The Impact of Online Education on Gifted Mathematics Students from Different Family Backgrounds

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

First, I would like to thank the authors for their contribution. This paper contributes to the research debate on bridging the gap between practice and academia about online learning.

 
It’s not clear the main question addressed by the research.
The authors analysed the learning patterns, grades, and family backgrounds of students participating in mathematics competitions in 10 key high schools in Liaoning Province from 2018 to 2024. The introduction can be strengthened further by elaborating on the research gap that this paper attempts to close

 
The authors give enough information in the methodology section, but a more detailed presentation of the themes and the subthemes in tables is needed. A table with the codes and sub-codes of the thematic analysis could be added to be clearer for the reader.

 
The conclusion should reiterate the purpose of the paper and state how the study has answered the research questions.

Author(s) need to mention ethical issues for their study and the relations between science and society. I propose to add the following reference:

Petousi, V., & Sifaki, E. (2020). Contextualizing harm in the framework of research misconduct. Findings from discourse analysis of scientific publications, International Journal of Sustainable Development, 23(3/4), 149-174, https://dx.doi.org/10.1504/IJSD.2020.10037655

Comments on the Quality of English Language

The grammar throughout the paper could be improved. I would suggest getting a native English speaker to edit the work. 

Author Response

Dear Editor and Reviewers,

We would like to express our sincere gratitude for the valuable feedback and constructive suggestions provided by you and the reviewers regarding our manuscript titled "[The Impact of Online Education on Gifted Mathematics Students from Different Family Backgrounds]" (Manuscript ID: sustainability-3164556). We have carefully considered each comment and have made revisions accordingly. Below, we provide a detailed point-by-point response to each reviewer’s comments and explain the changes made in the manuscript.

Response to Reviewer #1:

Comment 1:
It’s not clear the main question addressed by the research.

The authors analysed the learning patterns, grades, and family backgrounds of students participating in mathematics competitions in 10 key high schools in Liaoning Province from 2018 to 2024. The introduction can be strengthened further by elaborating on the research gap that this paper attempts to close.

Response:
Thank you for your valuable feedback regarding the clarity of the main research question and the need to better elaborate on the research gap. We have revised the introduction section, adjusting the previous four research questions into three new ones, more clearly emphasizing the main research question, which is: (1) What changes have occurred in the forms of participation in gifted mathematics education (in-class courses, extracurricular online or offline training, etc.) in recent years? (2) When participating in gifted mathematics education, which form do students from different family backgrounds tend to prefer? Is there a correlation between household registration and participation in online gifted mathematics education? If so, what are the key factors influencing their participation in online education? (3) What is the impact of online gifted mathematics education on the final achievement of different gifted students? Does online learning promote equity and sustainability in gifted mathematics education?

In addition, we expanded the section on the research gap and added a significant amount of previous research in the introduction to clarify this study's contribution to the existing literature.

Changes in the manuscript:
The introduction section has been revised to clarify the main research questions and provide a detailed explanation of the specific research gap. These changes can be found in section [1] "Introduction" of the revised manuscript.

 

Comment 2:
The authors give enough information in the methodology section, but a more detailed presentation of the themes and the subthemes in tables is needed. A table with the codes and sub-codes of the thematic analysis could be added to be clearer for the reader.

Response:
Thank you for your valuable suggestions regarding the methodology section. We agree that including a more detailed table outlining the themes and sub-themes will enhance clarity and help readers better understand the results of the thematic analysis. In response to your suggestion, we have added a table that categorizes the questionnaire questions by theme. This table is intended to provide a clearer and more organized presentation of the thematic analysis process.

Changes in the manuscript:
We have added a new table (Table [2]) in the methodology section, which lists the themes and sub-themes. This table can be found in section [3.2] "Questionnaire".

 

Comment 3:
The conclusion should reiterate the purpose of the paper and state how the study has answered the research questions.

Response:
Thank you for your suggestion to strengthen the conclusion by reiterating the purpose of the paper and explicitly stating how the study has addressed the research questions. We agree that this will enhance the clarity and impact of the conclusion. In response, we have revised the discussion and added a sixth section, Conclusion, which restates the main objectives of the study and clearly explains how the research findings address the research questions.

Changes in the manuscript:
The conclusion has been revised to reiterate the purpose of the study and explain how the research questions were addressed. These changes can be found in section [5] "Discussion" and section [6] "Conclusion".

