Embedding Mathematics in Socio-Scientific Games: The Mathematical in Grappling with Wicked Problems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper deals with a very topic transversal to scientific disciplines, namely if normal science approaches can contribute to post-normal science. And it presents a deep discussion on socio-scientific games in the modern age, and their mathematical approaches in problems defined as "wicked". It describes an application - ChoiCo - and some examples of students' protocols in using it. 

The paper is very well written and situated in the present literature on teaching mathematics in this millennium, after a critical period as the covid pandemic. It is positioned in the necessity of a shift from teaching mathematics as "visiting monuments" - as Chevallard says (please change the word "works" into the word "monuments"), to approaching mathematics as "questioning the world", using a constructionist background. It can be considered a theoretical discourse in the "red line" that historically touches Kaput, Noss, Hoyles, Trouche, to arrive nowadays. The debate on normal and post-normal science, and on the possible approaches to the disciplines in the educational system is really intriguing, for the challenge given to scholars, if and how science could give a contribution to fostering social innovation. And if it can be done through technological environments in educational settings.

The management of complexity as a goal for our society is examined through the use of microworld that combine values of different nature with didactical goals through the accomplishment of a task in an educational technology based game. 

The first part of the paper, more theoretical, can be left as it is, because it is complete and self-consistent.

the second part, of description of ChoiCo, can be improved according to some suggestions:

- to show the possible mathematics that can be done by students through ChoiCo: it is only commented at the end, but the reader cannot imagine it, according to the present description

- to contextualise the possible use of ChoiCo in an institutional view (age, kind of schools, etc.)

- To frame ChoiCo from a cultural-ethical-social-economic point of view: can it be used in every country? Is it inclusive? Can it be used at every social level? 

- To give ideas on the use of quantitative parameters in relation to the different choices: How have they been introduce in such values? Are they only randomly chosen or is there any proportional relation?

- to explain better the black and white box design (especially white)

- to take into consideration the institutional dimension (it is just quoted at the end) and to explain how this microworld can be used in a school by different teachers of different disciplines

- to give more insight on the interconnection between values and disciplines (especially mathematics)

- it would be very much appreciated if scholars as Schovsmose and Valero would be quoted in this paper.

 

Author Response

thank you very much for your constructive comments - I have added text to address the points you make about choico and its uses and affordances mainly in a long paragraph starting in line 401 under the bulleted main features of the tool , but also details scattered in the choico sections. Thank you for pointing me to Skovsmose and Valero's work which I have cited and which would have been an oversight otherwise, I also cited Hauge and Barwell the only piece i found specifically on post normal science and mathematics education. 

Reviewer 2 Report

Comments and Suggestions for Authors

I am puzzled as to why the author has submitted this to a peer-reviewed scholarly research journal. It is an opinion/information piece that would typically be published in an education magazine or on a blog. There's nothing wrong with it as such. Indeed, I find myself in general agreement with the points the author makes, and commend the effort to make them available to the education community. But it seems inappropriate for a research journal, and peer review would add nothing.

Author Response

Thank you for reading this paper. I do not agree with your point that this is not research, I consider the use of empirical evidence in the design part of design research to allow for an illuminative process to articulate research questions more succinctly. Journals addressing the questioning or the transformation processes of educational paradigms allow and welcome such contributions, see Chevallard for example. This is new stuff - we may agree in general but this paper suggests that it is time to become more succinct and specific about what to do about it. What would mathematical thinking in the context of addressing wicked problems look like? But thanks again - feedback is always useful and has been considered here and will be in future work. 

Reviewer 3 Report

Comments and Suggestions for Authors

I read with much interest the paper titled “Embedding Mathematics in Socio-Scientific Games: the Mathematical in Grappling with Wicked Problems”. This  theoretical paper  discusses the role of mathematics in educational transformation and the potential role for using digital media to engage students in mathematical thinking as a means of grappling wicked problems and global issues. The paper offers interesting insights on these matters and raises critical questions with regard to mathematics as discipline. The author presents an example of a digital media (ChoiCo) and discuss the potential of this tool for educational transformation. The paper is well written and the structure is clear. Statements are well explained, presented in a logical way and based on evidence from theory and/or research and own thought.

While the whole paper is characterized by a broad view on education the discussion is unexpected  too narrow. The paper ends with the concrete example of ChoiCo. I expected that after this example the discussion would move again to a more general level and some issues raised with ChoiCo would be discussed in a broader perspective. In addition the discussion would benefit from a reflection on the initial questions posed in pag. 2 about the role for mathematics in coping with complex, socio-scientific issues and how can digital media be designed and used to introduce these ones. 

Some minor and specific remarks that I believe that could improve the paper are listed below.

- lines 111 – 112: the author uses the terms ‘normal’ and ‘post-normal’ but only explain these ones  later in line 157; the reference and/or definition should be introduced when these terms are used for the first time

- lines 190 -196 refer to 8 competences but I only count 7 competences. I suggest to mention only the key competences and exclude the number (eight) .

- text in lines 197 - 205 is a repetition of what is already said. It could be skipped

- in text from lines 206- 217 there should be connection with the key competences defined previously

- the author wrote in lines 219 – 220 “To date, transformation in mathematics education has hardly addressed the role of mathematics and mathematical thinking in post-normal science”. It is not clear if this statement is based on scientific evidence or on author’s experience/opinion.  

- lines 226 to 228. In my view the statement contains contradictory information: how can something have a secondary role and remain as important as when it had a primary role? The statement induced the reader to believe that is possible to have both truths

- line 232. The section titled Digital Media as Tools to Transform Mathematics Education is about the Education Technologic Lab therefore the broad title should be adapted as it doesn’t reflect its specific content

- pag 8. in the text following lines 295 -298 all the aspects are explained except the one mentioned in line 297 (Reciprocal shaping of meaning and tool). The author should explain it or skip it from the list

- In the section starting with line 474 (The Mathematical in Grappling with Wicked Problems) the author could explain better what are the mathematical concepts and meanings involved in the examples.

 

-          line 515. Please explain the meaning of ‘ETL-grown 3D’

 -          The examples presented in the discussion section for mathematical reasoning are not very  strong.

Author Response

thank you for your valuable comments. I have addressed and made the appropriate revisions of all of the minor point you mention. Also, I take your point that in the discussion it may have not been so clear that the examples of choico use were meant to help better consider the challenge of addressing the role of mathematics and mathematics education in the education of wicked problems. As a result I revised the discussion section to make better connections with the broader views on education so that it is clearer how the choico example and experience has been employed to clarify the nature and potential of the challenges posed to mathematics education. This has been done in key places in the discussion text and also by adding a paragraph (the one before the last concluding one) to better draw out the main point of the paper .