From pedagogical content knowledge toward technological pedagogical content knowledge frameworks and their effectiveness in teaching mathematics: A mapping review

Background: A study to reveal existing pedagogical content knowledge or technological pedagogical content knowledge frameworks and their effectiveness in teaching mathematics is crucial to inform the reader, teacher, and researcher. This review study intended to explore the trends of the pedagogical content knowledge (PCK) framework, how it has changed over time until the most recent version of technological and pedagogical content knowledge (TPACK) was developed, and their effectiveness in teaching mathematics. Methods: We initially downloaded 273 articles from the first 30 Google Scholar pages and analyzed 229 journal articles. We got 24 frameworks from 64 journal articles since Shulman’s first model in 1986. About 52 out of 229 were mathematics studies. Among these studies, we found that 18 studies have extensively investigated the use of identified frameworks. Results: The frameworks were presented and descriptively discussed in chronological order. The empirical studies that compared the role of pedagogical content knowledge and technological pedagogical content knowledge models among classrooms with teachers who possess and do not possess such skills were demonstrated. Conclusions: The gap in empirical studies was identified, and further studies about the intervention of PCK and TPACK models were suggested to gain more insight into the mathematics classroom.


Introduction
Around the 1980s, a new era in subject matter and teacher pedagogy rose.Shulman (1986) argues that the emphasis on teacher material knowledge and pedagogy is conserved as special.He believes that teacher training should conglomerate these two areas of specialization.He introduced the concept of pedagogical content knowledge (PCK), which comprises pedagogical knowledge (PK) and content knowledge (CK), to address this dichotomy, amongst other classifications.His original portrayal of the teacher's knowledge encompassed information about the curriculum and knowledge of the educational context.
After two decades, a major revolution has been proposed by various researchers in the field of technology.Mishara and Koehler (2006) established the concept of technological pedagogical and content knowledge (TPACK) in reaction to the lack of theory guiding technology integration into teaching.TPACK characterizes an extension of Shulman's (1986) representation of what their colleagues looked for to teach explicit content (that is, PCK) by depicting the knowledge required to teach such content with technology (Mishara & Koehler, 2006).

Problem statement
The development of effective pedagogical strategies that integrate technology into the teaching of mathematics is a complex endeavor.In the landscape of educational research, a significant gap exists in understanding the evolution of PCK and TPACK frameworks, particularly within mathematics education.This gap becomes evident when considering the existing review articles found in the field.Our investigation revealed a review article from 2008 by Smith and Anagnostopoulos, which explored the development of PCK among English teachers within institutional networks.Conversely, a more recent review in 2020 by Njiku et al. focused on analyzing research instruments employed across 28 diverse studies to assess teacher TPACK.However, despite these contributions, a comprehensive and cumulative exploration of the evolution of PCK from its inception remains conspicuously absent in the literature.
In our analysis of 20 review articles, comprising 15 journal articles, two conference proceedings, two book chapters, and one book, we discovered a distinct lack of studies that systematically trace the progression of the PCK framework over time.Moreover, among the identified journal articles, none extensively examined teaching interventions facilitated by PCK and TPACK frameworks, nor did they provide a detailed investigation into the challenges teachers face when striving to acquire content knowledge.For instance, while notable efforts have been made to understand the methods and instruments of TPACK through studies by Abbitt (2011), Aydin andBoz (2012), andYoung et al. (2012), a comprehensive examination of PCK's development has been notably absent.Similarly, reviews conducted by Chai et al. (2013), Voogt et al. (2013), Depaepe et al. (2013), andWu (2013) have examined aspects of TPACK, but the narrative of PCK's evolution remains incomplete.
Furthermore, individual articles such as the critical review by HU (2014), the analysis of TPACK studies in Turkey by Yilmaz (2015), and the work by Rosenberg and Koehler (2015) have contributed unique perspectives to the field.However, the lack of a comprehensive investigation into the cumulative development of PCK hampers a holistic understanding of the subject.Similarly, while studies by Evens et al. (2016), Hubbard (2018), De Rossi and Trevisan (2018), and Grieser and Hendricks (2018) have provided valuable insights into specific aspects of PCK and TPACK, a coherent narrative spanning the entirety of PCK's evolution is still missing.In light of these observations, it becomes apparent that the literature lacks a consolidated and chronological exploration of the development of PCK and TPACK frameworks in teaching mathematics.While previous review articles have contributed valuable insights, they have not collectively addressed the evolution of PCK over time.This research aims to bridge this gap by providing a comprehensive mapping review that traces the evolution of both PCK and TPACK frameworks within mathematics education.In doing so, we seek to enhance the overall understanding of how these frameworks have evolved, how they have been applied in teaching mathematics, and their effectiveness in acquiring content knowledge.

