Research Proposal – Gamification and Engagement in Primary School Mathematics

Introduction

Numeracy underpins later academic achievement, workforce participation and everyday decision making, yet securing sustained engagement with mathematics is difficult across the primary years. National monitoring gives repeated cause for concern about Australian students’ mathematics outcomes. The most recent cycle of the OECD Programme for International Student Assessment recorded a long-run softening in mathematical literacy before a modest stabilisation, and a substantial share of students continues to perform below the national proficient standard on the National Assessment Program, Literacy and Numeracy (NAPLAN) (Thomson et al., 2023; Australian Curriculum, Assessment and Reporting Authority [ACARA], 2023). The Grattan Institute has argued that these results reflect a systemic problem rather than isolated underperformance, and that lifting the quality and appeal of mathematics teaching in the primary years is a national priority (Hunter & Haywood, 2025).

At the same time, digital tools have become routine in Australian primary classrooms. Adaptive practice platforms, tablet applications and web-based games are now widely used to supplement mathematics instruction, and the Australian Education Research Organisation (AERO) identifies student engagement as a mediating condition for the effectiveness of any such tool (AERO, 2023). Gamification, defined as the use of game design elements such as points, badges, levels, narrative and challenge in non-game contexts, has attracted particular interest as a low-cost way to make routine numeracy practice more motivating (Deterding et al., 2011). Whether gamification produces durable gains in engagement and achievement, however, or merely a short-lived novelty response, remains contested.

Problem statement

Two problems motivate this proposal. First, although meta-analytic evidence suggests that gamified and game-based learning can raise motivation and, less consistently, achievement, effects are heterogeneous and frequently confounded by novelty (Sailer & Homner, 2020; Clark et al., 2016). Many studies are brief, measure engagement by self-report at a single time point, and cannot separate a genuine motivational mechanism from the excitement of an unfamiliar activity. Second, few rigorous trials have been conducted in Australian primary settings against the Australian Curriculum: Mathematics, so teachers and school leaders lack local, causal evidence on which to base procurement and pedagogical decisions. This proposal addresses both gaps through a cluster-randomised trial that measures engagement and achievement across a full school semester.

Research aim and questions

The aim of this study is to determine whether a gamified numeracy program, delivered within regular mathematics units, improves student engagement and numeracy achievement relative to an equivalent non-gamified digital program, and to test the psychological mechanism proposed to explain any effect. The research is guided by three questions:

1. Does a gamified numeracy program produce greater gains in numeracy achievement than a non-gamified digital equivalent for students in Years 4 to 6?
2. Does the gamified program produce higher behavioural, emotional and cognitive engagement, and is any engagement advantage sustained beyond the initial weeks of exposure?
3. To what extent is the effect of the program on achievement mediated by satisfaction of the psychological needs for autonomy, competence and relatedness?

Literature review

Self-determination theory

Self-determination theory (SDT) provides the motivational foundation for the study. Ryan and Deci (2020) argue that intrinsic motivation is sustained when three basic psychological needs are met: autonomy, a sense of volition and choice; competence, a sense of effective mastery; and relatedness, a sense of connection to others. Well-designed game elements can, in principle, support each need. Optional quests and difficulty selection support autonomy, incremental levels and immediate feedback signal competence, and collaborative or team-based mechanics support relatedness. On this account gamification should raise engagement only when it satisfies these needs, and may even undermine motivation when points and badges are experienced as controlling rather than informational (Ryan & Deci, 2020).

Flow and optimal challenge

A complementary account comes from Csikszentmihalyi’s (1990) theory of flow, the state of absorbed concentration that arises when the challenge of a task is well matched to a learner’s skill. Adaptive gamified systems that adjust difficulty in real time are theorised to hold more students in this productive zone, avoiding both the anxiety of tasks that are too hard and the boredom of tasks that are too easy. Flow is therefore treated in this study as an indicator of cognitive engagement rather than a separate outcome.

Evidence on game-based and gamified learning

Empirical syntheses are cautiously positive. Wouters et al. (2013) found that serious games were more effective than conventional instruction for learning and retention, although not for motivation measured immediately afterwards. Clark et al. (2016), in a meta-analysis published in the Review of Educational Research, reported modest positive effects of digital games on learning while emphasising that design quality, not the game format itself, drives outcomes. Focusing specifically on gamification, Sailer and Homner (2020) reported small but significant positive effects on cognitive, motivational and behavioural outcomes, again moderated heavily by design and context. The consistent message is that gamification is not uniformly beneficial, and that mechanism and implementation matter more than the label.

