Learning the Mathematical Discussion (MD) Pedagogical Model in and from Practice: The Professional Development of Mathematics Teachers in a Technological Environment

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Overall, I think the manuscript could be strengthened with more references to teacher professional development literature, particularly those that support your approach to this type of intervention. I think that this type of professional development with pre-service teachers is important work, and I would like to see this work better situated (or in conversation with) similar interventions. I have left suggestions organized by sections of the manuscript below:

Abstract:

• Add the number of PSTs to the abstract
• Add a brief overview of the results to the abstract

Conceptual Framework:

This is where the authors could focus to strengthen the manuscript. First, if this is a conceptual framework, the authors should clarify from which concepts they are building and developing a new approach to teacher learning. This is currently more of a short literature review that states teacher professional development should include learning as a student and a reflective experience. What could be added is a larger discussion as to why meta-discussion could be an effective learning tool for teacher professional learning about mathematics. Many different approaches to reflection are based on various learning theories. For example, in cognitive and situated learning perspectives, classroom-based analyses involve an interpretive framework. Others use a task analysis and have teachers metacognitively reflect on their learning goals and use individual lesson videos to evidence instructional practices and student learning. There are linguistic perspectives, sociocultural perspectives, critical perspectives, etc. Mainly, the authors should frame how they are analyzing and evidencing PST learning and what perspective they are taking. Maybe expand on how you conceptualize the PSTs taking on the roles of mediator and moderator, and how that relates to MDPm, particularly for its effect on reflecting on a prior teaching experience. Relatedly, I was curious to learn more about how specific mathematical topics were chosen.

In the bullets about the new perspective starting at Line 128, it says that “back to the task” becomes “back to the experience,” but it is not clear how this is different from the MDc and what the pedagogical model (PM) is. It may help to define this more clearly above in the section on The Mathematical Discussion: an overview. Similarly, the second bullet point, I believe the authors are alluding to the idea that the PST then becomes the one directing their focus, but it is not clear how the PST is being directed to do so. Maybe give more explanations of the actual practices and roles to help understand what these MDPm constructs look like. After reading through section 4, I was still not clear how PSTs were getting to the point of being able to successfully and effectively recognize the characteristics of PM.

When I got to Section 5. Technological Environment’s Support, the authors claim that division in virtual rooms was supportive of learning. This could use more support since some research would argue that virtual environments can be challenging for participation and learning. Also, it sounds like technology allowed for more flexibility than collaboration, since participants seem to have had agency. This section could be expanded. Also, this section talks about “students,” but I thought the unit of analysis was PSTs. Do you all mean “teachers as students?”

Methods: There is no description of the data analysis. There were transcriptions, but how were they coded? And with what codes? How were the episodes you presented chosen for the findings? Additionally, you note the large corpus of teachers, but it is not clear what sample was chosen for analysis for this paper. All I can ascertain is that two episodes were chosen to show the cases around a geometric problem and an arithmetic problem. It would help to explain what and how the data were chosen. This is also important to distinguish because the problem seems to be more of a context for the discussion.

After reading the section 5.1 Structure of the Experimental Training Method, I am still left wondering how this is different from some of the teacher professional development models that are already out there, which have teachers reflect on others’ practices and think about how to apply their own. Is it the format? Are there ways questions were posed that made this reflection more effective/fruitful?

In reading the results, the authors refer to the “trainer,” but I thought that the role shifted to the PSTs. So, wouldn’t that person now be more of a “facilitator?”

In Section 7. Preliminary Results… does this mean that you only did a preliminary analysis of the data?

The manuscript could benefit from a Discussion section and a Conclusion.

Comments on the Quality of English Language

I only detected a few grammatical errors. I am sure I did not catch all of them. So, I recommend a close read. Here are some of the small errors I found below:

• Line 29, “It remains the difficulty …” changed to “It remains difficult…”
• Line 31, add “(MD)” after “Mathematical Discussion”
• Line 32, omit “a” in sentence, “This study, part of a deeper research…”
• Line 34, omit “(PSTs)” or replace “future teachers” with “pre-service teachers”
• Line 36, change “kind” to “kinds”
• Line 83, the title “Mathematical” is spelled incorrectly.
• Lines 217-218, do you mean “solution strategies,” not “resolution strategies?”

