The Role of Dynamic Geometry Software in Teacher–Student Interactions: Stories from Three Chinese Mathematics Teachers
Angie Hodge-Zickerman
Round 1
Reviewer 1 Report
This paper could be a very solid article if it was proofread for grammatical errors. These grammatical errors make it hard to follow the logic of the study/argument presented. There is great potential in this paper though.
Author Response
Response to Reviewer 1 Comments:
Point 1: This paper could be a very solid article if it was proofread for grammatical errors. These grammatical errors make it hard to follow the logic of the study/argument presented. There is great potential in this paper though.
Response 1: Thank you for the comments. We have asked language editors to help us check the grammatical errors and make our manuscript easily understood.
Reviewer 2 Report
The authors intend to study the role of dynamic geometry software (DGS) in teacher-student interaction during class time. Three teachers' teaching stories using DGS in their classrooms are presented as three cases in the paper. However, it is unclear if these three teachers were from the same school or if they were teaching the same course at the same grade level. The conclusion is that the teachers lack skills to integrate the DGS into their teaching. This conclusion is not convincing because there are other factors, such as class time, that are not considered by this paper. There is no information on the length of the class period. The depth of exploration can very well be limited by the class length.
The authors should make a thorough revision to the manuscript and fix many grammatical errors of the text.
Author Response
Respond to Reviewer 2 Comments:
Point 1: The authors intend to study the role of dynamic geometry software (DGS) in teacher-student interaction during class time. Three teachers' teaching stories using DGS in their classrooms are presented as three cases in the paper. However, it is unclear if these three teachers were from the same school or if they were teaching the same course at the same grade level.
Response 1: Thank you for your comments and questions. These three teachers are not from the same school. Two of them (Mr. ZH & Mrs. J) are experienced teachers in the same school. Another one (Mrs. Y) comes from another school. All the lessons included in this study are for students in Grade 7. We have added this information in our revised version in the method section.
Point 2: The conclusion is that the teachers lack skills to integrate the DGS into their teaching. This conclusion is not convincing because there are other factors, such as class time, that are not considered by this paper. There is no information on the length of the class period. The depth of exploration can very well be limited by the class length.
Response 2: Yes, there are many factors that will affect teachers to integrate technologies like DGS in classroom teaching like class time. In this research, we focus more on whether teacher-student interaction will be affected by using DGS and what kinds of questions the teacher asked during the lessons. We found that sometimes, teachers had tried to change their traditional ways to ask students questions for example, asking students how to construct triangles with the help of DGS, although the class time is still limited. But during our studies, these kinds of questions are few. So that we think it is because teachers lack enough skills to integrate DGS although some of them are willing to use it in different ways. We have added the information on the class time of each lesson included in our research in the method section. And we discussed there were other factors like limited time, heavy tasks and examinations that will affect teacher-student interaction when we talked about the limitation of our study.
Point 3: The authors should make a thorough revision to the manuscript and fix many grammatical errors of the text.
Response 3: We have asked language editors to help us check the grammatical errors and make our manuscript easily understood.
Reviewer 3 Report
Classroom teaching relies heavily on teacher-student interaction through questions and carefully considered teacher feedback. Questions can help teachers and students learn and discover simultaneously. Teachers should also learn to ask specific questions to help students discover mathematical concepts with technology. Technology gives students more effective chances to experiment and think mathematically. Thus, it provides an opportunity for more enriching teacher-student interaction. For example, technology may lead students to ask more profound questions that teachers may not predict when they prepare lessons or mathematical tasks. The feedback on these questions can help students and teachers consider changing their problem-solving and asking strategies.
Math teachers frequently use dynamic geometry software (DGS). According to this research, DGS does not change how teachers interact with students. They mostly use this software to 'present' mathematical questions. According to the study, teachers generally do not demonstrate that DGS can also be used for problem-solving and problem-finding. Teachers use and decide when and how to use the software. Although DGS has dynamic elements like moving points, teachers only use the software to present the final results. Although the research is well designed and has some novel features, one of the study's serious limitations is that it considered three teachers' lessons to analyse data. Further research is needed to understand how technology resources like DGS affect mathematics classroom teaching in different contexts.
Some examples of other corrections and typos that are required are:
Page 3 (line 97) Change '.....show that DGS is the generator of new tasks..' to ..show that DGS can also be used as the generator of new tasks..'
Section 3. Research questions .. modify the research questions to be more specific e.g.
1. What technology-specific actions do the mathematics teachers focus on.
2. What roles as amplifier and recogniser does DGS play...
(line 138) change "...we focus on how DGS as the main technological resource supports..." to "... we focused on how DGS appears as a technological resource to support ..."