Novelty effects

The most persistent threat to this literature is the novelty effect. Hamari et al. (2014) note that positive responses to gamified systems often fade as the novelty of the format wears off, yet many studies are too brief to detect this decay, so the size of the true effect is easily overstated. Australian classroom research reinforces the point: Attard and Holmes (2020) found that digital technologies engaged primary students most durably when they were embedded in meaningful mathematical tasks rather than used as a reward or a diversion. A credible test of gamification must therefore run long enough, and measure engagement often enough, to distinguish a lasting effect from an initial spike.

Conceptual framework

The study integrates SDT and flow into a single mediational model, shown in Figure 1. Gamified learning design is hypothesised to influence numeracy achievement indirectly rather than directly. Game elements first satisfy the psychological needs for autonomy, competence and relatedness; need satisfaction in turn drives behavioural, emotional and cognitive engagement, including flow; and engagement supports achievement. The novelty effect is modelled as a moderator that may weaken the engagement pathway over time, which is why the design measures engagement repeatedly rather than once.

Methodology

Design

The study will use a two-arm cluster-randomised controlled trial, with random allocation at the school level to prevent contamination between conditions within a school. Eight government primary schools in New South Wales and Victoria will be recruited and randomly assigned: four to the gamified program and four to a non-gamified digital comparison program that delivers identical curriculum content without points, levels, badges or narrative. Randomising at the cluster level reflects the reality that a whole-school platform decision cannot be split within a staffroom, and this nesting is carried through into the analysis (Raudenbush & Bryk, 2002).

Participants and sampling

Participants will be approximately 480 students across Years 4 to 6, around 60 per school, a stage at which numeracy engagement is known to decline and at which students can reliably self-report engagement. Schools will be purposively sampled to vary in advantage, using the Index of Community Socio-Educational Advantage, so that findings are not confined to high-advantage settings. A power analysis assuming a small-to-moderate effect (d = 0.30), an intraclass correlation of 0.10, power of .80 and alpha of .05 indicates that eight clusters of this size are sufficient to detect the target effect on achievement.

Measures

Outcomes will be assessed with a combination of curriculum-aligned achievement testing and validated engagement instruments, summarised in Table 1. All achievement items map to the Australian Curriculum: Mathematics achievement standards for the relevant year level (ACARA, 2023), so that the trial measures the numeracy the system actually expects students to learn.

Table 1: Constructs, instruments and timing of measurement

Procedure

Both programs will run for one school semester, approximately 12 teaching weeks, delivered in three 20-minute sessions per week within scheduled mathematics units so that instructional time is held constant across conditions. Teachers in both arms will receive equivalent professional learning, consistent with the Australian Professional Standards for Teachers, ensuring that any difference in outcomes is attributable to the gamification of content rather than to differences in teacher preparation or time on task (Australian Institute for Teaching and School Leadership [AITSL], 2022). Measuring engagement at Weeks 1, 6 and 12 allows the trajectory of any effect, and therefore the novelty question, to be tested directly.

Analysis

Because students are nested within schools, data will be analysed using multilevel, or hierarchical linear, models that partition variance between the student and school levels and yield unbiased standard errors under cluster randomisation (Raudenbush & Bryk, 2002). The primary analysis will regress post-test numeracy on condition, controlling for pre-test score and school advantage, with a random intercept for school. Repeated engagement measures will be modelled as growth trajectories to test whether any engagement advantage in the gamified arm is sustained or decays, providing a direct test of the novelty effect. Mediation will be examined by estimating the indirect path from condition to achievement through need satisfaction and engagement. All analyses will follow intention-to-treat principles.

Ethical considerations

Because the participants are children, ethical protection is central to the design. Approval will be sought from a university Human Research Ethics Committee (HREC) operating under the National Statement on Ethical Conduct in Human Research, together with the research approval processes of the relevant state education departments. Written informed consent will be obtained from parents or guardians, and age-appropriate assent from students, on the understanding that participation is voluntary and may be withdrawn at any time without academic penalty. Platform log data will be de-identified and stored securely, and reporting will occur only at aggregate level. To avoid disadvantaging the comparison group, schools allocated to the non-gamified condition will be offered access to the gamified program after the trial concludes.