Author Response

 

Comments 1: Abstract: Add the number of PSTs to the abstract Add a brief overview of the results to the abstract

Response 1: Thank you for pointing this out. Therefore, we have added the number of PSTs (line 8) and a brief overview of the results (line 13-15)

Comments 2: Conceptual Framework: This is where the authors could focus to strengthen the manuscript. First, if this is a conceptual framework, the authors should clarify from which concepts they are building and developing a new approach to teacher learning. This is currently more of a short literature review that states teacher professional development should include learning as a student and a reflective experience. What could be added is a larger discussion as to why meta-discussion could be an effective learning tool for teacher professional learning about mathematics. Many different approaches to reflection are based on various learning theories. For example, in cognitive and situated learning perspectives, classroom-based analyses involve an interpretive framework. Others use a task analysis and have teachers metacognitively reflect on their learning goals and use individual lesson videos to evidence instructional practices and student learning. There are linguistic perspectives, sociocultural perspectives, critical perspectives, etc. Mainly, the authors should frame how they are analyzing and evidencing PST learning and what perspective they are taking. Maybe expand on how you conceptualize the PSTs taking on the roles of mediator and moderator, and how that relates to MDPm, particularly for its effect on reflecting on a prior teaching experience. Relatedly, I was curious to learn more about how specific mathematical topics were chosen.

Response 2: Agree. We have, accordingly, modified this section to emphasize this point and to give a precise idea of how our research is aligned in the literature. In particulare see line 67-73 and line 95-101   In the bullets about the new perspective starting at Line 128, it says that “back to the task” becomes “back to the experience,” but it is not clear how this is different from the MDc and what the pedagogical model (PM) is. It may help to define this more clearly above in the section on The Mathematical Discussion: an overview. Similarly, the second bullet point, I believe the authors are alluding to the idea that the PST then becomes the one directing their focus, but it is not clear how the PST is being directed to do so. Maybe give more explanations of the actual practices and roles to help understand what these MDPm constructs look like. After reading through section 4, I was still not clear how PSTs were getting to the point of being able to successfully and effectively recognize the characteristics of PM.

Comments 3: In the bullets about the new perspective starting at Line 128, it says that “back to the task” becomes “back to the experience,” but it is not clear how this is different from the MDc and what the pedagogical model (PM) is. It may help to define this more clearly above in the section on The Mathematical Discussion: an overview. Similarly, the second bullet point, I believe the authors are alluding to the idea that the PST then becomes the one directing their focus, but it is not clear how the PST is being directed to do so. Maybe give more explanations of the actual practices and roles to help understand what these MDPm constructs look like. After reading through section 4, I was still not clear how PSTs were getting to the point of being able to successfully and effectively recognize the characteristics of PM.

Comments 4: Methods: There is no description of the data analysis. There were transcriptions, but how were they coded? And with what codes? How were the episodes you presented chosen for the findings? Additionally, you note the large corpus of teachers, but it is not clear what sample was chosen for analysis for this paper. All I can ascertain is that two episodes were chosen to show the cases around a geometric problem and an arithmetic problem. It would help to explain what and how the data were chosen. This is also important to distinguish because the problem seems to be more of a context for the discussion.   Response 4: We added further information about analysis and how the data were chose in a new sub-paragraph (line 301-312) is given.

Comments 5: After reading the section 5.1 Structure of the Experimental Training Method, I am still left wondering how this is different from some of the teacher professional development models that are already out there, which have teachers reflect on others’ practices and think about how to apply their own. Is it the format? Are there ways questions were posed that made this reflection more effective/fruitful? In reading the results, the authors refer to the “trainer,” but I thought that the role shifted to the PSTs. So, wouldn’t that person now be more of a “facilitator?” In Section 7. Preliminary Results… does this mean that you only did a preliminary analysis of the data? The manuscript could benefit from a Discussion section and a Conclusion.