REVISED Amendments from Version 1
The major change from the first to the second version was in the problem statement, discussion, and conclusion.
The reviewers advised to cumulatively explain the evolution of PCK from its inception.Therefore, the problem statement was rewritten by focusing attention first on PCK and then TPACK.We initially presented analyzed articles in tables and then discussed each of them in more detail.We were advised to discuss the trends in articles cumulatively instead of discussing each article separately.Therefore, we discussed the findings in more summarized and directional trends with commonalities and distinctions.One of the reviewers also suggested we frame our conclusion with main findings instead of through discussion.Thus, we reframed the conclusion, but the meaning did not change.
Any further responses from the reviewers can be found at the end of the article Therefore, our study aimed at reviewing: 1. Chronological trends in PCK models in teaching and learning mathematics (from beginning to date, how did researchers modify the original model that Shulman started with?Which models, what was modified, why were the modifications made, which teachers and/or students benefited from that change?) 2. Effectiveness of PCK and TPACK frameworks in teaching and learning mathematics (empirical studies that have used these frameworks to upgrade students learning.Any level, primary-secondary-university.Any year. Descriptive and inferential statistics each study used, etc.).

Data selection
We designed and employed a "one-term in one-source" method.This method involves using one term, a key, or search word in only one academic search engine.Thus, we have used "pedagogical content knowledge" as the search term in Google Scholar as an academic source.This search returned 20 review papers and 273 empirical studies at a glance (see Figure 1) on 19 August 2021.The choice of Google Scholar was influenced by its extensive coverage of scholarly articles and user-friendly interface facilitating efficient searches to access a wide array of academic publications.
Using the term "pedagogical content knowledge" in Google Scholar, we explored the results in the first 30 pages.We downloaded every article that contains the words "pedagogical content knowledge" in its title.We only included articles written in English.The first paper, "Pedagogical content knowledge in social studies," was published in 1987, while the latest "A virtual internship for developing technological pedagogical content knowledge" was published in 2020.The first seven pages exhausted all articles written in review form, such as a review of literature, systematic review, metaanalysis, etc.This means that we checked pages eight to 10 and had no results and stopped checking after page 10.There were many more empirical studies (articles that investigate with primary data), so we limited the search to the 30th page (entry); as you can see, the last page still had seven articles (see Figure 1) and no mathematics-related paper was available.
We did not limit ourselves to year of coverage, subject, or grades level.However, we intended to explore mathematical PCK explicitly.Thus, we retrieved all articles regardless of subject but then later excluded the non-mathematics articles.Literature review articles were visited only to frame our research problem, while empirical articles were focused on the analysis to answer our research objectives.The first author did initial screening and the co-authors checked the inclusion criteria.
Extended sources and nature of selected articles Although we used only one database, we found articles from other repositories.For instance, 24 articles were from the educational resources information center (ERIC), 17 from Academia, 13 from Research Gate, two from HAL (Hyper Articles en Ligne), and two from Durham University.However, all these were accessed via Google Scholar.Thus, articles in Google Scholar will take you to the website they are hosted on or repository they are deposited on.About the nature of articles selected, 229 were identified as journal articles, 22 were conference proceedings, 8 were book chapters, 2 were books, and 5 were generics (articles with unclear identification).Therefore, our analysis only considered journal articles due to their rigorous peer-review process that ensures a higher degree of academic scrutiny and quality.
12 subjects were identified across 229 articles.Articles discussing or investigating learning mathematics dominated the list (23% or 52 out of 229 articles).Science subjects and articles related to teacher education were 42 (18%) and 30 (13%) out of 229 articles, respectively, while unidentified articles or articles investigating PCK in a general sense accounted for 40 (17%).Figure 2 shows the distribution of articles among different subjects.
Among 229 retrieved journal articles, 110 (48%) were from 20 journals from various publishers.Table 1 shows that Teaching and Teacher Education, published by Elsevier, and the International Journal of Science Education, published by Taylor and Francis, were the two journals ranked first and second respectively among the top 20 contributors in this study (6% and 4%, respectively).After analyzing these 229 articles, we found 64 articles that clearly investigated or used PCK or TPACK frameworks or models (see grey color).Thus, others investigated these models.They did not formulate new models but used existing ones.Finally, among 229 articles, 52 articles were found to extensively investigate mathematics lessons, as shown in yellow.