 

Comment 4:
Author(s) need to mention ethical issues for their study and the relations between science and society. I propose to add the following reference:

Petousi, V., & Sifaki, E. (2020). Contextualizing harm in the framework of research misconduct. Findings from discourse analysis of scientific publications, International Journal of Sustainable Development, 23(3/4), 149-174, https://dx.doi.org/10.1504/IJSD.2020.10037655

Response:
Thank you for pointing out the need to discuss ethical issues and the relationship between science and society in the study. We recognize the importance of addressing these aspects, particularly in the context of educational research and the influence of socioeconomic factors on students. In response to your suggestion, we have added a new section on ethical considerations, detailing the ethical guidelines followed throughout the study, including participant consent, data privacy, and more. Additionally, we have discussed the ethical issues and the relationship between science and society. We also appreciate your recommendation to cite the work of Petousi & Sifaki (2020). We have reviewed the paper and agree that it provides valuable insights into the relationship between research ethics and social impact. As a result, we have cited this work in the revised manuscript to support our discussion on the impact of research ethics.

Changes in the manuscript:
A section on ethical considerations and the relationship between science and society has been added in section [3.3] "Measures". The reference to Petousi & Sifaki (2020) has been cited as reference number 117.

 

Comment 5:
The grammar throughout the paper could be improved. I would suggest getting a native English speaker to edit the work. 

Response:
Thank you for your feedback regarding the grammatical quality of the manuscript. We fully recognize the importance of ensuring that the language is clear and precise. To address this, the manuscript has already been professionally edited through the MDPI English editing service, which has improved the grammar, clarity, and overall readability of the text. We have reviewed the manuscript again to ensure it meets the highest language standards.

Reviewer 2 Report

Comments and Suggestions for Authors

Review for manuscript “The Impact of Online Education on Gifted Mathematics Students from Different Family Backgrounds”

Date: 14.8.2024

 

Dear all

Overall, the paper is good quality. The topic fits well to the journal’s scope. Structure is clear. There is a research gap and research question reflected to it. Theoretical framework is well-written, and the used literature is up-to-date and high-quality. Dataset is sufficient. Methods are clearly described, but there is few things to improve in methods (see suggestions). Results are aligned with RQs, and discussion section is quite good.

 

However, even though the manuscript is good quality, I have few recommendations how improve this manuscript from good to excellent.

 

Revision recommendations:

 

1) You have a major challenge in the introduction because the story changes without a warning from online education to gifted mathematics education. You need to bind different sections to a coherent wholeness.

“Future re-search should continue to explore and optimize the mode of online education to meet the needs of different learners and promote the popularization and quality of education.

Gifted mathematics education is critical in developing students with high potential and creativity.”

2) RQ2 has a term “rural” but is has not been introduced in the rationale. Please add it in the introduction.

3) The development of survey instrument has not been described. Is it from the reference 52? If yes, please elaborate.

4) Explain readers which statistical methods are used in answering which RQ and why. What are the key characteristics of a certain statistical methods and why they are suitable in this case.

5) Why there is no informed consent statement available?

6) In the discussion section you do not use your extensive theoretical background. Why not? I think it would be most useful for science if you reflect your findings to the used theoretical background and generate new insights for others to continue research through them

 

Summary: Good quality overall, but some minor and some major revision suggestions. I would like to read the paper again after revision and revision letter.

Author Response

Comment 1:
You have a major challenge in the introduction because the story changes without a warning from online education to gifted mathematics education. You need to bind different sections to a coherent wholeness.

Response:
Thank you for your valuable feedback on the introduction section. We agree that the transition from online education to gifted mathematics education could be more seamless and better integrated into the overall narrative. To address this, we have revised the introduction to ensure smoother transitions between the various topics in the introduction.

Changes in the manuscript:
The introduction section has been restructured to create a more coherent narrative, linking the various topics in the introduction. These changes can be found in section [1] "Introduction" of the revised manuscript.

 

Comment 2:
RQ2 has a term “rural” but is has not been introduced in the rationale. Please add it in the introduction.

Response:
Thank you for pointing out that the term "rural" mentioned in research question 2 was not adequately introduced in the argumentation section of the introduction. We agree that introducing and defining key terms early in the paper is crucial for maintaining clarity and coherence. To address this, we have revised the introduction to include a discussion on the equity of rural students' participation in online education in the section on online education and educational equity. This addition explains the term "rural" and elaborates on the challenges and disparities faced by students in rural areas, providing a rationale for focusing on these students in the research question. This revision ensures that the term "rural" is appropriately contextualized within the argument of the study.

Changes in the manuscript:
Changes in the manuscript: The term "rural" has been introduced and discussed in the revised introduction, found in section [1] "Introduction".

 

Comment 3:
The development of survey instrument has not been described. Is it from the reference 52? If yes, please elaborate.

