From Theory to Practice, and Back: Student Evidence Testing ZPD, APOS, CLT, and Constructivism in Mathematical Thinking Workshops
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsYour theoretical framework and connection to prior research strengthens your paper related to your research questions. Your first research question is about confirming and challenging the core assumptions. The paper has done a great job confirming but I am struggling to see how your research challenges the core assumptions. This paper could be strengthened by being explicit with the challenges that came out in your research.
A few other minor changes are the following:
1) The order of your frameworks is ZPD, APOS, CLT and constructivism; however, in your results sections this order is not followed.
2) 3.1 (Evidence, Judgement, Return to Design) Needs to be bolded.
3) 3.3 Missing your Evidence Section.
4) I struggled to read Table 1 and Table A1 because of the spacing.
5) 4.2, second paragraph, lines 466-468. The sentence is confusing, and I am not sure what you are trying to convey here.
Author Response
Responses to Reviewer 1 Comments
1. Summary
Thank you for taking the time to review this manuscript and for your constructive and encouraging feedback. We appreciate your positive evaluation of the theoretical framing and its alignment with the research questions. In response to your comments, we have revised the manuscript to (a) make the challenges to core theoretical assumptions more explicit, (b) ensure consistent ordering of theoretical frameworks throughout the paper, and (c) address several presentation and formatting issues you highlighted. All the revisions are highlighted using tracked changes in the revised manuscript.
2. Point-by-point response to Comments and Suggestions
Comment 1:
Your theoretical framework and connection to prior research strengthen your paper related to your research questions. Your first research question is about confirming and challenging the core assumptions. The paper has done a great job confirming, but I am struggling to see how your research challenges the core assumptions. This paper could be strengthened by being explicit with the challenges that came out in your research.
Response 1:
Thank you for this important observation. We agree that, in the original version, challenges to core theoretical assumptions were sometimes implicit rather than explicitly named. To address this, we have revised the Judgement subsections in the Results section for ZPD and CLT to more clearly articulate not only how student accounts confirm these frameworks but also which underlying assumptions are challenged by the evidence.
In particular, the revised Judgement text now explicitly identifies challenges to the sufficiency of psychological safety for equitable mediation in ZPD, and to narrow interpretations of CLT that locate extraneous cognitive load primarily in task or material design. The changes can be found in the Judgement subsections of the ZPD and CLT results and are marked in the revised manuscript.
Comment 2:
The order of your frameworks is ZPD, APOS, CLT and constructivism; however, in your results sections this order is not followed.
Response 2:
We agree, and thank you for pointing this out. We have revised the Results section to ensure that the frameworks are presented consistently in the same order throughout the manuscript (ZPD, APOS, CLT, and constructivism), aligning the Results with the Introduction, Discussion, and Research Questions. The changes are reflected in Section 3 and the corresponding subsection headings.
Comment 3:
3.1 (Evidence, Judgement, Return to Design) needs to be bolded.
Response 3:
Agreed. We have now consistently bolded the subheadings Evidence, Judgement, and Return to Design in Section 3.1.
Comment 4:
3.3 Missing your Evidence Section.
Response 4:
Thank you for noting this omission. We have reinstated the missing Evidence subsection in Section 3.3.
Comment 5:
I struggled to read Table 1 and Table A1 because of the spacing.
Response 5:
We agree and have revised the formatting of Table 1 and Table A1 to improve spacing, alignment, and overall readability. Column widths and row spacing have been adjusted so that the content is easier to follow.
Comment 6:
4.2, second paragraph, lines 466–468. The sentence is confusing, and I am not sure what you are trying to convey here.
Response 6:
Thank you for highlighting this. We have rewritten the sentence in question to improve clarity while preserving the original meaning.
Reviewer 2 Report
Comments and Suggestions for AuthorsI enjoyed the opportunity to review this manuscript. However, it was not fully blinded as references were included to your previous work. Whereas, other information was blinded for review.
Regarding the content of the paper, it was relevant and interesting. However, I encourage you to maintain the same order of the theories throughout. In the results section, you began with APOS and then discussed ZPD; throughout the rest of the paper, you always started with ZPD. Regarding grammar, I encourage thorough proofreading to ensure the correct words are used (e.g., "analyses" instead of "analyze" on line 105) and formatting (e.g., block quote on lines 265-269 and lack of bolded subheadings on lines 174, 197, and 201).
In the Discussion section, much of your narrative is supported by existing research, however, there are areas that lack clear connections (i.e., lines 437-461). Finally, the appendix should be placed after the references. However, I appreciated the inclusion of the table and its connection to prior research to support the understanding of the content of this manuscript.
Finally, can you support your theoretical perspectives and findings with more recent research?
Comments on the Quality of English LanguageThe manuscript requires thorough proofreading to ensure proper grammar and formatting.