Data analysis
To reveal trends of the PCK framework, we identified the year of publication, author of the study, model of PCK, and construct (whether PCK or TPACK) for each study.To reveal the effectiveness of PCK and TPACK interventions, we identified the construct, theoretical framework used to frame the study, research design, teaching intervention, topic, and analysis method for each study.PCK models were cited, presented in figures, and described.Teaching interventions were presented in sections, and their statistics were presented in tables and descriptively discussed.Teachers' knowledge was presented descriptively or in tables by discussing the type of study (survey, cases studies, interventions, etc.) that produced the results, the type of data such as quantitative or qualitative, the type of mode such as whether teachers'  knowledge was measured from him/herself or from his/her students, etc. Theoretical strands were also described accordingly.We used both NVivo 1.0 software and MS Excel 2016 to analyze data.Figure 4 is a typical example of the word analysis from NVivo using articles that were downloaded.

Results and discussion
PCK framework 65 (including 22 related to mathematics) out of 229 showed PCK trend models.About 24 articles (including 11 related to mathematics) showed original frameworks, while 41 referred to these 24 articles.Thus, Table 2 displays a review of 24 frameworks presented in the related 24 articles.Among these 24 frameworks, 17 are versions of PCK, and seven are upgrades of TPACK.
Table 2 outlines the models and constructs for each study.We are now going to discuss each of the 24 concepts in summary.The TPACK framework and its knowledge components TPACK These foundational studies unveil the multifaceted nature of PCK by highlighting its core constructs.Jones and Moreland (2003)

