Characteristics of Effective Elementary Mathematics Instruction: A Scoping Review of Experimental Studies
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript makes a significant contribution to the field by synthesizing findings from 44 experimental studies and identifying 27 characteristics of effective mathematics instruction. This work is valuable for guiding future research and informing educational practices. However, a deeper discussion on the practical implementation of these characteristics in diverse educational contexts could enhance its impact.
The manuscript is well-organized, with clear sections covering objectives, methodology, results, and discussion. Each section is detailed and provides sufficient information for understanding the study.
The study is scientifically strong, employing rigorous methodology with clear inclusion and exclusion criteria. The qualitative analysis is thorough, and the results are well-justified and supported by the data. There are no misleading statements or unsupported claims.
In my opinion, the manuscript includes appropriate and adequate references to related and previous work, demonstrating a strong understanding of the field.
In terms of format, line 394, should be “Figure 2” instead of “Figure 1”.
In general, the figures show poor quality, could you improve it?
In terms of English use, authors should break down long sentences into shorter, more manageable ones. For example, instead of "The study aims to identify the characteristics of effective interventions in elementary school mathematics education through a scoping review that included 44 experimental studies published between 2014 and 2023," consider "The study aims to identify the characteristics of effective interventions in elementary school mathematics education. It includes a scoping review of 44 experimental studies published between 2014 and 2023."
Author Response
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.
Comments 1: A deeper discussion on the practical implementation of these characteristics in diverse educational contexts could enhance its impact.
Response 1: In almost every section (from 3.3.1 to 3.3.9), we have added new content that deepens the discussion and outlines possibilities for implementing the identified characteristics. For example, at the end of section 3.3.2, we added the following text:
The prevalence of active learning strategies in the analyzed interventions aligns with the findings of a previously conducted meta-analysis, which reported an overall effect size of 0.47 when active learning was compared to traditional teaching methods (Freeman et al., 2014). According to Ting et al. (2023), active learning in Asian contexts has an even greater impact on student achievement in STEM subjects (d = 0.66). The authors attribute this to the fact that teaching in Asian contexts is “typically instructor-centered and highly content-oriented, whereby learners are passive recipients of information instead of actively engaged participants in the learning process” (p. 389). Consequently, the introduction of active learning represents a more significant change compared to Western contexts.
To implement active learning in settings less inclined toward this approach, challenges such as the “lack of time to actively involve students in teaching; the amount of content to be covered; lack of resources; lack of instructional materials; lack of administrative support; and that it took too much effort from teachers” (Takele, 2020, p. 12) must be addressed.
Digital tools, such as gamified learning platforms, can facilitate active student learning. However, in environments with limited access to technology, methods such as project-based tasks (Lazić et al., 2021) and hands-on activities can effectively connect mathematical concepts to real-life situations. Even in resource-constrained settings, teachers can design meaningful activities using everyday objects. For instance, buttons or sticks can be used to teach arithmetic, while role-playing games can illustrate concepts like money management in an engaging and relatable way. Embedding math tasks in real-world and culturally relevant contexts further enhances engagement. Tasks related to local markets or common household measurements, for example, highlight the practical relevance of mathematics in students' daily lives.
This review includes several interventions aimed at improving academic performance through various physical activities. These activities require no special equipment or conditions and can be easily integrated into daily math lessons. They not only enhance students' performance in mathematics but also “reduce the negative effects of a sedentary lifestyle” (Magistro et al., 2022, p. 8).
Comments 2: The next suggestion referred to the incorrectly numbered figure and the poor quality of the figures.
Response 2: All figures have been replaced with higher-resolution versions, and the mentioned figure in line 394 has been moved to the appendix and presented in a landscape orientation to ensure maximum clarity.
Comments 3: Finally, you suggested breaking down long sentences into shorter, more manageable ones. Response 3: We have reviewed the paper and, wherever possible, divided longer sentences into several shorter ones.
Thank you again for your insightful suggestions. We believe they have significantly strengthened the quality of our work.
Kind regards,
Authors
Reviewer 2 Report
Comments and Suggestions for AuthorsDear Authors,
The article is a significant contribution to understanding effective strategies in primary school mathematics education. It is informative, methodologically interesting, and provides a comprehensive perspective on the topic.
Based on the above questions, I’d like to demonstrate my partial rating results as follows:
1. Does the work make a significant contribution to the field?
The article addresses the important area of effective mathematics instruction in primary schools, which is essential for fostering mathematical literacy and equality in education. The results identify 27 characteristics of effective interventions, which are valuable for both researchers and educators. The research is contextualised with regard to previous and current studies.Recommendation for authors:
The introductory sections contain several general statements about the importance of mathematics, inclusivity, and equality in education. I recommend summarising these in a more concise format to make them more effective and focused. Additionally, the identified characteristics of interventions (e.g., use of technology, active learning) are not sufficiently linked to specific results from empirical studies that would confirm or challenge these characteristics.
2. Is the work well organised and comprehensively described?
The methodological steps are described in detail. The discussion is logically structured around the research questions. The identification of 27 characteristics of interventions and their grouping into nine thematic clusters provides a systematic framework for evaluating effective interventions. The research questions are clear and relevant, making sense in the context of the chosen method and allowing for a structured analysis.
