Abstract
This mixed-methods, quasi-experimental one-group pre–post study investigated whether a structured sequence of unplugged computational thinking (CT) activities embedded in regular primary mathematics lessons was associated with measurable changes in pupils’ CT practices and how such changes manifested in classroom interaction. Participants were 150 grade 4–5 pupils in a Vietnamese public primary school who completed eight 45-min, screen-free lessons aligned to five CT practices: decomposition, pattern recognition, abstraction, algorithm design, and evaluation/debugging. Quantitative analyses revealed statistically significant pre–post improvements across all five CT subscales (all
Introduction
Across the past two decades, education systems have moved beyond a narrow focus on literacy and numeracy toward competence-oriented curricula that foreground problem solving, modeling, and transferable reasoning. Within this shift, computational thinking (CT) has been widely promoted as a form of disciplined problem solving that can be expressed in procedures executable by humans or machines (Wing, 2006). Although rooted in computer science, CT is now treated as a cross-disciplinary construct with relevance for learning across STEM and beyond (Barr & Stephenson, 2011).
CT, however, is not a single, universally agreed construct. Definitions and component lists vary across frameworks and research traditions (Wu & Yang, 2022). To make our assumptions explicit and to support replicable classroom design and measurement, we adopt an operational definition aligned with taxonomy-oriented K-12 work (Li et al., 2020): CT is enacted through five observable practices—decomposition, pattern recognition, abstraction, algorithm design, and evaluation/debugging. This operationalization guides both (a) the design of our unplugged mathematics tasks and (b) the pre/post assessment of CT outcomes reported in this study. In primary mathematics, these CT practices are expected to surface through students’ mathematical thinking—for example, by using and revising representations, generalizing patterns, articulating stepwise strategies, and checking or comparing solutions.
Despite strong policy interest, three enduring challenges limit cumulative evidence and scalable practice. First, much of the CT evidence base originates in technology-rich contexts and plugged interventions, leaving open questions about how CT can be cultivated where device access is uneven, infrastructure is limited, or instructional time is tightly constrained (Chen et al., 2023). Second, many studies provide insufficient process-level explanation of how CT instruction connects to core mathematical processes (e.g., representational work, generalization, and strategic comparison) within authentic classroom activity, which weakens the theoretical justification for CT integration in mandated mathematics curricula (Chen et al., 2023; Wu & Yang, 2022). Third, empirical work focusing specifically on the primary grades remains comparatively limited and fragmented, constraining what we know about developmentally appropriate CT integration and its relationship to early mathematical learning trajectories.
Unplugged CT pedagogies—carefully designed, screen-free activities that externalize algorithmic ideas through manipulatives, games, and embodied enactment—offer a practical response to the first challenge by reducing reliance on hardware and software (Curzon et al., 2014). Crucially, they also speak to the second challenge: because the work is enacted publicly through talk, artifacts, and physical representations, unplugged tasks can be engineered to elicit and document mathematical processes (e.g., selecting and transforming representations, generalizing patterns, and justifying strategies), enabling clearer links between CT practices and mathematics learning mechanisms beyond technology effects (Battal et al., 2021; Chen et al., 2023). Nevertheless, rigorous evidence connecting unplugged CT to measurable CT growth and mechanism-consistent classroom processes in authentic primary mathematics lessons remains limited, especially in Global South contexts.
To address these gaps, we conducted an empirical study in a public primary school in a central Vietnamese city. Employing a mixed-methods, quasi-experimental (one-group pre–post) design, the study combines taxonomy-referenced quantitative measures with classroom observations, interviews, and student artifacts to examine both measurable outcomes and process-level mechanisms (Li et al., 2020; Ye et al., 2023).
Accordingly, the study pursues two aims: (i) to determine whether a structured sequence of unplugged CT activities embedded in regular mathematics lessons produces measurable gains in pupils’ CT practices and (ii) to identify and characterize the classroom mechanisms—such as representational work, strategic refinement and debugging, and forms of collaborative regulation—through which any observed gains may be explained.
Literature review
Computational thinking as a contested construct and our working stance
CT is widely promoted in K-12 education, yet it remains a contested construct with multiple definitions and partially overlapping component lists. In its influential formulation, Wing framed CT as a way of organizing problem solving in forms that can be carried out by humans or machines (Wing, 2006). Subsequent work broadened CT beyond computer science as a discipline, positioning it as a transferable competence relevant across domains (Barr & Stephenson, 2011). At the same time, this broadening has been noted to introduce conceptual ambiguity: depending on the lens adopted, CT may be treated as (i) computational practices closely tied to programming and automation, (ii) a general problem-solving competence emphasizing decomposition and abstraction, or (iii) an STEM-integrative practice involving modeling, representation, and data-based reasoning (Wu & Yang, 2022). This definitional plurality matters methodologically, because empirical studies often operationalize CT differently (e.g., coding performance, task-based problem solving, or self-report practices), complicating cross-study comparison and cumulative inference (Chen et al., 2023).