Synthesis and implications
Cumulatively, the studies reviewed here weave a tapestry of insights that converge on the significance of Pedagogical Content Knowledge (PCK) in mathematics education.PCK serves as a multifaceted framework that encompasses not only subject matter comprehension and teaching strategies but also the vital role of remedying misconceptions, addressing diverse student needs, and integrating technology into instruction.As PCK converges with content and technological knowledge, it becomes a key element within broader constructs like TPACK, highlighting the intricate network of expertise required for effective teaching.
Furthermore, these studies collectively emphasize the dynamic nature of PCK's interaction with other knowledge domains and its transformative role in shaping student learning trajectories.The synthesis of these insights underscores the integral role of PCK in scaffolding effective mathematics instruction, aligning pedagogical approaches with curriculum objectives, student characteristics, and diverse learning contexts.
The effectiveness of using PCK and TPACK interventions in Mathematics education 52 out 229 were identified as articles related to mathematics.Among 52 mathematics articles, 39 were related to TPACK, while 13 were investigating PCK.18 of the 52 articles fit our analysis framework and spanned from 1988 to 2020.They showed the implications of PCK and TPACK frameworks.Except for these 18 articles, 34 out of 52 articles reviewed showed survey results that only provided the outcome of PCK or TPACK.These 18 articles were only articles that investigated the outcome of comparative studies such as pre-and post-test designs, variables such as teachers' backgrounds, teachers' gender, teachers' geographical locations, etc.Most of the studies left out were surveys without comparison, and others were qualitative.Table 3 displays a review of 18 articles related to mathematics that showed the comparative outcome of PCK and TPACK.
Table 3 presents PCK and TPACK framework interventions.We are now going to discuss them in more detail and reveal their effectiveness in teaching mathematics.Within the realm of mathematics education, the exploration of PCK and TPACK interventions has yielded a plethora of studies that collectively shed light on their effectiveness.As we delve into this landscape, we will traverse a spectrum of research endeavors that have examined these frameworks' implications for educators and learners.
1. Enhancing Problem-Solving Instruction (Carpenter et al., 1988) Carpenter and colleagues ventured into the pedagogical content of grade-one teachers, scrutinizing their grasp of children's explanations of word problems in mathematics.The study underscored the significance of teachers' ability to comprehend critical differences in students' problem-solving approaches.This insight laid the groundwork for a deeper exploration of how effective teaching strategies can be aligned with diverse problem-solving challenges.
2. Fostering Pre-Service Teachers' PCK (Van Der Valk & Broekman, 1999) The investigation led by Van Der Valk and Broekman proposed a methodological approach for nurturing pre-service teachers' PCK.By urging trainee teachers to formulate lessons and harness their subject matter knowledge, the study pointed to the efficacy of engaging educators in designing and planning instructional activities.This approach echoed the idea that cultivating PCK can be a catalyst for effective teaching preparation.Blömeke and team embarked on a cross-cultural journey to assess the effectiveness of primary teacher training programs across 15 nations.The study unraveled a landscape of disparities, demonstrating the nuanced influences of cultural contexts on the outcomes of teacher education.This exploration broadened the understanding of PCK efficacy in diverse global settings.

Synthesis and implications
These studies weave a tapestry of insights into the efficacy and impact of PCK and TPACK interventions in mathematics education.Through these lenses, educators have sought to enhance problem-solving strategies, leverage technology to bolster teaching, and design comprehensive teacher education programs.While PCK and TPACK serve as pivotal frameworks, the studies collectively underline the need for a holistic approach to teaching mathematics.The recurring themes of knowledge integration, contextual relevance, and dynamic instructional methodologies transcend individual studies.However, gaps also emerge, particularly in integrating certain framework components.While PCK and TPACK offer valuable lenses, the studies suggest that they might not be the sole factors accounting for effective learning outcomes in mathematics education.The intricate interplay of content, pedagogy, and technology must align with diverse learner characteristics and changing educational landscapes.

Conclusion
In this study, we employed a focused method that proved effective in delving into the literature and extracting the relevant information necessary to address our research questions.The genesis of the concept of pedagogy's centrality in delivering effective lessons dates back to the early 1980s when Shulman (1986) laid the foundation.He advocated for an expanded view of a teacher's requisite knowledge, emphasizing the significance of content knowledge and pedagogical knowledge, including curriculum, students, and instructional insights (Shulman, 1987).Shulman's framework, as depicted in Figure 5, has since spurred a research continuum.The framework underwent adaptations to accommodate different contexts, ranging from diverse subjects to integrating information and communication technology (ICT).This dynamic evolution culminated in the introduction of the technological, pedagogical, content knowledge (TPCK) constructs, later streamlined as the technological, pedagogical, and content knowledge (TPACK) model, reflecting the increasing role of technology in 21st-century education (Mishra & Koehler, 2008).
Our study, driven by the aspiration to address a gap in the literature, delved into the hierarchical modifications of these frameworks across various teaching contexts.Specifically, we sought to discern their impact on refining mathematics education by analyzing empirical studies that employed PCK and TPACK frameworks as interventions to enhance learning outcomes.Our analysis revealed a pronounced emphasis on PCK, with 13 out of 18 reviewed papers centering around this construct.However, while these studies primarily surveyed teachers' performance in distinct components of these frameworks, few delved into fostering PCK and TPACK skills to enhance students' conceptual understanding, attitudes, and performance.Consequently, a pressing need exists to further explore these skills within the classroom context and their resultant impact on student learning.One notable area for future investigation is the comparison between teachers equipped with strong PCK skills and those without, discerning the ripple effects on their students' outcomes.
A pivotal avenue of research should encompass teachers' challenges in acquiring either content knowledge (CK) or pedagogical knowledge (PK), dissecting the nuances through empirical studies encompassing surveys, case studies, and interventions.The comprehensive illumination of teacher knowledge, regardless of its form, can guide pedagogical practices and elevate educational outcomes.In summation, our study's trajectory has elucidated the dynamic evolution of PCK and TPACK frameworks, prompting a proliferation of research that has, in turn, informed the landscape of effective teaching and learning strategies.As we move ahead, an agenda ripe with opportunities for uncovering the intricate relationship between these constructs, teacher capabilities, and student achievements emerges.The journey into the depths of effective education continues, with the tools of PCK and TPACK guiding us toward a brighter horizon of pedagogical excellence and improved learning outcomes.
got? Look at that again.

