The nature of integration among PCK components: A case study of two experienced chemistry teachers

Abstract

In this qualitative case study, we examined the nature of integration among pedagogical content knowledge (PCK) components. To attain the goal, two experienced chemistry teachers' teaching redox reactions and electrochemical cells was observed. The data were collected through card-sorting activity, content representation (CoRe) tool, observation, and interviews. The data analysis included three steps, namely; in-depth analysis, enumerative approach, and constant-comparative methods. Results reveal that knowledge of learner and instructional strategy components were central in the integrations. However, knowledge of assessment and curriculum were less effective in shaping teachers' teaching. Additionally, the integrations were specific to topic taught. More coherent integration was observed in both teachers' teaching electrochemical cells topic. With the quantification of PCK integration, this study provides an opportunity to discriminate integrations regarding their type, quality, and strength. Implications for both pre- and in-service teacher education programs were suggested.

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Introduction

Teachers are one of the most important factors in students' understanding and achievement (Hill et al., 2005), which increases the importance of professional development activities enriching teachers' knowledge and skills (King and Newman, 2000). This also makes teacher knowledge as a valuable construct in teacher education research since it offers useful information for the design and revision of professional development and teacher education programs (van Driel et al., 1998; Friedrichsen, 2008). As a knowledge base for teaching, Shulman (1986) introduced pedagogical content knowledge (PCK) and it has been used as a theoretical framework for investigating teachers' knowledge by many researchers.

Shulman (1987) described PCK as the knowledge that contains “the special amalgam of content and pedagogy that is uniquely the province of teachers, their own special form of professional understanding” (p. 8). In a way, PCK is the type of knowledge that distinguishes scientist from the teacher. PCK is important as a construct. First, PCK is formed through the transformation of many different knowledge bases for teaching; however, it is not the ordinary mixture of them. Rather, the components inform and interact with each other (Magnusson et al., 1999). ice and in-service teacher education. Additionally, PCK is also related to learners' understanding of science topics due to the fact that knowledge of learner component of PCK focuses on learners' difficulties, misconceptions, and pre-requisite knowledge (van Driel et al., 1998). Furthermore, PCK and its components are useful for researchers studying teacher knowledge and practice because they provide a road map to find your way (Second, PCK has a significant role in defining effective and competent teachers, and their practice. The practical value of PCK is related to its nature because it informs aspects of science teacher education programs, in terms of both pre-serv Marks, 1990; Friedrichsen, 2008). Therefore, in order to gain a better understanding of teachers' knowledge and to realize its importance, the thing that should be done is to uncover teachers' knowledge, which is the major purpose of research in teachers' PCK field (Loughran et al., 2004).

In the literature, scholars have proposed PCK models (e.g., Grossman, 1990; Marks, 1990). PCK models identified components of PCK; however, they do not indicate how the components interact with each other (Friedrichsen et al., 2011). Therefore, research should elaborate on how teachers use PCK components simultaneously in order to make the topic more understandable to learners (Abell, 2008; Friedrichsen et al., 2011; Park and Chen, 2012). A better understanding of the components' integration informs the literature about nature of PCK, which provides useful information for the design and revision of teacher education programs (National Research Council (NRC), 1996). “Given the integrative aspect and complexity of PCK, however, to provide insightful implications for practice, it is necessary to investigate how all components interact with one another and how they are integrated into PCK that enables a teacher to transform content knowledge into instructional events from a more holistic perspective” (Park and Chen, 2012, p. 923). In response to the call for research into examining the integration of PCK components, we sought to explore how experienced chemistry teachers' PCK components interact to make the topic more comprehensible for learners in the context of redox and electrochemical cells topics.

Literature review

This section consists of the literature review on PCK and its components, the nature of PCK, and the integration among PCK components. Finally, gaps in the literature are stated.

PCK and its components

PCK was first offered by Shulman (1986) and it has been described as a type of knowledge that “represents the blending of content and pedagogy into an understanding of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction” (Shulman, 1987, p. 8). In addition to Shulman's model, other scholars proposed different models of PCK, which means that there is no consensus on the conceptualizing of PCK (Abell, 2007). One of the PCK models used predominantly in the science education literature is Magnusson's model (Magnusson et al., 1999). In the model, PCK consists of five components that are orientations to science teaching (OST), knowledge of curriculum (KoC), knowledge of learner (KoL), knowledge of assessment (KoA), and knowledge of instructional strategies (KoIS). OST involves teachers' beliefs and knowledge about goals and purposes of science teaching at a specific grade level. KoL is related to learners' difficulties and misconceptions in learning specific topics, and prerequisite knowledge necessary to learn the topic. KoC consisted of knowledge of curriculum goals, and of curricular materials provided by the curriculum developers. KoA, another component, comprises knowledge of what to assess, and how to assess students' learning. KoIS involves both subject-specific strategy (e.g., 5E, inquiry, etc.), and topic-specific strategies that consist of knowledge of activities (e.g., simulations, demonstrations, and experiments) and representations (e.g., analogies, models, illustration, and examples).

