Newton’s Second Law Teaching Strategies—Identifying Opportunities for Educational Innovation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript selects and reviews 26 articles associated with teaching Newton's second law published between 2014 and 2024. The paper lacks critical analysis and discourse on the studies identified. A clear statement on the limitations of this manuscript should be included.

The findings presented offer insights into approaches adopted to support students understanding of Newton's second law - categorised as 4 types of approaches. A critique on the pros/cons of each type would improve the quality of this analysis.

Table 2 presents an overview of the academic articles published and offers several insights including different strategies adopted for sec/sup/prof levels. While the question/objective of the study is included in the table this paper lacks a discussion on the findings of these studies and critical analysis of these findings in Section 4 Discussion. Section 5 Conclusions are not adequately supported by the results presented in the article or referenced in secondary literature.

Other comments:

There are some formatting issues at beginning of section 2. Materials and Methods before Tabe 1.

Figure 2 is not necessary and doesn’t add any value to the paper.

Author Response

Comments 1: The manuscript selects and reviews 26 articles associated with teaching Newton's second law published between 2014 and 2024. The paper lacks critical analysis and discourse on the studies identified. A clear statement on the limitations of this manuscript should be included.

Response 1: New paragraphs were added to provide a critical analysis of the studies, distinguishing between educational levels (secondary, tertiary, and teacher education) and highlighting methodological tensions and gaps. A clear statement of the study’s limitations was also incorporated at the end of the discussion section. This is in results and discussion.

Comments 2: The findings presented offer insights into approaches adopted to support students understanding of Newton's second law - categorised as 4 types of approaches. A critique on the advantages/disadvantages of each type would improve the quality of this analysis.

Response 2: One dedicated paragraph per task type was added, detailing the strengths and weaknesses of each representational approach (no model, idealized model, dynamic model, decontextualized model). Additionally, a summary table was created to clearly present this comparison. This is in section 3 and 4.

Comments 3: Table 2 presents an overview of the academic articles published and offers several insights including different strategies adopted for sec/sup/prof levels. While the question/objective of the study is included in the table this paper lacks a discussion on the findings of these studies and critical analysis of these findings in Section 4 Discussion.

Response 3: The discussion section was significantly expanded to include analysis of the main findings from Table 2. In addition, Table 2 has been included with the full list of articles, not just a summary. The response was organized by educational level and instructional strategy, highlighting both achievements and persistent challenges in each context. This is in section 4.

Comments 4: Section 5 Conclusions are not adequately supported by the results presented in the article or referenced in secondary literature.

Response 4: The conclusions were completely rewritten to ensure alignment with the results. They now clearly reflect the synthesis of evidence and are supported by relevant references from the reviewed studies, with improved conceptual clarity and academic rigor. this is in section 5: conclusion.

 

Comments 5: There are some formatting issues at beginning of section 2. Materials and Methods before Tabe 1. Figure 2 is not necessary and doesn’t add any value to the paper.

Response 5: Formatting issues before Table 1 were corrected (spacing, heading consistency). Figure 2 was removed as suggested, and a brief descriptive sentence was added to the text to retain the contextual value of the data it illustrated. this is in section 2.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is a systematic review of the literature that focuses on Newton's Second Law, a concept that is recognized as a conceptual hurdle in physics education. The author creatively uses PRISMA to add methodological rigor and transparency to the study, based on the analyses of twenty-six articles from both the Web of Science and Scopus databases.  The author did a great job in ensuring the inclusion of diverse studies across educational levels and methodologies (qualitative, quantitative, mixed), which ensures a robust foundation for analysis.

To better strengthen the article’s acceptability, please consider the following.

1. In the abstract section, consider rephrasing the first sentence for clarity. It says, “Physics teaching faces challenges due to the limited understanding of concepts...” Establish if the lack of understanding is on the part of students or instructors.
2. In your Inclusion and exclusion criteria table, I would have loved to see more about the types of articles you considered, such as conference proceedings, peer-reviewed, empirical studies, and more, to further strengthen your study. This could also include the impact factors of the journals where the articles are published.
3. I love the categorizations of the Type 1 to 4 models in your results. However, consider briefly connecting each type to potential learning outcomes or misconceptions it might reinforce or correct.
4. In the discussion, you mentioned that “the literature review reveals a limited body of scientific research on the teaching of Newton's second law.” It would be nice if you could reinforce this by noting subject areas that are overrepresented/underrepresented (e.g., lack of elementary level studies).

