Playful and physically active mathematics learning in primary education: an exploratory comparison of pupils in schools with and without the darts math program

1 Introduction

Educational approaches that combine active participation, play, digital feedback, and curriculum-linked problem solving have received growing attention in mathematics and STEM education. Classroom-based physical activity has been associated with academic and cognitive outcomes, although effects vary across intervention design, exposure, age group, and outcome domain (Donnelly et al., 2016; Mavilidi and Vazou, 2021; Mullender-Wijnsma et al., 2016). Digital learning environments can also support immediate feedback, adaptive practice, and learner engagement when their design is closely aligned with instructional goals (Barana et al., 2021; Christopoulos and Mystakidis, 2023).

The Darts Math Program (DMP) combines these features within mathematics instruction. Pupils solve curriculum-related mathematical problems in connection with dartboard-based tasks, make decisions about possible solutions, receive immediate feedback, and repeat calculations and strategies across successive attempts (Bogdán, 2021). The program can therefore be understood not simply as gamification or physical activity, but as a learning environment in which movement, mathematical reasoning, feedback, and social participation are integrated.

1.1 Playful and physically active learning in mathematics education

The playful learning framework provides a useful lens for describing the pedagogical characteristics of the DMP. Bustamante et al., 2021 and related work on playful learning emphasize active, engaging, meaningful, social, iterative, and joyful learning. These characteristics are identifiable in the DMP at the level of instructional design. Throwing and interacting with the dartboard make the activity physically active; the digital interface and immediate feedback can sustain engagement; tasks remain meaningful because they are linked to the mathematics curriculum; whole-class and small-group use creates opportunities for social participation; and repeated attempts create an iterative cycle of calculation, feedback, correction, and retrying. The game-like format also gives the activity a potentially joyful character, although the present study does not directly measure joy or other affective outcomes.

Physically active learning may be relevant to mathematics because coordinated movement and visuospatial processing occur alongside calculation and decision making. Motor and cognitive development are related during childhood, and coordinated hand movements have been discussed in relation to school performance and cognitive development (Cameron et al., 2016). Activities involving aiming, spatial orientation, planning, and feedback recruit processes relevant to visuomotor control and decision making (Latash and Zatsiorsky, 2016; Olson and Colby, 2013). However, transfer from these processes to mathematics cannot be assumed. The motor demands of aiming and throwing may also compete for attention or working-memory resources. Consequently, the DMP should be evaluated empirically rather than treated as inherently beneficial.

This balance is important because meta-analytic and review evidence indicates that gamification and physically active learning do not produce uniform effects across settings or outcomes (Dicheva et al., 2015; Donnelly et al., 2016; Sailer and Homner, 2020; Toda et al., 2020). Design quality, curricular integration, exposure, learner characteristics, and implementation context may all shape observed differences.

In school practice, the DMP can be integrated into regular mathematics instruction through short activities in which pupils calculate, select strategies, interact with a dartboard, and receive immediate digital feedback. The program can be used in whole-class and small-group settings and is intended to complement, rather than replace, curriculum-based mathematics instruction. For pupils from Grade 3 onward, described task formats include number-selection, sector-puzzle, and calculation activities that practice the four basic operations and require pupils to identify or combine dartboard values, including single, double, and triple sectors (Bogdán, 2021).

1.2 Study aim and research questions

The aim of the present study was to compare mathematics and cognitive performance between third- and fourth-grade pupils attending schools with established DMP use and pupils attending comparable schools following the general mathematics program. The study was intended to identify domain-specific patterns that could inform more rigorous future research; it was not intended to estimate causal program effects.

The following exploratory research questions were addressed:

• RQ1: What differences can be observed between pupils in the DMP and GP groups in mathematics performance, and are the principal group differences robust to adjustment for grade level?
• RQ2: What differences can be observed between pupils in the DMP and GP groups in cognitive performance, and are the principal group differences robust to adjustment for grade level?