The nature of PCK

The literature has indicated that subject matter knowledge (SMK) is a must for solid PCK (van Driel et al., 1998; Abell, 2007). Additionally, PCK is a topic-specific construct that is developed through experience in teaching (Grossman, 1990; van Driel et al., 1998; Abell, 2007). However, experience may not always give rise to enhancement in PCK (Friedrichsen et al., 2009). When it is the case, workshops and professional development activities should be provided to teachers (Van Driel et al., 1998). Additionally, PCK should be viewed as whole rather than separate components. The reciprocal integration of the components is an indication of robust PCK (Marks, 1990; Fernandez-Balboa and Stiehl, 1995; Magnusson et al., 1999).

Due to the simultaneous use of different components, the line between components is not clear-cut (Grossman, 1990; Marks, 1990; Fernandez-Balboa and Stiehl, 1995). Grossman (1990) stated that PCK has five components but the division of them is not clear in practice. Marks (1990) also stressed the incorporation of components with each other, which makes it hard to structure PCK. In their model, Cochran et al. (1991) emphasized the same point and viewed pedagogical content knowing (PCKg) as combination of knowledge of environmental context, knowledge of pedagogy, knowledge of students and knowledge of subject matter. “…theoretically, the four components become so integrated and interrelated that they no longer can be considered separate knowledges” (Cochran et al., 1991, p. 12).

Research on integration among PCK components

Some research studies have been conducted about the integration among PCK components. For example, Fernandez-Balboa and Stiehl (1995) also paid attention to how those components are related to each other. To be a successful teacher, the integration among the components of PCK is essential. In other words, separate entities of components does not result in good teaching, therefore, PCK components should be employed simultaneously when it is necessary. In addition to that, the integration existing between the components is not linear, rather different integrations are possible for a specific situation. Similarly, Magnusson et al., (1999) argued that relations between the components of PCK are very important. They said that for being an effective teacher, having a solid knowledge of one component is not adequate. Moreover, there is a multifaceted relation between the components of PCK, which makes focusing on the relation and its influence on teaching valuable to the PCK field.

In another research type, the relation of science teaching orientation with other PCK components was explored. Padilla et al. (2008) focused on how instructors with different orientations to science teaching teach the same topic in different ways. For instance, one of the participants had atomistic paradigm that focuses on sub-microscopic level. His/her teaching was based on the particulate level. Different than Henze et al. (2008), Padilla et al., (2008) dig into different types of PCK including different types of integration of components. In type A PCK, there was synchronization between knowledge of goals and knowledge of instructional strategy. Namely, teachers focused on content so they used videos to help learners learn the content of the solar system and universe. Another relation was between knowledge of assessment and knowledge of learners. Data gathered from exam papers help teachers update their knowledge of learners. Finally, knowledge of instructional strategy and knowledge of assessment were also corresponding to each other. Teachers taught content of the model during instruction and assessed the content of it in the exam. Similar integrations were observed between knowledge of goals and of instructional strategy in type B PCK. The integration between knowledge of learner, of assessment and of instructional strategy was reciprocal. Both knowledge of instructional strategy and of assessment informed teachers about the possible difficulties that learners may have. Furthermore, the more developed knowledge of instructional strategy and learner that teachers possess, the better assessment was enacted by teachers. Henze et al. (2008) argued that each type of PCK has its own development and integration among the components. Finally, Friedrichsen et al. (2009) reported that intern teachers' PCK lacked relation between components while experienced teachers' PCK included integration among the components to some extent.

Similarly, Park and Chen (2012) explored the integration among PCK components for two different biology topics, photosynthesis and heredity. In order to explore the integration different than the other studies, they focused on the frequency of connections among the PCK components. The results of the study showed that integration among the components was topic-specific; the interaction among components was more for the photosynthesis topic than they were in the heredity topic. Moreover, knowledge of learner and knowledge of instructional strategies were the PCK components that had the strongest connection and had the strongest roles on teachers' PCK for both topics. However, knowledge of curriculum had the least connection with other components, therefore had little influence on teachers' practice.

