Differentiated Instruction in Problem-Based and Direct Instruction: The Moderating Role of Mathematical Disposition on Students’ Mathematical Communication Skills
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsBrief Summary
This study aims to investigate the individual and joint effects of two instructional models—Problem-Based Learning (PBL) and Direct Instruction (DI)—on students' mathematical communication skills, using mathematical disposition (high vs. low) as a moderating variable. Employing a quasi-experimental 2x2 factorial design with 75 Grade XI students in Indonesia, the main contribution is the finding of a significant interaction between the instructional model and mathematical disposition. Specifically, students with a high mathematical disposition performed significantly better under the PBL approach, whereas students with a low mathematical disposition achieved higher scores under the DI approach.
General Comments
The study is scientifically sound, and the experimental design is appropriate to test the hypothesis of an interaction effect, which is the manuscript's key strength. The significance lie in providing empirical evidence for the specific conditions under which PBL or DI are most effective, moving beyond a "one-size-fits-all" approach in mathematics education.
However, there are a few areas that affect the robustness and generalizability of the findings:
- Small sample size and generalizability: The sample size of N=75 is relatively small for a quasi-experimental study, which limits the generalizability of the findings. No worry. You should just explicitly acknowledge that the results may be specific to the context of the public high school in Indonesia.
- Short check: The study is strengthened by measuring the moderating variable (mathematical disposition) before the intervention. However, the internal validity would be significantly improved by reporting pre-test scores on the dependent variable (mathematical communication skills) for both classes (PBL and DI) to confirm their initial equivalence. This is a common requirement for quasi-experimental designs to strengthen causal claims. Try also to make clear and explicit the relationship among the variables, also with a short diagram.
- Add some data: The mathematical communication test only comprised five items used after five instructional sessions. Given that mathematical communication is a multi-dimensional construct (written explanations, visual representations, mathematical expressions), five items might not be comprehensive enough to capture the full scope of student skill enhancement. A justification for the adequacy of the five-item assessment should be added. Can you attach a sample of the items by the test? Same for some question from the questionnaire.
- Add external factors: The authors correctly identify in the limitations that the study does not account for other potential influencing factors such as learning motivation, interest, or social support. This should be mentioned in the discussion as a caveat to the interpretation of the results.
- Discussion emphasis: The first paragraph of the Discussion section (lines 239–242) currently emphasizes the overall main effect (PBL higher than DI). Given the novelty of the research, the discussion should be re-centered around the significant interaction effect between Model and Disposition (Table 5) as the primary and most important finding, as this is what addresses the stated gap in the literature.
Specific Comments
- Line 41: Instead of “acquired,” I would suggest using a softer verb such as “fostered.”
- Line 52: Typo in “(I(Ibrahim …”.
- Line 64: Instead of “all,” perhaps “each” would be more appropriate.
- Lines 77–81: I don’t quite understand the meaning of “flexibility” in the two models. Each model seems rather fixed; the flexibility appears to lie in the possibility of switching between them, correct? Please clarify this passage. The same applies to Lines 91–92.
- Page 3: I would suggest adding a small diagram to clarify the relationship among the three questions. As I understand it, each question seems to focus on the relationships between:
- Learning models → students’ mathematical communication skills;
- Students’ mathematical dispositions → students’ mathematical communication skills;
- Learning models & students’ mathematical dispositions → students’ mathematical communication skills.
You could, for instance, represent the relationships between learning models and students’ mathematical dispositions using dots and arrows to illustrate the whole structure.
- Lines 144–149: The notation “class XI I, XI.I, XI J, and XI.J” is unclear. Please ensure consistency or clarify what this notation means.
- Lines 150–159: Could you include a sample item from the test or a question from the questionnaire?
- Table 2: To improve readability, consider adding horizontal lines to separate each cell. I was also wondering about the connection between columns 1 and 2, as well as 3 and 4, in relation to the respective teaching models. For instance, teaching activities come first relative to student activities.
- Line 201: There is an inconsistency in the reported mean score for the Low Disposition (B2) group. Table 4 shows the mean as 62.50, whereas the text on Line 199 states it as 61.67. Please correct this discrepancy for consistency between text and table.
- Lines 210–214: Table 6 should be cited here.
- Figure 1: Use a capital letter in the caption. I would also suggest adding a unit of measure to the y-axis.
- Line 266: I would avoid grouping “sociocultural” and “constructivist” together. Vygotsky is often positioned between these two perspectives, but based on your text, your stance seems closer to a constructivist view. I would clarify this.
- Lines 347–348: I would include the terms “A1” and “A2” in brackets to make the acronyms clearer.
- Lines 353–354: This statement feels slightly disconnected from the preceding text. I suggest softening it with a phrase such as “the findings suggest that…”.
- Lines 357–363: These sentences are quite short; I would recommend expanding this section for a more substantial conclusion.
Pleasant to read. Well done. Good work! :)
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper addresses a relevant topic that is likely to draw interest from the mathematics education research community.
The article is written in a comprehensible and clear style, but see the comments of the quality of the English language below. The objectives are fully stated in the first part; the methods of the conducted research are clearly exposed, although I find the prose a bit dry, at times.
Regarding the aspects that can be improved, I would have liked to see more detail on the theoretical framework and its implication for the discussion of the results. For example, Vygotskian references are underlined but not fully integrated into the articulation and interpretation of the results, in my opinion. The final discussion could move beyond descriptive restatement of results aiming at a more comprehensive critical synthesis with existing literature.
Comments on the Quality of English LanguageA note on some linguistic and typographical issues.
I'm not a native speaker so I can comment only as far as my knowledge of English allows, and to me it seems the use of English in the paper appears to be correct, generally speaking.
There are, however, a few minor problems that need to be addressed before publication.
The paper seems to use American spelling but there are a few instances here and there (e.g. "centred") of a drift towards British spelling.
Last but not least, there are a few typographical inconsistencies in the presentation of quantitative results (e.g. t-table vs tₜₐᵦₗₑ or df vs Df).
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsIt is necessary to illustrate with examples of the mathematical skills developed. The following must be mentioned:
What mathematical topics were developed in the PBL and ID proposals?
If the topics were to vary, would the results presented change?
Was there any diagnosis prior to the application of the teaching situations?
The statistical work is very good, however, some examples of the students' reasoning need to be illustrated so that the development (or lack thereof) of mathematical skills is clear.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThe suggested corrections were made, and in its current state it is ready for publication and contributes to mathematics education.
Author Response
We are pleased that the reviewer found the manuscript satisfactory and ready for publication. We sincerely appreciate the reviewer's positive assessment of our revisions and the paper's contribution to mathematics education.