Author Response
1. Summary
Thank you for taking the time to review this manuscript and for your thoughtful and constructive feedback. We appreciate your positive assessment of the relevance and interest of the paper. In response to your comments, we have ensured consistent ordering of theoretical frameworks throughout the manuscript, improved formatting and clarity in the Results section, strengthened connections between the Discussion and existing literature, and corrected minor language and presentation issues. All revisions are highlighted using tracked changes in the revised manuscript.
2. Point-by-point response to Comments and Suggestions
Comment 1:
I encourage you to maintain the same order of the theories throughout. In the results section, you began with APOS and then discussed ZPD; throughout the rest of the paper, you always started with ZPD.
Response 1:
We agree, and thank you for this observation. We have revised the Results section to ensure that the theoretical frameworks are presented consistently in the same order throughout the manuscript—ZPD, APOS, CLT, and constructivism—aligning the Results with the Introduction, Discussion, and Research Questions.
Comment 2:
Regarding grammar, I encourage thorough proofreading to ensure the correct words are used (e.g., “analyses” instead of “analyze” on line 105) and formatting (e.g., block quote on lines 265–269 and lack of bolded subheadings on lines 174, 197, and 201).
Response 2:
We agree and have undertaken a careful proofreading of the manuscript. Grammatical issues and word-choice errors have been corrected, including the example you highlighted. Formatting has also been revised: the block quotation is now formatted, and the subheadings Evidence, Judgement, and Return to Design are now bolded throughout the Results section. These changes are visible in Section 3 and marked in track changes.
Comment 3:
In the Discussion section, much of your narrative is supported by existing research, however, there are areas that lack clear connections (i.e., lines 437–461).
Response 3:
Thank you for this helpful suggestion. We have strengthened the Discussion by making the connections between student evidence, theoretical interpretation, and existing literature more explicit, particularly in the sections you referenced. Specifically, we added targeted citations to recent research in educational psychology and mathematics education to support our interpretations of CLT and constructivist claims, while keeping the original analysis unchanged. These revisions appear in Section 4 and are highlighted in the revised manuscript.
Comment 4:
Finally, the appendix should be placed after the references. However, I appreciated the inclusion of the table and its connection to prior research to support the understanding of the content of this manuscript.
Response 4:
Thank you for this comment and for your positive feedback on the inclusion of the table. We note that, according to the journal’s submission template, appendices are placed before the References section. We have therefore retained the Appendix in its original position to remain consistent with the journal’s formatting guidelines.
Comment 5:
Finally, can you support your theoretical perspectives and findings with more recent research?
Response 5:
We agree and have addressed this by incorporating recent (e.g., Kirkil, 2025; Vasilakopoulou & Santamouris, 2025; Sedova et al., 2025; Villa & Sedlacek, 2025) literature at key interpretive points in the Discussion section for some of the theoretical frameworks. These additions include recent empirical and review studies related to cognitive load and learning environments (CLT), equitable participation and mediation (ZPD), and recent constructivist perspectives on social meaning-making. The relevant additions can be found primarily in Section 4 and are marked in track changes.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe theme of the paper is important. The work is original regarding its theme. This research adds a different perspective to the other published materials and researches. Overall, the conclusions drawn by the authors appear to be well-supported by the evidence and arguments presented.
An other paper is from the same project (Mokhithi et al., 2025) and documented students’ affective and identity-related gains, but it did not center the evaluation of these theoretical claims:
https://doi.org/10.1080/0020739X.2025.2564193
The study investigates how students’ experiences in Mathematical Thinking Workshops (MTWs) at a South African university affirm, nuance, or challenge assumptions associated with the Zone of Proximal Development (ZPD), Action–Process–Object–Schema (APOS) theory, Cognitive Load Theory (CLT), and constructivism. It draws on a qualitative secondary analysis of six focus-group interviews (n = 17), employing abductive reflexive thematic analysis and an Assumption–Indicator–Evidence matrix linking design rationales to student narratives.
The research questions are:
- To what extent do students’ accounts of participation and learning in the MTWs confirm or challenge core assumptions from ZPD, APOS, CLT, and constructivism?
- Where do the frameworks require extension or qualification to accommodatecontextual features such as multilingual interaction, uneven prior preparation, and environmental constraints?
- What design implications follow for subsequent iterations of the workshops?
The authors summarized their theoretical contribution as four propositions that refine canonical accounts of APOS, ZPD, CLT, and constructivism for this setting.
These propositions, together with their empirical grounding and design implications, are summarized in Table 2.
Main results:
ZPD worked if participation was designed to be inclusive, not only safe. APOS worked if there was time to come back to difficult tasks and close them at the level of approach. CLT worked if we treated room conditions and timing as part of the instructional design, not as neutral background. Constructivism worked if open, relational problem-solving was paired with brief, explicit signals of what counts as a good solution or explanation.