Recommendation for authors: The discussion is sometimes descriptive and less critical – there is a lack of deeper analysis of the reasons for the limited effect of technology in some cases. While the authors correctly identify several successful approaches (e.g., combining technology with active learning), these are not sufficiently linked to their feasibility in school environments. Why is this the case? Please elaborate. Tables and figures provide clear and specific data.
Additional recommendations:
Figure 1 and Table 2: I recommend moving these to the appendix (Figure 1 should also be moved due to poor resolution and should use an A4 landscape layout; Table 2 should be relocated due to its length, and references should be organised logically, e.g., by date rather than alphabetically).
Line 394: The labelling of Figure 1 is incorrect; it is the second figure in order (note: the figure is not sharp enough – resolution adjustment is essential, and its relocation to the appendix is advised).
Line 427: Figure 3 is also blurry – resolution improvement is necessary. (Some information is repeated in both the text and tables (e.g., the number of characteristics in individual interventions).)
3. Is the work scientifically sound and not misleading?
The arguments are supported by specific examples from the included studies, which enhances the credibility of the conclusions. The use of references such as NCTM (2014) and Prediger et al. (2022) adds depth and theoretical backing to the claims about the effectiveness of identified characteristics, which is a positive aspect. The conclusions are consistently supported by the findings from the analysed studies and logically derived, but they are not sufficiently elaborated. For instance, the conclusion that "multiple characteristics are important for the effectiveness of interventions" could be more thoroughly justified.
Recommendation for authors: Provide additional analysis of which specific combinations of characteristics are most effective. If this analysis is beyond the scope of the study, suggest it for future research to build upon these findings.
The authors chose a scoping review as the method, which is appropriate for mapping existing knowledge on effective interventions in mathematics instruction in primary schools.
Recommendation for authors: While the reason for selecting the scoping review method is provided (broad exploration of the literature), the choice could be defended more specifically – why was a meta-analysis not chosen, which might have allowed for deeper statistical comparisons?
4. Are there appropriate and adequate references to related and previous work?
The article is adequately referenced, covering a wide range of relevant literature. Most references are from high-quality sources.
Recommendation for authors: Include more studies from developing countries or countries with different educational systems to make the results more universal – or adequately justify why these steps are unnecessary.
There is a lack of linkage between citations mentioned in the article and the references listed in the "References" section.
Recommendation for authors: Ensure consistency in the formatting of references for pairs of authors, using either “XY and XZ” or “XY & XZ,” according to the template requirements.
Additionally, verify whether the references need to be presented in the order they appear in the article and numbered accordingly (the authors have listed them alphabetically in the References section). If required, reformat and reorder the references.
5. Is the English used correct and readable?
The English is generally professional and readable. The authors use precise scientific terminology, and the work is structured in a way that makes it accessible to a broad audience.
Overall: The article is of high quality, and I recommend it for publication with minor revisions (as outlined above) that would strengthen its practical applicability and theoretical contribution.
Best regards...
Author Response
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.
Comments 1: The introductory sections contain several general statements about the importance of mathematics, inclusivity, and equality in education. I recommend summarising these in a more concise format to make them more effective and focused.
Response 1: This section has been shortened and now reads:
The aim of mathematics education is multifaceted, reflecting various educational, societal, and personal goals. In general, the development of students’ problem-solving skills, which are necessary for coping with the real world, is the most important goal of mathematics education (OECD, 2023). The overarching goal is to create a mathematically literate population, capable of engaging with the world through a quantitative lens, thus contributing to the personal growth of individuals and the progress of society (Jablonka, 2003; OECD, 2023). To achieve this goal, it is important to focus on the quality of mathematics teaching.
Comments 2: The identified characteristics of interventions (e.g., use of technology, active learning) are not sufficiently linked to specific results from empirical studies that would confirm or challenge these characteristics.
Response 2: In Chapter 3.3, we expanded the text by linking our findings to other studies. For example, at the end of Section 3.3.3. we added the following text:
The central feature of this theme concerns formative assessment. In a recent systematic review of meta-analytic studies (Sortwell et al., 2024), formative assessment was found to have a positive impact on students' academic achievement. This is also true for mathematics, although the standardized mean differences (SMD) are not large (SMD = 0.09–0.34). By using formative assessments, teachers can group students according to their specific abilities and give them tasks that are tailored to their performance level. Computerized formative assessments, which have been shown to be effective (Kingston & Nash, 2011; Sortwell et al., 2024), can support this process. In low-resource settings, non-digital alternatives such as quick quizzes, exit tickets, student journals or structured question-and-answer sessions can be equally effective. Most importantly, clear and immediate feedback helps students to correct mistakes and make consistent progress.
In addition to the existing ones, we added 15 new references to connect the findings of our research with results from empirical studies.
Comments 3: The discussion is sometimes descriptive and less critical – there is a lack of deeper analysis of the reasons for the limited effect of technology in some cases. While the authors correctly identify several successful approaches (e.g., combining technology with active learning), these are not sufficiently linked to their feasibility in school environments. Why is this the case? Please elaborate.