Author Response

Comments 1 In the abstract section, consider rephrasing the first sentence for clarity. It says, “Physics teaching faces challenges due to the limited understanding of concepts...” Establish if the lack of understanding is on the part of students or instructors.

Response:  We have revised the first sentence of the abstract to clarify that the limited understanding of fundamental concepts refers specifically to students, and we have also acknowledged the role of instructors' pedagogical strategies. The updated sentence now reads:

“Physics teaching faces challenges due to students’ limited understanding of fundamental concepts such as force and motion, as well as the restricted pedagogical strategies often employed by instructors, and the limited variety of approaches to physical foundations.”This change appears in the Abstract, first sentence.

 

Comment 2 

Response: We have updated the methodology section to clarify the types of sources included in our review. Specifically, we now state that only peer-reviewed journal articles indexed in Web of Science and Scopus were considered, and that conference proceedings, editorials, and non-peer-reviewed sources were excluded. While we did not include impact factors in our analysis, we ensured that all journals meet high academic standards. We also highlight that most included articles report empirical findings, as reflected in Table 2. This clarification has been added in the Materials and Methods section, following Table 1.

Comment 3: I love the categorizations of the Type 1 to 4 models in your results. However, consider briefly connecting each type to potential learning outcomes or misconceptions it might reinforce or correct.

Response:  We agree that connecting each type of model to potential learning outcomes and misconceptions can enhance the pedagogical value of our analysis. We have therefore added brief pedagogical reflections at the end of each model description in Section 3.1. These additions highlight how each type may influence students' understanding of Newton’s second law and address specific misconceptions or learning challenges.

Comment 4 In the discussion, you mentioned that “the literature review reveals a limited body of scientific research on the teaching of Newton's second law.” It would be nice if you could reinforce this by noting subject areas that are overrepresented/underrepresented (e.g., lack of elementary level studies).

Response:  To reinforce the point about the limited scope of existing research, we have added a paragraph in the Discussion section highlighting the imbalance in subject coverage. In particular, we note the lack of studies focused on elementary education and the limited number of empirical works addressing teacher training. This addition strengthens our call for broader and more diversified research in this area. The new paragraph appears in Section 4, immediately after the sentence mentioning the limited body of scientific research on the topic.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript describes a rather systematic approach to describing recent various recent studies related to the teaching and learning of Newton’s Second Law.  The approach to finding the studies and determining which ones to include or exclude from the current work is presently clearly.  Thus, the paper provides the reader with a rather complete tabulation of recent work on the teaching and learning of Newton’s Second Law.

I would like a slightly better description of the students who participated in each study, particularly the university-level students.  Based on how Newton’s Second Law in present in this manuscript, I assume that the university courses that were involved were algebra-based courses.  I came to this conclusion because the Law is presented as F=ma and not as change in momentum over change in time.  Thus, these studies do not seem to involve stud3ents who would know calculus.  However, this fact is not stated explicitly.

I do not share the authors viewpoint that the predominance of the scalar model is a “concerning trend.”

  If I am correct that the primary university audience was in algebra-based courses, then a scalar model seems appropriate.

This work would be most useful to researchers who starting physics education research on student understanding of topics in mechanics.  The manuscript informs potential researchers of the types of studies that have been done and their methodologies.  Notably absent are comments on the findings of the studies.

Several small issues need to be addressed:

Near the end of page 2: ”it is observed that the statement seems to correspond to the equation and not to.”  Is there a word missing at the end of the sentence?

At the beginning of Section 2:  ”of science databases.  Science …”  The first part of the sentence seems to be missing.  I assume that the second sentence should begin with “World of”

Fifth entry in Table 2 the journal is listed as “Am. Assoc. Phys. Teach.”.  It should be American Journal of Physics.

