A Case Study of Prospective Teachers Engaged in Professional Noticing of their Students’ Mathematical Thinking

Round 1

Reviewer 1 Report

The topic of the article is very current. Teaching mathematics and educating future teachers is an interesting topic. In the second chapter, the authors mainly focus on the topic of Responsive Teaching, they did a decent literature review here. In the third chapter, the research problem and research methods are clearly formulated. In the Research Design section, I would recommend adding additional data, for example, when the study took place, how long it lasted, what the circumstances of the research were, etc. On what basis did the researchers select the participants? Data Analysis and research conclusions are clear and understandable. I recommend publishing the article after completing the data in the Research Design section.

Author Response

Thank you very much for taking the time to read our article and provide feedback. We appreciated your kind words and important suggestions that improved our paper.

The following table outlines your suggestions and notes related to our revisions.

Reviewer	Suggestion	Notes
Reviewer One	In the Research Design section, I would recommend adding additional data, for example, when the study took place, how long it lasted, what the circumstances of the research were, etc. On what basis did the researchers select the participants?	Thank you for this suggestion. On page 3 we added suggested details.

Reviewer 2 Report

This article reports on the analysis of prospective teachers while engaging in professional noticing of their students’ mathematical thinking in pieces of written work. The characterization have been made by using responsive teaching analysis.

To the opinion of this reviewer, this manuscript is overall well written and organized. Its findings might be interesting to many, specially for those involved on teacher training. However, the manuscript shows serious flaws that should be corrected:

Introduction

Introduction is way too brief and provides not enough background or context to fully understand the interest of the research. In this regard, research questions should be better introduced and grounded. To improve this, I’d suggest a deeper discussion about the challenges faced those working on training teachers. Some key questions should be clearly answered in this section, such like: what is this research useful for? why is different to previous research?

I miss a specific section discussing prospective teachers’ limitations and difficulties with respect to specific didactic-mathematic knowledge (this might have an impact on the interpretation of the obtained results!). To my opinion, this is a key discussion that the manuscript entirely bypass. This discussion could be presented in the introduction.

Figure captions

While the manuscript is overall well written, additional attention should be paid to figure captions… that are way too brief, becoming meaningless in some specific captions. To this regard, a good figure caption should first describe the related figure and, second, briefly analyze the figure itself. In doing so, a reader should be able to fully understand the figure without reading the related text -one could expand information by reading the related text-. For example, in figure 1, the caption states: “Barbara’s shared piece of student work”… which is an absolutely generic caption. Instead, I’d suggest: “Piece of student work analyzed by Barbara. The student’s response corresponds to a problem that requires to determine the total number of bottles of milk for 21 boxes -each one containing six bottles-. It can be seen that Barbara highlights specific elements of the written answer, interpreting that the student didn’t understand what the problem was asking.”

Data and results

Finally, the most critical aspect that should be corrected in the manuscript is -to my opinion- the lack of any transcription. On the “research design” section, it is stated that the authors analyzed several responses of prospective teachers, but the interviews and the prospective teachers’ responses are nowhere around. The reader has to trust and believe the delivered analysis, with no data supporting such analysis and with no meaningful evidences delivered. This is a key point of the manuscript. Transcriptions of the interviews should be provided, as far as these are key data needed to interpret and understand the delivered analysis. I suggest submitting an additional file of supporting information, annex or similar… and presenting some extracts of the mentioned interviews on the manuscript itself (the submitted manuscript reach to 15 pages, the maximum allowed size of 20 pages gives a room of 5 pages to solve this issue!).

In addition, the size of the simple is way too small to consider the results as “scientifically meaningful”. No generalizations can be made, because of the reduced sample of 8 participants in a single experience. The presented study has its value, and I find it interesting, but I’d recommend to change the title of the manuscript so that the reader quickly understand that the researchers are delivering a case study.

Final consideration

My main concern is that there is a lack of scientific rigor for a manuscript that aims to be published in a Q2 journal (such as Education Sciences). Original data should be provided, and some discussions should be better introduced and grounded. The study is interesting and could be useful to many -if well presented-. It deserves publication, but major revisions must be carried out prior to publish this manuscript.

Author Response

Thank you very much for taking the time to read our article and provide feedback. We appreciated your kind words and important suggestions that improved our paper.