Padilla and Van Driel (2011) also investigated the relationship among PCK components of university professors teaching quantum chemistry. In order to identify the relationships, after the interview data was analyzed qualitatively, PRINCALS, a quantitative technique was employed to find the loadings of sub-components of PCK components. It was found that orientations towards science teaching was strongly linked with knowledge of instructional strategies. Moreover, knowledge of students' difficulties was often linked with knowledge of curriculum while knowledge of assessment was less linked to other PCK components. In another study, Kaya (2009) examined the relationship among components of PCK in the context of ozone layer depletion. This study was carried out with pre-service science teachers. The data were analyzed quantitatively. In terms of PCK components, the most problematic one was knowledge of assessment. Results revealed that there was a strong positive correlation between SMK and PCK (r = 0.77, p < 0.0001). Moreover, SMK had a positive and significant correlation with all PCK components. Finally, there were moderate correlations between PCK components. However, knowledge of assessment did not have any significant correlation with other components.

Gaps in the PCK literature

Although PCK has been studied for more than 25 years, the integration of the PCK components has not been clearly explained in the literature (Abell, 2008; Friedrichsen et al., 2011; Park and Chen, 2012). Few studies have been conducted with respect to the integration of PCK components (e.g., Henze et al., 2008; Padilla and Van Driel, 2011; Park and Chen, 2012). Though these studies described various integration among PCK components, they did not explain the nature of those (i.e., how these integration are different regarding their strength). Park and Chen (2012) also criticized their research study by indicating that they tried to construct PCK maps of teachers in a way to determine the number of connections among PCK components by assuming the strength was the same for each connection. Therefore, all integrations were given “1”. In the present study, authors both aimed to construct PCK maps for chemistry teachers by considering the integration among PCK components and describe the nature of those relationships in detail. However, we would not simply assume the same strength for each connection; rather we coded them considering the quality of them regarding their support for learners' understanding. The research question guiding the study was: what is the nature of the integration among PCK components for two experienced chemistry teachers' teaching the redox reactions and electrochemical cells topics?

Methodology

Research design

This study is interpretative in nature. Specifically, the type of the study is secondary analysis of data collected and analyzed for different purposes (Heaton, 1998, 2004). Additional in-depth analysis, additional sub-set analysis, and new perspective/conceptual focus are three forms of secondary analysis (Heaton, 1998). Specifically, this research is new perspective/conceptual focus type due to the fact that we re-examined some part of the existing data with a different perspective. There are some methodological and ethical issues regarding secondary analysis. Heaton (1998) stated three main issues regarding secondary analysis studies, namely, compatibility of the data with secondary analysis, position of the secondary analyst, and reporting original and secondary data analysis. First, regarding “compatibility of the data with secondary analysis” (Heaton, 1998), the data are suitable for analyzing integration among PCK components. All data sources (i.e., field notes, CoRe, follow-up interviews) included rich data regarding how PCK components integrate with each other. Second, in terms of “position of the secondary analyst” (Heaton, 1998), we, as the analysts in this study, were part of the original research group. We are knowledgeable about the nature of the data and data collection procedure. Additionally, we have all parts of the data collected. Third, “reporting original and secondary data analysis” is necessarily provided. Necessary information about the purpose of the original research and the secondary analysis of it are given below. Finally, to meet the ethical issues regarding secondary analysis of the original data, participants were informed about the purpose of the secondary analysis (i.e., to examine how different components of their practical knowledge, for instance, instructional strategy knowledge and assessment knowledge integrate with each other). Informed consent that is also necessary for the re-use of the data (Taber, 2013) was obtained for the recent study.

In the initial study (i.e., Aydin, Friedrichsen, Boz, and Hanuscin, 2013), we attempted to compare and contrast two experienced teachers' PCK for teaching electrochemical cells and radioactivity topics. To achieve the goal, we collected the data through the whole electrochemistry and radioactivity units (i.e., more than two months). We focused on understanding the topic-specific nature of PCK, and examined teachers' PCK regarding all PCK components in the two topics. In this study, we are interested in examining the integrations among PCK components and understanding the nature of them regarding redox reactions and electrochemical cells topics.

Participants

First, research has shown that pre-service or novice teachers do not have robust PCK (van Driel et al., 1998; Abell, 2008). Hence, we decided to examine experienced chemistry teachers' PCK. We paid attention to the number of years that they have taught high school chemistry, professional development activities that they attended to, and the way of their teaching. Moreover, context influences how teachers teach (Berliner, 2001; Park and Oliver 2008a), hence, we studied with teachers working in the same context. Participants were two experienced chemistry teachers, Thomas and Carla (pseudonyms were used), with teaching experience of 15 and 8 years, respectively. Both teachers worked at the same high school. Both Thomas and Carla taught chemistry in a conceptual way and attended some professional development activities, related to performance based assessment and introduction of new chemistry curriculum.

The study was carried out in a private high school context in [a large university town]. There were about 450–500 learners in the high school. The learners are generally between 16 and 18 years old in the secondary level. In addition, the classrooms observed have about 20–24 students.

