Structure and development of pre-service physics teachers’ professional knowledge

ABSTRACT

Teachers’ professional knowledge is considered one of the most important predictors of instructional quality. According to Shulman, such professional knowledge includes content, pedagogical content and pedagogical knowledge. Although recent research shed some light on the structure of the dimensions of professional knowledge, little is known how teacher education impacts pre-service physics teachers’ professional knowledge. In an effort to address this issue, we examined the content, pedagogical content and pedagogical knowledge of N = 200 pre-service physics teachers enrolled in different years of teacher education at 12 major teacher education universities in Germany. We used structural equation modelling (1) to examine the relations amongst pre-service physics teachers’ content, pedagogical content and pedagogical knowledge, (2) to explore how the three kinds of knowledge and their relations differ across different stages of teacher education and (3) to identify factors affecting the level of each component of professional knowledge. Our findings suggest that content, pedagogical content and pedagogical knowledge represent distinct types of knowledge. Furthermore, our findings show that in the first years of professional education, pedagogical content knowledge is more closely related with general pedagogical knowledge while in later years, it is more closely related with content knowledge, suggesting that it develops from a general knowledge about teaching and learning into knowledge about the teaching and learning of specific content. Finally, beyond school achievement and years of enrolment as predictors, we find in particular the amount of classroom observations to have a positive impact on the professional knowledge of pre-service physics teachers.

KEYWORDS:

• Pedagogical content knowledge
• pre-service teachers
• physics education

Introduction

The education of teachers is commonly considered a crucial factor for securing the quality of science education (European Commission, 2015). Teacher education is supposed to provide pre-service teachers with the means to meet the challenges they are likely to face in teaching. Shulman (1986, 1987) identified seven areas in which teachers need professional knowledge in order to be adequately prepared for the challenges of teaching. Over the past 30 years, many researchers have built on this work (e.g. Berry, Friedrichsen, & Loughran, 2015; Cochran, DeRuiter, & King, 1993; Gess-Newsome & Lederman, 1999; Grossman, 1990; Loughran, Berry, & Mulhall, 2006). From this line of research, three of the originally proposed areas of knowledge have emerged as the key components of professional knowledge: content knowledge (CK), general pedagogic knowledge (PK) and pedagogical content knowledge (PCK). Particularly PCK as ‘that special amalgam of content and pedagogy that is uniquely the province of teachers, their own special form of professional understanding’ (Shulman, 1987, p. 8) is widely considered crucial for a teachers’ ability to create high-quality instruction.

Research has shown that teachers’ professional knowledge positively affects instructional quality and thus student learning (Baumert et al., 2010; Heller, Daehler, Wong, Shinohara, & Miratrix, 2012; Hill, Rowan, & Ball, 2005; Keller, Neumann, & Fischer, 2017; Park, Jang, Chen, & Jung, 2011; Roth et al., 2011). A high PCK has been found to ensure a high cognitive activation in the context of physics instructions (Keller et al., 2017), and on the level of reform-based science teaching in biology classrooms (Park et al., 2011). For elementary math teachers, a positive influence of content knowledge for teaching (a blend of CK and PCK) on student learning has been confirmed (Hill et al., 2005) and secondary-level math teachers’ PCK was found to influence students’ learning directly and mediated through cognitive activation (Baumert et al., 2010). Heller et al. (2012) as well as Roth et al. (2011) presented intervention studies fostering science teachers’ CK and PCK, which led to improved student learning. Further studies substantiate the relevance of teachers’ CK (e.g. Käplyä, Heikkinnen, & Asunta, 2009) as well as PK (e.g. Voss, Seiz, Hoehne, Kunter, & Baumert, 2014) as a prerequisite for high-quality instruction. The recently proposed model of teacher professional knowledge and skill (Gess-Newsome, 2015) provides a valuable theoretical framework describing the relationship of the three knowledge bases, unpacking different ideas related to PCK and linking the knowledge bases described above as a prerequisite for personal PCK and PCK/Skill, which are the abilities of a teacher to plan, teach and reflect effectively in the classroom context to support student learning.

