Fostering Reflection and Attention to Enhance Struggling Students’ Mathematical Problem Solving—A Case Study

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review of the study titled “Fostering Reflection and Attention to Enhance Struggling Students’ Problem-Solving: A Case Study”

This paper examines the cognitive obstacles to mathematical problem solving among high school students who struggle with learning mathematics. The authors focus on the development of attention, reflection, and metacognitive processes through the application of the CCRSRC (Connections, Choice, Reflection, Solving, Repetition, Choice) model, which encourages students to make connections between problems, select tasks, reflect on procedures, repeat processes, and become aware of their own progress. The text is well structured and theoretically grounded, combining cognitive theories with a practical instructional intervention. The results indicate that the intervention significantly improves flexibility of thinking and the development of strategies during problem solving, while also fostering students’ self-confidence. By the end of the process, students were able to solve more complex tasks independently and transfer the acquired skills to new problems.

Strengths of the study:

• The CCRSRC model represents an innovative approach to integrating attention and reflection into the problem-solving process. Attention and reflection play a central role in promoting the formation of long-term memory and cognitive flexibility in mathematical problem solving. Individual differences in learning outcomes are largely determined by the way knowledge is encoded and retrieved from long-term memory. In this context, solving tasks that encourage students to identify and use sources of relevant knowledge facilitates the construction of meaningful cognitive schemas. Repeatedly making connections between problems and reflecting on approaches to solving tasks enables more effective knowledge acquisition and long-term retention.
• The paper integrates insights from cognitive psychology (working memory, attentional shifts, metacognitive strategies) with mathematics teaching, enabling teachers to gain a deeper understanding of attentional dynamics and reflective processes in mathematics education.
• The study was conducted with 12 students in Grades 11 and 12 who experienced difficulties solving mathematical problems. Each student participated in three individual intervention sessions. The analysis involved microanalysis of discourse and written responses, with attention levels monitored. Prior to the intervention, all students completed a preliminary interview in which they solved mathematical tasks. The aim was to determine whether the students employed heuristic or other problem-solving strategies. Those who did not use such strategies were selected for the intervention. Each participant attended three individual sessions while continuing their regular classes throughout the school year, into which the intervention principles were integrated.
• The study offers clear recommendations for future practice, particularly for working with students who struggle with mathematics: “It offers educators a clear and flexible framework for fostering meaningful, transferable problem-solving skills in students who typically find routine tasks challenging.”

Limitations of the study:

• Although a qualitative approach is justified, the small number of participants (N = 12) limits the generalizability of the conclusions. The model should be tested with a larger sample to allow for broader generalization.
• Without a comparison group of students who did not participate in the intervention, it is difficult to determine the specific effect of the CCRSRC model.
• The microanalysis of discourse relies heavily on researcher interpretation. Although verification measures were applied (three raters), the risk of interpretive bias remains.
• One sentence in line 394 is written in the first person singular, whereas the remainder of the text is in the third person singular or passive voice.

Recommendations for improvement:

• Future research should include a larger sample and adopt an experimental design with a control group to more robustly assess the effectiveness of the intervention.
• This type of study should also be conducted in other STEM fields (e.g., physics, computer science), where problem-solving tasks play a similarly important role. Results across fields could then be compared.
• It would be useful to test the CCRSRC model in different educational systems and cultural contexts to examine its universal applicability.
• Ensure consistency in reporting by avoiding the first person singular.
• In lines 681, 707, 723, and 743, subheadings should be clearly separated from the body text and formatted in accordance with the author guidelines.

Conclusion:
The paper is highly relevant to the field of mathematics. It demonstrates how the CCRSRC model can bridge the gap between theory and classroom practice.

Author Response

Response to Reviewers' Comments

Manuscript Title: Fostering Reflection and Attention to Enhance Struggling Students' Problem-Solving: A Case Study

Dear Editor,

We are grateful for the thoughtful and constructive feedback provided by both reviewers. We have carefully considered all comments and have made substantial revisions to strengthen the manuscript. Below, we provide a detailed point-by-point response to each reviewer's concerns, indicating the changes made in the revised manuscript.

REVIEWER 1

We thank Reviewer 1 for their positive assessment of the study's strengths and for recognizing the CCRSRC model as an innovative approach. We appreciate the constructive suggestions for improvement.