The attached table outlines your suggestions and notes related to our revisions.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper addresses prospective teachers (PTs)’ professional noticing under the lens of responsive teaching. The topic of the manuscript is interesting and relevant to the potential audience of Education Sciences. It can make a contribution in the field of PTs’ noticing concerning PTs’ abilities to respond to students’ mathematical thinking. Below I provide some comments for improvement.

 1. The literature review should be enriched with some other important studies that focus on the nature of PTs’ responses to students’ errors, e.g., Son (2013). Also, there is a need to refer/categorize existing studies in relation to the structures given to PTs for noticing. In the present study, PTs worked on pieces of students’ work selected by themselves. In other studies PTs work with structures such as critical events, scripting dialogues  (e.g. Zazkis et al., 2009).  By referring to these studies the authors could also be able to describe more clearly the contribution of the study and position it better in the existing terrain in the field.  

Son, J. W. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational studies in mathematics, 84(1), 49-70.

Zazkis, R., Liljedahl, P., & Sinclair, N. (2009). Lesson Plays: Planning teaching vs. teaching planning. For the Learning of Mathematics, 29(1), 40–47.

 3. The authors should elaborate further at the theoretical part of the paper the connection between the third element of noticing  (‘deciding to respond, emphasis on the decision) to responsive teaching.

4. In the methods section the authors should inform the readers about PTs’ experiences in responsive teaching or responsive teaching actions/practices before the fourth year of their studies. In the current version of the paper, we read that ‘the participants had all been introduced to the construct of professional noticing, learning theory and educational research related to the importance of eliciting and using learner thinking during mathematics instruction’ (p. 3). Is this experience related to responsive teaching? This is critical because it constitutes a central element of the study and the research focus. Under which base it was expected by PTs to bypass procedures (as it is shown the literature) and pursue students’ mathematical thinking when responding to students?

5. The research questions should be aligned to research focus and become more accurate. The number of PTs who were able to notice students’ mathematical thinking can be mentioned in some way in the results – it is not a research question per se. As regards the research questions in general, the authors should clarify how they relate to the three elements of noticing. In my view, the most important thing is to clarify what / how PTs noticed students’ mathematical thinking and through which actions and aims. Also, the interrelation between actions and aims is important as well as the study of emerging shifts.

6. The results are interesting. However, the most critical part concerns the focus on specific cases that highlight the nature of shifts from one type of professional noticing to another. In my view, this should constitute the main part of the results section (1-2 more cases should be presented in detail) that leaves space for a deeper look to the nature of PTs’ noticing and individual/contextual factors explaining the specificities of each case. In this area the authors could highlight better the contribution of their study.

7. As regards the discussion and conclusion sections, the contribution of the study should be clearly related to the existing literature in the field. In the present version of the paper the results are mainly interpreted as indications/aids for teacher educators at the level of teacher education.  It is of course a valuable contribution at this level, but the status of the results to the existing research in the field is required.

Author Response

Thank you very much for taking the time to read our article and provide feedback. We appreciated your kind words and important suggestions that improved our paper.

The following table outlines your suggestions and notes related to our revisions.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

This article reports on the analysis of prospective teachers while engaging in professional noticing of their students’ mathematical thinking in pieces of written work. The characterization have been made by using responsive teaching analysis.

In a first review round, I noticed some aspects that should be improved. To this respect:

Introduction

Introduction is way too brief and provides not enough background or context to fully understand the interest of the research. In this regard, research questions should be better introduced and grounded. To improve this, I’d suggest a deeper discussion about the challenges faced those working on training teachers. Some key questions should be clearly answered in this section, such like: what is this research useful for? why is different to previous research?

Author’s response: We agree that the introduction was too short. On page 1 we have added a paragraph focused on the challenges facing prospective teachers learning to teach responsively and on page 2 we situated the current study.

This review has been partially fulfilled.

Authors have expanded the introduction section, providing additional background. However, research questions are still not presented or discussed instead, the authors delivered a paragraph summarizing the study (lines 43-48).

I miss a specific section discussing prospective teachers’ limitations and difficulties with respect to specific didactic-mathematic knowledge (this might have an impact on the interpretation of the obtained results!). To my opinion, this is a key discussion that the manuscript entirely bypass. This discussion could be presented in the introduction.

