On Reading Mathematical Texts, Question-Asking and Cognitive Load
Round 1
Reviewer 1 Report
Review
Article: On reading mathematical texts, question-asking and cognitive load
Journal: Educational Sciences
The study investigated the effects of incorporating question-asking activities and providing corresponding answers while reading historical mathematical texts on the self-reported cognitive load of prospective mathematics teachers. Two groups of 20 students each participated in the study. The experimental group was instructed to ask questions while reading the texts, whereas the control group received no specific instructions. The experimental group participants were also asked to verbalize their thoughts while reading and recorded their audio, which was then transcribed into written protocols. Both groups were required to complete a self-esteem index questionnaire, indicating the level of difficulty they experienced while engaging with the texts, as a measure of their cognitive load perception. The study revealed that question-asking led to a reduction in cognitive load, with a significant difference observed between the control and experimental groups; and question-asking facilitated the assimilation of new information, but this effect was limited and depended on the gap between existing knowledge and new information. Overall, the study was interesting, but I have some major and minor comments for the authors:
Major comments:
1) On line 99, the authors wrote “The participants were 99 assigned into two classes of 20 PMTs each (experimental and control groups) in accordance with the matching control technique [18]. “Can you provide more context or specific information about the matching control technique mentioned in the study?
2) Figure 1, since the range of the self-reported index of CL ranges between 1-9, I wonder, why the axis is ranging from -1 to 9? Will it not be appropriate the range the axis between 0 and 9?
3) If the purpose of the graph is to compare the experimental and control group's self-reported index of CL, I think it would be better to reorganize the bars. The current figure is more appropriate if the purpose is to compare control group’s self-reported index of CL for the extraneous and intrinsic. However, if the purpose of the paper is to compare the control and experimental groups’ self-reported index of CL for both extraneous and intrinsic, then the bars should be reorganized.
4) The study employed Friedman's test and observed that in the control group, there were no significant differences among the three measurements for all students, as well as for students with high ability (HA) or low ability (LA) [Table 3]. Conversely, in the experimental group, significant differences were found among the three measurements for all students, as well as for HA and LA [Table 3]. However, the authors did not assess whether there was a significant difference between the control and experimental groups. In the conclusion the author said, a significant difference observed between the control and experimental groups, but I am not sure if the authors measured that. Probably it would be helpful to the readers, if the authors clarify Table 3 to discuss their results.
5) In the qualitative data section, instead of presenting all the 22, 29, and 20 excerpts under protocol 1, 2, and 3 respectively, followed by the author's narrative of Rina's response to the QA session while reading the Egyptian texts, Babylonian texts, and Vedic method, I suggest that it would be more effective to present the entire episode as a cohesive story. Instead of using identifiers like (S1-2/ S3) beside each line, the authors could incorporate the actual excerpts within the narrative they have written. For instance, they could describe the situation by saying, "Upon reading the text containing the Egyptian algorithm for multiplying two natural numbers, Rina expresses her confusion. She exclaims, 'The Egyptian multiplication looks unclear... I've read it multiple times, but I can't understand why they multiplied the numbers by 2.'" This approach would make the narrative more engaging and provide a seamless flow to the reader.
Minor comments:
1) Line 59, the authors wrote, “The concept of 'cognitive load' was coined Sweller by [8] for describing the state of 59 memory storage and processing of information in a human's mind while coping with a particular task or complex situation, and it can serve as an indicator of the degree of difficulty learners experience while engaging in the task [13,14,10].” I think it would be “The concept of 'cognitive load' was coined by Sweller [8]”
2) On line 67, the authors described germane cognitive load (GCL). Please add one more line to explain GCL. I had trouble understanding the concept.
3) On line 79, the authors wrote “To that end, we sought to examine the effect of question asking (QA) by the PMTs while reading the mathematical texts and then answer these questions on the reduction of CL, as reported by the PSTs.” What is PST? Is it same as PMT?