Limitations and Recommendations

Comment 1.1: "Although a qualitative approach is justified, the small number of participants (N = 12) limits the generalizability of the conclusions."

Response: We appreciate the reviewer's acknowledgment that the qualitative approach is justified for this study. We have added clarification regarding sample size appropriateness for qualitative research.

The sample of 12 participants yielded 36 in-depth longitudinal interviews, as each participant was interviewed three times, with each interview lasting between 2 and 4 hours. This design resulted in 6-12 hours of in-depth engagement per participant. Research demonstrates that qualitative studies commonly achieve saturation within 9-17 interviews (Hennink & Kaiser, 2022), and our 36 interviews substantially exceed this threshold. The longitudinal qualitative interview (LQI) design provides comprehensive temporal data and allows for exploring processes and changes that cannot be captured in single cross-sectional interviews (Hermanowicz, 2013).

We have clarified that sample size assessment in qualitative research should consider not only the number of participants but also the depth and richness of data collected (Vasileiou et al., 2018). The longitudinal approach with multiple extended interviews per participant ensures substantial data richness and meaning saturation.

Additionally, we have noted that a complementary quantitative study employing an experimental design has been conducted and is currently under review for publication in a separate manuscript. The present qualitative study and the quantitative study serve complementary purposes within a broader research program: the qualitative findings provide depth and contextual understanding of how students experience and navigate the CCRSRC model, while the quantitative study addresses questions of effectiveness and generalizability.

Location in revised manuscript: Methods section, "Sample Size and Data Richness" subsection

References added:

Hennink, M., & Kaiser, B. N. (2022). Sample sizes for saturation in qualitative research: A systematic review of empirical tests. Social Science & Medicine, 292, 114523.

Hermanowicz, J. C. (2013). The longitudinal qualitative interview. Qualitative Sociology, 36(2), 189-208.

Vasileiou, K., Barnett, J., Thorpe, S., & Young, T. (2018). Characterising and justifying sample size sufficiency in interview-based studies. BMC Medical Research Methodology, 18(1), 148.

Comment 1.2: "Without a comparison group of students who did not participate in the intervention, it is difficult to determine the specific effect of the CCRSRC model."

Response: We have clarified the epistemological distinction between qualitative and quantitative research approaches. The reviewer's concern reflects a misunderstanding of the fundamental purposes of qualitative versus quantitative research designs.

Qualitative research is defined as "the study of the nature of phenomena," including "their quality, different manifestations, the context in which they appear or the perspectives from which they can be perceived," but explicitly excluding "their range, frequency and place in an objectively determined chain of cause and effect" (Busetto et al., 2020, p. 2). Unlike quantitative research, which is rooted in positivist philosophy emphasizing causality, generalizability, and replicability, qualitative research is especially appropriate for answering questions of "why" and "how" something is observed, assessing complex multi-component interventions, and focusing on intervention improvement rather than establishing causality (Busetto et al., 2020).

Qualitative studies do not use control groups (Busetto et al., 2020, p. 11), as their purpose is fundamentally different from experimental designs. The present qualitative study was designed to explore participants' lived experiences with the CCRSRC model and to understand the processes through which the model influences critical reading and reasoning. The research aim was to develop a rich, contextualized understanding of the phenomenon from participants' perspectives—a goal for which control groups are neither methodologically appropriate nor epistemologically necessary.

We have also noted that the complementary quantitative study (under review) employs an experimental design that addresses questions of causal effectiveness and generalizability. Together, the qualitative and quantitative studies offer a comprehensive understanding of both the mechanisms through which the CCRSRC model operates and its measurable impact on student outcomes.

Location in revised manuscript: Methods section, "Research Design and Epistemological Foundations" subsection

References added:

Busetto, L., Wick, W., & Gumbinger, C. (2020). How to use and assess qualitative research methods. Neurological Research and Practice, 2(1), 14.

Comment 1.3: "The microanalysis of discourse relies heavily on researcher interpretation. Although verification measures were applied (three raters), the risk of interpretive bias remains."

Response: We have added substantial clarification regarding the role of reflexivity and interpretation in qualitative research. The reviewer's concern reflects a misunderstanding of the epistemological foundations of qualitative research and the nature of discourse analysis as a methodology.