Response:
Thank you for your insightful comment regarding the development of the survey instrument. We apologize for not providing sufficient detail in the original submission. The development of the questionnaire was indeed based on an extensive literature review, and the theoretical framework for the questionnaire was adapted from Gu's semiprivate space theory, as outlined in references [115,116]. After conducting an in-depth review of the relevant literature on online education and family background, we chose Gu's questionnaire. We then modified the questionnaire to fit the specific characteristics of our study participants. To further ensure its suitability, we conducted multiple rounds of expert discussions, leading to revisions and improvements to the instrument. These steps helped guarantee that the adapted questionnaire also maintained high levels of reliability and validity, consistent with Gu’s original work.

Changes in the manuscript:
We have added a detailed explanation of the development and adaptation of the questionnaire in the methodology section, including references to Gu's semiprivate space theory and the process of expert consultations and revisions. This information can be found in section [3.2] "Questionnaire".

 

Comment 4:
Explain readers which statistical methods are used in answering which RQ and why. What are the key characteristics of a certain statistical methods and why they are suitable in this case.

Response:
Thank you for your valuable comment regarding the need to clarify the statistical methods used and their appropriateness for answering each research question (RQ). In response, we have revised the manuscript to provide a detailed explanation of the statistical methods used for each RQ and their suitability for this study:

To study the changes in the forms of gifted mathematics education and the impact of family income on educational forms, bar charts were created. Different colors were used to represent the quantities of different categories within each group, making it easier to compare sample sizes and observe trends between groups. Bar charts are particularly useful for visualizing categorical data and comparing quantities across different categories, which is essential for answering questions about variations in educational forms and income levels.

To examine the mediating effect of household registration (urban vs. rural) on the relationship between online education and factors influencing academic performance, we employed Pearson correlation analysis and Bootstrap mediation analysis using R software. Pearson correlation is used to measure the strength and direction of the linear relationships between variables, such as household registration, family income, and academic performance. Bootstrap mediation analysis was used to test the indirect effects of household registration on the relationship between online education and academic performance. The Bootstrap method is ideal for small sample studies because it does not rely on distributional assumptions, and it provides precise confidence intervals, which helps to improve the accuracy of estimates for the mediation effects.

Why these methods are suitable:

Bar charts provide a clear and intuitive comparison of categories within and between groups, making them suitable for visualizing trends in gifted mathematics education and the distribution of family income across different groups. Pearson correlation is appropriate for identifying relationships between key variables, helping to understand how factors like household registration and online education correlate with academic performance. Bootstrap mediation analysis is highly suitable for this study as it offers reliable estimates of mediation effects, even with a small sample size, and provides robust confidence intervals for more accurate conclusions.

Changes in the manuscript:
We have revised the methodology section to include a detailed explanation of the statistical methods used and their appropriateness for answering each research question. These changes can be found in section [3.4] " Statistics ".

 

Comment 5:
Why there is no informed consent statement available?

Response:
Thank you for your comment regarding the informed consent statement. We apologize for not clearly presenting this information in the initial submission. We would like to clarify that ethical considerations were carefully addressed throughout the study. This research was approved by the Ethics Committee of East China Normal University (approval number HR 806-2023). All participants voluntarily signed informed consent forms after being fully informed about the purpose, process, potential risks, and benefits of the study. The data collection was conducted anonymously to ensure privacy, and all data was securely stored and encrypted, with access restricted to the researcher. We have added this information to the manuscript to make the informed consent process more explicit.

Changes in the manuscript:
The informed consent statement has been added to the "Measures" section, along with a detailed description of ethical considerations and data protection. These changes can be found in section [3.3] "Measures" and at the end of the article.

 

Comment 6:
In the discussion section you do not use your extensive theoretical background. Why not? I think it would be most useful for science if you reflect your findings to the used theoretical background and generate new insights for others to continue research through them.

Response:
Thank you for your valuable feedback on the use of theoretical background in the discussion section. We fully agree that reflecting on the research findings within the context of the theoretical framework will help strengthen the discussion and contribute to future research. To this end, we have revised the discussion section to explore how the shift in learning modes (face-to-face, online, hybrid) for gifted mathematics education during the COVID-19 pandemic aligns with other studies on the shift in learning modes for general education during the pandemic. Additionally, we have more deeply integrated Gu's "semiprivate space theory," which underpins this study. Furthermore, we have connected our findings on the differing access to online gifted mathematics education based on economic factors (such as family income and urban-rural differences) with theories of educational equity. We emphasize that, while online education has the potential to democratize access to high-quality educational resources—as reflected in the reduced correlation between family income and mathematics competition performance—structural inequalities still persist, especially for rural students with limited resources. This perspective supports previous research on the dual nature of online education, which can both promote and hinder educational equity depending on the context. By linking these findings with the theoretical background, we provide new insights into how online learning environments can be optimized to reduce inequalities in gifted education, particularly for students from disadvantaged backgrounds. These reflections also open new avenues for future research, suggesting that future studies should continue to explore the intersection of socioeconomic status, access to technology, and educational outcomes in online gifted education.