Methodology
The method "one-term in one-source" (see page 3) is not well known to the research community.You may wish to look at it again.The sentence, "There were many more empirical studies (articles that investigate with primary data), so we limited the search to the 30th page (entry); as you can see, the last page still had seven articles."(see around line 5 under Figure, page 4) Should read "There were many more empirical studies (articles that investigate with primary data), so we limited the search to the 30th page (entry); as you can see, the last page still had seven articles (see Figure 1).

Data analysis
In Figure 4, the green colour is not showing well.It looks like grey colour.The authors referred to it as green colour (see sentence 3 under Figure 4, page 6)

Results and discussion
On page 7, the first sentence under Table 2 should rather read the summary of the articles and not … in more detail.

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The authors can consider looking at articles that relate to mathematics teaching as the title of the paper depicts.

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On page 8, the first sentence under "Seven components of the framework", from Table 2, it should be authors and not author.

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On page 8, in the first sentence under "Components of the PSTs' PCK investigated", from Table 2, it should be author and not authors.

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The effectiveness of using the frameworks did not show explicitly under "PCK interventions" as the title of the paper depicts.

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The discussions were not done in relation to literature by connecting articles that use the frameworks to enhance effective teaching of mathematics and those that did not.

References
The following cited works are not on the references list:

If applicable, is the statistical analysis and its interpretation appropriate? Yes
Are all the source data underlying the results available to ensure full reproducibility?Yes