Qualitative research relies on nuanced judgments that require researcher reflexivity. Unlike quantitative research, which strives to reveal truths as free as possible from researcher "bias," qualitative research depends on subjectivity (Olmos-Vega et al., 2022). Reflexivity is defined as "a set of continuous, collaborative, and multifaceted practices through which researchers self-consciously critique, appraise, and evaluate how their subjectivity and context influence the research processes," framing reflexivity as a way to embrace and value researchers' subjectivity (Olmos-Vega et al., 2022).

Discourse analysis involves subjective interpretation by its very nature. However, when discourse analysis is anchored in a theoretical approach with appropriate methodological safeguards, it constitutes a rigorous methodology (Hagen, 2023). The present study employed rigorous methodological safeguards to ensure trustworthiness: the use of three independent raters represents peer debriefing, which "is regarded as one of a complement of techniques used to enhance the credibility and trustworthiness of qualitative research through the use of external peers, comparable to internal validity in quantitative research" (Nguyen & Spall, 2008).

Investigator triangulation, applied by involving several researchers in addressing organizational aspects of the study and the process of analysis, significantly enhances credibility. When data are analyzed independently by multiple researchers and interpretations are compared and discussed until the most suitable interpretation is found, this represents a rigorous approach to ensuring trustworthiness (Korstjens & Moser, 2018).

Rather than representing a limitation, the interpretive nature of discourse analysis coupled with collaborative verification measures constitutes a methodologically sound approach that aligns with established standards for rigorous qualitative research.

Location in revised manuscript: Methods section, "Data Analysis and Trustworthiness" subsection; Discussion section

References added:

Olmos-Vega, F. M., Stalmeijer, R. E., Varpio, L., & Kahlke, R. (2022). A practical guide to reflexivity in qualitative research: AMEE Guide No. 149. Medical Teacher, 45(3), 241-251.

Hagen, P. (2023). Discourse analysis. In Qualitative research: A practical guide for health and social care researchers and practitioners. CAUL OER Collective.

Nguyen, T., & Spall, S. (2008). Peer debriefing. In L. M. Given (Ed.), The SAGE encyclopedia of qualitative research methods (pp. 603-604). SAGE Publications.

Korstjens, I., & Moser, A. (2018). Series: Practical guidance to qualitative research. Part 4: Trustworthiness and publishing. European Journal of General Practice, 24(1), 120-124.

Comment 1.4: "One sentence in line 394 is written in the first person singular, whereas the remainder of the text is in the third person singular or passive voice."

Response: We have corrected this inconsistency. Thank you for identifying it.

Comment 1.5: Future research recommendations (larger sample, experimental design, other STEM fields, different cultural contexts)

Response: We appreciate these constructive suggestions for future research directions. We have added a paragraph in the Discussion section acknowledging that:

1. A complementary quantitative study employing an experimental design has been conducted and is currently under review for publication in a separate manuscript. The qualitative and quantitative studies serve complementary purposes: qualitative research provides depth and contextual understanding of how the model operates, while quantitative research addresses questions of what works and under what conditions.
2. We agree that extending this research to other STEM disciplines and diverse cultural-educational contexts represents valuable directions for future investigation. Such studies would contribute to understanding the transferability of the CCRSRC model across different disciplinary cultures and educational systems, and represent natural next steps following the establishment of the model's theoretical foundations and empirical validation.

Comment 1.6: "In lines 681, 707, 723, and 743, subheadings should be clearly separated from the body text and formatted in accordance with the author guidelines."

Response: We have reformatted these subheadings according to the journal's author guidelines. All subheadings are now properly separated from body text with appropriate spacing and formatting.

Reviewer 2 Report

Comments and Suggestions for Authors

• LDM is not well described, line 90, what kind of symptoms are shown by such disabilities? related to intelligence ?any early detection or test to detect? 
• Double LDM line 84 makes the sentence confusing
• define cognitive flexibility line 101! can we measure it?
• PS schemas = P-S schemes? line 116. PS is problem solving?
• define heuristic strategies (HS) line 133!
• define PASS theory line 214
• Figure 1,2,3.. caption / title should be below the figure itself. explain blank diagrams in step: Choosing to finish process!
• Define similarity connection (SC) line 324, use SC abbreviation after that including  326, 329, etc
• P-S strategies==P-S schemes? line 350
• F A H definitions are repeated many times including line 402, its better to create a subsection for this and refers to this subsection 
• CCRSRC definitions are also repeated unnecessarily, line 396, 430 etc
• CCRSRC is sequential? if so then put arrow on the diagram of CCRSRC, one step after other. (Fig 1,2,3..)
• authors need to describe the students profiles in a separate subsection. Apparently, only one student is evaluated, this may mislead the data and conclusion
• the authors need to profile the problems relation with LDM. Do they have difficulties with specific subject on math like algebra, calculus, probability statistics, etc? 