Changes in the manuscript:
The discussion section has been revised to integrate the theoretical framework and reflect on the findings in relation to it. These changes can be found in section [5] "Discussion" and section [6] "Conclusion".

Reviewer 3 Report

Comments and Suggestions for Authors

Introduction:

·       Some long statements are not cited. References are quite old with few exceptions. A good number of research papers were published following the elapsed of COVID-19 pandemic, and critical reading and discussing the findings of related previous work after COVID-19 era is missing.

·       The title of the paper: The Impact of Online Education on Gifted Mathematics Students from Different Family Backgrounds. And the the study aims to investigate students’ learning patterns, achievements, and family background…

 ·       No research gap was articulated: It has been referred to only three studies that discussed relationship between parental involvement and students’ academic achievement. Where are the previous studies that investigated the impact of the online mode of learning? What are their findings?

·       Consequently, the research questions were not accurately developed to close a knowledge gap and contribute to current understanding of the subject matter.

·       The term sustainability required more elaboration. It is not related only to quality education. While authors stated in the introduction part the pillars of sustainable development, they haven’t developed further on how education would play a vital role on creating citizens that behave sustainably.

To sum up, the introduction section is usually written after completing all research sections to provide the reader with a crystal-clear picture about the whole research work, and this is missing.

Literature review

·       There is a need for critical reading and discussion of previous studies. Issues that were insufficiently investigated in previous studies, and the knowledge gap that motivated authors to carry out the current research should be outlined, and consequently the research gap to be clearly articulated.

Methods:

In a such study it is recommended that quantitative data be complemented by qualitative data to deeply capture respondents’ experiences and perceptions.

 

Population, sampling and survey dissemination.

·       What was the target population for this survey, the population size?

·       What a sampling method was utilized in getting students’ perceptions, how the sample size was calculated?

·       What are the percentages of the participants in each cohort?

·       How representatives are these numbers?

·       What criteria were set to recruit students?

·       What about anonymity and confidentiality of participants?

·       What are the questions according to the research domains?

·       In which format the survey was developed? And how was distributed?

·       What are the benchmarks to gather data on students’ achievements and comparison?

 

Reliability and validity of the collected data:

·       How researchers ensured the internal consistency of the questionnaire tools?

·       How the validity of the responses to the questionnaire was verified?

 Result and discussion section:

·       It is essential to show either the alignment or disagreements / new findings with previous studies. This is the way to demonstrate the contribution of the current paper to advancing knowledge in the field.

·       The discussion part appears to be a literature review rather than discussing findings in relation to the already known results.

 ·       It is recommended to add a conclusion and recommendations section.

 

General comments.

·       If the choice of the hybrid studying mode was included in the survey, it could reveal another dimension that may fit families and students to have alternatives of various learning resources to scoring well in competitions.

Comments on the Quality of English Language

Minor English language corrections are required.

Author Response

Dear Editor and Reviewers,

We would like to express our sincere gratitude for the valuable feedback and constructive suggestions provided by you and the reviewers regarding our manuscript titled "[The Impact of Online Education on Gifted Mathematics Students from Different Family Backgrounds]" (Manuscript ID: sustainability-3164556). We have carefully considered each comment and have made revisions accordingly. Below, we provide a detailed point-by-point response to each reviewer’s comments and explain the changes made in the manuscript.

Response to Reviewer :

Comment 1:
Introduction:

Some long statements are not cited. References are quite old with few exceptions. A good number of research papers were published following the elapsed of COVID-19 pandemic, and critical reading and discussing the findings of related previous work after COVID-19 era is missing.

The title of the paper: The Impact of Online Education on Gifted Mathematics Students from Different Family Backgrounds. And the the study aims to investigate students’ learning patterns, achievements, and family background…

No research gap was articulated: It has been referred to only three studies that discussed relationship between parental involvement and students’ academic achievement. Where are the previous studies that investigated the impact of the online mode of learning? What are their findings?

Consequently, the research questions were not accurately developed to close a knowledge gap and contribute to current understanding of the subject matter.

The term sustainability required more elaboration. It is not related only to quality education. While authors stated in the introduction part the pillars of sustainable development, they haven’t developed further on how education would play a vital role on creating citizens that behave sustainably.

To sum up, the introduction section is usually written after completing all research sections to provide the reader with a crystal-clear picture about the whole research work, and this is missing.

Response:
Thank you for the detailed and thoughtful feedback on our paper. We greatly appreciate your suggestions and agree that several aspects of the introduction can be improved. Below are the specific actions we have taken to address these issues:

Citations and References: We have revised the manuscript to ensure that all longer statements are properly cited and have updated the reference list to include more recent studies, particularly post-pandemic research.

