High School Students’ Performances in Transitions between Different Representations of Linear Relationships in Mathematics and Physics
Round 1
Reviewer 1 Report
The paper under evaluation presents an exploratory study from the perspective of quasi-experimental quantitative research. The topic under study is undoubtedly very interesting, especially with regard to the role of contexts and representations when measuring mathematical competence as well as that of some components of the affective domain in mathematics such as the perceptions of self-efficacy and self-confidence as relevant (mediator) variables to understand -and sometimes explain partially- students’ performances and behaviors.
The title of the article is clear and attractive, informative enough, although I suggest to remove the term “abilities” and use instead the word performances, since what is really being measures cannot be straightforward linked to skills or abilities in the sense these constructs are usually understood in Mathematics Education. The document presents a high degree of readability, with a coherent and fluid organization of the text and with statements that invite to reflect on the results that are being presented. The literature review shows relevant works in the area, although more references from recent years are missing, as well as some articles in which self-efficacy has been analyzed through multivariate approaches or, for example, by means of models of structural equations, showing possible relationships with academic performance itself. Moreover, some references to the role of contexts, at least in the sense PISA consider them might help to strengthen the paper. Concerning the theoretical framework some conceptual framework and some supporting theories are need to clarify what the authors understand by mathematical competence and by self-efficacy (is it understood in the sense provided by Bandura?).
The methodological section is undoubtedly one of the strengths of the article. The research design is adequate for the objectives pursued and the description of the process is detailed enough to assign a high degree of traceability. In turn, the execution of the different steps of the design is rigorous. There are, however, some small issues that can be improved: a) It is not clear how the underlying construct of the data collection instruments used is understood and if what they measure is really aligned with the position of the researchers themselves, as well as with the definition of their study variables. b) The arguments for the quality of the instruments selected is focused more on their reliability than on their validity, when reliability, being a necessary condition, in the terms in which it is presented, it is known that it is always more linked to the sample than to the instrument itself. Moreover, the use of Cronbach´s Alpha is usually constrained to some conditions or premises that are not clearly satisfied in the context of the study, apart from the limitation of such parameter itself. The use of McDonald´s Omega seems to me more suitable. c) Not enough psychometric analysis are performed on the self-efficacy scale. d) A more detailed description of the sample and the sampling method would be welcome.
In case the above mentioned drawbacks cannot be attended at this stage of the research I suggest to refer to them as limitations of the study.
The data are clearly and precisely presented as research results, although statistical details are sometimes abused that are not necessary for the reader or to shed more light on the research. Many of them are original and powerful, while opening future lines of research. The weakest point of the article is in its discussion and its conclusions. The discussion must offer a deep reflection on the results, and not insist on what has already been presented or being reduced just to a brief summary of previous results. Comparisons are made with other studies, but a more serene and thoughtful interpretation of what has happened is still pending, especially since the results shown, with regard to anxiety, are, to say the least, surprising. Both the discussion and the conclusions must go beyond the results. I encourage the authors to include these modifications, which will undoubtedly give even more quality to a good research work like the one they present.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The submitted manuscript investigates high school student’s abilities in transitions between different representations of linear relationships in mathematics and physics. Overall, this is a clearly written manuscript with justified research questions. I think it could be improved in some aspects.
Major points:
1. Sect. 3.1., Instruments: I do not think that “questionnaires” is the proper wording for the kinematics and mathematics instrument. In my opinion, it is instead a “test” (like the mental rotation test) instead of a “questionnaire”.
2. 310: I would judge the reliabilities as “satisfactory” instead of “excellent”.
3. I am entirely unsatisfied with the listwise deletion analysis. Please perform the multiple imputation technique to let all analyses rely on the same sample (size).
4. Figures: Please do not refer to colors in the description. Use black and gray (or white) for kinematics and mathematics for a better distinction on a back-white printer or colorblind readers.
5. Include d values in addition to mean differences and significance tests.
6. Appendix B, 675: It is unclear what is meant by the model matrix. Isn’t it the loading matrix?
Minor points:
7. Please use the same tense in the abstract.
8. 10: write “involved” instead of “has involved”
9. 13: write “it is shown”.
10. 157, 167, 242, and other places in the manuscript: There is too much space between two words in the corresponding lines.
11. 308: write “missing data” instead of “data missing”
12. 335: typo “7norma…”
13. 384: write “highly significant” instead of “very significant”
14. 684: write “obtained”
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