4) On line 96, the authors wrote “Forty middle and high school female PMTs of an average age of 24 years and seven months in the third year of their undergraduate studies participated in the study.”
5) I would recommend splitting this sentence as it can be confusing. Initially, it might be interpreted as the average age of the teachers being 24 years and 7 months. However, upon further reading, it appears to indicate that the study took place over a span of 7 months during the participants' third year of graduate studies. Additionally, could you please provide clarification on the specific program in which the PMTs were enrolled?
6) On line 101, the authors wrote “Given that prior knowledge affects the decrease of CL while performing learning tasks [19], and aiming to adhere to the matching control technique, the PMTs were matched based on their average grades in the compulsory mathematics courses they attended during the first two years of their training, which constitutes the dependent variable. Furthermore,” Please split the sentence. It is too long to comprehend.
7) On line 173, the authors wrote “Based on [14], the participants were asked to report on their invested mental effort during their 174 attempts to decipher the algorithm at hand.” What is 14? Is it some article or some concept discussed in article 14? Please rewrite the line to avoid such confusion.
8) Table 1. Please provide explanation of ICL and ECL Text 2 and Text 3.
9) Line 224, Shall the citation [13] (Paas et al., 2003) not numbered? Such as Paas et al. [number]?
10) Label of Figure 1 says “Figure 1. Average self-reported index of cognitive load (extraneous and internal) in three time points (1,2,3), control (c) and experimental (e) groups.” Shall it not be “Intrinsic”?
The manuscript has a lot of potential to improve. I have included the detail suggestions in the review.
Author Response
Dear reviewer,
First, we would like to thank you for your useful suggestions for changes. The following is our extended response:
- On line 99, the authors wrote “The participants were assigned into two classes of 20 PMTs each (experimental and control groups) in accordance with the matching control technique [18]. “Can you provide more context or specific information about the matching control technique mentioned in the study?
We added explanation to this request in the paper
- Figure 1, since the range of the self-reported index of CL ranges between 1-9, I wonder, why the axis is ranging from -1 to 9? Will it not be appropriate the range the axis between 0 and 9?
We replaced the figure to address the appropriate range.
3) If the purpose of the graph is to compare the experimental and control group's self-reported index of CL, I think it would be better to reorganize the bars. The current figure is more appropriate if the purpose is to compare control group’s self-reported index of CL for the extraneous and intrinsic. However, if the purpose of the paper is to compare the control and experimental groups’ self-reported index of CL for both extraneous and intrinsic, then the bars should be reorganized.
We believe the graph represents the comparison between the experimental and control groups' self-reported index of CL.
- The study employed Friedman's test and observed that in the control group, there were no significant differences among the three measurements for all students, as well as for students with high ability (HA) or low ability (LA) [Table 3]. Conversely, in the experimental group, significant differences were found among the three measurements for all students, as well as for HA and LA [Table 3]. However, the authors did not assess whether there was a significant difference between the control and experimental groups. In the conclusion the author said, a significant difference observed between the control and experimental groups, but I am not sure if the authors measured that. Probably it would be helpful to the readers, if the authors clarify Table 3 to discuss their results.
We explicitly added the information referring to the P-value of each case and hope it presents the results more clearly.
- In the qualitative data section, instead of presenting all the 22, 29, and 20 excerpts under protocol 1, 2, and 3 respectively, followed by the author's narrative of Rina's response to the QA session while reading the Egyptian texts, Babylonian texts, and Vedic method, I suggest that it would be more effective to present the entire episode as a cohesive story. Instead of using identifiers like (S1-2/ S3) beside each line, the authors could incorporate the actual excerpts within the narrative they have written. For instance, they could describe the situation by saying, "Upon reading the text containing the Egyptian algorithm for multiplying two natural numbers, Rina expresses her confusion. She exclaims, 'The Egyptian multiplication looks unclear... I've read it multiple times, but I can't understand why they multiplied the numbers by 2.'" This approach would make the narrative more engaging and provide a seamless flow to the reader.
