A Conceptual Model for Designing Anxiety-Reducing Digital Games in Mathematics Education

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Extended review of Model for Anxiety-Reducing Digital Games in Mathematics Education  

Thank you for sharing this interesting research. Your paper is well-organized and coherent. Your argument is sound. The one thing that I believe would strengthen this work would be applying your model to specific games so that your readers can understand what it looks like to evaluate the potential of a game for students based on the criteria you describe.

 This article brings together literature on game design with studies on math anxiety to theorize on how digital math games could be intentionally created to help lower math anxiety for students.

As the authors point out, math anxiety is multifaceted and does not simply go away with typical math instruction. They also point out that digital games have proliferated in classrooms, and thus they make a compelling argument for using digital games to address math anxiety.  

Specifically, the authors use Control-Value Theory to consider elements of game design and the mechanisms that address math anxiety's psychological and emotional components. This theory is appropriate for the paper’s goals because it emphasizes the way emotional responses are linked both to a game player’s senses of control over and value of the outcome.

In other words, if a student who is experiencing math anxiety feels helpless when approaching a task, then they perceive limited control and will experience negative emotions. Similarly, if they feel like they will learn nothing in the process, they will also experience negative emotions.

As the authors explain, to address math anxiety, a game would have to support students in feeling like a positive outcome was achievable and valuable.  

This paper is well-grounded in relevant and timely literature. The background builds solid support for the suggested game features (adaptive difficulty and feedback, safe environment for errors, immersive nature and meaningful context, collaboration, emotional regulation and reflection, and non-competitive/non-comparative).  

What would strengthen this paper significantly is a section following the description of the suggested game design features in which a sample game (or games) is described.

It is difficult for the reader to imagine a game that would include each of these components, and a description from the authors would make implementation of this theoretical paper seem much more feasible.

The authors do state that they intend to explore implementation of games in a classroom, but seeing these features within a game is important before classroom implementation can be further explored.  

Author Response

Reviewer Comment

What would strengthen this paper significantly is a section following the description of the suggested game design features in which a sample game (or games) is described.

It is difficult for the reader to imagine a game that would include each of these components, and a description from the authors would make implementation of this theoretical paper seem much more feasible.

The authors do state that they intend to explore implementation of games in a classroom, but seeing these features within a game is important before classroom implementation can be further explored.  

Response

We thank the reviewer for this valuable suggestion and agree that illustrating the proposed design elements through an example can improve clarity and feasibility. However,  aim of the present paper, was not to present a fully developed game, but to identify the core features necessary for alleviating mathematics anxiety.

For example, when a learner repeatedly struggles with a task (e.g., addition of rational numbers), the game may temporarily shift focus from problem-solving to emotional regulation. Our idea is for that the learner is invited to inflate a virtual balloon by breathing steadily into the device microphone. The balloon’s size increases in real time in response to controlled breathing, providing visual biofeedback. This short, non-punitive interruption will serve multiple purposes: it reduces physiological arousal, reframes failure as a manageable experience, and allows the learner to return to the mathematical task in a calmer state. This will be incorporated as part of the game narrative rather than presented as an external intervention.

Reviewer 2 Report

Comments and Suggestions for Authors

I'm attaching a file.

Comments for author File: Comments.pdf

Author Response

We thank you sincerely for your thoughtful, constructive, and detailed review of our paper. We appreciate the time you devoted to providing insights and suggestions that have significantly improved the clarity, structure, and contribution of our work. Below, we provide a point-by-point response to your comments, outlining how each concern has been addressed in the revised paper.

Reviewer Comment: Clarify in the abstract and introduction whether the article is (A) conceptual/theoretical (review + framework proposal) or (B) an empirical study. If (A), restructure to emphasize theoretical contribution, identify gaps in the literature, explain how the model advances theory, and propose explicit testable hypotheses.

Response: As suggested, we have explicitly clarified in both the abstract and the introduction that this article is a conceptual/theoretical study. The revised abstract now states that no new empirical data were collected or analyzed, and that the model is derived from a synthesis of theoretical perspectives and empirical findings from prior studies. In the introduction (page 1), we have reiterated that the manuscript presents a conceptual model grounded in Control-Value Theory and supported by systematic reviews and meta-analyses.

We have undertaken the following revisions:

• Strengthened the emphasis on theoretical contribution by highlighting how the proposed model integrates and extends existing research on mathematics anxiety (MA) interventions and digital game-based learning (DGBL).
• Identified clear gaps in the literature regarding the lack of psychologically grounded design principles in existing MA-focused educational games.
• Explained how our model advances theory, particularly by mapping game features to mechanisms proposed by Control-Value Theory (CVT).
• Proposed a set of explicit, testable hypotheses (see Section 5.3, Table 3) that future empirical studies can examine.
• Included a validation plan (Section 5.3, Table 4) outlining how each model component may be operationalized and assessed in empirical research.