To make our assumptions explicit and the study replicable, we adopt an operational definition that is observable in primary mathematics classrooms. Following taxonomy-oriented frameworks (Li et al., 2020) and core theoretical formulations (Barr & Stephenson, 2011; Wing, 2006), we conceptualize CT as a constellation of practices that can be enacted without requiring programming syntax: decomposition, pattern recognition, abstraction, algorithm design, and evaluation/debugging. This five-practice operationalization serves two purposes in the present study: it (a) guides task design so that CT practices are elicited through mathematical activity and (b) supports age-appropriate measurement of CT-related outcomes aligned with school curricula (Li et al., 2020). Importantly, adopting a transparent operationalization does not deny definitional debates; rather, it clarifies the particular “slice” of CT that this study targets, enabling interpretable design decisions and cumulative dialogue with prior work.
Theoretical foundations for linking CT and mathematical thinking in primary mathematics
A clear connection between CT and mathematics education requires more than parallel lists of skills; it requires a theoretically grounded account of how CT practices can be instantiated through mathematical work. In mathematics education, mathematical thinking is commonly characterized by selecting and transforming representations, identifying and generalizing patterns, coordinating procedures with justifications, and evaluating correctness and efficiency through strategic comparison. These processes align closely with CT dimensions when CT is framed as practice rather than as “coding.”
In primary mathematics, decomposition and algorithm design can be understood as forms of problem structuring and proceduralization (e.g., splitting a multistep task into subgoals and coordinating ordered solution steps that can be communicated and repeated). Pattern recognition and abstraction align with generalization and the identification of invariants across examples, which are central to early algebraic reasoning and functional thinking. Representational work—foregrounded in school mathematics through diagrams, tables, symbols, and manipulatives—functions as a bridge: representations externalize structure, reduce cognitive load, and create objects that can be inspected, revised, and justified. Finally, evaluation
Pedagogical modality: Why unplugged activities matter
A persistent pedagogical question concerns modality—whether CT is best introduced through coding-intensive (“plugged”) environments or through screen-free (“unplugged”) activity. Unplugged approaches use manipulatives, games, and embodied enactments to externalize algorithmic ideas, reduce entry barriers, and foreground talk, reasoning, and collaboration (Curzon et al., 2014). Plugged approaches (e.g., block-based coding, robotics, and digital simulations) can support authentic execution, debugging, automated feedback, and iterative refinement, but typically require devices, software, and teacher preparation that are not uniformly available (Chen et al., 2023; Pala & Türker, 2019).
Table 1 summarizes recurring affordances, constraints, and instructional roles of unplugged versus plugged activities as synthesized from the literature rather than from author-only considerations. The listed strengths, weaknesses, and “ideal roles” reflect design considerations emphasized in unplugged pedagogy guidance (Curzon et al., 2014), empirical and review-based discussions of classroom feasibility and learning mechanisms (Battal et al., 2021; Chen et al., 2023), and recommendations for sequencing unplugged-to-plugged progressions to build conceptual foundations before formal execution when resources permit (Pala & Türker, 2019). We use this synthesis to motivate an unplugged-first intervention design that is developmentally suitable for primary learners and realistic under resource constraints.
Unplugged versus plugged activities in primary CT integration.
Unplugged versus plugged activities in primary CT integration.
Note. CT= computational thinking.
As Table 1 suggests, unplugged activities are particularly well-suited to establishing early conceptual foundations—such as decomposing a task, noticing invariants, and articulating stepwise procedures—under realistic classroom conditions. Plugged extensions can subsequently broaden execution and feedback loops (e.g., automated debugging) when infrastructure and teacher capacity allow (Chen et al., 2023; Pala & Türker, 2019). This modality logic provides a principled rationale for studying an unplugged-first sequence embedded in routine mathematics lessons, while still recognizing a coherent pathway toward later hybrid designs.