Instruments

Data were collected by the use of card-sorting activity, content representation (CoRe), observation, field notes, and semi-structured follow-up interviews conducted after observations in order to examine the integration of PCK components for teaching the redox reactions and electrochemical cell topics.

Card-sorting activity

In order to determine participants' orientations and goals for teaching chemistry, card-sorting task was utilized (Friedrichsen and Dana, 2005). For the card-sorting activity, first of all, scenarios related to redox reactions and electrochemical cells topic were developed with help of the literature (i.e., Friedrichsen and Dana, 2005), Turkish high school chemistry curriculum implemented, and the context (i.e., university entrance system based on high stake exams). To illustrate, two examples of the scenarios written were provided: (a) a good way to teach students about oxidation and reduction reactions is to ask questions and/or to use a demonstration that will check on the students' prior knowledge of the topic and then try to eliminate their misconceptions with scientific conception. (b) One way to effectively teach students about the factors influencing the oxidation of iron is to allow students to design their own experiments using variables they decide upon. Then, teachers were requested to sort the cards into three groups, group of cards that are representative of their teaching, the other group of cards that do not represent their teaching, and final group of cards for which they are unsure whether these are representative or not of their teaching. To diagnose teachers' orientations, their reasons for sorting the cards were asked. Regarding the use of the card-sorting activity, Friedrichsen and Dana (2005) stated that conversation with the teachers during the sorting of cards provides rich information about teachers' orientations. To illustrate, teachers were wanted to discuss in what ways scenarios were different/similar to their own teaching and how the scenarios were related to their purposes and goals of chemistry teaching. In addition to data collected through the card-sorting activity, observation of teachers' teaching and follow-up interviews helped us decide on participants' orientations. The data collected through the activity, teachers' orientations and goals for teaching chemistry were tried to be determined. Not only those data, but also the data collected through the observations and interviews were helpful in understanding the participants' orientation as well. In the analysis of card-sorting activity, we mainly focused on how teachers teach, how they provide the content to learners, and whether they share the responsibility with learners or not to label teachers' orientations.

Content representation (CoRe)

One week before teaching each topic, the CoRe was employed by conducting interviews to teachers. The CoRe is a matrix that involves big ideas/concepts related to the topic on the horizontal axis and factors that influence teachers' decisions such as learners' difficulties, teaching procedures and ways of assessing students' understanding on the vertical axis (Loughran et al., 2004). In the CoRe, it was asked: “What are the difficulties related to teaching electrochemical cells topic?”, “Why do you think is it difficult to teach it? What are the factors making teaching it difficult?” The participants stated the difficulties that learners might have, how to use instructional strategies to address the difficulties, use of curriculum, and assessment of learners' understanding.

Observation

Although the data collected through interviews endow with valuable and rich data, it is not a full description of the participants' PCK. Therefore, for a complete picture of the situation in addition to taking participants' opinion, participants' teaching was observed (Patton, 2002). Teachers' instruction related to the redox reactions (eight class hours for each teacher) and electrochemical cells (six class hours for each teacher) topics were observed. A class hour is 50 minutes long. In the weekly-schedule, teachers teach chemistry three class hours at 11th grade. To conclude, for each topic, the researchers observed teachers' teaching practice more than two weeks. During the observation, field notes were taken simultaneously in the classes.

Follow-up interviews

Participants were asked about their teaching practice that are worthy of clarification by the help of semi-structured interviews carried out at the end of each week. For instance; “What were you thinking when this was occurring? Tell me more about what was happening when you…?” and “What do you think the student was thinking when s/he was doing…? Why do you think the student was having difficulty at that point?” The interviews took about half an hour. All interviews were audiotaped and then transcribed verbatim.

Data analysis

In this research, in order to examine the integration among PCK components, we utilized Park and Chen's (2012) approach. The data analysis was based on the Pentagon PCK model proposed by Park and Oliver (2008b). We identified the parts in which different types of teacher knowledge inform and/or influence each other. In this in-depth analysis of those parts that are called as PCK episodes, we used Park and Chen's (2012) operational definition of PCK that is “PCK as an integration of two or more components of in the [PCK] model” (p. 928). Similar to Park and Chen (2012), we focused on each PCK episode regarding which components of PCK take part in it, teacher's and students' role, and the quality of the instruction in terms of being parallel to the reform-based teaching. In the enumerative approach part, Park and Chen (2012) assumed that all connections have the same strength and gave 1 point to all connections identified. Different than Park and Chen (2012), we coded the PCK episodes regarding its strength in terms of its quality and usefulness of the integration for students' learning. To achieve that aim, we formed a rubric ranging from 3 to 1. The scoring (see Table 1) was focused on the consistency of the instruction with the science education reform documents (i.e., whether it provides an opportunity for students to learn), completeness (i.e., whether the integration has a diagnose and a re-design the instruction parts), and adequacy (i.e., whether the enactment part was adequate to help learners understand). In other words, we attempted to differ the connections regarding their strength by the use of the rubric, which is missing in the PCK literature.

