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

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 and Boz (2012), and Young 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), and Wu (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.

Therefore, our study aimed at reviewing:

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.

Figure 1. Number of studies downloaded from each page of Google Scholar.

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, meta-analysis, 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.

Figure 2. Subjects and number of articles.

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).

Figure 3 displays 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. Displaying the hierarchy of downloaded articles.

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.

Figure 4. Word frequency from all downloaded articles.

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.

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.

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.