Thank you for your suggestion. After considering it, we came to the conclusion that to be able for the reader to follow easily the analysis of each of the presented texts, it would be better to maintain the texts in their current state.
Minor comments:
- Line 59, the authors wrote, “The concept of 'cognitive load' was coined Sweller by [8] for describing the state of 59 memory storage and processing of information in a human's mind while coping with a particular task or complex situation, and it can serve as an indicator of the degree of difficulty learners experience while engaging in the task [13,14,10].” I think it would be “The concept of 'cognitive load' was coined by Sweller [8]” . done
- On line 67, the authors described germane cognitive load (GCL). Please add one more line to explain GCL. I had trouble understanding the concept.
We added explanation regarding germane CL.
- On line 79, the authors wrote “To that end, we sought to examine the effect of question asking (QA) by the PMTs while reading the mathematical texts and then answer these questions on the reduction of CL, as reported by the PSTs.” What is PST? Is it same as PMT?
We corrected the typo mistake
- On line 96, the authors wrote “Forty middle and high school female PMTs of an average age of 24 years and seven months in the third year of their undergraduate studies participated in the study.”
I would recommend splitting this sentence as it can be confusing. Initially, it might be interpreted as the average age of the teachers being 24 years and 7 months. However, upon further reading, it appears to indicate that the study took place over a span of 7 months during the participants' third year of graduate studies. Additionally, could you please provide clarification on the specific program in which the PMTs were enrolled? ×”×•×¡×¤× ×•
We spitted the sentence and added some clarifications.
- On line 101, the authors wrote “Given that prior knowledge affects the decrease of CL while performing learning tasks [19], and aiming to adhere to the matching control technique, the PMTs were matched based on their average grades in the compulsory mathematics courses they attended during the first two years of their training, which constitutes the dependent variable. Furthermore,” Please split the sentence. It is too long to comprehend.
Done.
- On line 173, the authors wrote “Based on [14], the participants were asked to report on their invested mental effort during their 174 attempts to decipher the algorithm at hand.” What is 14? Is it some article or some concept discussed in article 14? Please rewrite the line to avoid such confusion.
We added the name of the researchers.
- Table 1. Please provide explanation of ICL and ECL Text 2 and Text 3.
Done.
- Line 224, Shall the citation [13] (Paas et al., 2003) not numbered? Such as Paas et al. [number]?
It was numbered and corrected.
- Label of Figure 1 says “Figure 1. Average self-reported index of cognitive load (extraneous and internal) in three time points (1,2,3), control (c) and experimental (e) groups.” Shall it not be “Intrinsic”?
Done.
Reviewer 2 Report
It is gratifying to see the integration of mathematical history and mathematics teacher education in this study.
The abstract should be modified to provide a clear overview of the study's scope. The first sentence should be rephrased to clarify the key components of the quasi-experimental research design, such as question-asking activities, knowledge of mathematical history, and cognitive load. Furthermore, a more concise and improved presentation of the results should be provided in the abstract.
The introduction section is well-written. It effectively addresses the main issues related to the study and incorporates relevant research references.
However, the method section requires more careful consideration and should be written in a scholarly style. For example, while the Friedman test was used in data analysis, the null hypothesis has not been clearly stated in the paper. Additionally, inaccurate terminology is presented throughout the methodology descriptions. For instance, the term "research tools" should be replaced with "research instruments." Sub-section 3.1 on page 2 is too brief, and it would be beneficial to clearly identify the research question(s) before delving into the details of the research design. On page 3, lines 121 and 122, the reference should be cited according to the journal guidelines.
The interpretations of the results are generally clear, and the use of tables to present the statistical analysis in the result section is commendable. It is recommended that the data shown in sub-sections 4.2.1 to 4.2.3 should be moved to the appendix.
The discussion section is comprehensive but lengthy. To enhance clarity, it is advisable to divide the content into several sub-sections for better presentation.
