Milto (2018), who emphasize how narrative prompts can serve as vehicles for mathematics learning by inviting children into shared imaginative spaces where CT and mathematical explorations are naturally embedded. This suggests that educators can support early mathematical and computational thinking by designing activities that combine narrative contexts with opportunities for hands-on exploration and problem-solving.

A learning context combining analog and digital tools proved to be both productive and pedagogically demanding. Digital tools like Bee-Bot, while rich in potential, introduced abstract layers of logic and representation that were not always intuitively accessible, highlighting the need for intentional scaffolding and auxiliary representations (Nordby et al., 2024; Wang et al., 2022; Lee et al., 2022; Lv et al., 2023). At the same time, children engaged more readily with analog materials (e.g., DUPLO^®), which provided intuitue, tangible pathways into mathematical and computational concepts. These findings suggest that short, hands-on activities combining digital tools with unplugged, analog materials, embedded in playful, narrative-guided scenarios, can support both exploration and structured learning. Balancing guided instruction with open-ended, responsive play allows children to engage creatively while benefiting from scaffolding, emphasizing the crucial role of educators in shaping meaningful, interconnected learning experiences.

Aligned with previous research, the study affirms that CT need not be taught through explicit programming instruction alone. As Rahmawati et al. (2024) and Ye et al. (2023) note, CT can emerge when integrated into meaningful, narrative-rich, and exploratory experiences. Our findings extend this by showing how such experiences can align with Bishop’s six mathematical activities and Vygotsky’s view of imagination as a driver of cognitive development (Vygotsky, 1930/2004). When children collaboratively create a robot story or design a structure, they are not only engaging in imaginative play but also in sophisticated forms of abstraction, sequencing, and problem decomposition.

Finally, the findings highlight the role of the educator not as a mere deliverer of content but as a co-participant and designer of learning environments that respond to play. This aligns with calls for play-responsive pedagogy (Pramling et al., 2019; Wallerstedt & Pramling, 2023), where adult guidance, material affordances, and children’s intentions converge to create emergent learning experiences. Importantly, this perspective moves beyond viewing CT as a set of competencies to be transmitted, instead positioning it as a generative dimension of children’s meaning-making processes, shaped through intradtion, exploration, and play (Brooks & Sjöberg, 2023; Blikstein, 2018).

Building on these insights, the study proposes a reconceptualization of computational thinking and mathematics in early childhood as interdependent, embodied, and imaginative modes of sense-making. Within this perspective, computational play can be understood not merely as the integration of CT and mathematics within a playful framework, but as a pedagogical orientation that foregrounds children’s agency, material engagement, and narrative imagination as central to problem-solving. In this view, computational play is less about the mastery of predefined CT skills and more about cultivating conditions where children’s explorations with both unplugged analog and digital tools generate authentic opportunities for mathematical reasoning and computational thinking to co-develop. This expanded understanding positions computational play as a mediating space, where abstraction and creativity, logic and imagination, converge in developmentally meaningful ways.

While the small sample size and the study’s limited duration (a single workshop) present certain methodological constraints, these choices were deliberate given the exploratory character of the research. To ensure the collection of comprehensive and nuanced data, six researchers participated as observers and systematically documented the sessions. The intention was to generate context-specific insights that can inform the design of future, larger-scale investigations.

Accordingly, the findings should be interpreted as indicative and generative rather than definitive. Building on this foundation, future research could take the form of action research conducted over several weeks to track the development of children’s competencies. Such studies might examine how computational play evolves over time, the lasting effects of early experiences with analog and digital tools on mathematical reasoning and computational thinking, and how different scaffolding approaches and educator strategies shape engagement and the integration of computational play in early childhood settings. Insights from such research could directly inform the design of play-responsive curricula and professional development for educators, helping to operationalize computational play in ways that are developmentally appropriate and pedagogically meaningful.

7. Conclusions

This study demonstrates how play-responsive approaches that combine analog and digital tools can support young children’s engagement with early mathematical learning and computational thinking (CT). Drawing on Bishop’s (1988) six mathematical activities and a sociocultural framework, we examined how play-based interactions with DUPLO^® bricks and Blue-Bot robots supported competencies such as spatial reasoning, pattern recognition, sequencing, and problem-solving.

Our findings show that analog tools like DUPLO^® facilitated natural and spontaneous engagement with mathematical ideas. Through their construction and storytelling, children demonstrated intuitive understanding of patterns, spatial relations, and quantity. These activities often emerged without explicit instruction, highlighting the affordances of familiar, tangible materials in fostering early mathematical learning. Digital tools such as Blue-Bot, while offering opportunities to engage with CT concepts like sequencing and algorithmic logic, required more scaffolding and guidance from facilitators. Children’s engagement with the digital component was influenced by their comfort with abstraction, the clarity of the activity design, and the support provided.

The study highlights how the interplay of analog and digital tools can foster computational thinking and early mathematical learning in playful, child-centered environments. In particular, the unplugged analogue activities and the use of narrative often guided and structured the learning process. These findings have important implications for designing exploratory learning experiences in ECE, emphasizing play-responsive pedagogy and suggesting that educators can intentionally balance analog and digital materials to create developmentally appropriate pathways toward computational play.

In conclusion, this study contributes to a reconceptualization of computational thinking and mathematics in early childhood as intertwined, imaginative, and embodied forms of meaning-making. Within this view, computational play emerges as a pedagogical approach that enables these domains to co-develop through children’s playful exploration with both analog and digital tools. Narrative frameworks and unplugged analog activities, in particular, proved to be powerful drivers of children’s engagement and of their reasoning about possible solutions to tasks, illustrating how play can scaffold complex thinking. Rather than a framework for teaching discrete CT skills, computational play represents a generative space where mathematical reasoning and computational thinking are experienced as integrated, creative practices.