Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Thanks for the opportunity to review the article, which is a careful, well-focused manuscript that addresses an important pedagogical problem of how positive emotions interact with problem-based learning to shape engagement and sustainable competencies in a second-year university statistics course. The topic is timely, methodologically interesting, and the combined use of SEM and cluster analysis is appropriate for the research questions, however, to reach a publishable standard, the manuscript needs substantial revisions. Below, I give a, section-by-section review.

Introduction

The Introduction should start with a brief paragraph stating the stakes in plain terms, including statistical anxiety, transferable competencies, and relevance to SDG 4.7. Then reorganize the background into three tightly linked paragraphs (a) theory on emotions and learning in mathematics/statistics, (b) prior empirical work on PBL and affect, and (c) why a second-order model combining pre- and post-emotions is theoretically warranted.

Methods

Please provide exact counts, dates, and procedures, such as how many students were enrolled, how many were invited, how many declined, and final N by course (ADE, DADE), gender, age distribution, and repeat status. State ethics approval reference and informed consent procedures and include a short table with participant characteristics.

Also, report full survey items and response formats in an appendix or supplementary file. For each scale, provide descriptive statistics, inter-item correlations, Cronbach’s alpha, rhoA/rhoC, and AVE exactly as used. The Communication with teacher construct appears to have lower internal consistency in Appendix A, therefore explicitly report its reliability and discuss implications for interpretation.

The manuscript uses PLS-SEM, and a two-stage disjoint method to estimate second-order constructs, please state why PLS-SEM was preferred over covariance-based SEM given sample size and distributional assumptions. Report model identification checks, sample size/power justification for SEM, handling of missing data, and the number of bootstrap resamples used for inference and provide fit or quality indices appropriate to PLS-SEM and, if possible, cross-validate results using an alternative estimation strategy or provide a sensitivity analysis to show robustness of the main path coefficient.

Results

The Results present clear associations but need stronger evidentiary support. For each major claim, show exact statistics such as path coefficients with standard errors, t-values or p-values, bootstrap confidence intervals, R squared values for endogenous constructs, and effect size metrics such as f squared. Where you discuss group differences, report exact test statistics and effect sizes rather than only p-values.

For cluster descriptions, add 2 to 4 representative descriptive quotes or qualitative notes drawn from student project reflections or open responses if available. If not available, be explicit that clustering rests on quantitative constructs only. When discussing non-significant tests, report observed power and confidence intervals so readers can judge whether null findings reflect absence of effect or limited sample size.

Discussion

The Discussion links findings to theory but should do so more tightly and for each empirical theme, map it explicitly to achievement emotions theory, PBL literature, or ESD competencies. For example, explain mechanistically why pre-PBL positive emotions would shape perceived utility and teamwork outcomes. Consider alternative explanations such as selection effects or prior academic ability. The observed difference by degree program should be discussed as a potential confounder; if possible, present a robustness check controlling for entry grade or prior achievement.

Also, convert the general recommendations into a prioritized action list with actors and timelines and tie each recommendation to the specific empirical result that motivates it.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I have read your thoughtful piece with interest and here offer several observations for your consideration. First, as a theoretical proposition I suggest that you describe Muerza's conception of PBL and why you have adopted it -clearly and early in your piece. You will want also to explain how you derived your path model from it as well as your survey questions. Indeed, this seems very important to me. Likewise, since your findings suggest that "better prepared students" might fare better with PBL and enjoy it more as well, I suggest you wrestle with that finding a bit more. Why is your study not a candidate for a "so what "shrug on the basis of that finding? Third, you do not really take up the a priori problem of student emotional status when they enter into these courses as a complex set of concerns. How much can PBL, or any pedagogical strategy for that matter, be expected alone to address a lack of engagement on perhaps multiple grounds with roots well beyond the classroom? Fourth, you several times refer to PBL as somehow evidencing the "real world." Since there is only one world as a practical matter, I am uncertain to what you mean to refer. Perhaps you mean to distinguish between hypothetically and empirically derived scenarios? If so, I suggest you make that clear. Last, and perhaps more deeply, I found myself wondering where your analysis leaves professors? Is there a risk in "creating supportive environments" that some might lead some to work to take steps do that to the detriment of challenging their students adequately? One might raise a similar question concerning possible manipulation to enjoy a course rather than profit deeply from it. How would you argue such potentials can be avoided given your findings? 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The topic is relevant and the provided background sufficient. However, an extremely subjective and one way approach is selected based on a micro-pool of respondents. Genuinely, I have serious doubts about  the relevancy of the feedback provided by 30-70 students (some of them retaking the course). Namely, their replies can strongly depend upon the extent of curriculum, the personality of the professor and even their own expectations. They might not appreciate the course, but later in their life they might discover its usefulness or other way around. In sum, there is not a sufficient foundation justifying your methodological approach and this issue is further magnify by the lack of comparison and by the small size of the pool of respondents.