Research Gap and Previous Studies: We acknowledge the insufficient articulation of the research gap in the initial draft. To address this, we have revised the introduction to include a significant amount of previous research, clearly identifying the research gap in the existing literature, particularly the lack of studies on online gifted mathematics education. While many studies have explored the impact of online learning on general student populations, our research fills this gap by focusing on gifted mathematics students from different family backgrounds, especially those from rural and low-income families.

In addition, we have incorporated the latest research on online education before and after the pandemic, detailing their findings and their relevance to our study. The updated introduction provides a more comprehensive background for our research and highlights its contribution to the field.

Research Questions: Based on your feedback, we have revised the research questions, reducing the previous four questions to three new ones. These new questions more clearly emphasize the main research issues, ensuring they are better aligned with the identified research gap and contribute to the current understanding of online gifted education. The revised questions now more accurately address the impact of online learning on gifted mathematics students, the role of socioeconomic background in participation, and the influence of household registration on access to online gifted education.

Sustainability and Its Role in Education: We have expanded the discussion on "sustainability," emphasizing that education not only provides quality education but also promotes sustainable development by fostering students' sense of environmental, social, and economic responsibility. The revised introduction discusses how online education, by enhancing accessibility and flexibility, helps students develop skills such as problem-solving and critical thinking, which drive sustainable development. We also highlight that online gifted mathematics education contributes to cultivating future leaders in science and technology, who will play a key role in advancing sustainable innovation.

In summary, as you pointed out, the introduction should provide a comprehensive overview of the study and its contribution. After completing the other sections of the manuscript, we rewrote the introduction to ensure it clearly and coherently summarizes the study's objectives and its contribution to the field. The revised introduction now more clearly articulates the research gap, the importance of sustainability in education, and the relevance of online gifted mathematics education in promoting equity.

Changes in the manuscript:
A substantial number of references have been updated and added, including the latest research following the COVID-19 pandemic, as detailed in the references section. The research gap and research questions in the introduction have been revised, and the discussion on the role of sustainability in education has been expanded, as seen in section [1] "Introduction".

 

Comment 2:
Literature review

There is a need for critical reading and discussion of previous studies. Issues that were insufficiently investigated in previous studies, and the knowledge gap that motivated authors to carry out the current research should be outlined, and consequently the research gap to be clearly articulated.

Response:
Thank you for your valuable feedback. We agree that the literature review can be strengthened by providing a more critical discussion of previous studies and clearly outlining the research gap. In response, we have revised the literature review to include a more thorough analysis of the limitations of existing research on online education and gifted mathematics education. While previous studies have extensively explored the general impact of online education on student populations, several key areas remain underexplored. For instance, research has largely focused on how online education supports general student engagement and performance but has not sufficiently investigated its specific effects on gifted mathematics students, particularly those from rural or economically disadvantaged backgrounds. These students have unique needs and challenges, which have been relatively overlooked in current studies. In our revised literature review, we highlight the gap in research that fails to address the participation of mathematically gifted students in online education, as well as the impact of socio-economic factors on their access to and success in these programs. Moreover, existing studies have not fully explored how online gifted education promotes or hinders educational equity, especially in terms of addressing the digital divide experienced by students from lower-income families or remote areas. This gap is especially pertinent in the post-COVID-19 era, where the reliance on online education has increased, but the inequalities it may perpetuate have not been thoroughly examined in relation to gifted education. Our study aims to fill this gap by focusing on the participation and performance of gifted mathematics students in online education, analyzing how factors such as family income and rural background influence their learning outcomes. By doing so, we hope to contribute to the broader understanding of how online education can better serve gifted students while promoting educational equity and sustainability.

Changes in the manuscript:
The literature review has been revised to provide a more critical discussion of previous studies and clearly outline the research gap that motivated this study. These changes can be found in section [2] "Literature Review".

 

Comment 3:
Methods:

In a such study it is recommended that quantitative data be complemented by qualitative data to deeply capture respondents’ experiences and perceptions.

Response:
Thank you very much for your valuable suggestion. We sincerely apologize for not incorporating qualitative methods, such as interviews or focus groups, into the current study. We fully agree that qualitative data could have provided deeper insights into the participants' experiences and perceptions, which would have enriched the overall findings. Unfortunately, due to time and resource constraints, we were unable to include qualitative research methods in this study. We recognize this as a limitation and are committed to addressing it in future research. We will aim to complement the quantitative data with qualitative approaches in order to provide a more holistic understanding of the subject matter. Once again, we appreciate your suggestion and deeply regret not being able to implement it in this study. We will certainly prioritize it in subsequent research.

