Professional Support in Teaching Mathematics through Guided Discovery: The Role of Agency on Multiple Levels

Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article addresses a crucial and sensitive topic in mathematics education, the guided Discovery, which is especially suitable for the present quickly evolving and changing era as its main aim is not to transmit fixed knowledge, but to develop problem-solving and critical thinking skills that can be readapted in various future situations.
This type of approach, although quite widespread in Hungary, is not used by a small group of Hungarian teachers.
The article aims to: describe a case study of mentoring support provided to a novice mathematics teacher in using Guided Discovery in her classroom
Interested in examining the case of mentoring support provided to a novice mathematics teacher, the authors propose two questions:
- What are the challenges and the process of growth of a novice teacher while being immersed in using Guided Discovery in their classroom with mentoring support in planning and reflection?
- What aspects of the mentoring structure are effective for giving support in Guided Discovery, and how can it be improved and adapted to involve a larger number of teachers
Anchored in Támas Varga, they carried out a qualitative investigation based on three classes taught by Hanna (classes A, B, and C), for her students.
The empirical material consists of interviews carried out with Hanna and the students and the discussion.
a consisted of transcriptions of the meetings, field notes and questionnaire.
The thematic analysis highlighted the following themes:
Student affect and growth: students’ view.
Student affect and growth: teacher’s view.
Teacher affect and growth.
Teacher agency.
What helped teachers learn
Regarding the methodology, it is important to consider the representativeness of the sample used in the study and the generalization of the results to other sociocultural realities and specific contexts. However, the article addresses a significant social issue, offering valuable insights into domestic child labor and its impacts on children's development and providing support so that schools and teachers can intervene in this problem.
Points to Consider:
1. Explain better the context of the investigation, that is, the interventions carried out by Hanna. The class and the tasks developed are mentioned in a superficial, almost casual way so that it is not possible to understand some aspects that are highlighted in the analysis carried out. For example, on page 8, when talking about the failed class, without presenting any description of the class, the authors say: “In Lesson A Hanna felt frustrated, as she perceived that most students were passive and not cooperating. She said that when there was a specific task, they did it, but when they needed to think, or talk or cooperate they were passive, and some of them also missed instructions so she needed to repeat them several times. She said she was not sure why, and she gave several possible reasons. She mentioned various practical issues outside of class that probably contributed to low student energy levels, and added that she was in a bad mood herself. In terms of the tasks, she said that some of the tasks may have been very easy and some of them very difficult, so students may have been stuck.”
2. Sample and Generalization: It is important to consider the representativeness of the sample used in the study and the generalization of the results to other specific realities and contexts.
3. Methodological Limitations: The article could provide a more in-depth discussion about the methodological limitations encountered during the research, such as possible selection biases or data collection instruments.
4. The discussion of the agency category is critical from a scientific point of view because it was not within the scope of the article.
Author Response
Dear Reviewer,
Thank you for your review. Here are our answers to your comments.
Comment 1. Explain better the context of the investigation, that is, the interventions carried out by Hanna. The class and the tasks developed are mentioned in a superficial, almost casual way so that it is not possible to understand some aspects that are highlighted in the analysis carried out. For example, on page 8, when talking about the failed class, without presenting any description of the class, the authors say: “In Lesson A Hanna felt frustrated, as she perceived that most students were passive and not cooperating. She said that when there was a specific task, they did it, but when they needed to think, or talk or cooperate they were passive, and some of them also missed instructions so she needed to repeat them several times. She said she was not sure why, and she gave several possible reasons. She mentioned various practical issues outside of class that probably contributed to low student energy levels, and added that she was in a bad mood herself. In terms of the tasks, she said that some of the tasks may have been very easy and some of them very difficult, so students may have been stuck.”
Response 1. Thank you for pointing out that we need to add further details about the tasks and the lessons. We added more details to all three lessons (highlighted in yellow on pages 5-8). Concerning the cited expert from Lesson A, we are not able to add an objective description of the reasons why the teacher interpreted the class as a failure, as this was her subjective experience, which did not neccessarily match with the subjective experience of the mentors and the students. We hope that the objective description of what happened in the class is clear (page 4-5).
Comment 2. Sample and Generalization: It is important to consider the representativeness of the sample used in the study and the generalization of the results to other specific realities and contexts.
Response 2. We added details about this in the conclusion (highlighted in yellow on page 15).
Comment 3. Methodological Limitations: The article could provide a more in-depth discussion about the methodological limitations encountered during the research, such as possible selection biases or data collection instruments.
Response 3. We added details about this in the conclusion (highlighted in yellow on page 15).
Comment 4. The discussion of the agency category is critical from a scientific point of view because it was not within the scope of the article.
Respones 4: We agree that the agency category was originally not within the scope of the article, so let us explain why we still think it is relevant. Our research question was quite open, so we used thematics analysis, a method suitable for finding ideas we have not considered before the research. During thematic analysis agency emerged as a central theme, and hence we present it as a central idea in the results.
Note: we could not interpret the following sentence: "However, the article addresses a significant social issue, offering valuable insights into domestic child labor and its impacts on children's development and providing support so that schools and teachers can intervene in this problem."
Many thanks for providing insightful comments and thus helping us improve the paper.
Sincerely,
Reviewer 2 Report
Comments and Suggestions for AuthorsThis article is well written. The introduction of Guided Discovery is clear and precise, well done. The goals of the article are also clearly stated and discussed.
In line 179, Problem 2, a question in which students are to guess a point. There seem to be too many choices to guess here. How do we actually have it in a classroom? Simply telling the students the distance between the guess point and the target point may not be sufficient.
In line 186, Problem 3, the Lamb problem, I'm a little lost with the aim of the question. We do not see students working here. Do we get any information here?
Also, in Problem 4, we do not see any students working here.
Author Response
Dear Reviewer,
Thank you for your review. Here are our answers to your comments.
Comment 1. In line 179, Problem 2, a question in which students are to guess a point. There seem to be too many choices to guess here. How do we actually have it in a classroom? Simply telling the students the distance between the guess point and the target point may not be sufficient.
Response 1. Thank you for pointing out that we need to add further details about student thinking here. We added more student solutions and detailed explanations of strategies in order to clarify (highlighted in yellow on pages 5-7).
Comment 2. In line 186, Problem 3, the Lamb problem, I'm a little lost with the aim of the question. We do not see students working here. Do we get any information here?
Response 2. We agree that the wording of this problem is unclear (we use the wording written and used by the teacher). We added a note explaining the meaning, we hope this is helpful (highlighted in yellow on page 7).
Comment 3. Also, in Problem 4, we do not see any students working here.
Response 3: Unfortunately we have not collected student work for this problem. We added more detail to the description of the lesson (highlighted in yellow on page 7-8).
Many thanks for providing insightful comments and thus helping us improve the paper.
Sincerely,