 

Comments on the Quality of English Language

It is understandable, but it could be improved.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The article is relevant, well-founded theoretically, and methodologically sound. However, it presents limitations in the size and diversity of the sample, as well as in the depth of the qualitative analysis. Publication is recommended after substantial improvements are made to reinforce external validity, deepen the qualitative analysis, and nuance the conclusions in light of the limitations noted.

1. The study's findings are based on a sample of only 82 students from a single faculty at one university. This limits the external validity and generalizability of the results to other contexts, institutions, or countries. This limitation should be acknowledged more explicitly in the discussion and conclusions. The study should be framed as an exploratory single-campus case study, and it should be suggested that future research replicate the methodology with larger, more diverse samples across multiple institutions to confirm the findings.

2. The design lacks a control group of students taught using traditional lecture-based methods. Without this comparison, it is difficult to isolate the specific effect of PBL on emotions and engagement from other factors. In the limitations section, it should be noted that the absence of a control group means that strong causality cannot be established. It is recommended that future research employ a quasi-experimental design with a comparison group to more robustly test the unique impact of PBL.

3. The study relies exclusively on self-reported Likert-scale questionnaires. This introduces potential biases (e.g., social desirability bias, recall bias) and provides only a superficial understanding of complex emotional experiences. This point should be acknowledged as a limitation.

4. While the SEM analysis reveals strong correlations, the cross-sectional design cannot prove causality. It is unclear whether positive emotions lead to engagement, or if engagement in PBL fosters positive emotions (or both). It is necessary to revise the language throughout the article to avoid causal claims (e.g., replace "impacts" with "is related to" or "is associated with").

5. A sentence should be added in the methodology or limitations section acknowledging the potential for common method bias. It should be mentioned that future studies could use a combination of self-reports, teacher observations, and physiological measures (e.g., heart rate, facial expression analysis) to obtain a more objective measure of emotions.

6. The "Case Study" section should be expanded to include a detailed timeline of the PBL activities. The duration of the project, the frequency of team meetings, the role of the tutor, and any training or guidelines provided to the instructors should be specified. This would significantly enhance the reproducibility of the study.

7. A measure of effect size, such as Cohen's f² for the structural model, should be included. This would tell the reader how much variance in "PBL Engagement" is uniquely explained by "Positive Emotions," providing a clearer picture of the strength of the relationship.

8. The specific indices used to determine the number of clusters (e.g., silhouette width, elbow method, gap statistic) should be mentioned. The values for these indices should be reported to justify the choice of two clusters. This adds rigor to the clustering methodology.

9. The finding that gender was not a significant factor is mentioned, but not discussed in the context of the existing literature. This is a missed opportunity to engage with the broader academic conversation. A paragraph should be added discussing this null finding. Does it contradict previous studies that have found gender differences in emotional responses to mathematics? If so, why might this be the case (e.g., the specific nature of PBL, the business school context)? This would enrich the discussion.