Author Response

Response to Reviewers' Comments

Manuscript Title: Fostering Reflection and Attention to Enhance Struggling Students' Problem-Solving: A Case Study

Dear Editor,

We are grateful for the thoughtful and constructive feedback provided by both reviewers. We have carefully considered all comments and have made substantial revisions to strengthen the manuscript. Below, we provide a detailed point-by-point response to each reviewer's concerns, indicating the changes made in the revised manuscript.

REVIEWER 2

We thank Reviewer 2 for the detailed feedback on terminology, definitions, and study design. The reviewer's comments have helped us significantly improve the clarity and precision of the manuscript.

Terminology and Definitions

Comment 2.1: "LDM is not well described, line 90... Double LDM line 84 makes the sentence confusing"

Response: We have thoroughly revised the section on Learning Difficulties in Mathematics (LDM), removing redundancies and improving clarity. We have corrected the problematic sentence in line 84 from "the mathematical performance LDM students LDM has dropped" to "the mathematical performance of students with LDM has dropped." We have also ensured consistent terminology throughout the manuscript.

Comment 2.2: "Define cognitive flexibility line 101! can we measure it?"

Response: We have added a clear definition of cognitive flexibility: "Cognitive flexibility refers to the ability to switch between different mental tasks and adopt strategies to adapt to a changing environment (Orakcı, 2021)." We have also clarified that cognitive flexibility can be measured and has been shown to predict academic performance in multiple studies (Castro-Sánchez et al., 2019; Liem, 2019).

Comment 2.3: "PS schemas = P-S schemes? line 116. PS is problem solving?"

Response: We have standardized terminology throughout the manuscript. We now consistently use "problem-solving (P-S)" with the abbreviation clearly defined at first use. We use "P-S strategies" consistently rather than mixing "PS schemas" and "P-S schemes."

Comment 2.4: "Define heuristic strategies (HS) line 133!"

Response: We have added a comprehensive definition at the first use of the term: "heuristic strategies (HS)—defined as 'rules of thumb for successful problem solving' that help individuals understand problems better or make progress toward solutions (Schoenfeld, 1985)." We have also provided examples: "such strategies include working backwards, drawing figures, exploiting analogies, introducing auxiliary elements, decomposing and recombining problems."

Reference added:

Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.

Comment 2.5: "Define PASS theory line 214"

Response: We have added a detailed definition: "PASS theory—a neurocognitive model that defines intelligence through four interrelated brain-based processes: Planning, Attention, Simultaneous processing, and Successive processing (Das, Naglieri, & Kirby, 1994)." We have also clarified that "within this framework, Attention refers to selective focus and arousal mechanisms critical for inhibiting irrelevant information and maintaining concentration on task-relevant elements."

Reference added:

Das, J. P., Naglieri, J. A., & Kirby, J. R. (1994). Assessment of cognitive processes: The PASS theory of intelligence. Allyn & Bacon.

Comment 2.6: "Figure 1,2,3.. caption/title should be below the figure itself. Explain blank diagrams in step: Choosing to finish process!"

Response: We have moved all figure captions to below the figures in accordance with journal guidelines. We have also added explanatory text for the blank diagrams in the "Choosing to finish process" step, clarifying that this represents the decision point where students determine whether to continue with another problem or conclude the problem-solving session.

Location in revised manuscript: Figures 1, 2, 3 (captions repositioned; blank diagram explanations added)

Comment 2.7: "Define similarity connection (SC) line 324, use SC abbreviation after that including 326, 329, etc"

Response: We have added a clear definition at first use: "building similarity connections (SCs) among presented problems, defined as the cognitive process of recognizing structural relationships and common mathematical features that facilitate transfer of solution strategies across problems (Author, 2024; Hiebert & Carpenter, 1992)." We have also ensured consistent use of the SC abbreviation throughout the manuscript following the definition.

