The Idea and Conception of Pedagogical Content Knowledge

This paper was written with the intention to shed light on the idea and conception of pedagogical content knowledge (PCK). Lee Shulman in 1986 introduced this concept to represent the “special” knowledge of subject’s teacher's needs. It also represents a teacher’s ability to address and recognize misconceptions students have and how to properly address them. Many articles have examined and reviewed the concept of PCK, but few have brought together the plethora of research in PCK in the various education domains together. The purpose of this paper is to have a systematic review of the conceptualization of PCK, the impact PCK has had on education research, and criticisms PCK has had. Finally, the paper address lingering questions that have yet to be addressed in the academic community. This review should not be an exhaustive search of the literature, as over 1200 papers have cited the idea of PCK, but hopefully serves as a basis for future research and development of Shulman's (1987,1987) framework.

As a first-year pre-service teacher going through my first practicum, it soon became apparent that a difference in teaching capacity existed between myself and my mentor teacher. I reasoned this was because of the years of experience and knowledge he had on me. This idea that knowledge and experience greatly impacted teaching got me to consider the idea of “teacher knowledge” as a research topic. As I began my search, I stumbled across the concept of pedagogical content knowledge (PCK). The question I had going into the paper were: (1) What is PCK, and is the concept still useful (2) How has PCK influenced research and teacher education, (3) Do PCK effect student learning.

PCK was first introduced by Lee Shulman in 1986. He described it as the “missing” paradigm in research. In his paper, he commented on the apparent lack of research on effective teaching and training protocols for pre-service teachers.

With the introduction of PCK Shulman hoped to highlight the role of teacher education, and create a distinction between content knowledge (CK) and pedagogical content knowledge.

He criticized, that at the time the research was to much focus on classroom management, and assignment structure, and too little on the actual content of the lesson. He prompted scholars to research questions like “where do teacher explanations come from.” (Shulman, 1986. p. 8)

In his original paper, Shulman (1986) addresses the issue that many preservice teachers are asked to teach novel subjects when entering the teaching profession. For example, how an English major may be asked to teach on a novel or play they have never encountered before.

Shulman (1986) distinguishes 3 categories of knowledge: (1) subject matter, (2) content knowledge, (3) pedagogical content knowledge. According to Shulman (1986), PCK represented the knowledge to represent and formulate subjects to make it understandable for others. Additionally, it represented the teacher’s knowledge of common conceptions, and misconceptions student may have on the topic; more importantly the knowledge to address the misconceptions in a way that is “fruitful” in reorganizing the understanding of the learner.

In his following paper Shulman (1987), redefines the 3 categories and includes PCK as part of a teacher’s knowledge base. Defining it as the “special amalgam of content and pedagogy, that is uniquely the province of teachers. Their own special form of professional understanding” (p.8). The original 3 groupings were broken into 7 new knowledge categories for teachers: (1) content knowledge, (2) general pedagogical knowledge, (3) curriculum knowledge, (4) pedagogical content knowledge, (5) knowledge of learners and their characteristics, (6) knowledge of educational context, (7) knowledge of educational ends.

Among the categories, PCK was of special interest because it “represents the blending of content and pedagogy into an understanding of how particular topics, problems or issues are organized, represented and adapted into diverse interest and abilities of learners…… PCK is the category most likely to distinguish the understanding of the content specialist from that of pedagogue” (Shulman, 1986 p.8)

In summary, PCK represented the application of content knowledge during teaching and aimed to encapsulate the dynamic and unique interaction of the teacher and student. It also represents a teacher’s capacity to properly address the misconception of students and effectively engage the classroom in a meaningful manner.

Criticisms with PCK

Since its conception, PCK has sparked a plethora of research in education research. However, it is not without faults, PCK as a concept is hard to measure since it is not an explicit tool that teachers use (Kind, 2009). For example, teachers do not think consciously that they are using PCK when planning a lesson, rather PCK is applied subconsciously and integrated through the planning and enactment of the lesson itself (Kind, 2009). Another criticism of PCK is that it can not be empirically distinguished from CK, because teaching is dynamic in nature. There are often multiple dimensions that interact and it becomes extremely difficult to measure as a separate concept (Depaeppe, Vershaffel, & Kelchtermans, 2013). Similarly, McEwan and Bull (1991) reject that PCK and CK are separate concepts and argue that “all subject matter is pedagogic.” (p.331)

Shulman's model has also been faulted for holding too much of a static view on PCK. Bednarz & Proulx (2009), demonstrates the interaction a teacher has with his students, highlighting the dynamic and complex interactions an educator has while teaching. As a result of this dynamic relationship, PCK has been criticized, for not encapsulating the full extent of knowledge needed by teachers in the classroom (Depaeppe, Vershaffel & Kelchtermans, 2013).