Empirical evidence on CT integration in school settings is promising but uneven, particularly in primary mathematics. Recent reviews highlight growing interest and a range of reported outcomes, while also emphasizing limitations that constrain cumulative inference: short-duration interventions, small samples, heterogeneous CT operationalizations, and technology-dependent designs that do not transfer easily to low-resource contexts (Chen et al., 2023; Ye et al., 2023). Practice-oriented work suggests that unplugged or hybrid designs can be feasible in classrooms and can leverage collaboration and teacher mediation to surface algorithmic structure and evaluative talk (Battal et al., 2021; Shiau-Wei et al., 2021). However, the literature also indicates two persistent weaknesses for mathematics education purposes. First, many studies foreground CT outcomes without articulating a sufficiently explicit linkage to mathematical processes such as representational fluency, generalization, or strategic comparison—the mechanisms that would justify CT integration within mandated mathematics curricula (Chen et al., 2023; Wu & Yang, 2022). Second, Global South contexts remain underrepresented in the empirical base, leaving open questions about contextual fit, equity of access, and scalable implementation under typical constraints.
Methodologically, stronger designs increasingly triangulate quantitative measures with qualitative evidence from interaction and student artifacts, document implementation fidelity, and report uncertainty and robustness checks (Ye et al., 2023). On measurement, taxonomy-referenced instruments grounded in explicitly stated CT dimensions support construct clarity and allow alignment with local curriculum aims (Li et al., 2020). At the same time, locally adapted instruments are not always validated across languages and contexts, making transparent documentation of adaptation and psychometric reporting essential for interpretability and reuse (Chen et al., 2023).
Taken together, prior work points to a clear gap: we need rigorous, context-sensitive evidence that (a) makes CT operationalization explicit (given definitional plurality), (b) articulates a principled linkage between CT practices and mathematical thinking, and (c) tests whether an unplugged-first, curriculum-aligned sequence can support CT practices in typical primary mathematics classrooms under realistic constraints. Accordingly, this study asks: (RQ1) Do unplugged CT activities embedded in regular mathematics lessons produce measurable gains on CT subscales in Grades 4–5? (RQ2) Through which classroom mechanisms (e.g., representational fluency, strategic refinement/debugging, collaborative regulation) do any gains appear to emerge?
Method
Design and mixed-methods integration
We employed an embedded mixed-methods, quasi-experimental (one-group, pre–post) design to examine the impact of a structured sequence of unplugged CT activities integrated into regular primary mathematics lessons. The quantitative strand provided the primary estimate of pre–post change in CT practices, while the qualitative strand (collected during enactment) was used to explain and corroborate how and under what classroom conditions such changes emerged through pupils’ participation, strategies, and representational work (Battal et al., 2021; Ye et al., 2023).
Integration was planned and implemented at three points. First, at the design level, the intervention tasks and all instruments were aligned to the same five-practice CT taxonomy (decomposition, pattern recognition, abstraction, algorithm design, and evaluation) (Li et al., 2020). Second, at the analysis level, quantitative subscale changes were linked to qualitative indicators using joint displays and taxonomy-aligned coding. Third, at the interpretation level, classroom evidence (field notes, interviews, and artifacts) was used to contextualize statistical patterns and to ground mechanism claims and practice-oriented implications.
To make complementarity across instruments explicit, Table 2 maps each research question (RQ) to the quantitative and qualitative evidence and the intended inferential role of each strand.
Alignment of research questions, instruments, and mixed-methods integration.
Alignment of research questions, instruments, and mixed-methods integration.
Note. CT= computational thinking.
The study was conducted in a public primary school in Hue City, Vietnam, serving a typical urban and peri-urban catchment. Participants were 150 pupils in grades 4–5 (approximately 9–11 years old; n = 150), with demographic characteristics broadly typical of the setting. These grades were selected because they represent a developmental period in which abstraction, representational fluency, and strategic reasoning become more stable within Vietnam's mathematics curriculum (MoET, 2020).
Students’ prior exposure to CT: Regarding the students’ prior knowledge, the participants had no formal exposure to CT or computer science curricula before the study. CT was not taught as a standalone subject in the participating classes. Based on teacher reports and a brief informal baseline check, pupils had limited explicit knowledge of CT terminology (e.g., “algorithm” and “debugging”). Their academic background was strictly limited to the standard primary mathematics curriculum, which focuses on arithmetic operations and traditional word problems. While they were familiar with related mathematical practices such as identifying patterns, describing step-by-step procedures, and checking solutions, the unplugged activities in this intervention represented their first structured encounter with systematic algorithmic reasoning and symbolic representation. This profile motivated an unplugged-first approach emphasizing concrete representations, embodied enactment, and classroom discourse before any technology-dependent experiences.