Recommendation:
For each feature (Tables 1/2), include:
a) Direct empirical evidence linking the feature to MA reduction (not just motivation/performance)
b) Potential mediators (e.g., changes in self-efficacy)
c) Concrete evaluation measures.
Consider adding a hypothesis table (H1, H2...) that can be empirically tested.

Response: In Section 5.1, we now explicitly distinguish between:

• Strong empirical support (e.g., emotional regulation tools and combined interventions that directly reduce MA),
• Moderate or indirect support (e.g., adaptive feedback improving self-efficacy, which mediates MA).

In Table 1, we have labeled the type of evidence supporting each feature (e.g., “direct empirical (MA-specific)”, “moderate empirical”, “indirect empirical”) and cited the relevant meta-analyses and systematic reviews (e.g., Liu et al., 2025; Sammallahti et al., 2023; Dondio et al., 2023).

We have added a full section (5.3) where each game feature is linked to a psychological mediator (e.g., perceived competence, task value, appraisal regulation). This is now clearly summarized in Table 3, which connects each hypothesized mechanism (H1–H7) to both a mediator and an expected outcome (e.g., ↓MA, ↑engagement).

In Table 4, we provide a detailed validation plan for each game feature. This includes:

• What to measure (e.g., mathematics self-efficacy, fear of failure),
• How to measure (e.g., validated scales such as MARS, PANAS, Bandura-type task-specific self-efficacy),
• When to measure (e.g., pre-test, post-test, during gameplay).

Recommendation (strongly advised):

Include a proposed method section detailing: target population (age, school context), study design (RCT, cluster-RCT, or pre-post with control), instruments (e.g., AMAS, MARS, self-efficacy, performance), estimated sample size, and statistical analyses (e.g., mediation analyses, mixed models). This will increase the framework’s utility for researchers.

Response: We have added a detailed “Validation Plan” in Section 5.3 (Tables 3 and 4) outlining a proposed empirical approach for testing the conceptual model. Specifically, we have included the following elements:

• Target population: We propose a study focused on learners aged 10–14 years, as this group is particularly vulnerable to mathematics anxiety (MA) and well-suited for digital learning interventions.
• Study design: A cluster-randomized controlled trial (cluster-RCT) or a pre-post design with matched control schools is proposed, depending on resource availability.
• Instruments: We list validated measures for each psychological construct in Table 4, including:
• AMAS and MARS for mathematics anxiety
• Bandura-type self-efficacy scales for task-specific confidence
• PANAS for emotional self-awareness
• Cognitive Appraisal Scales
• Sample size: We recommend a minimum of 80–100 students per group (intervention/control) to detect moderate effects with adequate power (80%).
• Statistical analyses: The plan includes the use of multilevel modeling (e.g., linear mixed models) to account for nested data (students within classes), as well as mediation analyses to test whether perceived control and task value mediate reductions in MA.

 

Recommendation: Expand the “Limitations” section to discuss cultural heterogeneity in emotion interpretation, technological access gaps, educational level differences, and their impact on model applicability.

Response: We have substantially expanded the “Limitations” section in the Conclusion (Section 6) to address the following aspects:

• Cultural heterogeneity in emotion interpretation: We now acknowledge that learners' appraisal of emotional stimuli, such as feedback or game-based failure, may differ significantly across cultures.
• Technological access gaps: We discuss how variability in digital infrastructure and digital literacy may limit the feasibility and equity of implementing such games in different educational contexts.
• Educational level and developmental differences: We cautioned that learners at different developmental stages may respond differently to game mechanics such as narrative immersion, collaboration, or emotional regulation prompts. We suggest that age-appropriate adaptation will be necessary to ensure model effectiveness.

Observation: The literature review is broad but omits references to MA measurement tools (AMAS, MARS) and studies validating automated emotion detection in educational contexts (e.g., correspondence between facial signals and self-reported math anxiety). Recommendation: Include these references and discuss potential discrepancies between physiological signals and subjective experience, explaining how the proposed approach addresses these issues.

Response:

We have expanded the literature review to include explicit references to the two most widely used math anxiety (MA) measurement tools:

• AMAS (Abbreviated Math Anxiety Scale; Hopko et al., 2003)
• MARS (Mathematics Anxiety Rating Scale; Suinn & Winston, 2003)

These are now cited in Section 3.1 as the primary validated self-report tools used in MA research and proposed for future model validation (see also Table 4: Validation Plan). Additionally, we have added a new paragraph in the Conclusion (Section 6) discussing automated emotion detection technologies (e.g., facial recognition, physiological signals) and their limitations. Specifically, we now cite recent studies (e.g., Chen et al., 2024; Snow et al., 2025) showing that automated affective indicators may not align well with self-reported emotions.

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has been substantially improved and now satisfies the journal’s publication standards. I also encourage the authors to conduct an empirical study in the future, which would enhance the impact and generalizability of their research, thereby addressing broader scientific questions of interest.