Errors concerning Statistics and Probability in Spanish Secondary School Textbooks
Round 1
Reviewer 1 Report
"Misconceptions in Teaching and Learning Statistics" by XXXXX
In this paper, the authors carry out an analysis of Spanish secondary school mathematics textbooks. They describe some of these errors to show conceptual contradictions and statistics errors.
Before the article can be accepted, authors should consider the following comments:
1. Page 2. Line 38: The references given by the authors regarding the need for statistics in education are very old; it would be very convenient for some revisions to be made to update these references.
2. The method they use needs to be adequately described in detail. They mention some methods that appear in general research methodology references. Therefore, they should explain in more detail the methodology they used to find the errors they show in the Results Section.
3. The authors show great experience in statistical concepts. Still, the errors they mention in their Results seem to be separate from their analysis of the books, i.e., they seem to have come from experience rather than research. So, this perception should be changed by documenting more the methodology part.
Therefore, until they improve the description of the methodology, I cannot recommend its publication.
Author Response
Dear reviewer,
We find your suggestions very appropriate and useful to improve the manuscript. As consequence to these comments, and the comments made by the other reviewers, we have made some changes. Firstly, we modified the title and the second part of the abstract. Secondly, we added a new subsection (now 1.3) including theoretical aspects, and we improved section #2 with a detailed explanation of the methodology. Finally, we modified some sentences in order to clarify their meaning.
Please see the attachment with the responses of your comments.
Thank you very much for your suggestions and comments.
Best regards.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper is interesting especially in giving credit to statistics that is equal important as mathematics. Addressing misconceptions will uplifting the quality of teaching statistics among teachers. However, some comments are listed below so that the content of the paper can be improved;
The title is suggested to be improved to " Misconceptions in Spanish Secondary School Textbooks on Statistics and Probability". This is due to the focus of discussion is mainly based on the content of the textbook.
Abstract should be improved by considering to add research design, type of analysis. Brief result should be included as well as research implications.
Misconception of statistics is not being mentioned in the abstract. What is the focus of this research; statistical literacy or misconception of statistics? How these two are related?
Line 28 to 29, “Consequently, we consider that equipping teachers with good instructional materials 28 (i.e., appropriate, effective textbooks) could be a determinant factor in achieving statistical 29 literacy among the general population “ is rather contradict with the title of this paper.
Line 31 to 34, “In the present study, we analyse a range of mathematics textbooks for first and secondyear students in secondary education (Grades 7-8), finding that, despite the time and efforts invested and policymakers’ long-held interest in developing statistical literacy, certain errors systematically appear in statistics and probability chapters within mathematics textbooks” has more than 20 words which has confused the reader about the what the authors what to focus on. Please rephrase the sentence. Spelling error of secondyear, please add spacing.
Why statistics is chosen as the interest of this study and why the issue is related to teachers? How statistics is taught in Spain? Does the topic is part of mathematics or being taught as individual subject? Some background of study is required to be elaborated.
Authors should clarify whether the misconceptions of statistics in this paper are related to teaching or learning? Furthermore, description of misconceptions in introduction is not being clearly addressed.
Why statistics and probability being chosen as the main topic of the study? Please provide justification.
What learning theory or model that could be considered as the basis of this study? Please add.
Line 107 to 108, “In our opinion, the absence of research into errors in mathematics textbooks reflects the implicit assumption that no such errors exist” leads to inconsistency in addressing the main issue of the study.
Line 110, does the term systematic errors relate to misconception? Authors are suggested to add research objective(s).
Line 124 to 125, “For each book, all the units or topics related to statistics and probability were reviewed in depth. When an error was detected, its type was identified and analysed” must be explained in detailed by considering the below comments.
Please provide supporting data to indicate that these textbooks are required to be reviewed.
Line 124, who did the textbook review? How the process being done and how many reviewers involved? How the analyses of errors/misconceptions being done and how the results were verified? Any information of the experts involved and their credibility of knowledge in the related topic?
How the themes being developed, such as “Errors detected in texts on descriptive statistics”, “Errors detected in textbook chapters on probability” and their subtopics?
Authors have provided evidence from the textbook for 3.1.2, please provide evidence for other subtopics of errors found in the textbook.
How the findings contribute in reducing misconception in statistics? What ways that can be proposed to overcome this issue? How teachers could benefit from these findings?
How frequent that misconceptions found in the textbooks? Was it one misconception in every topic? Authors could provide data on number of misconceptions occur in every topic part from reporting the type of errors.
Please add subtopics of research implications and proposed future works. The implications should be based on the findings that could be discussed within the practical aspect of teachers and related theory.
Outdated references beyond the year of 2017 should be replaced by latest references except the references are meant for theory or model.
Author Response
Dear reviewer,
We find your suggestions very appropriate and useful to improve the manuscript. As consequence to these comments, and the comments made by the other reviewers, we have made some changes. Firstly, we modified the title and the second part of the abstract. Secondly, we added a new subsection (now 1.3) including theoretical aspects, and we improved section #2 with a detailed explanation of the methodology. Finally, we modified some sentences in order to clarify their meaning.
Please see the attachment with the responses of your comments.
Thank you very much for your suggestions and comments.
Best regards.
Author Response File: Author Response.pdf
Reviewer 3 Report
It is an interesting article, but, in my opinion, it has the problem that it does not establish a theoretical reference on what an error is. Many of the errors that the authors comment on are not exactly mathematical errors, but rather are imprecisions. Authors should make their theoretical referent explicit and use more categories, for example, imprecision or ambiguity. In this way, they could further clarify the typology of errors that they show.
Author Response
Dear reviewer,
We find your suggestions very appropriate and useful to improve the manuscript. As consequence to these comments, and the comments made by the other reviewers, we have made some changes. Firstly, we modified the title and the second part of the abstract. Secondly, we added a new subsection (now 1.3) including theoretical aspects, and we improved section #2 with a detailed explanation of the methodology. Finally, we modified some sentences in order to clarify their meaning.
Please see the attachment with the responses of your comments.
Thank you very much for your suggestions and comments.
Best regards.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The paper has improved in terms of what I commented on in the first review. So, although there are still some points that could be improved, they are not so bad as to not recommend the publication of this article.
Author Response
Dear reviewer:
Thank you very much for your report.
Following report of reviewer #2 we have improved the manuscript. In this review we include a section 4.2 called 'Research Implications' and we erase all & symbols and write "and" in their places.
We hope this version is now complete for publication.
Best regards.
Reviewer 2 Report
Some citations in the text should be improved such as Tversky & Kahneman; Burrill & Biehler; Rossman & Medina; Schubring & Fan; Wild & Pfannkuch; Vermette & Savard, the symbol of & should be replaced by 'and'.
The introduction part has been improved a lot yet more write up should be added in the Discussion part to indicate the strength of this study. Research implications are required to be written in detail which should be based on your findings.
Author Response
Dear reviewer:
Thank you very much for all your valuable comments.
We have improved the manuscript. In this review we include a section 4.2 called 'Research Implications' and we erase all & symbols and write "and" in their places.
We hope this version is now complete for publication.
Best regards.
Author Response File: Author Response.pdf
Reviewer 3 Report
I consider that in the new version the authors have followed my suggestions and now the new version of the paper "Misconceptions in Teaching and Learning Statistics" is a valuable contribution to mathematics education and it will be of great interest to Applied Sciences readers. My suggestion is to accept the article
Author Response
Dear reviewer:
Thank you very much for your report.
Following report of reviewer #2 we have improved the manuscript. In this review we include a section 4.2 called 'Research Implications' and we erase all & symbols and write "and" in their places.
We hope this version is now complete for publication.
Best regards.
