Mathematical Creativity: A Systematic Review of Definitions, Frameworks, and Assessment Practices

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this study, the authors conduct a systematic review of how mathematical creativity is defined and the theoretical frameworks on which it relies, as well as how it is assessed in K-12 education.

Overall, the manuscript is well written and easy to follow. I have only a few minor suggestions for improvement, and once these have been addressed, the manuscript should be ready for publication.

 

Below are my thoughts on the manuscript, ordered chronologically.

 

(1) In the abstract, you mention preliminary results. If this paper is to be published, I hope the results are more than preliminary.

(2) In the abstract, I would recommend talking not only about the results regarding definition and frameworks, but also about the results regarding assessment.

(3) Why are the lines of the introduction and methods sections not numbered, while the results and discussion sections are? Furthermore, the page numbers start again at 1 after Table 2, which makes it difficult for me to refer to page numbers when the same number can appear twice in the manuscript.

(4) Sections 1.1 and 1.2 feel very overlapping and redundant in places (e.g. the information on Balka, 1974), as the theoretical perspectives and definitions are closely interconnected. Is there any way to connect these sections, or perhaps discuss their close interrelation? In your three guiding questions, you discuss conceptualisation. Isn't this intrinsically linked to the definition? Is it at all possible to answer these questions separately?

(5) Why did you decide to only review studies with a K12 population? Why not also include adult samples? If I were on the lookout for a review on the definition and assessment of mathematical creativity, I would hope to find one as complete as possible.

(6) Why did you not mention the existing systematic review on the assessment of mathematical creativity?

Suherman, S., & Vidákovich, T. (2022). 'Assessment of mathematical creative thinking: A systematic review'. Thinking Skills and Creativity, 44. Thinking Skills and Creativity, 44, 101019.

Please specify what additional significance your study provides.

(7) On p. 3, you cite Bicer (2021). If this is a direct quotation, please provide a page number.

(8) I find the first paragraph of the Methods section unnecessary. I don't think you need to convince readers with so much detail about why a systematic review is beneficial.

(9) Is 'Major Databases' a subheading within section 2.1? If so, please make it more visible.

(10) On p. 5, you mention that you excluded studies that did not define mathematical creativity. Why did you exclude them? Shouldn't the important information on how mathematical creativity is assessed be included, if they still measured it?

(11) Personally, I find Figure 1 and Sections 2.1 and 2.2 a little redundant. I know it's always difficult to strike a balance between describing the figure and repeating information, but it might be worth reconsidering this aspect.

(12) With regard to Table 1, what does 'SU' stand for in the first box?

(13) This is a pet peeve of mine, but for consistency, if you decide to leave a space before and after an equal sign, apply this to all equal signs. In Figure 1, for example, there are some instances where there is a space before the equal sign but not after. The same is true of Table 1, where sometimes no spaces are used, sometimes all spaces are used, and sometimes only a space is used after the equal sign. Another thing I noticed in Table 1 is that sometimes you add a full stop at the end of the information about the sample and sometimes you don't. Please keep this consistent.

(14) Under 2.3, you state that 'initially a greater numbers of themes were proposed'. Could you clarify this? Does this refer to the definitions or the theoretical frameworks? If you are referring to an initial stage, this also suggests to me that there was a subsequent stage, so I would be interested to know what the initial stage was, what the subsequent stage was, and why this transition happened.

(15) If the information is available, I would strongly suggest that you report age as well as grades. For example, Schoevers et al. (2018) report a mean age of 9.68 years (SD = 0.45). As school starting age differs slightly depending on the country, this would be useful additional information. Alternatively, you could include the information about which country the study was conducted in. Another aspect connected to age is discussed in section 3.14, where you report the age of the target groups in months. Please transform this into years using the data from Leikin & Tovli (2019). Additionally, you state at the end that the sixth grade was the most frequently studied at elementary level. However, this also differs by country. For example, in my home country, only grades 1–4 are considered elementary school and grade 5 is considered secondary school. I mention this just to put things into perspective.

(16) In Table 1, you report the gender of some studies, but not others where the information is available (e.g. Sadak et al., 2022). I would therefore suggest either double-checking whether the original paper reports gender or not including it at all, given that you also don’t discuss gender in the rest of the paper.