Are the conclusions drawn adequately supported by the results? Yes
Competing Interests: No competing interests were disclosed.
Reviewer Expertise: Technology integration into the teaching of mathematics, Algebraic thinking of learners, Differentiated instructions I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.
trend in both PCK and TPACK frameworks usage.The paper would be good for researchers who want to employ PCK and TPACK as their theoretical framework.However, there are some concerns under the following headings that I suggest the authors should look at.
Author response: Thank you so much for your guidelines.We have adapted to the suggested title by including "…content knowledge…" Abstract "Pedagogical or technological pedagogical content knowledge frameworks" seems as if pedagogical and TPACK are the same.Also, is crucial to inform what?It must be stated explicitly.So, this sentence "A study to reveal existing pedagogical or technological pedagogical content knowledge frameworks is crucial to inform and their effectiveness in teaching mathematics" needs recasting."… and its effectiveness in teaching mathematics" is not specific.Is it PCK's or TPACK's effectiveness…?The last sentence under Background should be relooked at since it is not in relation with mathematics.The first sentence under Results, "The empirical studies that compared the role of pedagogical and technological pedagogical content knowledge model… seems like we have pedagogical model as well.
Author response: The first sentence of the background was changed as follows: "pedagogical" was replaced by "pedagogical content knowledge", and "is crucial to inform and their effectiveness in teaching mathematics" was replaced by "and their effectiveness in teaching mathematics is crucial to inform reader, teacher and researcher."The last sentence under background was changed as follows" "its" was replaced by "their."We added "content knowledge" after "pedagogical" in the sentence under results.
Problem statement Rossi and Trevisan (2018) investigated how TPCK is defined… seems like the authors are claiming Rossi and Trevisan (2018) tried to define TPCK.In 2005, it was TPCK and changed to TPACK in 2007 and context was added in 2008.The authors may wish to revisit the literature.The last sentence of 2 (see page 3), "Descriptive and inferential statistics each study got, etc.).Is it each study used or got?Look at that again.
Author response: The whole section was revisited to ensure clarity."got" was changed to "used." Methodology The method "one-term in one-source" (see page 3) is not well known to the research community.You may wish to look at it again.The sentence, "There were many more empirical studies (articles that investigate with primary data), so we limited the search to the 30th page (entry); as you can see, the last page still had seven articles."(see around line 5 under Figure, page 4) Should read "There were many more empirical studies (articles that investigate with primary data), so we limited the search to the 30th page (entry); as you can see, the last page still had seven articles (see Figure 1).Author response: We invented the "one-term in one source" method.We changed the sentence as you suggested: "There were many more empirical studies (articles that investigate with primary data), so we limited the search to the 30th page (entry); as you can see, the last page still had seven articles (see Figure 1)." Dar es Salaam University College of Education, University of Dar es Salaam, Dar es Salaam, Tanzania Summary: the study is a literature review.It is designed to discuss the trend in PCK and TPACK studies and how they influence effective learning, especially in mathematics.The study reviews different literature in the area to respond to two research questions.Data sources are obtained from the Google Scholar database and screened for relevance.Data analysis is done to uncover the trends in PCK and TPACK and their effectiveness in explaining learning.As such findings are presented first by listing and explaining studies that explain the PCK or TPACK framework and those that explain the use of the framework in explaining learning especially in mathematics.The topic is current and may inform future studies on the evolution and debate in PCK and TPACK and how they have been used to influence learning.Specific comments about possible areas for improvement of the paper are provided as follows: Keywords: although the authors used the Google Scholar database as the source of their articles, using google scholar as a keyword does not seem to fit what is discussed in the paper.
Statement of the problem: It identifies the lack of studies that cumulatively explain the evolution of PCK from its inception.However, the authors would consider presenting the arguments logically instead of mixing up PCK and TPACK in a zigzag way by focusing their attention first on PCK when done then TPACK.

Research questions:
Although the title and various places it is claimed that the study focuses on the learning of mathematics, none of the research questions is focused on mathematics.
Data selection: Selection of articles is well articulated.However, the authors have not explained why they chose google scholar as the sole database for their search.They may also explain why they ended on pages 10 and 30 in search of review articles and empirical studies respectively.

Nature of selected articles:
The author concluded that "therefore, our analyses only considered journal articles" without explaining why so.Were other types of sources not relevant/fit for the study?They may consider explaining why they selected only journal articles.

Writing style:
The authors have written several sentences that begin with numerals.They need to rephrase them and ensure no sentence starts with a numeral.They also use one-sentence paragraphs, a style uncommon in academic writing.
Data analysis: This section is supposed to explain how the results presented in the following sections were obtained.However, the authors seem to give more space to what the articles were about -an explanation that fits in their preceding section named "extended sources and nature of selected articles".For example, all the tables and figures in this section are about the articles selected (when they were published, where they were published, and their subjects) and not about how the selected articles were analyzed.Only the first paragraph of the section talks about how findings were presented but even this is not preceded by how such presented finding were found through analysis.The authors may consider focusing their attention on explaining how they went about analyzing the documents they selected.