 

Comment 4:
Population, sampling and survey dissemination

What was the target population for this survey, the population size?

What a sampling method was utilized in getting students’ perceptions, how the sample size was calculated?

What are the percentages of the participants in each cohort?

How representative are these numbers?

What criteria were set to recruit students?

What about anonymity and confidentiality of participants?

What are the questions according to the research domains?

In which format was the survey developed? And how was it distributed?

What are the benchmarks to gather data on students’ achievements and comparison?

Response:
Thank you for your insightful questions. Below, I provide detailed responses to each point based on the study’s methodology:

Target Population and Population Size: The target population for this study consisted of mathematically gifted high school students from ten key high schools in Liaoning Province, China. These schools host specialized experimental classes (e.g., rocket classes, competition classes), where students are selected based on their strong academic abilities in science and mathematics. The population included students who graduated between 2018 and 2024, with approximately 100 mathematically gifted students per grade in each school, making the total population size around 1,000 students per cohort.

Sampling Method and Sample Size Calculation: A convenience sampling method was utilized due to the availability of students within the experimental classes. We aimed to include approximately 10% of the total student population from each cohort. For example, the 2024 cohort had 103 participants out of approximately 1,000, representing around 10% of the total population.

Percentages of Participants in Each Cohort: The number of participants from each cohort is as follows: 2024 cohort: 103 students 2023 cohort: 88 students 2022 cohort: 79 students 2021 cohort: 61 students 2020 cohort: 67 students 2019 cohort: 53 students 2018 cohort: 59 students This distribution reflects around 10% of the total student population in each cohort, ensuring a balanced sample across different years.

Representativeness of the Sample: We compared the sample with the overall population in terms of academic performance, household registration (urban/rural), and family background. The proportions of these factors in the sample closely matched those of the general population, suggesting that the sample is representative of the larger population of gifted mathematics students in Liaoning Province.

Recruitment Criteria: Students were recruited from ten key high schools' experimental classes in Liaoning Province, where the most academically talented students were selected through examinations and other methods. These students, typically gifted in science and mathematics, were placed in specialized classes such as rocket or competition classes. Participation in mathematics competitions was a key criterion, confirming their status as mathematically gifted students.

Anonymity and Confidentiality: All participants were assured of anonymity and confidentiality. The survey was conducted anonymously, and no personally identifiable information was collected. The data was stored securely and was only accessible to the researcher, ensuring participants' confidentiality throughout the study.

Research Domains and Questions: The survey covered several key research domains:

Participation in online and offline gifted mathematics education.

Family background (income, household registration).

Academic performance in mathematics competitions.

Survey Format and Distribution: The survey was developed as an online questionnaire and was distributed electronically through school communication systems. Invitations to participate were sent to students in each cohort, and participation was voluntary.

Benchmarks for Data on Student Achievements: Academic achievements were measured using the students' performance in mathematics competitions, such as their rankings, awards, and overall scores. These benchmarks allowed for a comparison of students’ success based on their family background and participation in online gifted education.

Changes in the manuscript:
We have updated the "Participants" section to include more details about the sampling method, representativeness of the sample, and data collection process. These revisions can be found in section [3.1] " Participants".

 

Comment 5:
Reliability and validity of the collected data:

How researchers ensured the internal consistency of the questionnaire tools?  

How the validity of the responses to the questionnaire was verified?

Response:
Internal Consistency (Reliability): The development of the questionnaire was based on Gu's semiprivate space theory, which has been shown to have good reliability in previous research. We adapted Gu’s questionnaire to fit the context of online gifted mathematics education, and the modified version underwent multiple rounds of expert discussions and revisions. This iterative process, along with the use of a well-established theoretical framework, ensured the internal consistency of the questionnaire.

Validity of Responses: The validity of the questionnaire was ensured through several methods:

Extensive Literature Review: The questionnaire was developed after a comprehensive review of literature related to online education and family background, ensuring that the questions were grounded in relevant theoretical and empirical research.

Expert Review and Discussions: The questionnaire underwent multiple rounds of discussions with experts in the fields of online education and gifted education. These discussions led to revisions that ensured the questionnaire's content validity, aligning the questions with the study's objectives.

Theoretical Framework Alignment: Gu's semiprivate space theory was used as the foundational framework for the questionnaire, and modifications were made to ensure that the questions accurately captured the experiences of the study participants. This ensured strong construct validity.

These steps helped ensure both the reliability and validity of the data collected for this study. 

Changes in the manuscript:
A detailed explanation of how the questionnaire’s reliability and validity were ensured has been added to the methodology section. These changes can be found in section [3.2] "Questionnaire".

 

Comment 6:
Result and discussion section:  

It is essential to show either the alignment or disagreements / new findings with previous studies. This is the way to demonstrate the contribution of the current paper to advancing knowledge in the field.  