Reference added:

Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). Macmillan.

Comment 2.8: "P-S strategies==P-S schemes? line 350"

Response: We have clarified and standardized this terminology throughout the manuscript. We now consistently use "P-S strategies" to refer to problem-solving strategies and have eliminated the term "P-S schemes" to avoid confusion.

Comment 2.9: "F A H definitions are repeated many times including line 402, its better to create a subsection for this and refers to this subsection"

Response: Excellent suggestion. We have created a dedicated subsection titled "Levels of Similarity Connections: Formulation, Algorithmic, and Heuristic" in the Methods section. This subsection provides comprehensive definitions of all three levels (F, A, H), and we now reference this subsection throughout the manuscript rather than repeating the definitions.

Location in revised manuscript: Methods section, new subsection "Levels of Similarity Connections"

Comment 2.10: "CCRSRC definitions are also repeated unnecessarily, line 396, 430 etc"

Response: We have streamlined CCRSRC descriptions throughout the manuscript. We provide a comprehensive explanation at first mention and use abbreviated references (e.g., "the CCRSRC model" or "the six-phase model") in subsequent mentions, eliminating unnecessary repetition.

Comment 2.11: "CCRSRC is sequential? if so then put arrow on the diagram of CCRSRC, one step after other. (Fig 1,2,3..)"

Response: We have added directional arrows to all CCRSRC diagrams (Figures 1, 2, and 3) to clearly illustrate both the sequential progression through the six phases and the cyclical nature of the model (particularly the return to Reflection after each phase and the optional Repetition loop).

Participant Profiles and Study Design

Comment 2.12: "Authors need to describe the students profiles in a separate subsection. Apparently, only one student is evaluated, this may mislead the data and conclusion"

Response: This is an important concern, and we have made substantial revisions to address it comprehensively. We have added three new subsections to clarify the study design and participant information:

1. A) New subsection: "Participant Profiles"

We have added a comprehensive subsection providing detailed characterization of all 12 participants. This includes:

Selection criteria: (1) persistent low achievement on routine mathematics assessments, and (2) limited or absent use of heuristic strategies and systematic problem-solving approaches

Detailed cognitive profiles: The subsection describes the diverse cognitive challenges affecting participants' mathematical problem-solving performance, including:

• Attention difficulties: diagnosed attention-deficit disorders affecting sustained focus
• Memory difficulties: challenges with working memory and/or long-term memory retrieval
• Executive function difficulties: impairments in perseverance, self-monitoring, planning, and strategic control
• Information processing difficulties: challenges with processing speed and information integration
• Co-occurring difficulties: many participants presented with challenges across multiple domains

Clarification that despite varied cognitive profiles, all participants shared struggling with mathematical problem solving and demonstrating minimal strategic approach to novel tasks

1. B) New subsection: "Data Analysis"

This subsection clearly states:

• All twelve participants were analyzed according to the CCRSRC model across 36 intervention sessions (12 participants × 3 sessions each)
• Each session was video-recorded, transcribed, and subjected to discourse analysis
• The article presents a detailed case study of one representative participant to allow for in-depth microanalysis of moment-to-moment attentional shifts
• The Findings section includes a summary table providing a macro-level view of all 12 participants across the 36 intervention sessions, demonstrating patterns of attentional development across the broader sample

1. C) New subsection: "Rationale for Selecting an Illustrative Case"

This subsection explains:

• Why one participant (Ronny) was selected as the focal case for detailed discourse analysis
• That analysis of all 12 participants revealed four distinct attentional development profiles:
1. Tri-stage development (formulation → algorithmic → heuristic)
2. Bi-stage development: formulation to algorithmic
3. Bi-stage development: algorithmic to heuristic
4. Bi-stage development: formulation to heuristic
• That Ronny represents the first profile (tri-stage development), demonstrating the fullest progression through all levels
• That all twelve participants successfully engaged with the CCRSRC model and exhibited similar patterns of attentional development
• That a macro-level summary of all participants is presented in Table X in the Findings section

These additions ensure readers understand that:

1. The study encompasses all 12 participants
2. All participants were fully analyzed
3. One case is presented in depth for detailed microanalysis purposes
4. The selected case is representative of patterns observed across the sample
5. Summary data for all participants is provided

Location in revised manuscript: Methods section, new subsections: "Participant Profiles," "Data Analysis," and "Rationale for Selecting an Illustrative Case"

Comment 2.13: "The authors need to profile the problems relation with LDM. Do they have difficulties with specific subject on math like algebra, calculus, probability statistics, etc?"