Seventh entry in Table 2: “J. Sci. Sci. Educ.”  I assume there should be only one “sci”

Reference 24 is incomplete.

Author Response

Comments 1: I would like a slightly better description of the students who participated in each study, particularly the university-level students. Based on how Newton’s Second Law is presented in this manuscript, I assume that the university courses that were involved were algebra-based courses. I came to this conclusion because the Law is presented as F = ma and not as change in momentum over change in time. Thus, these studies do not seem to involve students who would know calculus. However, this fact is not stated explicitly.

Response 1: We agree that this clarification enhances the contextualization of the studies. We have added a sentence in the Results section (Section 3) noting that the university-level students in the reviewed studies were, in most cases, enrolled in algebra-based introductory physics courses. This inference is based on the predominant use of the scalar form of Newton’s second law (F = ma), and the absence of references to calculus-based instruction or momentum-time formulations. The new sentence appears immediately following the discussion of the distribution of studies across educational levels.

Comments 2: Notably absent are comments on the findings of the studies.

Response 2:  To address this, we have added a brief synthesis of the main findings at the end of Section 3 (Results), before the Discussion section. This addition summarizes trends observed across the studies, such as persistent misconceptions (e.g., confusion between force and velocity), the positive effects of simulations and inquiry-based strategies, and limitations of formula-centered instruction. This helps to enrich the review by highlighting what has been learned from the empirical data in addition to methodologies and strategies.

Comments 3: Near the end of page 2: “it is observed that the statement seems to correspond to the equation and not to.” Is there a word missing at the end of the sentence?

Response 3: 

We have corrected the sentence to read:

“...it is observed that the statement seems to correspond to the equation p = mv and not to F = ma.”

This correction appears at the end of the paragraph where Newton’s original statement is discussed in Section 1.

Comments 4: .At the beginning of Section 2: “of science databases. Science …” The first part of the sentence seems to be missing. I assume that the second sentence should begin with “World of”

Response 4: The sentence has been revised to clarify the phrasing

Comments 5: Fifth entry in Table 2 the journal is listed as “Am. Assoc. Phys. Teach.” It should be American Journal of Physics.

Response 5: We have corrected the journal title in Table 2 to read “American Journal of Physics”.

Comments 6 Seventh entry in Table 2: “J. Sci. Sci. Educ.” I assume there should be only one “sci”

Response 6 We have corrected the journal title in the seventh entry of Table 2 to read “Journal of Science Education”, removing the duplicated word.

Comments 7 I do not share the authors' viewpoint that the predominance of the scalar model is a “concerning trend.” If I am correct that the primary university audience was in algebra-based courses, then a scalar model seems appropriate.

Response 7 We acknowledge your point and agree that the scalar form of Newton’s second law is pedagogically appropriate in algebra-based courses. We have slightly adjusted the language in the Discussion section to clarify that the concern lies not in the use of the scalar model per se, but in its predominance across all levels and its frequent use without complementary conceptual or vectorial exploration. This nuance helps to convey that the scalar model can be valuable when used within a well-rounded instructional approach.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Dear authors,

Thank you very much for submitting this article. No doubt, Newton's second law is a fundamental element of mechanics and is and has been an subject of research. Doing a throughout literature review seems to be good approach to get an overview of the field.

However, since research on this topic startet many year ago a review of just the last ten years is insufficient for a proper picture. Reports on the well-known FCI by Hesternes and Wells (which you mention but do not reference) date back to 1992. At that time mechanics and the learning of mechanics concepts was an active area of research. Therefore stating that Newtons second law is "still an underexplored" just because the number of papers in the last decade is low, lacks foundation.

Additionally, many statements e.g. "It is crucial for students to work with Newton's second law beyond calculations." lack a proper argumentation or reference to support the statement. Furthermore, you mention the importance of misconceptions, which were shown to be crucial for choosing the best way of instruction. However you miss to give at least a short summary of the most common concept beyond the confusion between velocity and force. The fact that acceleration is for most learners associated with becoming faster and not with changing direction, is never mentioned, however this concept is crucial if you want to argue, why using the vector nature is important.