Project timeline

The project will run over twelve months, as set out in Table 2. The schedule front-loads ethics approval and instrument preparation, because school-based data collection cannot begin until consent processes are complete and must be aligned with the school semester.

Table 2: Twelve-month project timeline

Significance

The study offers three contributions. Theoretically, it tests an explicit SDT-based mechanism rather than treating gamification as a black box, clarifying why and when game elements help. Methodologically, its cluster-randomised design, objective achievement testing and repeated engagement measurement address the two weaknesses that limit much of the existing literature: weak causal identification and an inability to separate durable effects from novelty. Practically, it generates Australian evidence, aligned to the Australian Curriculum and to NAPLAN numeracy expectations, that schools and systems can use when deciding whether to invest in gamified numeracy platforms. Given the national policy attention now directed at primary mathematics, evidence of this kind speaks directly to the priorities identified by the Grattan Institute and AERO (Hunter & Haywood, 2025; AERO, 2023).

Limitations

Several limitations should be acknowledged. First, a one-semester intervention, although longer than most gamification studies, cannot establish whether effects persist across years; a longer follow-up would strengthen claims about durable engagement. Second, eight schools provide adequate power for a moderate achievement effect but limited ability to detect small effects or to model school-level moderators in detail. Third, self-reported engagement is vulnerable to social desirability, which is why the design triangulates student report with objective platform logs and teacher observation. Finally, restricting the trial to Years 4 to 6 in two states supports internal validity but limits generalisation to other year levels and jurisdictions.

Conclusion

Gamification is widely promoted as a remedy for flagging engagement in primary mathematics, yet the evidence base is uneven and rarely Australian. This proposal sets out a theory-driven, cluster-randomised trial that tests not only whether a gamified numeracy program improves engagement and achievement for students in Years 4 to 6, but also why, through the satisfaction of basic psychological needs, and whether any benefit outlasts its novelty. By combining a defensible causal design with curriculum-aligned measurement and a clear ethical framework for research with children, the study is positioned to produce evidence that is academically rigorous and directly useful to Australian schools and policymakers.

References

Attard, C., & Holmes, K. (2020). “It gives you that sense of hope”: An exploration of student engagement in mathematics through digital technologies. Mathematics Education Research Journal, 32(3), 431-451.

Australian Curriculum, Assessment and Reporting Authority. (2023). Australian Curriculum: Mathematics (Version 9.0). ACARA.

Australian Education Research Organisation. (2023). Engaging students: Creating classrooms that improve learning. AERO.

Australian Institute for Teaching and School Leadership. (2022). Australian Professional Standards for Teachers. AITSL.

Clark, D. B., Tanner-Smith, E. E., & Killingsworth, S. S. (2016). Digital games, design, and learning: A systematic review and meta-analysis. Review of Educational Research, 86(1), 79-122.

Csikszentmihalyi, M. (1990). Flow: The psychology of optimal experience. Harper & Row.

Deterding, S., Dixon, D., Khaled, R., & Nacke, L. (2011). From game design elements to gamefulness: Defining gamification. In Proceedings of the 15th International Academic MindTrek Conference (pp. 9-15). Association for Computing Machinery.

Hamari, J., Koivisto, J., & Sarsa, H. (2014). Does gamification work? A literature review of empirical studies on gamification. In Proceedings of the 47th Hawaii International Conference on System Sciences (pp. 3025-3034). IEEE.

Hunter, J., & Haywood, A. (2025). The maths guarantee: How to boost primary students’ mathematics learning. Grattan Institute.

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Sage.

Ryan, R. M., & Deci, E. L. (2020). Intrinsic and extrinsic motivation from a self-determination theory perspective: Definitions, theory, practices, and future directions. Contemporary Educational Psychology, 61, 101860.

Sailer, M., & Homner, L. (2020). The gamification of learning: A meta-analysis. Educational Psychology Review, 32(1), 77-112.

Thomson, S., De Bortoli, L., Underwood, C., & Schmid, M. (2023). PISA 2022: Reporting Australia’s results. Volume I: Student performance and equity in education. Australian Council for Educational Research.

Wouters, P., van Nimwegen, C., van Oostendorp, H., & van der Spek, E. D. (2013). A meta-analysis of the cognitive and motivational effects of serious games. Journal of Educational Psychology, 105(2), 249-265.