2 Materials and methods

The total sample consisted of 124 pupils in Grades 3 and 4. Seventy pupils attended the two schools implementing the Darts Math Program (DMP), whereas 54 attended the two schools following the general program (GP). The DMP group included 31 third-grade and 39 fourth-grade pupils, while the GP group included 25 third-grade and 29 fourth-grade pupils. Grade composition did not differ significantly between the groups, χ²(1) = 0.05, p = 0.823. A summary of the sample characteristics is presented in Table 1. The DMP group comprised 33 boys and 37 girls and had a mean age of 10.03 years (SD = 1.19). The GP group comprised 22 boys and 32 girls and had a mean age of 10.01 years (SD = 1.08). No individual-level socioeconomic-status or ethnicity variables were available in the study dataset. These characteristics therefore could not be described with validated indicators or included as covariates and should be regarded as unmeasured potential confounders rather than inferred from broad school-level characterizations.

Table 1. Characteristics of the study sample.

DMP, darts math program; GP, general program.

The research was conducted with the support of the participating school leadership. Parents or legal guardians provided written informed consent for pupil participation. Ethical approval was granted by the Research Ethics Committee of Eszterházy Károly Catholic University under approval number RK/90/2025.

2.1 Study design and setting

A cross-sectional, non-randomized comparative design was used. The study involved third- and fourth-grade pupils from four primary schools in Northern Hungary. Schools were selected purposively based on existing Darts Math Program (DMP) implementation and on comparable institutional characteristics, including settlement type, school size, and geographic region. Two schools had implemented the DMP in both Grades 3 and 4, whereas two comparison schools followed their general mathematics program without DMP implementation.

Program exposure was therefore determined at the school level rather than through random assignment. Consequently, school- and teacher-level characteristics are inherently linked to group membership and cannot be disentangled from the DMP–GP comparison in the present design. The study should therefore be interpreted as an exploratory comparison of existing educational conditions rather than as an evaluation of causal program effects.

2.2 Participants

The total sample consisted of 124 pupils in Grades 3 and 4. Seventy pupils attended the two schools implementing the Darts Math Program (DMP), whereas 54 attended the two schools following the general program (GP). The DMP group included 31 third-grade and 39 fourth-grade pupils, while the GP group included 25 third-grade and 29 fourth-grade pupils. Grade composition did not differ significantly between the groups, χ²(1) = 0.05, p = 0.823. A summary of the sample characteristics is presented in Table 1. The DMP group comprised 33 boys and 37 girls and had a mean age of 10.03 years (SD = 1.19). The GP group comprised 22 boys and 32 girls and had a mean age of 10.01 years (SD = 1.08). At the school level, the participating institutions had highly homogeneous student populations: approximately 99% of pupils belonged to the same ethnic group, and the schools predominantly served socioeconomically disadvantaged student communities.

The research was conducted with the support of the participating school leadership. Parents or legal guardians provided written informed consent for pupil participation. Ethical approval was granted under approval number RK/90/2025.

2.3 Educational conditions

2.3.1 DMP condition

At the time of data collection, pupils in the DMP schools had been exposed to the program for approximately one academic year. The program was used twice per week during regular school instruction, typically in 20 min units, and was delivered by the pupils' regular primary school teachers. A typical unit followed a recurring sequence: the teacher introduced a curriculum-linked numerical problem or target; pupils calculated possible solutions and selected a strategy; pupils then completed the corresponding dartboard task; the digital interface provided immediate feedback; and pupils recalculated, revised their strategy, and repeated the task as needed, followed by brief whole-class or small-group discussion of alternative solutions. In Grades 3–4, the program can use number-selection, sector-puzzle, and calculation formats involving addition, subtraction, multiplication, and division with values represented on the dartboard, including single, double, and triple sectors (Bogdán, 2021). Before implementation, the participating teachers attended a preparatory workshop held over one afternoon. The workshop covered the practical use of the Darts Math Program, the integration of dartboard-based and digital activities into mathematics lessons, classroom organization, and the main procedures required for program delivery.