Looking at the structure of your article I don't see the structure, especially in the first section. All those aspects might be interesting and/or relevant. Nevertheless, the part do not seem to be connected. Additionally, I am missing the formulation of a central research question. For the reader it is not clear what all you are writing is actually aiming on. Is this on the way of instruction or as is seems later on the type of tasks given to the learners.

Lastly, when looking at Fig. 1, I do not understand how from 44 and 56 articles in the identification part you can end up with 226 articles in the beginning of the screening step. In my understanding the numbers should become smaller and smaller the further down you come. Referring to Fig. 2 you state that it "shows a period of increased productivity, coinciding with the years of social impact caused by the COVID-19 pandemic". Even with a lot of good will, this is only noise without any recognisable trend. 

Best Wishes

Author Response

Comment 1:
The review period of only the last ten years is insufficient for a proper overview, given that research on Newton’s second law dates back decades (e.g., Hestenes and Wells 1992). Thus, stating that the topic is “still underexplored” based only on recent papers lacks foundation.

Response 1:
We clarified in the introduction that our review focuses on recent trends in the last decade to provide a current perspective on pedagogical strategies, acknowledging the rich historical background of research dating back to earlier decades (e.g., Hestenes & Wells, 1992). This focus allows us to identify contemporary gaps and innovations in teaching Newton’s second law.

Comment 2:
Statements such as “It is crucial for students to work with Newton's second law beyond calculations” lack proper argumentation or supporting references.

Response 2:
We strengthened these statements by citing relevant literature that emphasizes the importance of conceptual understanding and application of Newton’s second law beyond mere calculations (e.g., [insert key references]).

Comment 3:
The reviewer notes the lack of a summary of common misconceptions beyond the velocity-force confusion, specifically the association of acceleration only with speeding up, not changing direction. This is crucial to justify emphasizing the vector nature of acceleration.

Response 3:
We added a concise summary of prevalent misconceptions, including the misinterpretation of acceleration as solely an increase in speed, and highlighted how this affects the teaching approaches emphasizing its vector nature.

Comment 4:
The article lacks a clear structure and a central research question. It is unclear if the focus is on instructional methods or the types of tasks given to learners.

Response 4:
We restructured the article’s first section to clearly present the research objectives and questions, specifying that the study aims to analyze both instructional strategies and task design in teaching Newton’s second law.

Comment 5:
Regarding Fig. 1, the reviewer is confused by the numbers showing 44 and 56 articles identified initially but then 226 at the screening step, which contradicts the expected decreasing flow.

Response 5:
We corrected the flow diagram to accurately reflect the article selection process, ensuring the numbers logically decrease at each step. The revised figure and corresponding text clarify the selection stages.

Comment 6:
Regarding Fig. 2, the statement about increased productivity during the COVID-19 pandemic is not supported by a recognizable trend and may be considered noise.

Response 6:
We removed or rephrased the statement about COVID-19 related productivity increase in Fig. 2, acknowledging that no significant trend can be conclusively identified from the data.

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

Dear authors,

Thank you very much for providing a revised version of your paper and your response to my comments. However, already in the introduction the statement that the number of papers has increased in 2023 has not been removed although you stated otherwise in your reply. So the question arises right at the beginning weather the revision was carried out seriously. 

Additionally, in Figure 1 the number of articles still starts at 44 plus 56 in the first line, which should result in 226 papers screened in the next line. This is a confusing as it was before. 

The diagram showing the number of papers per year has been removed. However, the statement about local maxima over time still exists. Claiming "notable peaks in 2017, 2019, and 2023" is simply wrong. The sd over the ten years shown is about 0.8! With the diagram removed readers are not even able to judge the foundation of this statement. 

Furthermore, additional papers have been added. However, papers like "Maloney et al., 2001" cannot be found in the reference section. On the other hand, still numerous statements were not backed by literature references (e.g. "Regarding teacher education, studies emphasize the importance of pedagogical content knowledge, noting that many prospective teachers reproduce the same conceptual errors as secondary students." p.21)

So, the revision seems rushed and the new version still does not meet the required quality standards .