Response: We have expanded the Participant Profiles subsection to address this concern. The subsection now includes:

• Detailed information about participants' cognitive challenges (attention, memory, executive function, information processing)
• Clarification that all participants demonstrated persistent low achievement on routine mathematics assessments across content areas
• Explanation that participants' difficulties were characterized primarily by minimal use of systematic problem-solving strategies rather than content-specific deficits in particular mathematical domains (algebra, calculus, etc.)
• Note that participants struggled with both routine and non-routine problems regardless of specific mathematical topic

The cognitive profiles provided give readers a comprehensive understanding of the nature of participants' mathematical difficulties.

Location in revised manuscript: Methods section, Participant Profiles subsection (expanded)

Additional Improvements

Beyond addressing the specific reviewer comments, we have made the following improvements:

1. Enhanced coherence in theoretical framework: We have strengthened the connections between cognitive load theory, cognitive flexibility, and the intervention design. The revised text now explicitly explains how the intervention addresses both cognitive load management and cognitive flexibility development, creating a clearer theoretical rationale for the study.

Location in revised manuscript: Introduction, "Learning Mathematics and Individual Differences" section

2. Improved internal consistency: We have conducted a thorough review of terminology, ensuring consistent use of abbreviations and technical terms throughout the manuscript.

Summary of Major Revisions

Methodological Clarifications:

1. Comprehensive explanation of sample size appropriateness for qualitative research, including discussion of saturation and data richness
2. Clear epistemological rationale for qualitative design without control groups
3. Detailed explanation of reflexivity and trustworthiness measures (investigator triangulation, peer debriefing)

Enhanced Definitions and Terminology:

1. Added definitions for: heuristic strategies, PASS theory, similarity connections, cognitive flexibility
2. Standardized all abbreviations (P-S, HS, SC, F-A-H, CCRSRC, LDM)
3. Created dedicated subsection for F-A-H levels to eliminate repetition

Improved Study Design Transparency:

1. Added comprehensive Participant Profiles subsection describing all 12 students' cognitive characteristics
2. Added Data Analysis subsection clarifying that all 12 participants were fully analyzed
3. Added Rationale for Case Selection subsection explaining the four developmental profiles and why Ronny was selected as the focal case
4. Clarified that macro-level summary of all 12 participants is included in Findings

Visual and Formatting Improvements:

1. Added directional arrows to CCRSRC diagrams (Figures 1, 2, 3)
2. Repositioned all figure captions below figures
3. Added explanations for blank diagram elements
4. Reformatted subheadings per journal guidelines
5. Corrected person inconsistency (line 394)

Strengthened References:

1. Added 10 new high-quality academic references to support methodological approach and definitions

New References Added

For sample size and qualitative methodology:

• Hennink, M., & Kaiser, B. N. (2022). Sample sizes for saturation in qualitative research: A systematic review of empirical tests. Social Science & Medicine, 292, 114523.
• Hermanowicz, J. C. (2013). The longitudinal qualitative interview. Qualitative Sociology, 36(2), 189-208.
• Vasileiou, K., Barnett, J., Thorpe, S., & Young, T. (2018). Characterising and justifying sample size sufficiency in interview-based studies. BMC Medical Research Methodology, 18(1), 148.
• Busetto, L., Wick, W., & Gumbinger, C. (2020). How to use and assess qualitative research methods. Neurological Research and Practice, 2(1), 14.

For reflexivity and trustworthiness:

• Olmos-Vega, F. M., Stalmeijer, R. E., Varpio, L., & Kahlke, R. (2022). A practical guide to reflexivity in qualitative research: AMEE Guide No. 149. Medical Teacher, 45(3), 241-251.
• Hagen, P. (2023). Discourse analysis. In Qualitative research: A practical guide for health and social care researchers and practitioners. CAUL OER Collective.
• Nguyen, T., & Spall, S. (2008). Peer debriefing. In L. M. Given (Ed.), The SAGE encyclopedia of qualitative research methods (pp. 603-604). SAGE Publications.
• Korstjens, I., & Moser, A. (2018). Series: Practical guidance to qualitative research. Part 4: Trustworthiness and publishing. European Journal of General Practice, 24(1), 120-124.