Under table 3 - Task used by Madame J (page 5) .. Point N is not mentioned.
(line 206). Remove .." This process shows a typical teaching episode in almost all Chinese lessons."
The conclusion and Discussion section must also be rewritten and be more precise.
Author Response
Point 1: Classroom teaching relies heavily on teacher-student interaction through questions and carefully considered teacher feedback. Questions can help teachers and students learn and discover simultaneously. Teachers should also learn to ask specific questions to help students discover mathematical concepts with technology. Technology gives students more effective chances to experiment and think mathematically. Thus, it provides an opportunity for more enriching teacher-student interaction. For example, technology may lead students to ask more profound questions that teachers may not predict when they prepare lessons or mathematical tasks. The feedback on these questions can help students and teachers consider changing their problem-solving and asking strategies.
Response 1: Thank you for your comments. We totally agree with this. In China, based on our own experiences of observing mathematics teaching in schools, we found that mathematics teachers always focus on the mathematical results during the lessons no matter whether DGS is used or not. It seems that DGS seldom affects teacher-student interaction in Chinese lessons. So we want to find more evidence and think about how to deal with this phenomenon. It is the main objective of why we did this research.
Point 2: Math teachers frequently use dynamic geometry software (DGS). According to this research, DGS does not change how teachers interact with students. They mostly use this software to 'present' mathematical questions. According to the study, teachers generally do not demonstrate that DGS can also be used for problem-solving and problem-finding. Teachers use and decide when and how to use the software. Although DGS has dynamic elements like moving points, teachers only use the software to present the final results. Although the research is well designed and has some novel features, one of the study's serious limitations is that it considered three teachers' lessons to analyse data. Further research is needed to understand how technology resources like DGS affect mathematics classroom teaching in different contexts.
Response 2: Thank you for the comments. In the conclusion section, we talked about the limitation of our research. Because we have limited data (three mathematics teachers), we did not want to make more general conclusions in Chinese mathematics lessons, but to present a detailed picture, showing teachers’ strategies regarding the use of DGS in mathematics education. Of course, we also think further research is needed in the future.
Point 3: Page 3 (line 97) Change '.....show that DGS is the generator of new tasks..' to ..show that DGS can also be used as the generator of new tasks..'
Response 3: Thank you for your correction, we have changed this sentence.
Point 4: Section 3. Research questions .. modify the research questions to be more specific e.g.
- What technology-specific actions do the mathematics teachers focus on.
- What roles as amplifier and recogniser does DGS play...
Response 4: Thank you for your correction, we have changed our research questions and made them more specific.
Point 5: (line 138) change "...we focus on how DGS as the main technological resource supports..." to "... we focused on how DGS appears as a technological resource to support ..."
Response 5: Thank you for your correction, we have changed this sentence.
Point 6: Under table 3 - Task used by Madame J (page 5) .. Point N is not mentioned.
Response 5: Thank you for your comments, we have added the related information in table 3 to mention point N.
Response 6: (line 206). Remove .." This process shows a typical teaching episode in almost all Chinese lessons."
Response 6: Thank you for your correction, we have removed this sentence.
Point 7: The conclusion and Discussion section must also be rewritten and be more precise.
Response 7: Thank you for your comments, we divided the final section of our paper into two parts and reorganized our conclusion part. In our revised version, we added some previous research that can support our results and conclusions. Like the study found that teacher–student interactions are often guided by the initiation–response–evaluation pattern [29]. Additionally, questions and answers may not be derived from students’ thought processes during lessons [4]. Using DGS in this way does not impact students’ problem-solving process and does not modify student learning situations and teacher practices in geometry. With DGS, teachers were also required to address new mathematical practices [32,33] and pay more attention to how to design suitable teaching and learning activities [34]. It seems that teachers lack sufficient strategies for their effective integration into mathematics education [35].
Reviewer 4 Report
The paper looks into the link between technology and mathematics education with an emphasis on DGS.
Details related to the theoretical framework that this paper is addressing is needed at this stage to highlight how technology can play a role in the type of interactions between teachers and students. It seems that the contextual background of mathematics education in China gives emphasis on finding the right answer or in other words the final products. With DGS more probing can take place to elicit student’s deep conceptual learning and how technology can be used beyond an amplifier to include an additional role of a reorganiser.
Also there needs to be some directions of what teachers are expected to do with such new learning environment especially if students are given the chance to have direct interaction with DGS.
As for the methods section, more details are needed while combining some text from the paper with reference to the tools and analysis that was found later in the paper.
