Using Game-Based Learning for Engaging with Determinants in Mathematics Education at the University Level

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This is an interesting and well-written paper presenting results of a study examining the impact of a custom game-based learning intervention, a UNO-based card game called DETerminator, on students’ understanding of determinants in linear algebra at the university level. The authors compare the performance and perceptions of an experimental group that played the game to a control group that did not play it, using pre- and post-tests, mid-term exam results, and a student perception questionnaire.

The topic is timely and relevant, and the paper is well-written, with good and easy to follow structure. The language is also good. The authors provided a detailed literature review and, what I really liked, a very detailed description of the game, making it easy to repeat or modify the experiment. The inclusion of both cognitive and affective measures is great, I always like to see measurable results, but also the affective side of the intervention...

However, there are two important methodological concerns that need to be fixed/addressed before the paper can be considered for publication:

The most critical issue is unequal treatment of groups. The experimental group had 150 more minutes of course lectures/practical work (180 min + 90 + 60, that is almost double time than the control group), did this influence the knowledge? Did the control group have additional non-game sessions comparable to these? Because, this way we are not sure if the increase of time or the GBL are causing better results, maybe if we organized 150 minutes of in-class practice for control group, they would also achieve similar results?
In my opinion, this makes it impossible to isolate the effect of the game from the effect of the additional instructions time. The intervention, as described, is a result of multiple variables, and attributing any learning gains to the game alone is not valid.

Secondly, this was not clearly described, but it seems that grouping was not randomized, instead the participation in the experimental group was voluntary. This introduces the so-called "self-selection bias", as more motivated or engaged students may have opted for the game-based activity. This further weakens the validity of the findings.

Given these issues, the paper requires substantial revision. The authors need to clarify the structure of the intervention, address the unequal treatment, and more cautiously interpret their results in light of these limitations. I do understand that it is not possible to redo the experiment, so I would suggest the authors to focus more on other (student perception) results, and for this part, clearly state the limitation and interpret the academic achievement results with extreme caution. In case the authors are sure that this issue had no meaningful effect on the outcomes, they must justify this statement, ideally by drawing on relevant literature and presenting arguments that will convince the reader.

While the paper is really interesting, the GBL intervention is promising and the game itself is well described and interesting, the current study design does not support the strength of the conclusions drawn so I would suggest a major review to fix these issues.

Also, probably a typo, I found the following error in the Table 1:
- the row with value 1, red cards matrix is wrong. det is 2, not 1. Please double check this and all other entries, I didn't calculate all of them.

Author Response

Answers for Reviewer 1

Thank you very much for your valuable review. We have taken your comments into account and revised the article accordingly. Changes are highlighted in blue in the manuscript.

 We answer as follows to your comments and questions:

1. The most critical issue is unequal treatment of groups. The experimental group had 150 more minutes of course lectures/practical work (180 min + 90 + 60, that is almost double time than the control group), did this influence the knowledge? Did the control group have additional non-game sessions comparable to these? Because, this way we are not sure if the increase of time or the GBL are causing better results, maybe if we organized 150 minutes of in-class practice for control group, they would also achieve similar results?
   In my opinion, this makes it impossible to isolate the effect of the game from the effect of the additional instructions time. The intervention, as described, is a result of multiple variables, and attributing any learning gains to the game alone is not valid.

Answer:  We thank the reviewer for this important observation and fully acknowledge the concern regarding unequal treatment. As clarified in the revised manuscript, the additional 150 minutes were not primarily used for delivering new instructional content. The majority of this time was dedicated to introducing the students to the rules, structure, and practicalities of the game, as well as to the gameplay itself. Only about 30 minutes were devoted to revision activities, and no new subject knowledge was provided beyond what the control group received. Moreover, the teachers in the experimental condition acted more as “more knowledgeable others” facilitating the game process, rather than as lecturers providing extra explanations. We agree that this setup introduces a limitation in isolating the precise effect of game-based learning from time-on-task factors. However, as we note in the revised text, extending class time within strict curricular frameworks is rarely feasible, making the intervention closer to a realistic teaching scenario. We have now explicitly reflected these nuances and limitations in the manuscript, and we appreciate the reviewer’s input, which helped us clarify this point more carefully. New lines: 442-455, 490-505, 864-869, 889-898, and 985-992.

2. Secondly, this was not clearly described, but it seems that grouping was not randomized, instead the participation in the experimental group was voluntary. This introduces the so-called "self-selection bias", as more motivated or engaged students may have opted for the game-based activity. This further weakens the validity of the findings.

Answer: We agree with the reviewer's comment. We expanded the article with lines 971-984.  

3. Also, probably a typo, I found the following error in the Table 1:
   - the row with value 1, red cards matrix is wrong. det is 2, not 1. Please double check this and all other entries, I didn't calculate all of them.

Answer:  There were two incorrect determinants in Table 1, which we have corrected and checked all other items. The mistake was caused by a copying error.

We trust that after the changes and amendments, you will find the article suitable for publication. 