2.3.2 General program condition

Pupils in the GP schools followed conventional mathematics instruction delivered by their regular primary school teachers. Mathematics lessons did not include the DMP, movement-integrated mathematics activities, or the routine use of digital devices for mathematics learning. Desktop computers were available during information technology lessons but were not used as a regular component of mathematics instruction. The GP pupils were taught by teachers from their own schools; consequently, the same teachers did not teach pupils in both study conditions.

2.4 Measures

2.4.1 Mathematics assessment

Mathematical performance was assessed using a curriculum-aligned achievement test developed by mathematics educators. The assessment comprised six task blocks covering number representation and place value, number ordering, arithmetic with positive and negative numbers, mirror symmetry, and spatial geometry. For descriptive purposes, Tasks 1–4 represented predominantly number-, arithmetic-, and algebra-related content, whereas Tasks 5–6 represented geometry-related content. The algebra and geometry domain scores used in the analyses were derived from the corresponding task blocks according to the study scoring protocol and were analyzed separately alongside the total mathematics score.

The scoring protocol used in the present study yielded a maximum total score of 100 points.

Grade-appropriate versions followed the same general assessment framework, with task content and difficulty adapted to the curriculum and developmental level of the respective grade. Internal consistency in the present sample was acceptable (Cronbach's α = 0.779). The assessment has not undergone independent formal psychometric validation and should therefore be interpreted as a curriculum-based achievement measure rather than a standardized validated test. The structure of the mathematics assessment, including the maximum scores and observed score ranges in the present sample, is presented in Table 2.

Table 2. Structure and scoring of the curriculum-aligned mathematics assessment.

2.4.2 Cognitive assessment

Cognitive performance was measured using selected tasks from the Gyarmathy Cognitive Profile Test (Gyarmathy, 2009). The analyzed domains were figure-based reasoning, shape recognition, directions, attention, and spatial perception, together with a cognitive total score. The maximum score for the applied cognitive battery was 50 points. Internal consistency was good in the present sample (Cronbach's α = 0.807). The applied cognitive tasks, their maximum scores, and the observed score ranges in the present sample are presented in Table 3.

Table 3. Applied tasks from the cognitive profile test.

2.5 Data collection procedure

Data collection took place after approximately one academic year of existing DMP use in the participating DMP schools. The researchers did not randomly assign pupils or schools to conditions and did not introduce the DMP as part of the study. Mathematics and cognitive assessments were administered to pupils in both conditions using the same study procedures. The design therefore represents a cross-sectional observational comparison of existing educational conditions.

2.6 Statistical analysis

Analyses were conducted on the final dataset of 124 pupils using IBM SPSS Statistics 25. Descriptive statistics were calculated for all outcomes. Distributional assumptions were examined with Shapiro–Wilk tests within each group, and equality of variances was assessed with Levene's test. Independent-samples Student's t tests were used when homogeneity of variance was supported; Welch's t tests were used for figure-based reasoning, cognitive total score, and mathematics total score because Levene's test was significant for these outcomes. Cohen's d was reported as an effect-size estimate together with 95% confidence intervals.

To address multiplicity, Holm familywise-error correction was applied separately within the mathematics outcome family (three outcomes) and the cognitive outcome family (six outcomes), reflecting the two prespecified research questions and the conceptual distinction between the two outcome domains. Both unadjusted and Holm-adjusted p values are reported, with inferential emphasis placed on the adjusted results. Robustness to grade level was examined using the General Linear Model procedure. Grade and group were first entered as categorical fixed factors in full-factorial models to test group-by-grade interactions. Because no interaction was statistically significant, additive models containing group and grade were then used to estimate grade-adjusted group main effects. The same family-specific Holm correction was applied separately to the mathematics and cognitive grade-adjusted group effects. Partial eta squared (ηp²) was reported for the adjusted group effects.

