How Teaching Practices Relate to Early Mathematics Competencies: A Non-Linear Modeling Perspective

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Point 1: The article clearly situates the study within the context of previous research on early mathematics, quality teaching, and the limitations of existing quality measures. It appropriately justifies the need to use COEMET and nonlinear approaches, drawing on a robust theoretical and empirical foundation.

Point 2: The research questions are explicit and well-motivated; the design is solid and appropriate for the purpose (secondary analysis of TRIAD data using nonlinear methods), and the methods are explained in detail (RF, GAM). The description of samples, measures, and procedures is comprehensive.

Point 3: While the discussion reflects the results well and connects them to the literature, it could benefit from a more critical analysis of the limitations of the nonlinear methods and the potential practical implications for teacher professional development.

On the limitations of nonlinear methods

Currently, the discussion mentions the benefits of applying Random Forest and GAM but does not address their limitations. The authors could point out, for example:

• The possible lack of intuitive interpretability of some results compared to traditional linear models.

• The risk of overfitting, especially when working with a relatively small number of classrooms and many predictors.

• The dependence on the quality and nature of the data to properly capture nonlinear relationships.

Although the nonlinear methods used allow capturing complex relationships between variables, their practical interpretation may be less intuitive for teachers or educational decision-makers, and the risk of overfitting in relatively small educational samples should be considered in future studies.

On practical implications for teacher training and professional development

The discussion describes how certain teaching practices are associated with better mathematics outcomes, but it does not delve into what these findings mean for teacher professional development or how they could be incorporated into initial and ongoing training.

The findings on the importance of specific practices, such as “supporting listeners’ understanding” or “adapting tasks to a range of abilities,” suggest key areas for teacher professional development. Specifically, training programs could focus on developing teachers’ capacity to identify students’ levels of competence and adjust their interventions accordingly.

On the generalization and contextualization of the results

The discussion does not question to what extent the results are generalizable to contexts different from the original study (two U.S. cities in urban settings).

Since the study was conducted in a specific urban context, it is necessary to investigate the extent to which these relationships are replicated in other educational settings, including rural contexts or those with culturally distinct populations.

Point 4: The article includes an extensive and up-to-date relevant bibliography, demonstrating a strong engagement with both recent and classic literature.

Point 5: The conclusions are well-grounded in the empirical findings and align with previous evidence. They also open avenues for future research on the revision of COEMET. The article would benefit from making an effort to connect how the findings can contribute to better mathematics teaching in early childhood and how these findings can be transferred to teacher training (both initial and ongoing)

Point 6: The English is generally correct, but in some passages the writing is redundant and somewhat dense. A style review is recommended for greater conciseness and fluency.

Point 7: This article is original, relevant, and rigorous. Its methodological strengths and its contribution to the field are evident. With minor improvements in the writing and the discussion, it will be an excellent addition to the literature on early mathematics education.

I believe that a detailed qualitative analysis of the items associated with the dimensions ‘Classroom culture’ and ‘Specific mathematical activity’ could provide very valuable indicators and descriptors for both research and the training and professional development of future teachers. For example, understanding the different ways in which teachers ‘promoted mathematical thinking’ successfully making explicit how, when, and why they selected certain strategies would be highly valuable for understanding and disseminating contextualized strategies that foster the teaching and learning of mathematical knowledge in early childhood.

I am aware that the nature and objectives of the present research are different, and I do not intend to diminish in any way the remarkable work already done. However, I encourage the authors to consider the possibility of leveraging the data already collected to conduct future qualitative research aimed at advancing the understanding of situated teaching strategies that influence the development of students’ mathematical competencies. I am convinced that this type of analysis would complement and enrich the solid contributions of the current study.

Author Response

Please see the response letter attached. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Reviewer Comments on Manuscript: “How Teaching Practices Relate to Early Mathematics Competencies: A Non-linear Modeling Perspective”

This manuscript investigates the relationship between early mathematics teaching practices, measured by the Classroom Observation of Early Mathematics Environment and Teaching (COEMET), and children’s mathematical competencies, measured by the Research-Based Early Mathematics Assessment (REMA). Using data from 106 classrooms in the TRIAD study, the authors apply Random Forest to identify key COEMET items predictive of mathematics outcomes and then use Generalized Additive Models (GAM) to examine non-linear relationships between these practices and posttest math scores, controlling for pretest performance and intervention status. The authors conclude that item-level observational data, analyzed through non-linear modeling techniques, provides a more nuanced and predictive understanding of how specific teaching practices influence children's early mathematics competencies compared to traditional scale-level or linear approaches.

In the following, I provide comments and feedback informed by my reading of your manuscript:

Comment 1: The connection to prior research in the introduction section of the paper needs to be strengthened. The introduction is notably under-referenced from my perspective. Several key claims (for example that “The significance of children’s proficiency in early mathematics is gaining widespread recognition The mathematical knowledge that children possess upon entering kindergarten serves as the most reliable predictor of high school graduation, and a recent meta-analysis has demonstrated that early mathematics significantly influences mathematical development throughout a student’s educational journey.”) are presented without supporting citations, which weakens the academic rigor of the paper. I also suggest the authors include references to prior work on early mathematics instruction, classroom observation tools, and the use of advanced modeling techniques in educational research. Incorporating such references would help readers situate the current study within the existing literature and better understand its novel contributions.