Intervention: Unplugged CT activity sequence
The intervention consisted of eight 45 min lessons embedded in existing mathematics units (e.g., number patterns and elementary geometry). Each lesson targeted one or more CT practices while remaining faithful to the mathematics learning goals. A detailed intervention protocol, including materials and enactment guidance, is provided in Supplemental Appendix A.
Classroom organization and role rotation
To support a practice-oriented experience, pupils worked in heterogeneous triads. Roles rotated across tasks to promote participation and collaborative regulation:
a Commander/Navigator who analyzed the map and planned the route, directly enacting decomposition and algorithm design; a Programmer/Mover who translated the plan into symbolic command strings on the worksheet, practicing representational fluency and abstraction; a Tester/Checker who executed the “program” using physical markers and monitored for errors, explicitly driving the evaluation/debugging process.
This structure encouraged pupils to externalize reasoning and engage in collective debugging. As illustrated in classroom photographs (see Supplemental Appendix A and Figure 4), the presence of a dedicated Checker tracing the path with a physical marker helped validate each command against the spatial constraints of the task.
Lesson structure and launch
Each lesson followed a consistent four-phase structure to scaffold a transition from concrete enactment to abstract symbolic representation:
Launch (5–8 min): The teacher framed the activity as a “navigation challenge.” CT language was introduced through worked examples rather than formal definitions. Team enactment (25–30 min): Groups enacted procedures using physical materials. The assigned roles made reasoning publicly inspectable. Share and compare (8–10 min): Groups presented algorithms; the class compared representations and efficiency. Evaluation/debugging (3–5 min): Groups tested their strategy, identified failure points, and refined command strings. This phase emphasized errors as productive information.
Core tasks and materials
Robot Grid Navigation: A core task was Robot Grid Navigation, targeting algorithm design, decomposition, and debugging. Pupils wrote movement command strings on a
As shown in Figure 1 (Group “Hope Supernach”), pupils documented an initial collision (“hit obstacle”), localized the faulty step, and produced a final corrected sequence. This behavioral shift was echoed in student reflections; one grade 5 pupil remarked: “At first, I thought a mistake meant I failed, but now I see it's just a signal to fix my arrows. It's like solving a puzzle.” This pattern of iterative testing aligns with the high effect sizes observed for evaluation/debugging (
An example of a student worksheet showing the iterative debugging process. The pupils identified a collision (“hit obstacle”), analyzed the failure, and provided a corrected command sequence. This qualitative artifact corroborates the gains observed in the evaluation/debugging subscale. CT = computational thinking.
Sorting Networks: A second task, Sorting Networks, focused on pattern recognition and abstraction (see Supplemental Appendix C for the full worksheet). Pupils enacted compare–swap routines by physically walking across a network drawn on the floor while holding number cards. At each comparison node, they followed a strict routing rule: the smaller number moved left, and the larger number moved right. This embodied enactment externalized algorithmic logic and supported pupils in articulating reusable rules (e.g., “the largest number always drifts to the far right”) and checking correctness through repeated runs.
Taken together, these tasks operationalized CT as observable classroom practices: unplugged activities externalized structure, reduced representational load, and made reasoning publicly inspectable through physical artifacts and collaborative discourse.
All instruments were aligned to the five-practice CT taxonomy to ensure construct consistency across strands (Li et al., 2020). Below we summarize each instrument and provide illustrative examples; full protocols and materials appear in the appendices listed.
CT assessment (quantitative)
CT practices were assessed using a 20-item instrument developed for this study and aligned with the five-practice CT taxonomy guiding the intervention (decomposition, pattern recognition, abstraction, algorithm design, and evaluation/debugging). The instrument was constructed by the authors drawing on established CT frameworks in mathematics and computing education (e.g., Li et al., 2020), and adapted to reflect classroom-based mathematical problem solving rather than programming proficiency.
Item development followed three steps: (1) mapping each item explicitly to one of the five CT constructs; (2) contextualizing statements to grade 4–5 mathematical activities enacted during the intervention (e.g., sorting tasks, grid navigation, and debugging routines); and (3) reviewing item wording for linguistic clarity and age appropriateness. Each subscale contained four items, yielding five subscales (4 items × 5 practices = 20 items).
Items were administered in Vietnamese using a five-point Likert response format (1 = strongly disagree to 5 = strongly agree). Subscale scores were computed by summing item responses within each practice and rescaled for comparability across constructs. The self-report format was selected for two reasons. First, for upper-primary pupils, short and activity-referenced Likert items are developmentally appropriate and feasible within regular lesson time. Second, the study aimed to capture students’ perceived engagement and metacognitive awareness of CT practices (e.g., noticing patterns, testing solutions, and revising steps) enacted during collaborative mathematical tasks.