For example, RQ1 should include if the videos will be divided to certain time intervals to analyse the type of questions posed by teachers to their students in addition to the feedback. Since there were 3 teachers, 3 expert and 1 novice, further comparisons could be made in the discussion section. For RQ2, since teachers are interviewed, more on the questions asked during the interviews and how their responses were analysed need to be added.
Suggest that you divide the last section titled conclusions and discussions into 2 separate sections to ensure that each part serves its purpose.
Author Response
Point 1: Details related to the theoretical framework that this paper is addressing is needed at this stage to highlight how technology can play a role in the type of interactions between teachers and students.
Response 1: Thank you for the comments. Researchers think DGS can improve learning and teaching mathematics via its dragging mode. Students need to use this mode to solve problems, including construction, searching for commonalities, conjecturing, and proving and refuting conjectures. And we think when students used DGS as a problem-solving tool, teacher-student interaction may be changed. The interaction will focus more on how to use DGS to explore and create mathematics knowledge.
Point 2: It seems that the contextual background of mathematics education in China gives emphasis on finding the right answer or in other words the final products. With DGS more probing can take place to elicit student’s deep conceptual learning and how technology can be used beyond an amplifier to include an additional role of a reorganiser.
Response 2: Yes, you are right, in our studies, teachers more focus on how to help students find correct answers and sometimes may dismiss the moving process. So they seldom ask students to explore mathematics during the lessons. At this point, we think DGS was used as an amplifier.
Point 3: Also there needs to be some directions of what teachers are expected to do with such new learning environment especially if students are given the chance to have direct interaction with DGS.
Response 3: Thank you for your comments. We added some research in China that deal with how technologies like DGS affect teachers’ practice in the lessons and what teachers are expected to do with DGS. For example, teachers had to directly teach students mathematical concepts [16], whereas, with DGS, teachers can let students independently explore and experiment [17]. They are also expected to use DGS to help students in the problem-solving process.
Point 4: As for the methods section, more details are needed while combining some text from the paper with reference to the tools and analysis that was found later in the paper.
For example, RQ1 should include if the videos will be divided to certain time intervals to analyse the type of questions posed by teachers to their students in addition to the feedback. Since there were 3 teachers, 3 expert and 1 novice, further comparisons could be made in the discussion section.
Response 4: Thank you for the comments. For analyzing videos, we first divided each of them into a certain time based on the tasks and problems teachers and students deal with. What I mean is we divided the videos into two or more parts if teachers change the mathematical tasks or problems students need to solve. For example, in Mrs. J’s lesson, the main task contained two sub-questions. So we would divide the video into two sub-sections at first. Then we focus on teacher-student interaction that happened in each sub-section. And if teachers asked different students to answer questions, the analysis would be done separately.
Point 5: For RQ2, since teachers are interviewed, more on the questions asked during the interviews and how their responses were analysed need to be added.
Response 5: Thank you for the comments. In the methods section, we added the process of analyzing our interview data on page 6. One example was provided in appendix.
Point 6: Suggest that you divide the last section titled conclusions and discussions into 2 separate sections to ensure that each part serves its purpose.
Response 6: Thank you for your suggestions. We have divided our last section into two parts and reorganized the related contents and also found more other research to support our point of view.
Round 2
Reviewer 1 Report
This paper reads much better now that the grammar and structure has been revised.
Author Response
Response to Reviewer 1 Comments:
Point 1: This paper reads much better now that the grammar and structure has been revised.
Response 1: Thank you for your positive comment.
Reviewer 2 Report
The manuscript has gone through a thorough revision and its English is now much easier to understand. Through case studies of three Chinese mathematics teachers, the authors discover that the teachers still lack sufficient skills to integrate the DGS software into mathematics teaching.
I recommend that the paper be accepted for publication in Sustainability with the following suggested revisions.
(1) Page 1, Line 8 of Introduction: Delete "asking" in " ... to asking ask worthwhile questions ..."
(2) Page 2, Line 1: Fix the typo of Section 2 by deleting "1. Introduction"
(3) Page 2, Section 2.2: Number the four roles using 1, 2, 3, 4 instead of 1, 2, 1, 2.
(4) Page 4, Last row of Table 1: fix the typo in "Try to conclude ways to prove draw triangles"
(5) Page 5, Table 2: The word "remains:" needs to be replaced by something else.
(6) Page 5, Table 4: Fix the typo in "When point A has dragged ..."
(7) Page 6 and 7: The upper case letters A, B, C should be replaced with lower case letters a, b, c so that the notation for side length is consistent with that in Table 2.
(8) Page 10, Line 7 in Section 5.3: Change (Table 3) into (Table 4).