Response 5: Information about the difference between the MDPm and others teacher professional model is given in line 295-300 and 98-106. We rearrange the last paragraph by adding the two suggested sections, to answer the comments regarding the conclusions.   We also modified and corrected the grammar issues

 

 

 

 

 

 

 

 

 

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Learning the Mathematical Discussion pedagogical model in  and from practice: the professional development of mathematics teachers in a technological environment

This paper anchors on key theories of teacher education, emphasising the work of Shulman and Ball.  This paper emphasizes the importance of participating in learning how to solve a mathematical problem and then reflecting on the solution process.  A total of 180 PSTs participated in the first experiment and 220 in the second experiment.  All were fourth-year students in a Primary Education degree programme specialising in Mathematics Education.  The training was done via Microsoft Teams platform.

In Phase 1, the PSTs and the trainer participated in a discussion to conceptualize a specific mathematical problem.  The trainer provided the pedagogical model via a lecture.

In Phase 2, focused on the mathematical content.  The participants were required to solve an open-ended mathematical problem.  Mathematical discussions were held where the participants shared their solution processes with the rest of the group.

In Phase 3, the focus was not on the mathematics but rather the process of teaching and learning.  The PSTs reflected on their phase 2 experience.  The discussion in Phase 3, Meta-Discussion, involved the PSTs and the trainer.  The aim of Meta-Discussion was to provide the participants the opportunity to identify key aspects of the pedagogical model – to understand teacher’s role and actions in the classroom. 

The reflections of the participants supported the effectiveness of the different phases of the experiment. 

The paper presented conclusions which did not overclaim the effectiveness of the experiment.

This paper has presented a useful model for mathematics teacher education.  Although the participants’ feedback was encouraging, it does not mean that these participants would be effective teachers.  The effectiveness of the programme could only be ascertained by observing these PSTs in real-time teaching, i.e. when these PSTs are in front of a classroom of learners with diverse needs.

Amendment: Page 2, line 61, should read pedagogical content knowledge, not pedagogical knowledge.

References are appropriate to the study.

Author Response

Comments 1: This paper anchors on key theories of teacher education, emphasising the work of Shulman and Ball.  This paper emphasizes the importance of participating in learning how to solve a mathematical problem and then reflecting on the solution process.  A total of 180 PSTs participated in the first experiment and 220 in the second experiment.  All were fourth-year students in a Primary Education degree programme specialising in Mathematics Education.  The training was done via Microsoft Teams platform. In Phase 1, the PSTs and the trainer participated in a discussion to conceptualize a specific mathematical problem.  The trainer provided the pedagogical model via a lecture. In Phase 2, focused on the mathematical content.  The participants were required to solve an open-ended mathematical problem.  Mathematical discussions were held where the participants shared their solution processes with the rest of the group. In Phase 3, the focus was not on the mathematics but rather the process of teaching and learning.  The PSTs reflected on their phase 2 experience.  The discussion in Phase 3, Meta-Discussion, involved the PSTs and the trainer.  The aim of Meta-Discussion was to provide the participants the opportunity to identify key aspects of the pedagogical model – to understand teacher’s role and actions in the classroom.  The reflections of the participants supported the effectiveness of the different phases of the experiment.  The paper presented conclusions which did not overclaim the effectiveness of the experiment. This paper has presented a useful model for mathematics teacher education.  Although the participants’ feedback was encouraging, it does not mean that these participants would be effective teachers.  The effectiveness of the programme could only be ascertained by observing these PSTs in real-time teaching, i.e. when these PSTs are in front of a classroom of learners with diverse needs. Amendment: Page 2, line 61, should read pedagogical content knowledge, not pedagogical knowledge. References are appropriate to the study

Response 1: Thank you very much, we checked your amendment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors did a better job of citing relevant research and attending to the reviewers' feedback. I appreciate how well the authors framed the study as reporting on preliminary finding more clearly and how well they clarified how their intervention was distinct from others.