Mathematics lessons are introduced to primary school students at the age around seven for three key reasons. First, cognitive readiness occurs during the concrete operational stage (ages 7 to 11), during which children develop the ability to use logic in concrete ways (e.g., applying rules for sorting and classifying physical objects) (Lemoyne & Favreau, 1981; Piaget, 1953). Second, brain activity at age seven is elevated in the prefrontal cortex during numerical processing, facilitating the understanding of approximate magnitudes and novel mathematical concepts (Clark et al., 2020; Geary & Moore, 2016). Third, mathematics has practical applications in various real-life situations, such as handling money, measuring objects, and understanding time.

Although number sense or numerosity is inherent in the general population (Dehaene et al., 2003; Wynn, 1992; Xu & Spelke, 2000) and early mathematics can be taught in primary school, some primary school students experience mathematical difficulties (MD). According to existing studies on MD among primary school students in various countries, the estimated prevalence rates are as follows: 8.97% in mainland China (Y. Wang et al., 2024), 5.70% (Morsanyi et al., 2018) and 6% (Shalev, 2007) in the UK, 5-9% in the US (Geary, 2011), 7.70% in Pakistan (Kausar et al., 2021), 8% in India (Scaria et al., 2023), 4-5% in Malaysia (Aquil & Ariffin, 2020), and 11.90% in Thailand (Khangdee et al., 2017). Early mathematics skills in formal schooling have a positive and cumulative influences on later advanced mathematics skills, though poor mathematics development over time may exert a long-term and negative impact on mathematical achievement for students (Liu et al., 2025).

In response to these challenges, various intervention programs have been developed to support children with MD. Overall, both computer-based and face-to-face mathematical interventions—grounded in instructional, neurological, empirical-pragmatic, or developmental psychology frameworks—have been found effective in meta-analytic studies (Chodura et al., 2015; Filiz, 2023). Notably, interventions targeting children at risk of MD demonstrated greater improvements in mathematical achievement (MA) when implemented in single-subject settings and through computer- or digital-based formats (Benavides-Varela et al., 2020; Chodura et al., 2015). Nonetheless, few studies have employed theory-based interventions and the findings regarding their effectiveness compared to non-theory-based approaches remain inconsistent (Chodura et al., 2015). Moreover, interventions specifically designed to enhance mathematical competence based on strong neurodevelopmental perspectives on mathematical learning remain under-investigated (H. Chang et al., 2022; Menon, 2010; Menon & Chang, 2021).

The Triple-Code Model (TCM) of developmental numerical cognition posits the existence of three distinct representational codes for number: a visual symbolic code (e.g., Arabic numerals like “7”), a verbal symbolic code (e.g., spoken number words like “Seven”), and a non-symbolic analogue magnitude code (e.g., approximate quantities such as “■■■■■■■”). These numerical systems enable individuals to process numerical information through different modalities depending on the task and context (Dehaene, 1992; Dehaene et al., 2005). The TCM framework has also been partially supported by empirical fMRI-based investigations, which have identified distinct but overlapping neural networks associated with each code (Arsalidou et al., 2018; Skagenholt et al., 2021; Skagenholt et al., 2018; Dehaene et al., 2003). Furthermore, the TCM framework has been shown to predict MA through studies employing both individual differences (Bugden & Ansari, 2011; Lyons et al., 2014; Schleepen et al., 2016; Wongupparaj & Kadosh, 2022) and neuroimaging approaches (De Smedt et al., 2013).

Although the link between the TCM and MA has been observed, few studies have explicitly designed interventions based on the TCM framework for children with MD. Additionally, digital game-based interventions have been shown to enhance brain activation in numerical processing regions among children with developmental dyscalculia (F. Wang & Jamaludin, 2025). Hence, computer-based interventions have also demonstrated greater effectiveness in improving mathematical competence compared to other modes of delivery in children with MD (Chodura et al., 2015; Ren et al., 2023). Apart from MD, working memory (WM) deficits are another major concern for this population, as the visuospatial sketchpad is associated with processing mathematical symbols and performing mental computations, while the phonological loops is linked to word problems and retrieving arithmetic facts (Kroesbergen et al., 2023; Matejko et al., 2023; Mohammed et al., 2024; Peng & Fuchs, 2016).

Rigorous intervention studies that integrate established theoretical frameworks and align with national school curricula are still needed to determine their effectiveness in addressing MD among children. The ADDIE model—an acronym for Analysis, Design, Development, Implementation, and Evaluation—is a robust and widely used framework that has significantly influenced the fields of education and psychology (Allen, 2006). It offers a systematic and dynamic approach to instructional design and development through its five structured stages, facilitating the creation of effective and learner-centered educational interventions (Abuhassna et al., 2024; L. Chang & Abidin, 2024). Accordingly, the present investigation aims to design a digital game-based intervention grounded in the TCM and ADDIE frameworks, with the goal of enhancing both MA and WM in children at risk of MD. The conceptual framework and relevant theories of the current study is demonstrated in Figure 1.

The present study comprised two main phases: the development of the intervention and the evaluation of its effectiveness. The ADDIE framework was employed to guide the intervention development, while a pretest–posttest control group design (Edmonds & Kennedy, 2017) was utilized to assess the effectiveness of the developed intervention.