The empirical part of the article are detailed and accurate.
The work includes 44 references: 33 are from after 2000, and 11 are from before 2000.
I have a few comments:
1.I find the article lacking a brief theoretical section in which the authors present the key concepts of the theories used in the paper: ZPD; APOS theory; Cognitive Load Theory; constructivism.
- Throughout the article, the order is as follows: ZPD, APOS, CLT and constructivism.
The same order should be maintained during the presentation of the results as well; it is strange that they start with APOS here.
The same in this case:
3.5. Cross-framework synthesis: “....(a) APOS progressions should be spiralized with scheduled returns; (b) ZPD requires designed equity in participation, not only safety;
or in this case:
“Drawing on the framework-specific analyses above, we summarize our theoretical contribution as four named propositions that refine canonical accounts of APOS, ZPD, CLT, and constructivism for this setting”
3.In line no. 174 Evidence must be in bold.
In line no. 197 Judgement must be in bold.
In line no. 201 Return to design must be in bold.
4.In lines 265-269. Since this is a student’s comment, it should be placed in quotation marks.
- I suggest explicitly including the specific answers to the research questions in section 4.5 Conclusions.
Author Response
1. Summary
Thank you for your careful reading of the manuscript and for your encouraging and constructive feedback. We appreciate your recognition of the originality and relevance of the study, as well as your assessment that the conclusions are well supported by the empirical evidence. In response to your specific suggestions, we have clarified the presentation of the theoretical frameworks, ensured consistent ordering throughout the manuscript, strengthened the visibility of the study’s answers to the research questions in the Conclusion, and addressed several formatting and presentation issues. All revisions are highlighted using tracked changes in the revised manuscript.
2. Point-by-point response to Comments and Suggestions for Authors
Comment 1:
I find the article lacking a brief theoretical section in which the authors present the key concepts of the theories used in the paper: ZPD; APOS theory; Cognitive Load Theory; constructivism.
Response 1:
Thank you for this suggestion. We agree that readers benefit from a clear orientation to the theoretical frameworks used in the study. The core assumptions of ZPD, APOS theory, Cognitive Load Theory, and constructivism are briefly described in Section 1.3, specifically in relation to how they informed the design of the Mathematical Thinking Workshops. In addition, Section 2.1 directs readers to Table A1 in Appendix A1, which provides a concise comparative summary of the key features of the four frameworks as they relate to the intervention.
We believe this approach offers a focused theoretical orientation without expanding the manuscript with a separate stand-alone theory section. However, we would be happy to include a dedicated theoretical overview section if the editor or reviewer feels this would further strengthen the paper.
Comment 2:
Throughout the article, the order is as follows: ZPD, APOS, CLT and constructivism. The same order should be maintained during the presentation of the results as well; it is strange that they start with APOS here.
Response 2:
We agree, and thank you for pointing this out. We have revised the Results section to ensure that the four frameworks are presented consistently in the order ZPD, APOS, CLT, and constructivism, aligning the Results with the Introduction, Discussion, and Research Questions.
Comment 3:
The same in this case: 3.5. Cross-framework synthesis: “(a) APOS progressions should be spiralized…” and “Drawing on the framework-specific analyses above, we summarize our theoretical contribution as four named propositions that refine canonical accounts of APOS, ZPD, CLT, and constructivism…”
Response 3:
Thank you for noting this inconsistency. We have revised the Cross-framework synthesis (Section 3.5) and the subsequent summary of propositions to ensure that the frameworks are discussed in the same order throughout the manuscript (ZPD, APOS, CLT, constructivism).
Comment 4:
In line no. 174 Evidence must be in bold. In line no. 197 Judgement must be in bold. In line no. 201 Return to design must be in bold.
Response 4:
Agreed. We have now consistently bolded the subheadings Evidence, Judgement, and Return to Design across all Results subsections. This formatting change has been applied throughout Section 3 and is visible in the revised manuscript.
Comment 5:
In lines 265–269. Since this is a student’s comment, it should be placed in quotation marks.
Response 5:
Thank you for this comment. We have revised the formatting of the excerpt so that it is clearly presented as a block quotation by indenting it, in accordance with APA guidelines for quotations of 40 words or more. As per these guidelines, quotation marks are not used for indented block quotations. This revision appears in Section 3 and is marked in track changes.
Comment 6:
I suggest explicitly including the specific answers to the research questions in section 4.5 Conclusions.
Response 6:
We agree and appreciate this suggestion. We have revised the Conclusion (Section 4.5) to explicitly and clearly address each of the three research questions. The revised conclusion now states how the findings confirm and challenge the core assumptions of the four frameworks (RQ1), how contextual features required theoretical extensions or qualifications (RQ2), and what concrete design implications follow for future workshop iterations (RQ3). These changes are marked in the revised manuscript.