(17) Why did you not include Stolte, M., García, T., Van Luit, J. E., Oranje, B. and Kroesbergen, E. H. (2020)? 'The contribution of executive functions in predicting mathematical creativity in typical elementary school classes: A twofold role for updating' in your review?

(18) I am not sure if you really need Table 2, since you never refer to it elsewhere in the study. If you want to keep the table, I would suggest indicating in the column 'Studies using the assessment' which studies came up with the test and which only used it. For example, the Mathematical Creativity Test (MCT), which was used by Schoevers et al. (2018), was developed by Kattou et al. (2013) and translated into Dutch for this study. Stolte et al. (2019) also report using an adapted version of this task.

(19) Please double-check the citations throughout the study. Most of the time they are correct, but on p. 3, line 120, for example, it should be “and” instead of “&”. There are also some examples on pp. 7 and 8.

(20) Under section 3.9, what is the difference between (a) the scoring approaches and (c) the specific components scored? Please clarify.

(21) It would be easier to understand the results if you provided examples when reporting them. What does a criterion-referenced scoring approach actually entail?

(22) Shouldn’t 3.10 actually be a subheading of 3.9 instead of being at the same level as the other points?

(23) You also report an unclassified approach. If they didn’t use norm- or criterion-referenced approaches, what did they actually do?

(24) Page 9, lines 418 and 419: This sentence appears to be incomplete.

(25) As you mention AI in combination with mathematical creativity, this paper, Marrone, R., Cropley, D. H., & Wang, Z. (2023). Automatic assessment of mathematical creativity using natural language processing. Creativity Research Journal, 35(4), pp. 661–676, might be of interest to you. It could also be a candidate for inclusion in your review.

(26) On p. 11, you state that creativity involves not only cognition, but also beliefs. Are beliefs actually part of creativity, or are they simply a predictor of it?

(27) On p. 12, you mention mathematics-specific processes that are central to authentic mathematical creativity as implications for practitioners. How does authentic mathematical creativity differ from non-authentic mathematical creativity? Could you give an example of what this should look like?

(28) Why is the conclusion written in a different font?

(29) Why is there an appendix that tells me what an appendix is?

Author Response

Thanks very much for your valuable feedback! Please see the attachment for our detailed responses.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for the opportunity to read and review this engaging and well-structured paper.

Overall, I find the manuscript to be methodologically sound and conceptually rich. The analysis is compelling, and the topic is both timely and relevant. I have only a few suggestions that I believe could enhance the clarity and coherence of the paper.

1. I recommend referencing the research questions throughout the entire Findings section, rather than only in section 3.9. Additionally, a more precise alignment between the terminology used in the research questions and the headings and meta-text in the findings would be beneficial. For instance, the term' theoretical foundations' in the research questions appears as a framing in the findings. While this may be a matter of interpretation, framing can imply several things beyond theoretical underpinnings, which may confuse, particularly for readers who are not native English speakers.

   I also found myself revisiting the research questions repeatedly due to the considerable overlap between Research Question 1 (RQ1) and Research Question 2 (RQ2). Clarifying the distinction between these two questions would strengthen the overall structure, especially since this overlap is acknowledged in the manuscript.

2. The discussion of target groups in the findings section raises some questions. Does this fall within the scope of how creativity is operationalized and assessed? The inclusion of age-related observations is interesting and relevant, particularly given the noted underrepresentation of certain age groups. However, age is introduced in the findings without prior mention in the introduction or research questions. If there is existing research on this topic, it might be helpful to reference it and consider incorporating this aspect into RQ3. Preparing the reader for this part of the findings earlier in the manuscript would improve coherence.

3. The description of the coding and analysis process is relatively brief. Expanding this section, especially with regard to the analysis of RQ1 and RQ2, would be valuable. Was a deductive approach employed, based on pre-existing themes? Clarifying this would help readers better understand the distinction between definitions/conceptualizations and theoretical foundations.

4. There are a few instances where the language could be clarified:

   • Lines 14–16
   • Lines 418–419
   • Lines 439–441: In particular, the phrase close numerical representation is unclear. 

Comments on the Quality of English Language

I made comments about language above.

Author Response

Thanks very much for your valuable feedback! Please see the attachment for our detailed responses.

Author Response File: Author Response.pdf