Comment 2: Please clarify the methodological rationale before presenting research questions. The research questions are introduced before the reader has been sufficiently prepared with methodological and theoretical context. While the introduction provides a broad rationale for the importance of early mathematics and the limitations of general observational instruments, it does not adequately explain why Random Forest and Generalized Additive Models (GAM) are appropriate analytical choices for this study. Nor does it clarify why item-level analysis is central to the research design. As a result, readers unfamiliar with these models may find the research questions abrupt or disconnected from the preceding narrative. I recommend that the authors revise the introduction to include a brief but clear explanation of the strengths of RF and GAM in modeling complex, non-linear relationships, and why item-level data offers advantages in this context. This would improve the paper and better prepare readers for the study’s aims.

Comment 3: I appreciate the authors’ use of innovative analytical approaches, combining Random Forest (RF) regression and Generalized Additive Models (GAM) to explore relationships between teaching practices and early mathematics outcomes. However, from my understanding, some statistical issues require clarification.

1. The analysis is conducted at the classroom level (n = 106) with initially 28 predictors and later 17 predictors in GAM models. The substantial increase in adjusted R² from .50 (Model 2) to .72 (Model 3) may reflect the added explanatory power of non-linear terms, but it also warrants caution and further scrutiny to rule out potential overfitting. This impressive gain is noteworthy, but given the small n is it possible that it may partly reflect model complexity?
2. The paper presents methodologically innovative analyses (Random Forest and GAM). However, the concept of “non-linear relationships” is not explained very clearly. For readers less familiar with advanced statistical modeling, it would be helpful to provide a more pedagogical explanation of what such patterns mean in practice. For example, why “moderate” levels of teacher support (as seen in the inverted U-shaped relationships for Q16 and Q21) may be more beneficial than either too little or too much. A clearer, practice-oriented interpretation would make the findings more accessible to a broader audience and highlight their instructional significance.
3. Motivate your variable removal rationale. Eleven COEMET items were excluded due to zero or negative importance in RF. IS it possible that these low values could result from multicollinearity or scale characteristics rather than true irrelevance?
4. Likert-scale items and percentage-category items are treated as continuous without discussion of potential distortions. Given that measurement validity is central to the paper’s argument, please justify this treatment in your paper.
5. Is it possible that the inverted U-shaped relationships observed for Q16 and Q21 may be driven by few observations at extreme values? The discussion of the inverted U-shaped relationships for items Q16 and Q21 is intriguing and potentially important. However, I found the explanation somewhat brief and abstract. It would be helpful if the authors could elaborate on what these patterns mean in practical terms. A clearer pedagogical interpretation would make the findings more accessible to readers who are not familiar with non-linear modeling (I have also commented on this in relation to the discussion section below).

Based on my reading and my understanding, addressing the points above would strengthen the statistical foundation of the manuscript and improve confidence in the reported findings.

Comment 4: The study uses data from a single large-scale intervention (TRIAD) conducted in the U.S. While the findings are compelling, the extent to which the identified relationships apply to other contexts, such as non-intervention classrooms, different educational systems, or international settings, remains unclear. I recommend that the authors include a brief discussion on the generalizability of their findings and how these insights might inform teacher education or professional development beyond the TRIAD context.

Comment 5: The discussion section presents several important findings, including the added value of item-level analysis and non-linear modeling. However, I suggest the authors clarify the practical implications of the inverted U-shaped relationships, particularly for Q16 and Q21. What do these patterns mean for instructional practice? Additionally, the discussion could benefit from a more explicit reflection on the study’s limitations, such as potential overfitting, context specificity, and the interpretability of RF importance scores. Strengthening these aspects would enhance the relevance and transparency of the conclusions.

Comment 6: While the manuscript discusses the strengths of the COEMET tool and its predictive value, it would benefit from a more explicit reflection on its limitations as a measurement instrument. For example, the paper does not address issues such as inter-rater reliability, contextual sensitivity, or the extent to which individual items capture complex teaching practices. Given that the study’s conclusions rely heavily on item-level data, a brief discussion of COEMETs potential constraints would strengthen the credibility and transparency of the findings.

Comment 7: The reference list does not consistently follow APA 7 guidelines. For example, journal titles should be italicized, and volume numbers should also be italicized. I recommend that the authors revise the formatting to ensure compliance with APA 7 standards.

The comments above are based on my careful reading and interpretation of your manuscript in its current form. I recognize that some points, particularly those related to statistical modeling, may benefit from further clarification. I hope that my comments and suggestions prove useful in enhancing the clarity, rigor, and practical relevance of your paper.

Author Response

Please see the response letter attached. 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have carefully addressed my comments from the first round of review and have revised the manuscript in a clear and constructive way. These improvements have strengthened the paper, and I have no further comments.