Internal consistency reliability was examined using Cronbach's alpha. The overall scale demonstrated strong reliability (
Because self-report instruments measure perceived engagement rather than objective CT performance, responses may be influenced by metacognitive awareness, interpretation of items, or social desirability tendencies. To address this limitation, quantitative findings were triangulated with qualitative evidence from classroom observations, student artifacts, and semistructured interviews (see Supplemental Appendices D–F), thereby strengthening interpretive validity.
Sample items (illustrative):
Decomposition: “When a problem seems difficult, I can split it into smaller parts to solve one by one.” Algorithm design: “I can write clear step-by-step instructions so someone else can repeat my solution.” Evaluation: “I check my solution by trying another example or another method to see if it still works.”
Translation and construct validity: The Vietnamese version followed forward–backward translation with expert reconciliation. To verify the theoretically proposed five-factor structure of the instrument, a confirmatory factor analysis was conducted. The model fit indices demonstrated an acceptable to good fit to the data:
Classroom observation and artifacts (qualitative)
Classroom observations were guided by a structured protocol aligned to the five CT practices. Field notes focused on (i) representational moves (e.g., drawing, re-drawing, and use of manipulatives), (ii) strategy formation and revision, (iii) peer explanation and collaborative regulation, and (iv) evaluation/“debugging” moments (testing, identifying errors, and revising procedures). Student artifacts (annotated worksheets, strategy cards, and group outputs) were collected as complementary evidence of enacted CT and mathematical thinking. An anonymized observation excerpt with CT coding is provided in Supplemental Appendix E; sample integrated worksheets/artifact traces are provided in Supplemental Appendix F.
Student interviews (qualitative)
Semistructured interviews were conducted with a purposive sample of pupils (balanced by grade and gender) to elicit students’ perceived strategies, representational choices, and how they tested and revised solutions during the unplugged tasks. Interviews were time-constrained (approximately 5–7 min) and followed a rapid protocol consisting of seven core questions, with at most one brief follow up used when clarification was needed. Illustrative prompts include:
“Can you explain your group's steps so another group could follow them?” “Where did your first plan fail, and what did you change after that?” “Why did you choose this drawing/table/model instead of another one?”
The complete interview protocol (D6: Rapid Student Interview Protocol; 7 questions) is provided in Supplemental Appendix D.
Codebook and analytic categories (qualitative)
We used a codebook grounded in the CT taxonomy and refined inductively during analysis. Core categories included Decomposition talk, Pattern noticing, Abstraction/generalization, Algorithm articulation, Evaluation/debugging, and cross-cutting mechanism categories emphasized in the research questions (e.g., Representational fluency, Strategic comparison/strategy refinement, and Collaborative regulation). Coding conventions and an illustrative coded excerpt are provided in Supplemental Appendix E; tables supporting interpretation are provided in Supplemental Appendix G.
Procedures
After obtaining parental consent and pupil assent, the teacher implemented the eight-lesson sequence during regular mathematics periods. The CT assessment was administered 1 week before and 1 week after the intervention under standardized conditions. Observations were conducted across early and late lessons to capture shifts in classroom discourse and strategy use over time. Interviews were scheduled after selected lessons to elicit immediate reflections while minimizing disruption. Artifacts were collected at the end of each observed lesson and catalogued by lesson and group.
Data analysis and integration
Quantitative analysis: Score distributions were screened using normality checks (Shapiro–Wilk) and variance diagnostics (Levene). Pre–post changes were examined with paired t-tests on CT subscale scores, reporting effect sizes (Cohen's
Qualitative analysis: Qualitative evidence (classroom observations, interviews, and artifacts) was analyzed using reflexive thematic analysis (Braun & Clarke, 2006). Coding proceeded in two stages: (i) a deductive cycle anchored in the CT taxonomy (D, PR, A, AD, and E) and (ii) inductive refinement to capture classroom mechanisms relevant to the research questions (e.g., representational fluency, strategy refinement, and collaborative regulation). Discrepancies during double-coding of an initial subset were discussed to refine code definitions, after which the remaining corpus was coded using the stabilized codebook.
Mixed-methods integration: Integration was conducted through joint displays and meta-inferences. First, quantitative changes by CT subscale were aligned with qualitatively documented episodes and artifact traces from the corresponding lessons (Supplemental Appendices E and F). Second, evidence across sources was synthesized to determine whether findings converged (agreement), expanded one another (complementarity), or diverged (tension). These patterns were used to interpret both outcomes (what changed) and mechanisms (how change emerged) while grounding practice-oriented implications in observed classroom processes.