Author’s response: Thank you for this suggestion. We have added citations on Page 1 about the difficulties faced by prospective teachers in learning to professionally notice and to teach responsively.

This review has not been fulfilled.

To my opinion, little to no improvement has been made regarding this issue.

Figure captions

While the manuscript is overall well written, additional attention should be paid to figure captions… that are way too brief, becoming meaningless in some specific captions. To this regard, a good figure caption should first describe the related figure and, second, briefly analyze the figure itself. In doing so, a reader should be able to fully understand the figure without reading the related text -one could expand information by reading the related text-. For example, in figure 1, the caption states: “Barbara’s shared piece of student work”… which is an absolutely generic caption. Instead, I’d suggest: “Piece of student work analyzed by Barbara. The student’s response corresponds to a problem that requires to determine the total number of bottles of milk for 21 boxes -each one containing six bottles-. It can be seen that Barbara highlights specific elements of the written answer, interpreting that the student didn’t understand what the problem was asking.”

Thank you for this suggestion. It is the first time I have been given this suggestion and I liked the way it contributes to the flow of the manuscript. We have made these changes for each figure included in the manuscript.

This review has been fulfilled.

While figure captions are displaced and bad positioned in the submitted pdf (probably due to the “track changes” option), such captions have been clearly improved.

Data and results

Finally, the most critical aspect that should be corrected in the manuscript is -to my opinion- the lack of any transcription. On the “research design” section, it is stated that the authors analyzed several responses of prospective teachers, but the interviews and the prospective teachers’ responses are nowhere around. The reader has to trust and believe the delivered analysis, with no data supporting such analysis and with no meaningful evidences delivered. This is a key point of the manuscript. Transcriptions of the interviews should be provided, as far as these are key data needed to interpret and understand the delivered analysis. I suggest submitting an additional file of supporting information, annex or similar… and presenting some extracts of the mentioned interviews on the manuscript itself (the submitted manuscript reach to 15 pages, the maximum allowed size of 20 pages gives a room of 5 pages to solve this issue!).

Thank you for this suggestion. We have incorporated your suggestion by emphasizing places in the manuscript that share direct quotes from transcripts (e.g. in the methods section) and adding an additional illustrative example. The four illustrative examples show the analytical work, and shares transcript excerpts so the reader can understand how the results were achieved. In other words, each illustrative example is meant to show transcript and utilized analysis. (pp. 8-14)

This review has been partially fulfilled.

Research data consist on 8 interview transcripts and 16 pieces of student written work. Author’s stated that “each participant engaged in semi-structured insterview in which they examine two pieces of student written work”. In my last communication I suggested the inclusion of evidences (transcriptions of the interviews). I’d also recommend providing supplementary material with the 16 pieces of student written work, and also discussing the criteria used for selecting such 16 pieces.

Regarding the inclusion of evidence, minor improvements have been made, by including some paragraphs describing the discussions (lines 483-454). I’d recommend expanding these transcriptions a bit more.

In addition, the size of the simple is way too small to consider the results as “scientifically meaningful”. No generalizations can be made, because of the reduced sample of 8 participants in a single experience. The presented study has its value, and I find it interesting, but I’d recommend to change the title of the manuscript so that the reader quickly understand that the researchers are delivering a case study.

Thank you for this reminder. We have changed the title and revisited the language throughout the manuscript to emphasize that this is a case study.

This review has been fulfilled.

Final consideration

My main concern is that there is a lack of scientific rigor for a manuscript that aims to be published in a Q2 journal (such as Education Sciences). Original data should be provided, and some discussions should be better introduced and grounded. The study is interesting and could be useful to many -if well presented-. It deserves publication, but major revisions must be carried out prior to publish this manuscript.

The manuscript has been improved, but it still has room for improvement in my opinion. It is worth publishing and I still consider that its findings might be interesting to many, but minor amendments should be addressed. Please note that Education Sciences is now a Q1 journal, so the excellency in research should be our priority.

 

 

Author Response

Thank you for the opportunity to respond to a second round of reviews. I have attached a table of responses. 

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors addressed all the points raised by the reviewers. So I suggest the paper to be accepted in each current form.

 

Author Response

Thank you for your review and support towards publication.