In short, the article represents a relevant and methodologically rigorous contribution that addresses a significant gap in the literature. However, to achieve the impact and robustness it deserves, it is essential to address the noted limitations regarding the sample, design, and depth of analysis. The implementation of the proposed improvements will strengthen the external validity of the study, appropriately nuance its conclusions, and consolidate its contribution to the field of statistics education and active learning methodologies.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The revised manuscript is improved and the authors have taken several of the earlier concerns seriously. The introduction is stronger than before and now opens with a clearer paragraph on statistical anxiety, transferable competencies, and the relevance of SDG 4.7, and the background is more coherently organized around emotions in mathematics/statistics, PBL, and the rationale for the second-order model. The paper also now includes a fuller description of enrolment, participation, degree-program breakdown, age categories, and first-enrolment status in the Methods, along with the questionnaire in an appendix and additional reliability/validity material in the appendices. These are real improvements and they make the manuscript more transparent than in the previous round. The authors have also added explicit reporting of bootstrap confidence intervals, R² values, and an f² effect-size estimate for the second-order path model, as well as a brief sensitivity analysis for the main path coefficient.

That said, some of the central concerns remain only partially resolved. First, while the sample description is fuller, the Methods still do not provide a genuine sample-size/power justification for SEM, and the rationale for choosing PLS-SEM over covariance-based SEM remains rather formulaic and generic (“small sample size and non-normal data”) rather than being properly defended for this specific design. The manuscript also still does not report model identification checks in a way that would reassure a methodologically demanding reader, and the handling of missing data is only indirectly visible through the descriptive appendix rather than being explicitly addressed in the main text.

A further unresolved issue concerns for stronger evidentiary support and interpretive caution around the cluster analysis. The authors have been explicit that clustering rests on quantitative constructs only, which is preferable to implying a qualitative dimension that is not there, but the cluster interpretation remains somewhat overextended. Statements such as Group 1 “may face challenges in emotionally connecting with PBL” and may need adapted intervention are plausible, yet they remain inferential extensions from quantitative profiles rather than directly observed explanations. Since no qualitative reflections or open-response material are included, these claims should be phrased more cautiously. Likewise, while the discussion now links findings more explicitly to achievement emotions theory, PBL literature, and ESD competencies, the mechanistic explanations are still somewhat broad. The paper is strongest when it shows that post-PBL positive emotions are more strongly associated with engagement than pre-PBL emotions; it is weaker when it moves quickly from those associations to broad pedagogical recommendations without adequately ruling out alternative explanations such as self-selection, prior ability, or degree-program differences. The authors do acknowledge the likely role of prior academic preparation and the absence of direct prior-achievement measures, which is a useful revision, but this remains a limitation that continues to matter for the interpretation of the degree-program pattern.

There are still minor language problems that would benefit from another round of careful editing. The recommendation section is more prioritized than before, but it still does not fully match the more operational structure suggested in the previous review (specific actors, timelines, and direct links to particular empirical findings).

Comments on the Quality of English Language

 

     

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for your sharing your revision, which I believe reflects a very good faith and successful effort to address the suggestions/observations I shared concerning your earlier draf. 

Comments on the Quality of English Language

I noticed several sentences in passive voice on this read (such have no subject- one useful way to identify them is if you can place "zombies" as a subject in such sentences and have it make sense". One appears at line 557, for example: "an analysis was conducted" BY ZOMBIES??? A few sentences also exhibited tense issues and a few contained extra/unnecessary articles. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Thanks for your work, your paper has been improved, but I still see some issues regarding the conceptual and practical definition and delimitation of "Problem-Based Learning (PBL)" and regarding a rather fragmented and small pool of references. I suggest that you engage more with the PBL and while refering to other authorities and authors, you explain it as such as well as within the context of your study and comparatively.

 

Comments on the Quality of English Language

It is understandable, but it could be improved.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have addressed all reviewer comments satisfactorily. The changes made have notably improved the robustness, transparency, and framing of the study. Some aspects to consider:

• In the Conclusions section (p. 19), the authors explicitly acknowledge the limitation: "the sample consists of 82 students from a single faculty at one university, which limits external validity and restricts the generalizability of the findings." They also suggest future research with larger and more diverse samples. However, the key phrase "framed as an exploratory single-campus case study" does not appear verbatim in the abstract or the introduction. Although the discussion of limitations is clear, the overall framing of the study has not been modified to reflect this characterization in the main sections. This is a minor point but could be considered for fine-tuning.

• Verify that all references to figures and tables are correct and that the figures are numbered sequentially without gaps.

These adjustments are minor and editorial in nature. They do not affect the scientific validity, methodology, or conclusions of the study.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf