Mathematical Modeling Approach and Exploration of Geometric Properties as Part of an Outdoor Activity for Primary-School Pupils in Out-of-School Learning

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for giving me the opportunity to review this interesting approach.

The aim of this article is "to highlight the link between mathematical modeling, which is often used in geometric problem solving, and teaching outside the classroom, where there is a suitable space to use modeling in activities that are interesting for pupils."

This is an interesting aim, which is followed up by a combination of practical indoor and outdoor activities. Congratulations to fascinating outdoor activities.

However, I suggest the following major revisions:

Most important: A discussion section is lacking, which discusses the results toward the initially cited literature.

- The manuscript needs restructuring, especially regarding the methods section,

- The first paragraph leading to the aim lacks a convincing rationale, supported by an overview over existing literature toward the aim.

-1.1. Modeling in Mathematics Education: The quality of the English language makes it difficult to understand the argument.

- The literature used is of varying quality, for instance: International Journal of Research and Analytical Reviews (IJRAR) is often seen as a predator journal. There are doi missing as well.

-1.2. Outdoor Activities in Math Education is not acceptable in its current form. A thorough, up to date, literature review of the field is missing, several sentences lack references, for instance the claims in line 76 and 113ff., while the results of other references are just stated as bullet points without further connecting to the theme of this paper.

The materials and methods section lacks scientific rigor. It remains unclear if the participants of this study are the same indoors and outdoors, how these activities are logically connected or unrelated studies? It seems as if this manuscript consists of two unrelated research projects?

-2.2 vs. abstract: are the pupils from 2nd grade or from 9th grade? This is confusing and a clear description of the research context is needed. You give more information about the context in section 4.1.2, this might be good to use in the method section.

-Problem 1 needs further description and linking to the outdoor educational approach. Problem 2 seems much more suitable as a relevant problem-based context, but it remains unclear how this is connected to the actual outdoor activities.

- The qualitative analysis in section 3 is clear and precise for the reader, while there lacks context about the students preexisting competence toward this type of assignments and related content knowledge.

- How is section 4 linked to section 3? These seem to be independent research projects?

-Line 248-9: TDS is based on the principles of the French school, for more information, the reader may refer to [19-22]. --> Please provide this information as it makes it easier for the reader to follow. I also suggest to include this into the methods section, as it describes how your design-based teaching was created.

Line 281:" as weaker pupils may not be involved in solving 281
the problem" --> is this a claim you made, or based on literature? I would recommend to rephrase the wording and avoid "weaker pupils", as well as cite the related literature behind this claim.

Would it be better to use the word compass or divider for the drawing tool to avoid confusion towards circle (shape)?

Your qualitative results toward the outdoor activities seem to be based solely on researcher's observations. This should be reflected on in the methods section, both advantages and limitations.

In the conclusion, you state a series of claims that are not empirically supported in your research design: "It can be concluded that the pupils enjoyed the activities based on their positive feed- 398 back. Pupils enjoyed working in groups, the use of non-traditional resources (string, chalk, 399 ruler) and working outside their school. The activities encouraged discussion in groups. 400 Pupils helped each other to solve problems and complemented each other's knowledge. 401 Such activities can foster a positive attitude towards geometry. Pupils see its practical ap- 402 plications and learn a lot of new knowledge"

--> These claims need empirical backup or a rigorous in-depth discussion, which links them to the presented results. Therefore they have to either be avoided or backed up by data, which are currently lacking.

It remains unclear, how the different parts of this manuscript are connected, and if it is logically valid to connect the different research results toward the proposed aim of the paper. The last comment may originate in the current language quality, see below.

Comments on the Quality of English Language

This manuscripts is difficult to follow, partially due to its language quality. Some of the above points may be due to language problems and will be clear after extensive language editing.

Author Response

Dear colleague,

We would like to thank you very much for your review and your comments and recommendations on our manuscript. We accept them, of course, and have tried to add them to the manuscript (more in attachment).

We hope we have completed the manuscript appropriately. We greatly appreciate your recommendations.

Sincerely,

Authors

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article is well-composed and emphasizes that mathematical modeling is crucial. It is essential to explain the strong rationale behind linking it to geometry, even though mathematical modeling encompasses more than just that. Explain why, in this study, the topic leans towards geometry

Author Response

Dear colleague,

We would like to thank you for your review and your comments and recommendations on our

manuscript. We certainly accept them and have tried to incorporate them into the manuscript.

Comments 1: It is essential to explain the strong rationale behind linking it to geometry, even

though mathematical modeling encompasses more than just that. Explain why, in this study, the

topic leans towards geometry.

Response 1: In recent years we have observed a very low level of geometric knowledge among

pupils in Slovakia. This tendency is indicated by the national test on the second level of primary

school, which is intended for pupils in 9th grade (measurements: Testing 9 – external testing of

pupils of 9th grade in Slovakia). For this reason, in our research we focus on the solution of two

geometric problems solved by pupils from different schools in the Slovak Republic.

We hope we have completed the manuscript appropriately. We greatly appreciate your

recommendations.

Sincerely,

Authors

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

thank you for the revised version. Some aspects become clear now, and the readability has improved.

However, there are some serious logical problems regarding both, how these two empirical studies are connected, as well as to claims that are made, especially in the end of the paper.

1. It still is not clear, what exactly the findings from the first study are, which are addressed in the second, as well as how exactly the second study managed to address exactly the problems that arouse in the problem-tasks of the first study.

2. As in the theory in the beginning, it is simply stated that outdoor-education is an approach that seems to fix everything, which it definitely is not. A critical discussion of both literature and own findings lacks.

3. It now appears there have been interviews, which the positive claims are based on. This has to be documented in detail and empirical data, as well as a systematic analysis of these interviews presented. Otherwise the claims in the last two paragraphs of the paper cannot be made.

Especially since the topics change from conceptual problems in the first part of the paper, which are documented quite well, to motivational/attitude-focus in the second, which lacks empirically valid analysis.

If I am not mistaken and misjudge the kind of data that feed this manuscript, my suggestion would be to divide this paper into two, as you change from a post-positivistic paradigm to a interpretivistic in study two. This could for example be done as follows:

1. A detailed quantitative study, from which potential for more suitable approaches can be deduced. This part is already well developed, and discussing outdoor education more critically and discussing critically how distinct problems of the first part could be addressed helped by the a-priory-analysis is promising and could result in an interesting paper.

2. A detailed qualitative study that enacts these suggestions and may provide substantiated empirical suggestions how the outdoor approach may contribute to solve the initial problems in study 1, based on a detailed documented methodology that analyses the observations and interviews, which lacks at the moment. This one, I fear, needs a lot of work, will become an interesting paper, but would be too long to be together with the first one, if containing and presenting rich qualitative data.

------

Some distinct comments:

113The outdoor environment is inspiring for the pupils, as we have personal experience of implementing an out-of-school club with them.

--> Is this a result? This claim has to be rooted in some data? This claim is repeated in the end of the paper

126 Depending on the type and focus of the secondary
school, the differentiation of the geometry curriculum takes place only during further 127
studies. Depending on the type of secondary school they will attend, some pupils will not 128
continue to develop their knowledge of geometry.

--> These sentences do not make sense.

419
[3], pupils can develop and reinforce connections between different geometric knowledge 420
in these activities, leading to deep and lasting learning.

--> another unsubstanciated claim.

The last paragraph has more of these in the current form invalid claims.

 

 

Comments on the Quality of English Language

The language has become better, but there are still small errors, as well as sometimes difficult to assess logical ones, which might arise from translational challenges.

Author Response

Dear colleague,

please find attached the replies to your comments.
Thank you for them.

Yours sincerely,

Authors

Author Response File: Author Response.pdf