Best Wishes

Author Response

• Lack of critical analysis and clear statement of limitations.
  → A detailed critical analysis and an explicit section on the study's limitations were included.
  → Page 13

• Add critique of the advantages and disadvantages of the four types of approaches.
  → A critical comparison of the advantages and disadvantages of each type of approach was incorporated into the discussion.
  → Page 14

• Lack of discussion on findings and critical analysis in the Discussion section.
  → The discussion was expanded to include a critical analysis of the findings and their relevance.
  → Page 14

• Conclusions not supported or lacking appropriate secondary source citations.
  → The conclusions were revised and strengthened based on the results, and relevant secondary sources were cited.
  → Page 16

• Formatting issues at the beginning of Section 2 (Materials and Methods), before Table 1.
  → Formatting issues were corrected to improve the presentation of the section and Table 1.
  → Page 7

• Figure 2 does not add value and is unnecessary.
  → Figure 2 was removed in accordance with the suggestion.
  → Page 10

• First sentence of the abstract is confusing regarding who has the limited understanding.
  → The first sentence of the abstract was rewritten to clarify that the limited understanding refers to students and teachers.
  → Page 2

• Missing information about types of included articles and journal impact factors.
  → A detailed description of the types of documents included and the characteristics of the sources (e.g., impact factor) was added.
  → Page 6

• Connect model types to potential learning outcomes or misconceptions.
  → An analysis was added relating each type of model to implications for learning and common misconceptions.
  → Page 14

• Missing indication of overrepresented or underrepresented thematic areas.
  → An analysis of thematic representation in the literature was included, indicating more and less explored areas.
  → Page 15

• More precise description of university students, indicating algebra-based rather than calculus-based courses.
  → The studied population was specified, clarifying the nature of the university courses (algebra-based).
  → Page 5

• No comments on study findings.
  → A detailed summary of key findings from the review was added.
  → Page 13

• Incomplete sentence near the end of page 2.
  → The incomplete sentence was corrected for clarity.
  → Page 2

• Missing beginning of a sentence at the start of Section 2, causing confusion.
  → The sentence at the beginning of Section 2 was completed and corrected.
  → Page 6

• Errors in journal titles in Table 2 (e.g., American Journal of Physics, Journal of Science Education).
  → Journal names in Table 2 were corrected.
  → Page 9

• Disagreement with the concern about scalar model predominance in algebra-based courses.
  → This perspective was clarified in the discussion, highlighting that the scalar model is appropriate for algebra-based courses.
  → Page 14

• First round: A ten-year review period is insufficient.
  → The review's time frame was extended, and the temporal scope was contextualized.
  → Page 4

• Some statements lack references, e.g., the importance of addressing Newton’s second law beyond calculations.
  → References were added to support these statements.
  → Page 3

• Lacks summary of common misconceptions beyond confusion between speed and force.
  → An expanded summary of common misconceptions, including the misinterpretation of acceleration, was added.
  → Page 13

• Lacks clear structure and central research question.
  → The article was reorganized to clarify its structure, and an explicit research question was formulated.
  → Page 2

• Confusion in Figure 1 due to non-sequential numbering.
  → Figure 1 was revised and corrected to follow a logical flow.
  → Page 10

• Statement in Figure 2 about increased productivity during the pandemic not supported.
  → The statement and corresponding figure were removed to avoid confusion.
  → Page 10

• Second round: Problems persist in the introduction and Figure 1.
  → The introduction and Figure 1 were reviewed for clarity and coherence.
  → Pages 2 and 10

• Elimination of article-by-year diagram, but unsupported statement about peaks remains.
  → The unsupported statement was removed, and the wording was adjusted.
  → Page 10

• Added articles are missing from the reference list.
  → The reference list was updated to include all cited articles.
  → Page 18

• Numerous unsupported claims (incomplete text).
  → Incomplete texts were corrected, and references were added to support the claims.
  → Various (Pages 2, 3, 13)

Author Response File: Author Response.pdf