A sensitivity analysis was conducted to characterize the detectable effect size for the two-group comparison. With n = 70 and n = 54, a two-sided α = 0.05, and 80% power, the design could reliably detect an effect of approximately d = 0.51. Accordingly, non-significant findings should not be interpreted as evidence of equivalence or absence of smaller effects.

3 Results

3.1 Assumption checks and grade composition

The DMP and GP groups had similar grade composition, χ²(1) = 0.05, p = 0.823. Shapiro–Wilk tests did not indicate departures from normality for any analyzed outcome within either group (p ≥ 0.188). Levene's test indicated unequal variances for figure-based reasoning (p = 0.003), cognitive total score (p = 0.004), and mathematics total score (p = 0.035); Welch's t test was therefore used for these outcomes. Levene's tests for the remaining outcomes were non-significant.

3.2 Group differences in mathematics performance

The DMP group had a higher mean algebra score (M = 44.16, SD = 14.92) than the GP group (M = 38.24, SD = 14.82), t(122) = 2.210, unadjusted p = 0.031, d = 0.40 (Table 4). This difference did not remain statistically significant after Holm correction within the mathematics outcome family (adjusted p = 0.093). Geometry scores were nearly identical between groups, t(122) = 0.110, p = 0.909, d = 0.02. The DMP group also had a higher total mathematics mean (M = 51.20, SD = 14.75) than the GP group (M = 45.16, SD = 19.71), but the Welch test was not statistically significant, t(95.06) = 1.880, p = 0.063, Holm-adjusted p = 0.126, d = 0.35. The mathematics results are demonstrated in Table 4. Thus, no mathematics outcome met the Holm-adjusted significance criterion.

Table 4. Mathematics performance in the DMP and GP groups.

Student's t-tests were used when the homogeneity of variance assumption was met. Welch's t-test was used for total mathematics because Levene's test indicated unequal variances. Holm-adjusted p values were calculated within the mathematics outcome family comprising the three mathematics outcomes.

3.3 Group differences in cognitive performance

Among the cognitive outcomes, the DMP group had higher spatial-perception scores (M = 4.52, SD = 0.78) than the GP group (M = 4.20, SD = 0.85), t(122) = 2.180, unadjusted p = 0.031, d = 0.39 (Table 5). The DMP group also had a higher cognitive total score (M = 37.92, SD = 7.65) than the GP group (M = 35.41, SD = 5.01); because variances differed, the Welch test was used, t(119.12) = 2.201, unadjusted p = 0.030, d = 0.38. Neither contrast remained statistically significant after Holm correction within the cognitive outcome family (both adjusted p = 0.180). Figure-based reasoning, shape recognition, directions, and attention showed no statistically significant group differences. Full descriptive and inferential results for the cognitive outcomes are presented in Table 5. Consequently, no cognitive outcome met the multiplicity-adjusted significance criterion.

Table 5. Cognitive performance in the DMP and GP groups.

Student's t-tests were used when the homogeneity of variance assumption was met. Welch's t-tests were used for figure-based reasoning and cognitive total score because Levene's test indicated unequal variances. Holm-adjusted p values were calculated within the cognitive outcome family comprising the six cognitive outcomes.

3.3.1 Robustness to grade level

In the full-factorial general linear models, no group-by-grade interaction was statistically significant, indicating no evidence that the DMP–GP contrast differed between Grades 3 and 4. In additive models containing group and grade as categorical fixed factors, the group term was nominally significant for algebra, F = 4.70, p = 0.032, ηp² = 0.037; spatial perception, F = 4.85, p = 0.029, ηp² = 0.039; and cognitive total score, F = 4.32, p = 0.040, ηp² = 0.034. Total mathematics approached but did not reach the conventional threshold, F = 3.76, p = 0.055, ηp² = 0.030. None of the grade-adjusted group effects remained significant after family-specific Holm correction (adjusted p = 0.096 for algebra, 0.110 for total mathematics, 0.174 for spatial perception, and 0.200 for cognitive total score). The grade-adjusted analyses therefore reproduced the direction of the unadjusted exploratory findings without providing multiplicity-adjusted confirmatory evidence. Grade robustness analyses are summarized in Table 6.