Ball, Thames, and Phelps (2008) have also criticized the lack of empirical and theoretical grounding for the existence of PCK. They state that Shulman's concept of PCK is too loosely defined and was formulated without much empirical research thus limiting its usefulness.

Models Based On PCK.

Following the conception of PCK, many models have been introduced in response to the criticism, and to better understand and apply PCK in various educational subjects. Cochran et al. (1993), used the term pedagogical content knowing (PCKg), rather than PCK, to highlight the dynamic nature of teaching. PCKg addresses the importance of the teacher-student interaction, and the environmental context in which teaching occurs (Cochran et al., 1993) The authors explain that knowledge as a term was too static, and by using knowing they are able to differentiate between training, (as a pre-service teacher) and teaching (In-service teacher). Cochran et al, (1993) define PCKg as “a teacher’s integrated understanding of four components of pedagogy, subject matter content, student characteristics, and the environmental context of learning” ( p.266). Applying this framework in a more practical sense the authors advocate for teacher education programs to educate pre-service teachers differently then subject matter experts. For example, a science teacher needs to learn and understand science so that they can help students understand concepts and distinguish between similar concepts, rather than strictly learning about scientific facts. Surprisingly, the term PCKg has not been used by many researchers, and PCK despite its limitation is still the dominant framework that researcher and scholars have gravitated towards.

Veal and Makinseter (1999), suggested that PCK should be part of a taxonomy of knowledge. With general PCK at the bottom of the pyramid, which includes a wide range of subjects, and building up to the top which represented subject-specific PCK. This subject-specific PCK represents how one teaches depending on their background. For example, a chemistry major will explain a concept differently than a physics major (Kind, 2009).

More recently the conception of Technological Pedagogical Content Knowledge (TPACK) was created. By building on the works of Shulman and others, TPACK was conceptualized in response to the new challenges of teaching with technologies (Koehler and Mishra, 2009). The idea was that the integration of technology in the educational context would benefit from an alignment of content, pedagogy, and the use of technology (Voogt et al., 2013). More simply, teachers that wish to successfully integrate technology into their curriculum would require a level of competency in the new domain of technology in addition to both content knowledge and pedagogy.

Like other frameworks based on off PCK, TPACK includes both CK and PCK in the framework. However, there is the addition of technology knowledge. Technology knowledge (TK) is defined as acquiring knowledge of technology broadly enough to apply it to work and everyday life (Koehler and Mishra, 2009).

Overlapping areas of the three domains result in the formation of new categories, PK and TK form Technological pedagogical knowledge, CK and TK form Technological content knowledge, and CK and PK form PCK. Ultimately, TPACK as a concept emerges when the three domains (PK, CK, TK) overlap. Koehler and Mishra (2009) define it as “the basis of effective teaching with technology, requiring an understanding of the representation of concepts using technologies; pedagogical techniques that use technologies in constructive ways to teach content; knowledge of what makes concepts difficult or easy to learn and how technology can help redress some of the problems that students face.” (p.66)

Another framework that was created in response to Shulman's original work, was in the realm of mathematics. Authors such as Ball et al. (2008), Hill et al. (2004, 2008), Hill, Rowan & Ball (2005) reference the concept of a mathematical knowledge of teaching (MKT).

Ball, Thames, & Phelps (2008) explained MKT as the mathematical knowledge needed by teachers to perform the recurrent tasks of teaching math to students.

Like TPACK, MKT combines both content knowledge and pedagogy knowledge, however, in the MKT framework, PCK is conceptualized as a combination of multiple components rather than one single idea. The MKT framework has 6 domains, 3 of them are related to the teacher CK, while 3 are related to PCK.

The three related to CK is (1) common content knowledge (CCK, i.e. Math knowledge and skills to solve problems outside of teaching. (2) specialized content knowledge (SCK, i.e. math knowledge that is specific to teaching) (3) horizon content knowledge (HCK, i.e. a knowledge of what students need to know for future grades, and what they should know coming into the classroom).

The next 3 domains are related to PCK: (1) Knowledge of content and students (KCS, i.e. knowledge needed to select appropriate math material for students that is motivating and interesting) (2) Knowledge of content and teaching (KCT, i.e. ability to know math, and how to teach it effectively.) (3) Knowledge of content and curriculum (KCC, i.e. knowing what must be taught at the specific grade levels) (Ball, Thames, & Phelps, 2008).

Following the introduction of MKT, a test coined “Mathematical knowledge for Teaching” (Hill et al.,2004 2005) was created to determine the MKT of teachers. It is a multiple-choice test that focuses on math related concepts teacher should know. (Hill et al. 2004,2005) With the creation of the test, researchers were able to compare epically if better grades on the test resulted in increased student learning.

