Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students
Round 1
Reviewer 1 Report
The paper demonstrates the results of the study of reasoning styles, representations used, and levels of generality in geometric proof
problems. There is a presentation of the results of students' work on solving the geometric problem. There are examples of visual and verbal work of students. The authors estimate the reasoning style, scope of argumentation, and representation. At the same time, it is not clear what conclusions the authors draw from this study. It is necessary to show the main results of the study more clearly.
Also, it will be a benefit to add a short description of the application Geogebra that is used in the research and forms of its implementations.
Author Response
We sincerely appreciate the comments.
In order to solve your suggestion of clearing conclusions, we have added a new paragraph in the end of the manuscript that summarise our main results.
In addition, reponding the second suggestion, we have included a short paragraph (lines 272-276) to describe the use of Geogebra.
Reviewer 2 Report
Thank you for the opportunity to participate in the review process of the paper entitled "Reasoning, representing and generalizing in geometric proof problems". For clarity, I will list my points on the relevant topic:
1. Resources. The first thing I noticed is that many sources are out of date. For example, the authors cite sources older than ten years. I recommend not using these resources. In terms of quantity and choice of resources, their list is sufficient.
2. I lack a chapter called Study Limits that would justify or justify certain steps. One of them is the use of a deliberate sample.
3. The evaluation itself is descriptive and the work has a very didactic impression, although given the focus of "Research on Powerful Ideas for Enriching School Mathematical Learning", I believe that the article could fit thematically.
4. I do not consider some pictures suitable. I recommend the following adjustments:
- Figure 2: Image too dark. Although I understand the reason for including the image, for the purposes of the magazine, it would be appropriate to redraw the solution.
- Figure 3: The same.
- Figure 4: without algebraic window
- Figure 5: the same
Author Response
We sincerely appreciate the comments.
We modified brightness, contrast and saturation in figures 2, 3, and 5. In addition, we removed the algebraic window in figure 4.
The sugestion of including a chapter about Study Limits that would justify or justify certain steps is very interesting. We have referred the limitations of the study in the last paragraph of the paper claiming our corncern about the results. More concretely, considering the comment on the sample, we have also included a sentence describing more precisely the selection of subjects (lines 238-246)
Reviewer 3 Report
Please find the comments below.
Comments for author File: 
Comments.pdf
Author Response
We sincerely appreciate the revision as well as the interesting comments provided.
In the following lines, we briefly describe the changes included in the new version to answer the suggestion proposed:
- Title: We added “among talented 8th grade students”
- Abstract: we have included the information required.
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Introduction:
Lines 22-90
As the reviewer points, these paragraphs express the authors’ ideas eventually supported by citing other sources. This is the structure of the paragraphs. Any change in this composition would affect the rest of the paper and it will force us to change the entire manuscript.
Any case, since we have included some changes corresponding to other suggesions, we have also added changes in this sense.Line 100. We added research objectives in bullet format
Line 117. We added citations -
Methodology:
We have added the description of the study as well as several sentences to solve the question of the reviewer (lines 247-255).The coding is clarified in table 1.
- Discussion and Result:
We have included a summary of result in conclusions. A separation in this part will require major changes in the composition. We suggest a new implementations of the experience in different contexts and with different students’ profiles
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References: We have rectified the references
Reviewer 4 Report
I, personally, do not agree with a lot of issues, regarding proofs in mathematics, especially in work with younger students. But it is my personal and general opinion, and I tried to not affect to reviewing process of this nice paper. Various mathematicians have different opinion about proofs.
Regarding paper:
Table 1 is to big. It ruins consistent look of whole paper. I suggest (not obligatory) to change its shape somehow, in order to fit better.
Maybe even to split it in two tables?
Or to reduce font size?
I do not like use of scanned student handwriting in scientific papers (Figs 2, 3 and 5). They ruin nice and smooth look of scientific paper. But if authors think that this is necesery, then OK.
Sample is small. That means that findings could be a topic for larger discussion. But authors are aware of that and they mentioned it in Conclusion.
Anyway, this could be even better for this paper - a lot of researcheres could have opportunity to coment those findings and to cite this paper. So it could increase referencing and visibility of this paper and this journal.
Finally, it is interesting approach and nice paper, that is worth of publishing.
Author Response
We sincerely appreciate your comments as well as the effort made for reviewing external to your interests.
Table 1 is hard to be changed. We tried to split it in several ways, but we have not be able to get any satisfactory version. Any other chage like the reduction of font size is not possible due to the journal editing directions. Probably editors will take it into account in the final version of the paper
Concerning figures, we agree that they ruin the appearance of the manuscript. However, to to clarify the expressed ideas, we consider the necessity of illustrating the text with images.