Additional details on measurement translation/validation checks and sensitivity analyses are provided in Supplemental Appendix H. Supplemental Appendix H summarizes the assumption screening and robustness checks used to corroborate the primary pre–post inferences.
Ethical considerations
Ethical approval was granted by the University of Education, Hue University. Informed consent (parents/guardians) and assent (pupils) were obtained. Data were anonymized and stored securely in accordance with Vietnam's Personal Data Protection Decree (No. 13/2023/ND-CP). Participation was voluntary and did not affect pupils’ grades or access to instruction.
Results
The findings are organized in relation to the two research questions (RQ1 and RQ2). Quantitative outcomes are presented together with convergent qualitative evidence—field notes, interview transcripts, and student artifacts—to illuminate both the magnitude of change (what changed) and the classroom processes through which change appeared to emerge (how change emerged).
RQ1: Changes in CT practices
Quantitative outcomes: Pre–post analyses indicate statistically significant gains across all five CT subscales: decomposition, pattern recognition, abstraction, algorithm design, and evaluation/debugging. Paired t-tests yielded large effect sizes (Cohen's d = 2.58–3.29, all p < .001), as summarized in Table 3. For illustration, algorithm design increased from M = 8.5 (SD = 2.1) to M = 14.7 (SD = 1.8), while pattern recognition increased from M = 9.1 (SD = 2.0) to M = 15.2 (SD = 1.7). Figure 2 depicts a consistent upward shift in mean scores across all subscales, accompanied by reduced dispersion postintervention.
Pre- and postintervention CT scores by subscale
Summary of paired
Note. CT= computational thinking.
While the observed effect sizes are substantial, they should be interpreted cautiously given the one-group pre–post design and the reliance on a self-report instrument. Accordingly, the results indicate marked within-cohort growth rather than definitive causal impact.
Qualitative corroboration: Classroom observations and artifacts provide process-level evidence that aligns with the quantitative gains. In the Sorting Networks task, pupils enacted the local compare–route rule (algorithm design) while simultaneously anticipating potential failure points and revising decisions (evaluation/debugging). They also articulated invariant patterns that were generalized beyond the immediate instance (pattern recognition and abstraction).
For example, in Obs-SN-03 (Supplemental Appendix E), a pupil predicted an incorrect output—“If you don’t swap here, then at the end the number 22 will be in the wrong place”—and subsequently generalized the network behavior—“the largest number is pushed step by step to the far right.” These episodes illustrate the coordination of procedural execution with reflective evaluation.
Similarly, in the Robot Grid task, pupils localized faulty commands and proposed specific revisions before re-testing their sequence (Obs-RG-05; Supplemental Appendix E). One group remarked, “Step 3 is wrong … we need to move forward one more square before turning,” demonstrating explicit identification of an error source followed by corrective action. Such episodes suggest that post-test improvements correspond to observable shifts in enacted computational practices rather than to test familiarity alone.
Thematic analysis identified three interrelated mechanism clusters that help interpret the observed gains.
Mechanism 1—Representational fluency (pattern recognition/abstraction): Across lessons, pupils increasingly coordinated embodied actions, verbal rules, and written notations. Representations compressed sequences of actions into reusable forms (e.g., “always/if–then” rules; command strings), making structural invariants more visible. This compression appears to support pattern recognition and abstraction by stabilizing shared reference points for reasoning.
Mechanism 2—Strategic reasoning and iterative debugging (algorithm design/evaluation): A second mechanism involved stepwise planning followed by iterative test–revise cycles. In Sorting Networks, the checker role supported anticipatory evaluation (Obs-SN-03; Supplemental Appendix E). In Robot Grid tasks, pupils localized faulty steps, revised command strings, and re-tested (Obs-RG-05; Supplemental Appendix F).
Artifacts revealed visible traces of revision, including crossed-out commands and color-coded corrections. Errors were treated as informational signals rather than terminal failures. This iterative refinement aligns with growth in evaluation/debugging and algorithm design, indicating convergence between enacted classroom practices and measured subscale development.
Mechanism 3—Collaborative regulation and social decomposition (decomposition): Role rotation and peer monitoring structured group interaction and distributed cognitive load. Pupils divided tasks into subcomponents (e.g., planner, executor, and checker), thereby enacting decomposition at a social level. Planning talk and worksheet segmentation (Obs-RG-02; Supplemental Appendices E and F) indicate that collaboration functioned not only as classroom management but as a mechanism supporting structured problem decomposition.