Response 3: We expanded the discussion in almost all sub-sections of Chapter 3.3. To address the mentioned recommendation, we added the following text:
Previous research on the effectiveness of technology use on mathematics achievement is inconsistent. In meta-analytic studies, Li and Ma (2010) found a mean weighted effect size of 0.28, Cheung and Slavin (2013) determined an effect size of 0.16, Higgins et al. (2017) reported a mean weighted Cohen’s d of 0.68, while Pellegrini et al. (2018, 2021) concluded that technology-based interventions had minimal impact on student outcomes. Based on such results, it is difficult to determine the extent to which technology is effective in mathematics education. Furthermore, it can be assumed that other factors besides technology influence the outcomes of mathematics instruction. Li and Ma (2010) found that this applies to the use of technology in special education. They also found that “the method of teaching showed a magnitude of 0.79 SD in favor of using technology in school settings where teachers practiced a constructivist approach to teaching over school settings where teachers practiced a traditional approach to teaching” (p. 230). In our study, technology was combined with other characteristics of effective interventions. It appears that digital technology is more effective when combined with other features of effective mathematics instruction. It is therefore important to ensure that technology is used in elementary mathematics education in a way that also takes into account other features such as (meta)cognitive engagement, conceptual understanding, procedural fluency and formative assessment.
Comments 4: The next section of recommendations pertains to Table 2 and the figures:
Figure 1 and Table 2: I recommend moving these to the appendix (Figure 1 should also be moved due to poor resolution and should use an A4 landscape layout; Table 2 should be relocated due to its length, and references should be organised logically, e.g., by date rather than alphabetically).
Line 394: The labelling of Figure 1 is incorrect; it is the second figure in order (note: the figure is not sharp enough – resolution adjustment is essential, and its relocation to the appendix is advised).
Line 427: Figure 3 is also blurry – resolution improvement is necessary. (Some information is repeated in both the text and tables (e.g., the number of characteristics in individual interventions).)
Response 4: Table 2 has been moved to the appendix. Although the references in Table 2 could be organized according to another criterion (e.g., year of publication), we have kept them arranged alphabetically because the publication date is not crucial for this review. Additionally, we believe it is easier to navigate the list of studies when they are organized alphabetically. All figures have been renumbered and replaced with higher-resolution versions. Additionally, the figure mentioned in line 394 has been moved to the appendix and presented in a landscape orientation to ensure maximum clarity.
Comments 5: Provide additional analysis of which specific combinations of characteristics are most effective. If this analysis is beyond the scope of the study, suggest it for future research to build upon these findings... While the reason for selecting the scoping review method is provided (broad exploration of the literature), the choice could be defended more specifically – why was a meta-analysis not chosen, which might have allowed for deeper statistical comparisons?
Response 5: We addressed those comments at the end of chapter 6. Limitations:
To identify the characteristics of instruction present in effective elementary mathematics education interventions, we selected a scoping review as the appropriate methodological approach (Munn et al., 2022). Additionally, determining which specific combinations of characteristics are most effective would be interesting but falls outside the scope of this review. However, this could serve as a research focus for a future meta-analytic study.
Comments 6: Include more studies from developing countries or countries with different educational systems to make the results more universal – or adequately justify why these steps are unnecessary.
Response 6: In the inclusion and exclusion criteria, we stated the following: “The study must be available in English, regardless of the country in which it was conducted.” This means that we included all studies published in various countries. Most interventions were carried out in developed countries (32), followed by developing countries (11). Only one study was conducted in a least developed country (Malawi). However, the number of studies from developing countries was not influenced by the selection process but is likely due to the fact that these countries often have fewer resources and less developed research institutions, resulting in lower scientific output. Considering the other references included in the review, we added studies from different countries whenever possible, including around twenty references from developing countries
Comments 7: There is a lack of linkage between citations mentioned in the article and the references listed in the "References" section.
Response 7: Regarding this comment we reviewed all references included in the article and made the necessary corrections.
Comments 8: Ensure consistency in the formatting of references for pairs of authors, using either “XY and XZ” or “XY & XZ,” according to the template requirements.
Response 8: To ensure consistency in the formatting of references for pairs of authors, using either “XY and XZ” or “XY & XZ” according to the template requirements, we reviewed all in-text references to align them with APA style:
“In-text citations may be parenthetical or narrative.
- In parenthetical citations, use an ampersand (&) between names for a work with two authors or before the last author when all names must be included to avoid ambiguity.
In narrative citations, always spell out the word 'and'.” (https://apastyle.apa.org/style-grammar-guidelines/citations/basic-principles/author-date)
Comments 9: Additionally, verify whether the references need to be presented in the order they appear in the article and numbered accordingly (the authors have listed them alphabetically in the References section). If required, reformat and reorder the references.
Response 9: The new template and the Instructions for Authors (https://www.mdpi.com/journal/education/instructions) recommend using APA style, which requires listing references alphabetically in the References section.
Thank you again for your insightful suggestions. We believe they have significantly strengthened the quality of our work.
Kind regards,
Authors