Results and discussion:
The section seems to be divided into two major subsections namely PCK framework and PCK interventions.Under each subsection, there are presented lists of studies that the authors discuss one after another.The studies are discussed as isolated ideas that do not inform or complement each other.There is no explanation why the second study or the third study etc. are important in/or add to the idea presented in the preceding studies.Also, there is no synthesis as to what we cannot learn from the listed studies.What is (not) common about them?What do we now learn about PCK and TPACK from them?How about mathematics?What have the studies shown in general about the learning of mathematics?Is PCK or TPACK sufficient in explaining effective learning of mathematics?What component of the frameworks should/has not been well addressed by teachers for effective learning of mathematics?Also, the studies are presented separately from each other, each having its own heading, where some are discussed using one sentence paragraph.The authors may consider explaining in a logical flow how PCK for example, is understood from some two to three papers and how this understanding is corroborated/advanced/contradicted/etc.by other studies.They may do so by connecting the ideas from the studies to one another and explicitly showing what we can now learn from the cumulative trend.

Conclusion:
Although the conclusion hits the point, especially in the last paragraph, the preceding paragraphs seem to supplement what may have been missed in the discussion.As such much of its content does not sound as concluding.

Is the work clearly and accurately presented and does it cite the current literature? Partly
Is the study design appropriate and is the work technically sound?Yes

Are sufficient details of methods and analysis provided to allow replication by others? Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Not applicable
Are all the source data underlying the results available to ensure full reproducibility?Yes

Are the conclusions drawn adequately supported by the results? Partly
Competing Interests: No competing interests were disclosed.
Reviewer Expertise: Mathematics education, teacher education, and technology integration in education.
I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.
stopped checking after page 10.Eventually, the search for empirical studies ended on page 30 because no mathematics-related paper was available.
Nature of selected articles: The author concluded that "therefore, our analyses only considered journal articles" without explaining why so.Were other types of sources not relevant/fit for the study?They may consider explaining why they selected only journal articles.
Author response: We considered journal articles due to their rigorous peer-review process that ensures higher academic scrutiny and quality.
Writing style: The authors have written several sentences that begin with numerals.They need to rephrase them and ensure no sentence starts with a numeral.They also use onesentence paragraphs, a style uncommon in academic writing.
Author response: The journal editor suggested beginning with numerals in the preassessment review round.
Data analysis: This section is supposed to explain how the results presented in the following sections were obtained.However, the authors seem to give more space to what the articles were about -an explanation that fits in their preceding section named "extended sources and nature of selected articles".For example, all the tables and figures in this section are about the articles selected (when they were published, where they were published, and their subjects) and not about how the selected articles were analyzed.Only the first paragraph of the section talks about how findings were presented but even this is not preceded by how such presented finding were found through analysis.The authors may consider focusing their attention on explaining how they went about analyzing the documents they selected.Results and discussion: The section seems to be divided into two major subsections namely PCK framework and PCK interventions.Under each subsection are presented lists of studies that the authors discuss one after another.The studies are discussed as isolated ideas that do not inform or complement each other.There is no explanation why the second study or the thirdstudy etc. are important in/or add to the idea presented in the preceding studies.Also, there is no synthesis as to what we cannot learn from the listed studies.What is (not) common about them?What do we now learn about PCK and TPACK from them?How about mathematics?What have the studies shown in general about the learning of mathematics?Is PCK or TPACK sufficient in explaining effective learning of mathematics?What component of the frameworks should/has not been well addressed by teachers for effective learning of mathematics?Also, the studies are presented separately from each other, each having its own heading, where some are discussed using one sentence paragraph.The authors may consider explaining in a logical flow how PCK for example, is understood from some two to three papers and how this understanding is corroborated/advanced/contradicted/etc.by other studies.They may do so by connecting the ideas from the studies to one another and explicitly showing what we can now learn from the cumulative trend.
Author response: Each article's discussion in more detail was changed to a more thorough connection, and discussion together to provide compromise, same trends, opposing trends, and contradiction from one to the other.

Conclusion:
Although the conclusion hits the point, especially in the last paragraph, the preceding paragraphs seem to supplement what may have been missed in the discussion.
As such much of its content does not sound as concluding.
Author response: The whole conclusion was revised.