Taken together, these mechanisms suggest a coherent pathway from embodied, low-cost activity to the consolidation of CT practices within mathematics lessons. Unplugged tasks externalized structure, reduced representational load, and made reasoning publicly inspectable, thereby increasing opportunities for explanation, testing, and revision.
Summary
Across RQ1 and RQ2, quantitative and qualitative evidence converge toward an integrated account of change and mechanism. Pre–post improvements across CT subscales were observed alongside classroom-documented shifts in representational work, strategic planning and iterative debugging, and collaborative regulation. The joint display (Table 4) links subscale patterns to observed episodes and artifact traces, supporting an interpretation that unplugged activities functioned as epistemic scaffolds within this instructional context: they appeared to externalize algorithmic structure, stabilize shared problem frames, and expand opportunities for explanation and evaluation during regular mathematics lessons.
Joint display integrating quantitative CT gains with qualitative corroboration.
Joint display integrating quantitative CT gains with qualitative corroboration.
Note. CT= computational thinking.
This study examined whether a structured sequence of unplugged CT activities embedded in routine primary mathematics lessons can support the development of pupils’ CT practices in a Vietnamese public-school setting. Quantitative findings indicated substantial pre–post gains across five taxonomy-referenced CT practices (RQ1), while qualitative evidence documented mechanism-consistent shifts in representational work, iterative debugging, and collaborative regulation (RQ2). In this section, we interpret these findings in relation to prior theory and empirical research and articulate the conceptual progression from classroom evidence to pedagogical implications, grounding each step in documented episodes and artifacts (Supplemental Appendices A, E, and F).
Interpreting the gains: CT as enacted mathematical practice
The direction and breadth of gains align with theoretical accounts that position CT and mathematical thinking as overlapping forms of structured reasoning involving decomposition, abstraction, representation, and evaluation (Barr & Stephenson, 2011; Wing, 2006; Wu & Yang, 2022). By aligning both task design and measurement with Li et al.'s five-practice taxonomy (Li et al., 2020), the study examined CT as enacted within mathematical activity rather than as a decontextualized coding skill.
Importantly, the quantitative gains establish that measurable change occurred within the cohort (Table 3 and Figure 2). The joint display and field evidence (Table 4 and Supplemental Appendix E) clarify how these gains corresponded to observable classroom practices: pupils articulated invariants, recorded reproducible procedures, localized faulty steps, and revised representations. Given the one-group pre–post design, the results should be interpreted as evidence of substantial within-group growth rather than definitive causal impact. Nonetheless, the convergence between quantitative subscales and enacted practices strengthens the interpretive coherence of the findings.
Mechanisms linking unplugged activity to CT development
The qualitative analysis identified three interrelated mechanisms that help interpret the observed gains (RQ2).
Representational fluency: Across sessions, pupils increasingly coordinated embodied enactment, verbal articulation, and written notation. Representations compressed sequences of actions into reusable structures (e.g., “if–then” rules and command strings), making invariants more salient. This compression plausibly supported growth in pattern recognition and abstraction by stabilizing shared objects for inspection and generalization.
Strategic reasoning and iterative debugging: Observed test–identify–revise cycles in Sorting Networks and Robot Grid tasks (Supplemental Appendices E and F) indicate that pupils treated errors as informational signals rather than as terminal failures. Artifact traces—crossed-out steps, color-coded revisions, rewritten command strings—externalized iterative refinement. This pattern aligns with gains in algorithm design and evaluation/debugging, suggesting that structured opportunities for re-testing and revision were central to the developmental trajectory documented in RQ1.
Collaborative regulation and social decomposition: Role rotation (e.g., planner, mover, and checker) distributed cognitive load and structured explanation. Groups segmented tasks into subcomponents and monitored each other's reasoning, effectively enacting decomposition at a social level. This organization appears to have supported stable execution and reflective dialogue, corresponding to growth in decomposition-related practices.
Taken together, these mechanisms suggest a plausible pathway linking embodied, low-cost activity with the observed consolidation of CT practices in this context.
Positioning the contribution within existing research
Prior syntheses report promising effects of CT interventions but note methodological and contextual constraints, including small samples, short duration, and technology dependence (Chen et al., 2023; Ye et al., 2023). The present study contributes classroom-scale evidence
Consistent with prior discussions of modality (Battal et al., 2021; Chen et al., 2023; Curzon et al., 2014; Pala & Türker, 2019), the findings are consistent with a complementary rather than oppositional stance toward unplugged and plugged approaches. The observed mechanisms indicate that foundational CT practices can be enacted and consolidated without device reliance. Plugged extensions may later add affordances such as automated feedback or expanded iteration cycles, but the present evidence suggests that meaningful CT development does not require immediate access to digital tools.