Table 1 Scoring rubric for coding the data

Scores	Explanation	Example
3 points	An integration including an understanding part of students' difficulties, pre-requisite knowledge, and/or a point about the topic and then enactment part in which teacher tailors the instruction to address it. The teacher reflects on the difficulty and/or requirement and design/re-design an instruction that is informed by reforms in science education (i.e., including student centered discourse, providing opportunities for students to construct knowledge such as hands-on, and minds-on activities).	One of the students, Michelle, in Carla's class had difficulty in understanding how to use the half-cell potentials for determining anode and cathode of the cell. Carla provided an example and gave reduction potentials of copper and silver half-cell reactions and asked Michelle to help her determine anode and cathode. Carla asked: “what should we do?” She did not tell her how to determine them, rather took Michelle's idea about the process. Carla did not dominate the discourse. Michelle had a chance to learn by experiencing the whole process with support of the teacher. When asked in the interview, Carla stated: ‘I thought that Michelle could not understand that point [how to use the half-cell potentials for determining anode and cathode]. I specifically asked her help me.’
2 points	An integration including diagnosing students' difficulties and/or problems about the topic and/or tailoring instruction to solve the problem. The instruction is not informed by reforms in science education (i.e., teacher-centered discourse, no activities for knowledge construction, and teacher provides the knowledge directly). Although the instruction is teacher-centered, it is adequate regarding to solve learners' problem or address it.	Thomas knows that learners have difficulty in understanding standard hydrogen electrode (SHE) and the reason of why SHE is necessary. In order to help learners understand SHE, he used an analogy. He stated that the use of SHE is similar to the use of sea level in determining the altitude. In order to determine the altitude of a place, a reference point is needed.
1 point	An integration including diagnosis of students' difficulties and/or problems about the topic, and tailoring instruction to solve it. The instruction is not informed by reforms in science education (i.e., teacher-centered, no activities for knowledge construction, and teacher provides the knowledge didactically). Moreover, the instruction is not adequate for students' knowledge construction.	In Carla's class, learners could not realize that oxidation and reduction reactions occur simultaneously. Carla diagnosed the problem and stated that they occur simultaneously. She explained that one of the species gives electron and the other receives it. She warned learners not to forget this rule.

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The integrations identified were coded by the use of the scoring rubric. Then, the frequencies of the integrations and the total points given to each pair were summed up. Then, PCK maps for each teacher were formed. In the final step, by the use of constant-comparative method (Strauss and Corbin, 1990), we attempted to see the patterns existing in teachers' PCK integration.

In this study, data triangulation (use of CoRes, interview transcripts, and field notes from observations), the investigator triangulation (by inviting three researchers to observe both participants' teaching), and methodology triangulation (use of in-depth analysis, enumerative approach, and constant-comparative method) were used to ensure credibility (Patton, 2002).

Results

In the result section, first, PCK maps drawn for each teacher's teaching the two topics, frequencies of connections, and their strength are presented in Table 2. The strength of the integrations among the components was discriminated by the use of different lines. Second, the results revealed from the constant-comparative analysis are presented.

Table 2 PCK maps for teaching redox reactions, electrochemical cells, and total

Topics	Thomas	Carla
Redox reactions
E. cells
Total

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The analysis of the PCK episodes identified from observations and field notes, and triangulated by the use of other data sources (i.e., card-sorting activity, CoRe, follow-up interviews) revealed that, in total, 52 and 46 PCK episodes were labelled in Thomas and Carla's teaching, respectively. In teaching redox reactions, Thomas got 32 points from 22 PCK episodes. In the electrochemical cells topic, he got 45 points from 30 episodes coded. Thomas got three points only once. In that PCK episode, KoL and KoIS integrated for teaching electrochemical cells. In Carla's teaching of the redox reactions, she got 33 points from 19 episodes. In electrochemical cells topic, more integration was observed (i.e., 27 episodes) than those in redox reactions topic. She received 39 points from the episodes identified. There were two episodes (i.e., between KoC–KoIS and KoL–KoIS) from which she got three points in the electrochemical cells topic. When the total points were summed, Thomas got 77 and Carla got 72 in total from the connections. As Table 2 shows, some of the connections were stronger and more frequent than the others. For instance, in both of Thomas and Carla's teaching, knowledge of learner (KoL) and knowledge of instructional strategy (KoIS) components had played a central role in their teaching both topics. However, the connection of knowledge of assessment (KoA) with other components was very few (e.g., connections between knowledge of curriculum (KoC) and KoA).