For key concepts:

• Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
• Das, J. P., Naglieri, J. A., & Kirby, J. R. (1994). Assessment of cognitive processes: The PASS theory of intelligence. Allyn & Bacon.
• Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). Macmillan.

Conclusion

We believe these substantial revisions have significantly strengthened the manuscript. The additions provide greater clarity regarding:

• The appropriateness and rigor of the qualitative methodology
• The theoretical foundations of key concepts
• The comprehensive nature of the study (all 12 participants analyzed)
• The rationale for presenting one detailed case study
• The trustworthiness measures employed

We are deeply grateful to both reviewers for their careful reading and constructive feedback. Their insights have helped us produce a much clearer and more rigorous manuscript that better communicates the value of this research to the field.

We hope you will find the revised manuscript suitable for publication.

Sincerely,

Author

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

thanks for the revision. 

Author Response

Thank you for the opportunity to revise our manuscript titled "Fostering Reflection and Attention to Enhance Struggling Students' Mathematical Problem Solving - A Case Study." We are grateful for the constructive feedback provided by the reviewer, which has helped us improve the quality and rigor of our work.

We have carefully addressed all comments and suggestions raised in the review. Below, we provide a point-by-point response to each comment, along with a detailed explanation of the revisions made to the manuscript. All changes have been highlighted in the revised manuscript for your convenience.

Response to Reviewer Comments

Comment 1: Citation of Xin et al. (2023) in the Theoretical Background Section

Reviewer's Comment:
"Under 'Theoretical background,' the first paragraph and at least a couple of sentences in the second paragraph (lines 81-92) are pretty much paraphrased from Xin et al. (2023) article including the reference citations used by Xin et al. (2023). However, Xin et al. (2023) was not cited here. I respectfully request the authors make proper citation of 'Xin et al., 2023' in this part of the manuscript. Although the author perhaps cited Xin et al. 2023 elsewhere in the paper, they need to cite Xin et al. (2023) in this part and use quotation marks if the phrases are directly taken from Xin et al. (2023), including the term 'LDM' which is unique to Xin's publications."

Response:
We sincerely thank the reviewer for this important observation. We have now properly cited Xin et al. (2023) throughout the Theoretical Background section (lines 81-92). Specifically:

We added the proper citation format "as cited in Xin et al. (2023)" for all secondary sources originally cited by Xin et al. (2023), including:

U.S. Department of Education (2022)

Jitendra et al. (2018)

CCSSI (2012)

We added an explanatory sentence clarifying our use of the term "LDM" (Learning Disabilities/Difficulties in Mathematics), acknowledging that this terminology was proposed by Xin et al. (2023) and citing the original source (Xin, Tzur, & Thouless, 2022) where the rationale for this term was explained.

We also added a slash in the term to read "learning disabilities/difficulties in mathematics (LDM)" to accurately reflect Xin et al.'s terminology.

The full reference to Xin et al. (2023) has been added to the reference list:

Xin, Y. P., Kim, S. J., Lei, Q., Liu, B. Y., Wei, S., Kastberg, S. E., & Chen, Y. (2023). The Effect of Model-Based Problem Solving on the Performance of Students Who are Struggling in Mathematics. The Journal of Special Education, 57(3), 181-192. https://doi.org/10.1177/00224669231157032

Location of changes: Lines 81-92 (Theoretical Background section, first and second paragraphs)

Comment 2: Terminology Consistency - "generalized strategic PS schemas"

Reviewer's Comment:
"On page 3, line 125, replace 'generalized strategic PS schemas' with 'generalized PS strategies', as proposed by the authors, so that it is consistent across the paper."

Response:
We agree with this suggestion. We have replaced "generalized strategic PS schemas" with "generalized PS strategies" on line 125 to maintain consistency throughout the manuscript.

Location of changes: Page 3, line 125

Comment 3: Typographical Error

Reviewer's Comment:
"On page 9, line 403, delete the ')."

Response:
Thank you for catching this typographical error. We have deleted the erroneous ")." on line 403.

Location of changes: Page 9, line 403

Comment 4: Pronoun Consistency

Reviewer's Comment:
"On page 11, line 475: replace 'I' with 'we'?"

Response:
The entire article was written with "I".