Please be advised that there are several grammatical errors present in the paper. For example, in the abstract on page 1, at line 13, the phrase "The data was..." should be amended to "The data were..." Therefore, I strongly recommend conducting a thorough proofreading to rectify these issues.
Author Response
Dear reviewer,
First, we would like to thank you for you useful suggestions for changes. The following is our extended response:
It is gratifying to see the integration of mathematical history and mathematics teacher education in this study.
Thank you!
The abstract should be modified to provide a clear overview of the study's scope. The first sentence should be rephrased to clarify the key components of the quasi-experimental research design, such as question-asking activities, knowledge of mathematical history, and cognitive load. Furthermore, a more concise and improved presentation of the results should be provided in the abstract.
The abstract was rewritten accordingly.
The introduction section is well-written. It effectively addresses the main issues related to the study and incorporates relevant research references.
However, the method section requires more careful consideration and should be written in a scholarly style. For example, while the Friedman test was used in data analysis, the null hypothesis has not been clearly stated in the paper. Additionally, inaccurate terminology is presented throughout the methodology descriptions. For instance, the term "research tools" should be replaced with "research instruments." Sub-section 3.1 on page 2 is too brief, and it would be beneficial to clearly identify the research question(s) before delving into the details of the research design. On page 3, lines 121 and 122, the reference should be cited according to the journal guidelines.
We added research questions and our research hypotheses in section 3.1.
We replaced the research tools to research instruments.
We corrected the cited reference- since it is a website, we moved it to a footnote.
The interpretations of the results are generally clear, and the use of tables to present the statistical analysis in the result section is commendable. It is recommended that the data shown in sub-sections 4.2.1 to 4.2.3 should be moved to the appendix.
Thank you for your suggestion. After considering it, we came to the conclusion that to be able for the reader to follow easily the analysis of each of the presented texts, it would be better to maintain the texts in their current state.
The discussion section is comprehensive but lengthy. To enhance clarity, it is advisable to divide the content into several sub-sections for better presentation.
We divided the discussion section into two parts and added subtitles.
Please be advised that there are several grammatical errors present in the paper. For example, in the abstract on page 1, at line 13, the phrase "The data was..." should be amended to "The data were..." Therefore, I strongly recommend conducting a thorough proofreading to rectify these issues.
We conducted a proofreading of the text.
Reviewer 3 Report
I appreciated reading this report. I was particularly interested in learning more about the organization and content of chapters used in the model (inclusion of questions, etc.) since I too teach a course on history of mathematics to preservice teachers. I was also a bit concerned that references to scaffolding was not offered. I perceive the issue of embedded Q/A to be a form of scaffolding.
I understand the value of providing opportunities for students to rank and evaluate their own efficacy and confidence when encountering disciplinary text but I found absence of references to what was actually gained from the intervention somewhat alarming. I remain unsure of how this issue may be addressed in a revised version of the report.
Author Response
First, we would like to thank you for you useful suggestions for changes. The following is our extended response:
I appreciated reading this report. I was particularly interested in learning more about the organization and content of chapters used in the model (inclusion of questions, etc.) since I too teach a course on history of mathematics to preservice teachers. I was also a bit concerned that references to scaffolding was not offered. I perceive the issue of embedded Q/A to be a form of scaffolding.
In line 88 We added clarification regarding QA as a scaffolding tool.
I understand the value of providing opportunities for students to rank and evaluate their own efficacy and confidence when encountering disciplinary text but I found absence of references to what was actually gained from the intervention somewhat alarming. I remain unsure of how this issue may be addressed in a revised version of the report.
The actual gain of the QA process was reflected in the significant difference between the groups in terms of final grades in the course. However, this paper does not focus on this issue but rather on the connection between QA and perceived CL.
Thank you again for your careful reading of the paper and insightful comments.
Round 2
Reviewer 1 Report
The authors have addressed most of the comments. I think the article is ready for acceptance.