Second, with the help of the episodes analyzed and maps drawn, we came up with 5 characteristics of integration among PCK components: (a) the integrations were idiosyncratic vs. topic-specific in nature. (b) Some of the interactions are very simple whereas some of them are so complicated. (c) Orientation to science teaching (OST), an overarching component in the PCK model, shaped instructional decisions. (d) Some of the integrations detected were more frequent than others. (e) The integrations have diverse parts, namely, diagnose, performance, and reflection.

The integrations among PCK components are idiosyncratic and topic-specific

As seen from PCK maps (Table 2), integration between PCK components differed between the topics for the same teacher. For example, regarding redox reactions, there were fewer connections among PCK components in Thomas's teaching (i.e., 32 in total), whereas his PCK map was more coherent and involved more integration (i.e., 45 connections totally) in his teaching of electrochemical cells. In addition, no integration between KoA and KoL was detected for Thomas's teaching of redox reactions. Furthermore, integration between KoA and KoC and KoA and KoIS did not exist in electrochemical cells. Similarly, Carla's PCK maps were different for teaching redox reactions and electrochemical cells topics. The frequencies of the connections among PCK components were 33 and 39 for redox reactions and electrochemical cells topic, respectively. While teaching redox reactions, Carla could not link KoA and KoIS components of PCK. In her teaching of electrochemical cells, on the contrary, no integration was observed between KoC and KoA as well as KoC and KoL.

Some of the integrations are simple whereas others are complicated

When all of the PCK episodes belonging to both teachers were coded, a range of complexity of the integration was noticed. For instance, there was an objective related to the Nernst equation and performing some algorithmic exercises related to it in the 11th grade chemistry curriculum. By the use of the objective, Carla integrated some exercises within her lectures. In this example, KoC informed the use of instructional strategies. The integration was so simple that one PCK component informed the other one (Fig. 1).

Fig. 1 An example of simple integration between PCK components.

On the other hand, some of the integrations were so complicated that at least two components informed and/or influenced the others (Fig. 2). For instance, Thomas stated that because the signs of anode and cathode are opposite in electrochemical cells and electrolytic cells, learners have difficulty in learning them. He also attributed the difficulty to prior learning in physics course. Students had learnt that electron flow is from positive terminal to negative in physics. However, in chemistry they learn that it is from anode, negative terminal, to cathode, positive terminal. Thomas knew the confusion and the possible reasons of it. He taught electrochemical cells first and then started to teach the electrolytic cells. Due to the fact that he is aware of the confusion, he did not use signs of anode and cathode when teaching electrochemical cells. He postponed the use of them to electrolytic cells purposefully. When he started to teach electrolytic cells, he provided a comparison table that shows the signs of anode and cathode, and which reaction occurs in those terminals in electrochemical and electrolytic cells. Moreover, he was aware the curriculum objective regarding to the cells, namely; “learners should be able to discriminate electrode, half-cell, and electrochemical and electrolytic cell concepts.”

Fig. 2 An example of complicated integration of PCK components.

OST, an overarching component in the PCK model, shaped the instructional decisions

OST component was found to shape both teachers' instructional decisions. To clarify, Thomas was aware of students' misconception that “anode is always on the left side of the cell”. To address this misconception, he could have utilized different instructional strategies. For instance, he could have used a demonstration in which he forms two Zn–Cu cells. In the first one, anode which is Zn electrode is on the left and in the second one anode (Zn electrode) on the right. Then, he could have asked learners what they expect and take their reasons. In the next step he could have measured the potential difference in both cells with learners. After seeing that the potential difference does not depend on the position of the electrodes, they could have discussed it. However, he preferred to draw an electrochemical cell on the blackboard and told that it was not correct to think in that way. He stressed that, not the position, but the half-cell potentials determine which electrode would be the anode or cathode. In this example, Thomas's didactic orientation shaped the way how to address the misconception.

Similar manipulative influence of OST component on instructional decisions was observed in the integration provided above. In the complicated PCK integration example, Thomas decided to stress the differences among electrochemical and electrolytic cells regarding the signs of electrodes (Fig. 3).

Fig. 3 The shaping influence of OST component on instructional strategy use.

Some of the integrations detected were more frequent than others

When all of the integrations were examined, it was clear that some of the PCK components were more strongly connected whereas the integration among some PCK components was weak. For example, in both Thomas's and Carla's teaching, the strongest connection took place between KoL and KoIS components. Moreover, KoL and KoIS were the PCK components that were the most frequently connected with other components. We could infer that both KoL and KoIS were influential in shaping both teachers' PCK.