(9) Page 11, Line 6 under the Table 8: Fix the typo in " using technology vit he use of terminology ..."
The authors are strongly encouraged to do another round of complete check and fix some other typos of the text.
Author Response
Respond to Reviewer 2 Comments:
Point 1: The manuscript has gone through a thorough revision and its English is now much easier to understand. Through case studies of three Chinese mathematics teachers, the authors discover that the teachers still lack sufficient skills to integrate the DGS software into mathematics teaching.
Response 1: Thank you for your positive comments.
Point 2: I recommend that the paper be accepted for publication in Sustainability with the following suggested revisions.
(1) Page 1, Line 8 of Introduction: Delete "asking" in " ... to asking ask worthwhile questions ..."
(2) Page 2, Line 1: Fix the typo of Section 2 by deleting "1. Introduction"
(3) Page 2, Section 2.2: Number the four roles using 1, 2, 3, 4 instead of 1, 2, 1, 2.
(4) Page 4, Last row of Table 1: fix the typo in "Try to conclude ways to prove draw triangles"
(5) Page 5, Table 2: The word "remains:" needs to be replaced by something else.
(6) Page 5, Table 4: Fix the typo in "When point A has dragged ..."
(7) Page 6 and 7: The upper case letters A, B, C should be replaced with lower case letters a, b, c so that the notation for side length is consistent with that in Table 2.
(8) Page 10, Line 7 in Section 5.3: Change (Table 3) into (Table 4).
(9) Page 11, Line 6 under the Table 8: Fix the typo in " using technology vit he use of terminology ..."
The authors are strongly encouraged to do another round of complete check and fix some other typos of the text.
Response 2: Thank you for the all above suggestions. We have already checked the above mistakes in our manuscript and also other typos of the text.
Reviewer 3 Report
Thanks for the extensive corrections. I am overall happy with the changes.
There are still some English typos e.g. "Feedbacks" should be 'Feedback'.
Page 2 - 1. Introduction and 2. Literature Review headings appear in the same line
Author Response
Respond to Reviewer 3 Comments:
Point 1: Thanks for the extensive corrections. I am overall happy with the changes.
Response 1: Thank you for the positive feedback.
Point 2: There are still some English typos e.g. "Feedbacks" should be 'Feedback'.
Page 2 - 1. Introduction and 2. Literature Review headings appear in the same line
Response 2: Thank you for your feedback. We have checked the above typos and also others in our manuscript.
Reviewer 4 Report
Two points are still needed:
1) there is no theoretical framework that oversees the main ideas presented in the paper
2) the discussion section needs to come before the conclusion, with the later to be reduced to main findings. As for the discussion this needs to be linked with the studies that are presented in the lit review of the paper to indicate where it echos any of the previous findings or not and why.
Author Response
Respond to Reviewer 4 Comments:
Point 1: there is no theoretical framework that oversees the main ideas presented in the paper
Response 1: Thank you for your advice. In this study, we analyze our data based on the framework posed by Hollebrands and Lee which is based on the idea of a didactic tetrahedron presented by Tall. In their study, they divided teachers’ questions and feedback into four different categories (see Table 1). And we also see the four different roles DGS played in mathematics teaching (Laborde 2001 & Soury-Lavergne 2017) as another framework in our study. So all the results we found in Chinese mathematics lessons are explained through these two important frameworks. Detailed information was presented in section 2.2.
Point 2: the discussion section needs to come before the conclusion, with the later to be reduced to main findings. As for the discussion this needs to be linked with the studies that are presented in the lit review of the paper to indicate where it echos any of the previous findings or not and why.
Response 2: Thank you for your suggestion. We have reorganized the last two sections of our manuscript. In the conclusion part, we listed the main results we found based on our data. For example, 1, teacher–student interactions are often guided by the initiation–response–evaluation pattern [29]; 2, the teachers in this study seldom linked their questions with DGS. In this study, most questions focused only on mathematics, which means that students were able to answer them without DGS; 3, DGS is more for presenting content. This implies that the dragging mode is controlled by teachers, not students; therefore, the meaning of the interactivity of DGS is ambiguous, and DGS is used just for clicking buttons or touching objects on the screen [6]. In the discussion part, we presented the possible factors which may affect the use of DGS in mathematics lessons. For example, 1, teachers may lack enough knowledge and strategies to integrate DGS [3][35]; 2, teachers learned mathematics in a totally different environment to that of modern students; therefore, it is difficult for teachers to evaluate students’ learning process [3]. And other factors like the limited teaching time, and examination in China which are not the focus of our study, so we presented them in the limitation part.