Thank you very much for your contribution,

The Authors

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper “Using Game-Based Learning for Engaging with Determinants in Mathematics Education at the University Level” addresses an important and timely topic in higher mathematics education. The integration of game-based learning into linear algebra teaching is innovative and relevant, particularly given the challenges of student motivation and retention. The manuscript is generally well-structured, with a clear introduction, literature review, description of the DETerminator game, methodology, and results.

Strengths:

• The paper presents a novel and creative teaching tool (the DETerminator card game) that adapts a popular format (UNO®) for mathematical learning.

• The quasi-experimental design with a large sample (n=580) provides credibility to the findings.

• The statistical analyses (Wilcoxon and Mann–Whitney tests) are appropriate for the non-normal distributions and strengthen the validity of the conclusions.

• The integration of literature on determinants, game-based learning, and UNO® adaptations shows a strong theoretical foundation.

Weaknesses and Suggestions for Improvement:

1. Clarity and Conciseness:

   • Some sections, especially the literature review, are lengthy and could be more concise. The focus should remain on literature directly relevant to determinants and game-based learning in mathematics.

   • Consider reducing historical details of determinants to shorten the manuscript without losing relevance.

2. Methodological Transparency:

   • More information is needed on the pre- and post-test instruments (e.g., types of questions, reliability measures). Including sample items in an appendix (or more details if already present) would enhance replicability.

   • The role of instructors during the gameplay sessions could be clarified further. Were they facilitators, evaluators, or active participants?

3. Data Interpretation:

   • While the statistical results are convincing, the practical significance of the small effect size in the midterm exam (r = 0.16) could be discussed more critically.

   • It would strengthen the discussion to acknowledge potential biases, e.g., voluntary participation in the experimental group.

4. Language and Style:

   • Some sentences are overly complex and could be simplified for better readability.

   • Minor grammatical corrections are needed (e.g., article usage, verb tenses).

5. Future Directions:

   • The conclusion would benefit from suggestions for future research, such as testing DETerminator in other mathematical topics, in different cultural contexts, or comparing digital vs. non-digital versions.

Comments on the Quality of English Language

• Some sentences are overly complex and could be simplified for better readability.

• Minor grammatical corrections are needed (e.g., article usage, verb tenses).

Author Response

Answers for Reviewer 2

Thank you very much for your valuable review. We have taken your comments into account and revised the article accordingly. Changes are highlighted in blue in the manuscript.

We answer as follows to your comments and questions:

1. Clarity and Conciseness:

1. 1. Some sections, especially the literature review, are lengthy and could be more concise. The focus should remain on literature directly relevant to determinants and game-based learning in mathematics.
   2. Consider reducing historical details of determinants to shorten the manuscript without losing relevance.

Answer: We deleted five sentences from subsection 2.3. We think that this article may be of interest not only to educators and researchers involved in mathematics, which is why we have included a somewhat longer review about the history and importance of determinants.

2. Methodological Transparency:

1. More information is needed on the pre- and post-test instruments (e.g., types of questions, reliability measures). Including sample items in an appendix (or more details if already present) would enhance replicability.
2. The role of instructors during the gameplay sessions could be clarified further. Were they facilitators, evaluators, or active participants?

Answer: We agree with the reviewer's comment. Of course, both tests were validated before the experiment. We expanded the manuscript with lines 469-472 and detailed the validation process in Appendix A.3. New lines are 1120-1144. We clarified the role of teachers in the experiment. New lines are 442-455.

3. Data Interpretation:

1. 1. While the statistical results are convincing, the practical significance of the small effect size in the midterm exam (r = 0.16) could be discussed more critically.
   2. It would strengthen the discussion to acknowledge potential biases, e.g., voluntary participation in the experimental group.

Answer: Sections 7 and 8 have been significantly revised, taking a more critical view of the results and taking into account the limitations. In lines 442-455, we provide further details regarding the conduct of the experiment. Voluntary participation in the experimental group as a limitation factor is detailed in new lines 971-984.

4. Language and Style:

1. Some sentences are overly complex and could be simplified for better readability.
2. Minor grammatical corrections are needed (e.g., article usage, verb tenses).

Answer: The manuscript was checked by a native speaker, who made minor changes. These changes are not highlighted in blue in the manuscript.

5. Future Directions:

1. 1. The conclusion would benefit from suggestions for future research, such as testing DETerminator in other mathematical topics, in different cultural contexts, or comparing digital vs. non-digital versions.

Answer:  

We thank the reviewer for this valuable suggestion. The conclusion has been revised to include directions for future research, specifically highlighting the potential of testing DETerminator style games in additional mathematical topics, across diverse contexts, and through comparisons of digital versus non-digital forms. The digital form of DETerminator is already in its beta testing phase. We believe these additions strengthen the conclusion by situating the study within a broader research agenda. New lines are 1002-1015.

We trust that after the changes and significant amendments, you will find the article suitable for publication. 

Thank you very much for your contribution,

The Authors

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors considered all my revision comments and improved the manuscrupt. In my opinion, it is suitable for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

In my view, the revision was adequate, and the paper can be accepted for publication.