On the other hand, the least connection was between KoC and KoA. We could state that participants' KoC did not inform their use of KoA. For example, in both teachers' teaching, the only integration between the KoC and KoA was that their KoC informed them what to assess, in terms of objectives stated in the curriculum. They asked questions to assess whether or not they reached the objectives in the curriculum. Moreover, KoC and KoA were less frequently connected with other components in both teachers' teaching. Therefore, we could say that KoC and KoA were less effective in shaping their PCK. In conclusion, for both teachers, some of the PCK components are more available (e.g., KoL and KoIS) than the others (e.g., KoC and KoA).

The integrations can be assumed to have diverse parts, namely, understand, decision-making, enactment, and reflection

A close analysis of the integration showed that integrations had parts that are related to each other. The first part is the understanding of the difficulty, misconception, and/or a problem (Fig. 4). Then, the decision for addressing it is taken through the filter of orientation to science teaching. The enactment of the strategy decided is the third step. After the application of the strategy, the teacher reflected on the decision taken regarding to what extent it helps learners to understand and solve the problem detected. After reflection, if the teacher thinks that it is useful, s/he puts it into his repertoire.

Fig. 4 Steps included in the integrations among PCK components.

When these parts of the integrations were examined, it was observed that KoL and KoC had essential roles in diagnosing the difficulty or problem that learners faced. OST component, on the other hand, mediated teachers' choices about how to remedy it. For example, due to their didactic orientation, the participants of this study usually responded to the difficulties and/or misconceptions didactically. They preferred to provide scientific explanation, and to eliminate them through asking questions to learners, which makes them think on the point and creates dissatisfaction with their conception. Therefore, at the enactment step, KoIS took the main role. In addition to KoIS, KoA took part as well. For example, as mentioned in the examples above, due to the fact that learners had difficulties in determining anode, cathode, electron and ion flow in the electrochemical cells, both Thomas and Carla used an open-ended question asking learners to form a cell between two metals and determine all of the details about the cell. In this example, the problem was diagnosed with help of KoL. Then their didactic orientation shaped their decision and they decided to enact the same traditional assessment which is test but with different types of questions. Rather than multiple-choice items, they included open-ended items. Finally, after the first try they reflected on it and realized that open-ended items were better than multiple-choice ones to see how much learners learn and at which points they have difficulties (Fig. 5). Through this way, they accumulated the strategy, which is one piece of their PCK.

Fig. 5 The PCK formation cycle.

Discussion, conclusion, and implications

The present study explored the nature of two experienced teachers' PCK components' integration in teaching redox reactions and electrochemical cells topics. First, it was found that the integration among PCK component was idiosyncratic and topic-specific, which was also supported by Park and Chen (2012). Second, both teachers' PCK maps were more coherent regarding the electrochemical cells topic. Electrochemistry unit is one of the most difficult ones in chemistry for both learners and teachers (De Jong and Treagust, 2002). In this unit, electrochemical cells topic has more concepts (e.g., oxidation, reduction, anode, cathode, SHE, electrolytic cell, electrochemical cell, ion and electron transfer, etc.) than redox reactions topic does. Moreover, redox reactions topic includes two ways of balancing redox reactions (half reaction method and oxidation number method), which is based on following the rules and balancing the reactions. However, in order to learn the electrochemical cells topic, learners need to have much pre-requisite knowledge (e.g., spontaneous reactions, chemical equilibrium, and reactivity of metals) (De Jong and Treagust, 2002), which may be another possible explanation of teachers' coherent PCK maps in this topic. In other words, they were aware of the pre-requisite knowledge that learners need, the topics taught in the previous grades and the previous chemistry topics. Then, they assessed learners' prior knowledge and related the cells topic to the previous ones. To conclude, the nature of the electrochemical cells topic may let them use the PCK components in harmony to design and enact the instruction. This result supported Park and Chen's (2012) study regarding the influence of topic's nature on how and to what degree components integrate.

Third, different than the results received in the previous studies, it was noticed that the level of complexity of integrations might vary. The present study showed that some of the integrations were simple, while some were complex; at least two components informed and/or influenced each other. To the best of our knowledge, this point has not been revealed by the previous studies yet. It is important to show how complicated PCK is. By the use of the scoring rubric, we tried to discriminate the complexity and the quality of the integrations for facilitating learners' understanding. Teachers' representation of subject matter to make the content more comprehensible to others is called PCK that is knowledge discriminating teachers from content specialists (Shulman, 1986, 1987). However, the representation of the content varies from teacher to teacher. At this point, our data revealed that OST plays a vital role in teachers' decisions, which is discussed in the following paragraph.