Table 6. Grade-adjusted general linear model analyses.

Grade was entered as a categorical fixed factor (Grade 3 vs. Grade 4). Grade-adjusted group effects were obtained from additive general linear models including group and grade. Group × grade interactions were obtained from full-factorial models. Holm-adjusted p values for the grade-adjusted group effects were calculated separately within the mathematics outcome family (three outcomes) and the cognitive outcome family (six outcomes).

4 Discussion

The present study compared mathematical and cognitive performance in pupils attending schools with approximately one academic year of DMP exposure and pupils attending comparison schools using conventional mathematics instruction. The central result is not a confirmed DMP advantage: none of the mathematics or cognitive group comparisons remained statistically significant after Holm correction within their respective outcome families. Rather, the unadjusted analyses showed small-to-moderate differences in algebra, spatial perception, and cognitive total score, and grade-adjusted models reproduced these same nominal patterns. These findings are best interpreted as exploratory signals rather than evidence of program effectiveness.

4.1 Mathematics findings

The mathematics findings do not provide multiplicity-adjusted evidence that pupils in the two educational conditions differed systematically in mathematics performance. The unadjusted algebra contrast favored the DMP group with a small-to-moderate effect, while the total mathematics contrast was of similar direction and magnitude but did not reach the conventional significance threshold. Adjustment for grade did not materially alter the algebra pattern, but the adjusted result also failed to survive Holm correction within the mathematics outcome family. Algebra may therefore represent a useful target for future confirmatory research rather than a domain in which the present study establishes a DMP-related advantage.

Taken together, the mathematics results suggest a selective rather than broad pattern of group differences. This selectivity is consistent with the wider literature on physically active and game-supported learning, in which academic effects vary across intervention characteristics, outcome domains, and educational contexts rather than appearing uniformly across all measures (Donnelly et al., 2016; Mavilidi and Vazou, 2021; Mullender-Wijnsma et al., 2016). Similarly, research on gamification has reported heterogeneous effects across learning outcomes and has emphasized the importance of instructional design and context in shaping observed results (Dicheva et al., 2015; Sailer and Homner, 2020).

The relatively limited instructional dose of two 20-minute DMP sessions per week, delivered alongside regular mathematics instruction, may also be relevant when interpreting why the observed patterns were selective rather than broad across all mathematical domains. The observed algebra pattern may therefore warrant further investigation in studies specifically designed and adequately powered to test domain-specific differences.

4.2 Cognitive findings and possible mechanisms

The cognitive results were similarly selective and exploratory. Spatial perception and the cognitive total score were nominally higher in the DMP group before multiplicity correction, with small-to-moderate effect sizes. Grade-adjusted models yielded the same nominal pattern, although neither effect survived Holm correction within the cognitive outcome family. The recurrence of these domain-specific patterns across both unadjusted and grade-adjusted analyses suggests that spatial processing may represent a particularly relevant area for further investigation.

This pattern is theoretically compatible with research linking motor coordination, visuospatial processing, and aspects of children's academic and cognitive functioning (Cameron et al., 2016). The aiming, spatial orientation, calculation, and feedback demands embedded in dartboard-based activities also provide a plausible basis for examining visuospatial processes more specifically, although the present findings do not establish a transfer mechanism (Latash and Zatsiorsky, 2016; Olson and Colby, 2013).

These findings add useful empirical evidence to the still limited research base on the Darts Math Program and help identify cognitive domains that may be most informative in future studies. In particular, the spatial-perception pattern provides a focused basis for developing and testing more specific hypotheses about the relationship between playful, movement-integrated mathematics activities and cognitive performance.