Table 2 presents the means, SDs, minimum and maximum scores, and skewness and kurtosis values across the three outcome parameters—MA, VWM, and SWM—for both the control and experimental groups. The skewness and kurtosis values for all variables were within the acceptable range for normality (i.e., ≤ ±2; Kim, 2013), and Box’s test indicated equality of covariance matrices of the dependent variables across groups. MA, VWM, and SWM pretest scores were similar between the two groups (see Figure 4). A significant main effect of time was observed for MA, indicating that the average posttest scores were significantly higher than the pretest scores, F(1, 68) = 63.05, p < .01, = .48. In addition, a significant group × time interaction was found, F(1, 68) = 7.31, p < .01, = .10. Simple effects analysis revealed that the gain in MA scores was greater for the experimental group, t(34) = 7.85, p < .01, Cohen’s d = 1.33, compared with the control group, t(34) = 3.56, p < .01, Cohen’s d = 0.60 (see Table 3 and Figure 4A).

For both VWM and SWM, significant main effects of group and time were also found. Specifically, for VWM, F(1, 68) = 12.49, p < .01, = .15 (group) and F(1, 68) = 39.70, p < .01, = .37 (time); and for SWM, F(1, 68) = 4.41, p = .04, = .06 (group) and F(1, 68) = 257.54, p < .01, = .79 (time). Moreover, significant group × time interaction effects were found for both VWM, F(1, 68) = 9.69, p < .01, = .12, and SWM, F(1, 68) = 14.86, p < .01, = .18. Simple effects analyses indicated that the gains in both VWM and SWM were greater in the experimental group, t_VWM(34) = 5.77, p < .01, Cohen’s d = 0.97; t_SWM(34) = 13.17, p < .01, Cohen’s d = 2.23, than in the control group, t_VWM(34) = 2.76, p < .01, Cohen’s d = 0.47; t_SWM(34) = 9.30, p < .01, Cohen’s d = 1.57 (see Table 3 and Figures 4B and 4C).

The primary aims of the present study were to develop and evaluate the effectiveness of a digital TCM game intervention for children at risk of MD in primary school settings. The intervention was grounded in the TCM and aligned with the standardized mathematics curriculum, incorporating the ADDIE and DGBL frameworks. Focus group discussions were conducted with key stakeholders and domain experts to guide the development process. A feasibility study involving 45 children was undertaken to validate the MA measure and the stimuli used in the digital TCM game. Expert evaluations indicated very high satisfaction ratings across all aspects of the intervention, which were further supported by positive feedback from 35 participating students in the experimental group.

The main findings demonstrated that the digital TCM game intervention effectively enhanced cognitive functions, particularly verbal and spatial WMs, and promoted achievement of learning objectives. This educational intervention, which integrates elements of challenge, complexity, and entertainment through digital gamification, successfully fostered motivation, engagement, and measurable learning gains. The greater improvement in MA observed in the experimental group indicated a transfer effect of the intervention beyond regular classroom instruction. Furthermore, the enhanced WM performance appeared to indirectly facilitate learning processes in the experimental group, surpassing the typical developmental trajectory observed in the control group.

Furthermore, the finding of the current study was in line with the previous review suggesting that the DGBL can improve learning outcomes while reducing cognitive load in young children (Behnamnia et al., 2023). From the perspective of the Cognitive Load Theory (Sweller, 2011), the interactive and adaptive nature of DGBL can optimize intrinsic and germane cognitive loads by presenting information in engaging and meaningful contexts. This digital TCM game intervention helps participants in the experimental group allocate cognitive resources more efficiently during mathematical problem-solving. Moreover, according to the Control-Value Theory of Achievement Emotions (Pekrun, 2006), positive emotions as the arousal of achievement emotions such as enjoyment, interest, and values, which are often elicited during gameplay, may enhance WM functioning by facilitating goal-relevant processing and sustained attention (Figueira et al., 2018; Hou & Cai, 2022; Yüvrük et al., 2020).

Consequently, the dynamic interplay among emotion, domain-general cognitive processes, and domain-specific mathematical cognition may underlie the observed improvements in mathematical learning among children at risk of MD (Wongupparaj & Kadosh, 2022). Additionally, the sense of engagement and challenge embedded in the digital TCM game could induce a flow state (Pan et al., 2025), particularly when task difficulty is optimally matched to players’ skill levels (Pujol et al., 2024), thereby further supporting motivation and learning gains. Empirically, the mean MA scores significantly increased from 14.77 to 18.37 points following the intervention, representing an improvement of approximately +1 SD. A gain of 1 SD reflects a meaningful enhancement equivalent to performance at around the 84th percentile, indicating that participants outperformed roughly 84% of their baseline distribution. Although a post-intervention mean of 18.37 out of 35 points suggests that the digital TCM game effectively strengthened arithmetic ability, it also implies that this supplementary intervention could be used to complement regular classroom instruction for children at risk of MD. Nonetheless, the findings leave scope for the integration of additional targeted interventions or instructional activities to further accelerate mathematical learning and consolidate long-term skill retention.