Fourth, when the integrations were examined, it was obvious that OST is an over-arching component that moderates teachers' decisions (and Dana, 2005; Friedrichsen et al., 2011). Teachers' FriedrichsenOST directed the way in which teachers respond learners' misconceptions. In our cases, the didactic orientation of participants made teachers warn learners about the misconceptions that learners had in previous years or made teachers give the scientific explanation. They mostly provided the correct explanation directly rather than letting learners take responsibility for their learning. Similarly, the didactic orientation most probably influenced teachers' way of assessment and use of the assessment results. Didactic OST' influence was observed when the scores were examined. Two participants got three points only three times (Thomas got once and Carla got twice). Therefore, we could recommend that teachers' OST should be considered before they are formed, for instance, in pre-service teacher education programs. As Brown et al. (2009) stated, pre-service teachers' OST should be made explicit and in order to change their didactic orientation, first, they should become dissatisfied with their own orientation and then other alternative orientations that are intelligible, plausible and fruitful should be offered to them.

Fifth, although teachers bring into play different components of PCK to respond to an instructional event in chorus, the accessibility of the components were not the same. For example, KoC and KoA were the components that were less frequently connected to other PCK components. Moreover, no integration between KoC and KoA was noticed. On the other hand, KoIS and KoL had more connections among other components. This study indicated that experience does not make all PCK components expand; therefore, teachers need support through professional development, which is also supported by other studies (van Driel et al., 1998; De Jong et al., 2002). The missing integrations make us think that teachers may necessitate more support in those components than the others. Especially, it seems that support for KoC and KoA are crucial to build up robust PCK. It appears that if teachers' PCK development is assisted by professional support through the time, it is more likely that teachers are able to draw on more PCK components simultaneously. Additionally, it is also clear that the development of one component does not mean that others develop as well. “[L]ack of coherence among the components would be problematic within an individual's developing PCK and increased knowledge of a single component may not be sufficient to stimulate change in practice” (Park and Oliver, 2008a, p. 264). As Abell (2008) indicated, PCK is neither one or two components nor just a mere addition of them, but it is more than this. Therefore, all PCK components should be paid attention in professional development activities.

Finally, when the teacher's PCK components integrate in order to respond to a difficulty that learners have, and/or to take an instructional decision, the use of PCK contains different divisions, namely, understanding, decision-making, enactment, and reflection. Park and Oliver (2008a) mentioned divisions, namely, understanding and enactment in their study. They argued that teachers' self-efficacy belief forms a link between teachers' understanding and their enactment. However, the results of this study revealed that some parts of the integration are missing in Park and Oliver's (2008a) assertion. We assert that between the understanding and enactment, there is a decision-making step in which teacher's orientation to science teaching plays a role. The assertion is also congruent with the research stating that orientation to science teaching is the over-arching component that influences other components (Magnusson et al., 1999; Friedrichsen and Dana, 2005). “If the teachers believe that students learn best through careful listening (didactic and rigor orientation), then the teacher will likely choose lectures as the most appropriate strategy” (Friedrichsen et al., 2007, p. 5). When teachers need to think for an instructional decision, their choices are filtered through their orientation. In addition to a decision-making step, there is also a reflection step in which teachers reflect on the decision that they made. Park and Oliver (2008a) stated that teachers reflect on the decision during the decision moment that is reflection-in-action and after the decision that is reflection-on-action. They focused on the reflection regarding PCK development. However, we assert that in addition to PCK development, it is also part of the decisions that include integrations of PCK components. In other words, it is important regarding how teachers draw on PCK. Furthermore, regarding the parts of integration, when teachers' instructional strategy repertoire is imperfect, the enactment step may be weak. In our example, although the teacher could diagnose the specific learner difficulties and misconceptions, they could not implement effective strategies to remedy them. To sum up, the completion of the integration depends on the quality of the PCK components. The deficient part would bring about disconnection between the components and/or unproductive treatment for the difficulty that learners experience.

We believe that this study contributed to the relevant literature in several ways. First of all, we not only portrayed integration among PCK components quantitatively, but we also analyzed the nature of the integration. Secondly, we think that PCK maps suggested by Park and Chen (2012) are beneficial to reveal participants' PCK but as Park and Chen (2012) indicated, the missing part in their study was that they considered the same strength among PCK components. However, the present study revealed that considering the level of strength between components of PCK it is also possible to map out integration of PCK components. We believe that this approach is more suitable to explore participants' PCK. It also gives opportunity to correlate the scores obtained from PCK maps with students' achievement scores. As Abell (2008) states, the relationship between teachers' PCK and their students' understanding is an unanswered question in PCK literature. As a future study, we may suggest a study that investigates the relation between PCK and students' understanding by using our approach in data analysis to form PCK maps.

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