Competing Interests: None
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Figure 1 .
Figure 1.Number of studies downloaded from each page of Google Scholar.

Figure 3
Figure3displays the hierarchy of downloaded articles.The blue color chart shows the number of all empirical studies downloaded across the years of publication.The first study that investigated PCK, after its launch from Shulman in 1986, was published in 1987, while the latest came out in 2020.After filtering out proceedings, books, book chapters, theses, and generics, 229 journal articles are shown in red.After analyzing these 229 articles, we found 64 articles that clearly investigated or used PCK or TPACK frameworks or models (see grey color).Thus, others investigated these models.They did not formulate new models but used existing ones.Finally, among 229 articles, 52 articles were found to extensively investigate mathematics lessons, as shown in yellow.

Figure 3 .
Figure 3. Displaying the hierarchy of downloaded articles.

Figure 4 .
Figure 4. Word frequency from all downloaded articles.

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The following references were not cited: De Miranda MA: Pedagogical Content Knowledge and Technology Teacher Education: Issues for thought.Journal of the Japanese Society of Technology Education.2008; 50(1): 17-26.○ De Rossi M, Trevisan O: Technological Pedagogical Content Knowledge in the literature: how TPCK is defined and implemented in initial teacher education Technological Pedagogical Context Knowledge (TPCK) in letteratura: come viene definito e implementato il ○ modello TPCK nei conte.Ital.J. Educ.Technol.2018; 26(1): 7-23.References 1. De Miranda MA: Pedagogical Content Knowledge and Technology Teacher Education: Issues for thought.Journal of the Japanese Society of Technology Education.2008; 1 (50): 17-26 2. De Rossi M, Trevisan O: Technological Pedagogical Content Knowledge in the literature: how TPCK is defined and implemented in initial teacher education.Italian Journal of Educational Technology.2018; 1 (26): 7-23 Is the work clearly and accurately presented and does it cite the current literature?Yes Is the study design appropriate and is the work technically sound?Yes Author response: This section refocused on explaining how we analyzed the documents we selected.We then moved other texts under the previous subsection of extended sources and the nature of selected articles.The following was added: "To reveal trends of the PCK framework, we identified the year of publication, author of the study, model of PCK, and construct (whether PCK or TPACK) for each study.To reveal the effectiveness of PCK and TPACK interventions, we identified the construct, theoretical framework used to frame the study, research design, teaching intervention, topic, and analysis method for each study."Figure1was changed to Figure4and maintained in this section, showing data analysis software usage.

Table 1 .
Journals that mostly contributed to the present study.

Table 1 .
Continued AACE: Association for the Advancement of Computing in Education, NCTM: National Council of Teachers of Mathematics.

Table 2 .
ContinuedAdditionally,Andyani et al. (2020)assert that PCK's convergence with content and technological knowledge culminates in the comprehensive Technological Pedagogical and Content Knowledge (TPACK).These works collectively underscore the intricate interplay of PCK with other dimensions of teachers' expertise.4.Examining PCK's Influence on Student Learning(Marks, 1990; Simon, 1995; Chai et al., 2019)Marks (1990) explored PCK's influence on student learning by emphasizing its interconnectedness with instructional processes, student focus, and media.Simon (1995)further contributed to this understanding by highlighting the pivotal role of teachers' capacity to hypothesize students' knowledge and tailor learning activities accordingly.Chai et al.'s (2019) model advances this by mapping PCK within the Revised Scaffolded TPACK Lesson Design Model, linking it intricately with instructional and learning activities.Collectively, these studies illuminate how PCK shapes instructional practices and learning trajectories to maximize student learning outcomes.

Table 3 .
Effectiveness of PCK and TPACK interventions.Niess delved into the intricate fusion of PCK and technology, presenting the Technological Pedagogical Content Knowledge (TPACK) concept.Through a multidimensional training program for science and math teachers, the study showcased the evolving nature of PCK when infused with technology.This intervention highlighted the need to integrate subject matter knowledge, pedagogical insights, and technological tools seamlessly.