Taken together, the findings articulate a coherent progression from classroom evidence to pedagogical implication. In contrast to technology-heavy narratives, substantial CT gains and mechanism-consistent practices were observed under unplugged conditions. These results support an unplugged-first progression that is context-sensitive and equity-aware, while remaining open to later hybrid designs when infrastructure and teacher capacity allow.
Implications for curriculum and instruction
The implications below derive directly from the mechanisms observed (RQ2) and the implementation structure documented in Supplemental Appendix A.
Integrate CT within existing mathematics units: Because CT practices emerged during routine mathematical problem solving, integration can occur through carefully designed task families embedded in core content (e.g., ordering, patterns, and grid navigation). Recurrent structures enable repeated enactment of decomposition, abstraction, and evaluation without displacing curricular time.
Make invariants visible through representation: Embodied comparison followed by explicit notation (diagrams, rules, and command strings) supported pattern recognition and abstraction. Instructionally, sequencing enactment with representation appears to help pupils compress actions into transferable structures.
Institutionalize structured debugging routines: Short cycles requiring groups to test on a new instance, locate failure steps, and revise procedures for peer execution operationalize evaluation as a classroom norm. The artifact evidence suggests that making revision visible strengthens engagement and procedural clarity.
Stabilize collaboration through explicit roles: Role rotation and peer monitoring structured explanation and verification, particularly in larger classes. Explicitly scripting planner/executor/checker roles may support decomposition and reflective regulation under realistic classroom constraints.
Implications for teacher learning and assessment
Practice-based refinement cycles: Teacher prompts that externalized reasoning (e.g., identifying which step failed) appeared to mediate mechanism activation. Professional learning structured around short design–enact–reflect cycles, using artifacts and brief observation notes, may strengthen alignment between intended and enacted CT practices.
Assessment triangulated with artifacts: Because pupils produced observable traces of CT practices (Supplemental Appendix F) aligned with the taxonomy-referenced instrument (Li et al., 2020), teachers can triangulate rubric judgments with classroom artifacts. This approach enhances interpretability and reduces reliance on test-only evidence.
Staged unplugged-to-plugged progression: In this context, unplugged materials were sufficient to elicit measurable growth and mechanism-consistent practices (RQ1 and RQ2). A staged approach—conceptual consolidation first, selective technological extension later—aligns with the complementary affordances described in prior reviews (Chen et al., 2023; Pala & Türker, 2019).
Limitations and future directions
Several limitations qualify interpretation. First, the quasi-experimental single-site design constrains causal inference and generalizability. Second, long-term retention and transfer to mathematics achievement were not examined. Third, although reliability indices were adequate, cross-context measurement invariance was not tested. Future research should include comparison conditions, longitudinal follow up, and cross-site replication, while examining how specific task features most reliably activate representational fluency, iterative debugging, and collaborative regulation.
Conclusion
Within the bounds of a classroom-based quasi-experimental design, the findings provide convergent evidence that carefully structured unplugged CT activities can be integrated into primary mathematics lessons and are associated with substantial growth in taxonomy-referenced CT practices. By linking measurable outcomes with observable mechanisms, the study contributes to a context-sensitive account of CT integration—conceptual foundations enacted through mathematical activity, with technological extensions added as capacity permits—responsive to curricular demands and resource constraints.
Supplemental Material
sj-pdf-1-mea-10.1177_27527263261447560 - Supplemental material for Fostering computational thinking in primary mathematics through unplugged activities: Evidence from a Vietnamese case study
Supplemental material, sj-pdf-1-mea-10.1177_27527263261447560 for Fostering computational thinking in primary mathematics through unplugged activities: Evidence from a Vietnamese case study by Manh Ha Le in Asian Journal for Mathematics Education
Footnotes
Ethical Considerations
Ethical approval was granted by Hue University of Education, Hue University.
Consent to Participate
Informed consent was obtained from all participants involved in the study, as well as from the pupils’ parents or legal guardians prior to data collection.
Funding
The author received no financial support for the research, authorship, and/or publication of this article.
Declaration of Conflicting Interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Data Availability Statement
De-identified data and materials are available from the corresponding author upon reasonable request, subject to applicable ethics approval and data protection requirements.
Use of AI Tools
AI-assisted tools were used for language editing and structural refinement only. All methodological decisions, analyses, interpretations, and final wording are the author’s responsibility.
Supplemental Material
Supplemental material for this article is available online.
Author biography
References
Supplementary Material
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