PCK/MKT and student learning

Due to the nature of MKT being built on empirical research and in response to some of the deficits of Shulman's original work, it provides a unique way to see the effect of PCK and the effects it may have on students. Hill et al. (2005), found that teacher knowledge in math was related to student improvement. Teachers who scored higher on the Mathematical knowledge for teaching test were able to more effectively teach their students. However, this study is not without its limitations as most of the students came from lower social economic status backgrounds and the results may not have been the same, had the sample been more normative. Building off this study, Hill et al. (2008) were able to demonstrate that teachers who had higher MKT scores, had fewer errors while teaching, were better able to respond to their students and choose examples that helped the students build meaning. Along the same lines Izsak (2008), contrasted two, grade six teachers. The author concluded that the teacher with a deeper understanding of the subject matter was better able to explain concepts, generated better examples, and was better at identifying the misconceptions of their students. Charalambous (2010) was also able to demonstrate that a teacher’s knowledge of mathematics impacted their decision making in the classroom, which in part impacted the experience of the students and their learning. Teachers in the study who had a higher MKT were able to keep tasks more cognitively challenging for their students creating a more dynamic and meaningful lesson.

Although the research seems promising, MKT represents many aspects of knowledge; it is still unsure that PCK is the main contributor to the improved student learning that we see.

Commonalties of PCK in research

Although there exists much controversy regarding PCK, and many authors have updated and built upon the framework most authors agree that it connects two domains of knowledge. Content knowledge and pedagogical knowledge. According to Sibbald (2009), it is “The intersection of pedagogy and content is pedagogical content knowledge, which combines specific content objectives with particular instruction techniques” (p.454). PCK is also seen as the overlap of the two domains in multiple frameworks. This is shown in the TPACK framework as the two domains of pedagogical knowledge (PK) and CK overlap to create PCK (Koeler & Mishra, 2009) Lastly, even in the MKT framework, although not a separate concept, is still conceived as the integration of both PK and CK.

Gaps in the PCK Research

Interestingly, in my research, I did not come across any studies that have examined how PCK may be different in the various levels of teaching (Abell, 2008). For example, does a teacher that goes from educating a class of first graders, to a group of grades 7 require a higher level of PCK. Additionally, although PCK has branched off into different fields such as mathematics, science, and even physical education (e.g. Hill et al., 2008, Kind, 2009, Tsangaridou, 2002,) none, or few studies have looked at PCK across the various education domains, to see how PCK may be applied differently depending on the subject. For example, is the level of PCK needed for mathematics, the same needed for teaching science of the same grade level? Similarly, does addressing the misconceptions in science compared to math require varying levels of PCK? This is of interest because Ontario elementary teachers often need to teach a wide range of subjects to their students. Expanding on this, does an elementary teacher that teaches multiple subjects, require varying levels of PCK in the various subjects? Although Veal and Makinster (1998) introduced the idea of a domain-specific PCK; studies on how PCK impacts a teacher that teaches multiple subjects are limited.

Also, PCK as a concept has been dominating mainly in mathematics and science; limited studies have examined the usefulness of PCK in subjects such as history, and social studies. Finally, PCK is not widely taught as a concept in teacher education, and many professional teachers are unfamiliar with the idea (Kind, 2009). It would be interesting to examine if explicitly teaching PCK as a concept would have any impact on pre-service teachers as they transition into novice teachers.

It is evident that PCK as a concept is much more complex and intricate than when Shulman (1986;1987) first thought. Researchers have yet to come to an agreement as to what exactly PCK is. However, PCK has unarguably been a powerful concept that has been pervasive in the research community. There is strong research to suggest that PCK is indeed a useful tool in contributing to our understanding of the complexities of teaching, and professional practices. It is widely agreed that PCK encapsulates the combination of content knowledge and pedagogy. However, the concept is not without issues. Difficulties arise when trying to fully understand PCK, and many argue that PCK does not exist as a separate concept ( Depaeppe, Vershaffel, & Kelchtermans, 2013; McEwan and Bull, 1991; Baumert et al., 2010). Nonetheless, PCK has been fundamental in understanding how teachers teach, and the importance of specialized context knowledge for teaching. PCK has also sparked, the creation of multiple teachers knowledge models, such as MKT and TPACK. Additionally, these models have been applied empirically to determine if higher scores could have a positive impact on students; with multiple studies suggesting it can (e.g. Ball, Thames, Phelps, 2008; Charalamnbous, 2010; Hill et al., 2008).

Many areas of PCK still remain unexplored in-part because of the difficulty to explicitly identify PCK in the teaching process (Kind, 2009) but as new research comes to light a better understanding of PCK will without a doubt be beneficial to both educators and students alike.