Viewed through the playful learning framework, these patterns emerged in an educational setting that combined active participation, meaningful curriculum-linked tasks, immediate digital feedback, social interaction, and repeated opportunities for iterative practice (Bustamante et al., 2021). Rather than treating these characteristics as outcomes themselves, the present study provides an empirical basis for future research examining which dimensions of playful learning may be most closely related to specific mathematical and cognitive outcomes.

4.3 Practical significance

The present study provides practically useful information about the magnitude and pattern of differences observed between pupils in DMP and GP educational settings. Effect sizes ranged from trivial to small-to-moderate, with the largest contrasts observed in algebra, spatial perception, and cognitive total score (d = 0.38–0.40). These domain-specific effects are particularly informative because they identify areas in which future research can formulate more focused hypotheses and estimate the sample sizes required for adequately powered confirmatory studies.

The sensitivity analysis indicated that the present sample was adequately powered primarily for effects of d = 0.51 or larger. The largest observed effects therefore fell below the effect size that the study was optimally positioned to detect. This finding is important for interpretation: the absence of multiplicity-adjusted statistical significance does not exclude smaller differences that may still be educationally meaningful. Rather than supporting broad claims of program effectiveness, the results provide a clear empirical basis for prioritizing specific mathematical and cognitive domains in subsequent longitudinal and experimental research.

From a practical research perspective, the study therefore contributes by narrowing the range of plausible outcomes, identifying the domains in which the strongest patterns emerged, and providing effect-size estimates that can directly inform the design and statistical planning of future DMP studies.

4.4 Limitations and future research

The cross-sectional, non-randomized design limits causal interpretation because the study captures group differences at a single point in time and does not establish temporal ordering. In addition, the study included only four purposively selected primary schools from Northern Hungary, which limits the extent to which the findings can be generalized to other educational settings and pupil populations.

The curriculum-aligned mathematics assessment was developed for educational use and showed acceptable internal consistency in the present sample, but it has not undergone independent formal psychometric validation. Separate grade-appropriate versions were used for Grades 3 and 4; although they followed the same general task structure and scoring framework, their cross-grade measurement equivalence has not been formally established. Domain-level mathematics findings should therefore be interpreted with appropriate caution.

The sensitivity analysis also indicated that the available sample was adequately powered primarily for effects of d = 0.51 or larger. Because the largest observed effects were smaller than this threshold, the study may have had limited ability to detect smaller but potentially educationally meaningful differences.

Future research would benefit from longitudinal or experimental designs incorporating baseline and follow-up assessments, larger samples, and a greater number of participating schools. Randomized or carefully matched comparison designs would provide stronger evidence regarding program-related differences, while a larger number of school and classroom clusters would also allow the use of multilevel analytical approaches. Future studies should additionally employ independently validated mathematics measures and examine the reproducibility of the domain-specific patterns identified in the present study. Particular attention could be given to algebra and spatial processing, where the most consistent exploratory differences emerged, including theoretically specified pathways examining whether changes in visuospatial processing precede or statistically mediate changes in specific mathematics outcomes, particularly algebra-related performance.

5 Conclusion

The present study contributes new empirical evidence on the Darts Math Program by identifying a selective pattern of mathematical and cognitive differences across the examined educational settings. The most consistent signals emerged in algebra, spatial perception, and overall cognitive performance, suggesting that these domains may be particularly relevant for understanding how playful and physically active mathematics learning relates to pupil outcomes.

Rather than indicating a broad and uniform pattern across all measured domains, the findings help define more specific and theoretically meaningful directions for subsequent research. By providing domain-level effect-size estimates and identifying the outcomes in which the clearest exploratory patterns emerged, the study offers a useful empirical foundation for the design of larger longitudinal, matched, and experimental investigations. In this way, the present findings advance the emerging evidence base on playful, movement-integrated mathematics learning and provide focused targets for future evaluation of the DMP.

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Footnotes

Edited by: Karyn Allee, Mercer University, United States

Reviewed by: Eduardo Gutiérrez-Turner, Universidad Adventista de Chile, Chile

Zaid Alkouri, Al-Balqa Applied University, Jordan