The discussion part appears to be a literature review rather than discussing findings in relation to the already known results.

It is recommended to add a conclusion and recommendations section.

Response:
Thank you for your valuable feedback. We have revised the Discussion and Conclusion sections to address your concerns as follows:

Alignment, Disagreements, and New Findings: The Discussion section has been revised to clearly highlight how the findings align with or differ from previous studies.

Discussion Focused on Findings: We have revised the discussion to focus more on interpreting the study’s findings in relation to known results, rather than reviewing the literature.

Conclusion and Recommendations Section: In response to your recommendation, we have added a Conclusion and Recommendations section that summarizes the main findings of the study. We outline practical recommendations for improving the accessibility and effectiveness of online gifted mathematics education, especially for students from rural and low-income families. These recommendations include improving digital infrastructure in rural areas, providing subsidies for necessary technological resources, and exploring hybrid education models that combine the strengths of both online and offline learning environments.

Changes in the manuscript:
The Discussion section now clearly shows the alignment or disagreements with previous studies and focuses on discussing the findings in relation to known results. A new Conclusion and Recommendations section has been added to summarize key insights and provide practical suggestions for educators and policymakers. These changes can be found in section [5] "Discussion" and section [6] "Conclusion".

 

Comment 7:
General comments.  

If the choice of the hybrid studying mode was included in the survey, it could reveal another dimension that may fit families and students to have alternatives of various learning resources to scoring well in competitions.

Response:
Thank you for your insightful suggestion. We agree that including the option to explore hybrid learning modes in the survey could have revealed an additional dimension in understanding how students and families utilize various educational resources to enhance performance in mathematics competitions. While our current study focused on the comparison between online and offline education, we recognize that hybrid learning—combining both online and offline resources—may offer unique advantages, particularly for students seeking flexibility in their learning. This would have been a valuable area to explore, especially considering how different family backgrounds and resource availability could influence the choice of hybrid learning. In future research, we plan to incorporate the hybrid studying mode as an explicit option in the survey to further explore its impact on student outcomes. This will allow us to examine how students balance online and offline resources and whether this approach contributes to improved performance in gifted mathematics competitions.

 

Comment 8:
Minor English language corrections are required.

Response:
Thank you for your feedback regarding the grammatical quality of the manuscript. We fully recognize the importance of ensuring that the language is clear and precise. To address this, the manuscript has already been professionally edited through the MDPI English editing service, which has improved the grammar, clarity, and overall readability of the text. We have reviewed the manuscript again to ensure it meets the highest language standards.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The revision was done very well and the paper can be published now.

Author Response

Thank you for your valuable revision suggestions and finally approved us to publish this paper! It is precisely because of your review suggestions that we can effectively improve the quality of the article.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for the revised manuscript and authors' response.
I went through the authors' response in which the authors:
1) Stated that some comments are unable to be handled at this stage.
2) Assured that they incorporated most of the comments.

In fact, going over the manuscript, the comments were not sufficiently addressed as it claimed in the authors' responses. 

• This is a structural and linguistic issue in this Manuscript, the ideas are not flowing easily while reading it. It is not a grammar issue; Authors may need to revisit and reorganize their research work.
• It has been noticed in both documents, the manuscript and authors' responses, that different statements indicate a single author (I, researcher's,..etc). While in fact the title of the manuscript shows three authors?!
• There are repeated paragraphs in the manuscript.
•  

I hope these comments would be beneficial to the authors to improve their work.

 

Comments on the Quality of English Language

Minor English language corrections are required.

Author Response

Thank you for your detailed feedback. We sincerely apologize for any inconvenience caused by the insufficient responses to the comments. We have carefully reviewed your feedback and made the necessary revisions to the manuscript. Changes from the previous revision are indicated in red, while changes made in this revision are highlighted in yellow.

 

Comment 1:

The comments were not sufficiently addressed as claimed in the authors' responses.

 

Response:

We acknowledge the concerns raised regarding our initial responses. In the revised manuscript, we have thoroughly reviewed all prior feedback and ensured that each suggestion has been fully incorporated.

In section 3.1 (Participants), we have provided further clarification on the sampling method and the proportions of participants in each group.

In section 3.2 (Questionnaire), we have added an explanation about the format of the questionnaire used in the study.

In section 3.3 (Measures), we have expanded on how anonymity and confidentiality were ensured for participants, as well as clarified the distribution method of the questionnaire, enhancing the methodological transparency of the data collection process.

In section 6 (Conclusion), we have further elaborated on the concept of “sustainability” to provide a more comprehensive discussion on its role within the context of online gifted mathematics education.

 

Comment 2:

The ideas are not flowing easily while reading the manuscript; this is a structural and linguistic issue, not a grammar issue.

 

Response:

Thank you for your insightful feedback. We acknowledge that the flow of ideas in the manuscript may not have been as smooth as expected. To address this, we have carefully reorganized the sections of the manuscript to improve clarity and enhance the logical progression of ideas. Below is a detailed description of the manuscript’s structure, which now reflects a more coherent and systematic presentation:

Research Background:
The study begins with a response to the United Nations Sustainable Development Goal (SDG 4), emphasizing the need for inclusive and equitable education, particularly in the field of gifted mathematics education. The research situates itself within the context of the rapid development of online education, especially during the pandemic, offering new perspectives on how students from different family backgrounds engage in gifted mathematics education.

Research Purpose:
The study aims to address critical issues in gifted mathematics education, including resource shortages, rural-urban disparities, and income inequality, which all affect educational equity. Specifically, the research explores how online education can contribute to improving equity and fostering sustainable development in gifted education, particularly after the transition to online formats during the COVID-19 pandemic.

Research Questions:
The study investigates several key questions:

How have the forms of participation in gifted mathematics education evolved in recent years?

What are the preferences and influencing factors for students from different family backgrounds in choosing educational formats?

How does online gifted education affect the academic outcomes of students from diverse backgrounds, and does it promote educational equity?

Literature Review:
The literature review has been restructured to focus on the development of online education, its relationship with educational equity, and its impact on student performance. This section critically examines previous research and highlights how this study contributes to understanding the effects of online education on gifted mathematics students, particularly in addressing rural-urban disparities.

Research Methods:
We have clarified the sampling process and methodology. The study focuses on mathematically gifted students from 10 key high schools in Liaoning Province who participated in mathematics competitions. Data were collected through a well-structured questionnaire covering family background, study habits, and educational choices. The questionnaire was designed based on established theoretical frameworks and adapted to fit the study’s objectives. Correlation analysis and Bootstrap mediation analysis were used to explore the relationships between family background and online learning participation and outcomes.

Research Results:
The results section presents a detailed analysis of the impact of the pandemic on gifted mathematics students' learning modes. It shows that online education increased significantly during the pandemic, particularly for low-income families, who favored online formats. However, rural students faced challenges due to limited material resources, which affected their ability to benefit fully from online education. The results also highlight that the correlation between family income and mathematics competition performance decreased as online education became more prominent.

Discussion:
The discussion section has been restructured to analyze both the advantages and limitations of online education in promoting educational equity. While online education has expanded access to resources and reduced barriers related to time and location, challenges such as hardware availability and internet access remain significant, especially for students from rural and low-income families. This section emphasizes the need for further infrastructure development and technical support to fully realize the potential of online education in addressing educational disparities.

Conclusion:
The conclusion clearly summarizes the study’s findings, noting that while online education has reduced the impact of income inequality on educational outcomes, challenges remain in achieving complete equity and sustainability. The study recommends addressing the digital divide through improved internet infrastructure and technology support, alongside exploring hybrid learning models to enhance the sustainability of gifted education.

By following this structure, the manuscript now presents a clearer and more logical flow, progressing from the background and rationale of the research to the analysis of the data and policy recommendations. These revisions ensure that the ideas flow smoothly, improving the overall coherence and readability of the paper.

 

Comment 3:

The manuscript and authors' responses indicate a single author, while the title shows three authors.

 

Response:

We apologize for the confusion in the manuscript and responses, where references to a single author were made. This was an oversight, and we have corrected all mentions of "I" or "researcher" to reflect that this work was conducted by three authors.

 

Comment 4:

There are repeated paragraphs in the manuscript.

 

Response:

Thank you for highlighting the issue of repeated paragraphs in the manuscript. After a careful review, we identified that some sections in Chapter 1 (Introduction), Chapter 2 (Literature Review), and Chapter 5 (Discussion) contained paragraphs with overlapping or repetitive content. We have since revised these sections by either adjusting or removing the redundant paragraphs to ensure that each chapter provides distinct and valuable insights.

Repeated or overlapping paragraphs in Chapters 1, 2, and 5 have been either revised for clarity or removed to avoid redundancy, ensuring that each section presents unique and relevant information.

We appreciate your careful review and believe that these changes have improved the overall structure and readability of the manuscript.

 

Comment 5:

Minor English language corrections are required.

 

Response:

Thank you for your feedback regarding the grammatical quality of the manuscript. To address this, the manuscript has already been professionally edited through the MDPI English editing service, which has improved the grammar, clarity, and overall readability of the text. Additionally, we have conducted a further review to ensure the manuscript meets the highest language standards.

We appreciate your suggestion and believe the language quality now aligns with the required standards for clarity and precision.