As a first step towards understanding how to educate future teachers, it is crucial to gain more insights into the development of each area of pre-service teachers’ professional knowledge during teacher education. Despite the broad consensus on the importance of CK, PCK and PK for the quality of science teaching, much less is known about the development of each component as well as the interplay of them during teacher education (for details, see Abell, 2007; van Driel, Berry, & Meirink, 2014). Differences in the interplay of the components are especially important for the evolution of PCK due to its conceptualisation as an amalgam of content and pedagogy. It is therefore necessary to examine what differences in the structure manifest itself during teacher education and which learning opportunities are able to support each component of the professional knowledge of pre-service physics teachers. In this paper, we seek to examine (1) the structure of pre-service teachers’ professional knowledge, (2) differences in the structure of professional knowledge across different stages of teacher education and the interplay between its components and (3) the influence of different types of learning opportunities on professional knowledge.

Theoretical background

The goal of science teacher education is to provide future teachers with the ‘intellectual tools’ (Grossman, Schoenfeld, & Lee, 2005, p. 208) to further develop over the course of their careers. To support this development in an optimal manner, research needs to identify the components of professional knowledge, their relationship as well as factors supporting their development.

Structure of professional knowledge

The idea of professional knowledge was first introduced by Shulman (1986, 1987). Shulman aimed to describe the knowledge needed by teachers to make meaningful decisions in their teaching and to critically reflect about the decisions made during teaching. He identified multiple components of professional knowledge such as content knowledge (CK), general pedagogical knowledge (PK), curriculum knowledge, pedagogical content knowledge (PCK), knowledge of learners and their characteristics, knowledge of educational contexts and knowledge of educational ends, purposes and values (Shulman, 1987). In subsequent research, the three components CK, PCK and PK developed into what is nowadays considered the core components of professional knowledge (Abell, 2007; Grossman, 1990).

The main challenge for teachers is to transform knowledge about a domain such that it becomes comprehensible for students (Shulman, 1987). Teachers therefore need to have the relevant CK (or sometimes called subject matter knowledge – SMK) themselves (Grossman et al., 2005). At which level of depth teachers have to have CK is still subject to an ongoing debate. Some researchers conceptualise CK as knowledge taught at a school level (Hill, 2010). Grossman et al. (2005), however, suggest that teachers have (1) to know the content they have to teach and (2) to know about the disciplinary structure of the content domain to enable their students to pursue a career in the discipline. Shavelson, Ruiz-Primo, and Wiley (2005), in their effort to develop a conceptual framework for teaching goals, identified four different levels of knowledge about a domain a person can have: declarative knowledge (‘knowing that’), procedural knowledge (‘knowing how’), schematic knowledge (‘knowing why’) and strategic knowledge (‘knowing when, where and how to apply knowledge’). Within this framework, knowledge at the school level consists mainly of facts (declarative knowledge) and to some extent applicable knowledge (procedural knowledge). In order to be able to effectively teach, teachers also need to exhibit a sound understanding of how this knowledge is applied in specific situations and about the reasoning for (schematic knowledge) as well as the way of employing specific knowledge in a given situation (strategic knowledge). While early assessment of CK used rather distal measures like the number of content courses (Abell, 2007), a growing variety of more complex and proximal measures account for the different aspects of CK (e.g. Jüttner, Boone, Park, & Neuhaus, 2013; Käplyä et al., 2009; Maerten-Rivera, Huggins-Manley, Adamson, Lee, & Llosa, 2015). Research based on this new approach to measure CK provides evidence that CK is of importance for quality instruction (Käplyä et al., 2009).

The definition of PCK is not as clear as the definition of CK (Smith & Banilower, 2015). According to Shulman (1987), PCK is an amalgam of content and pedagogy that allows teachers to teach effectively. Several researchers tried to elaborate on the definition of PCK in terms of its theoretical foundation or components (Kind, 2009). Park and Oliver (2008) attempted to characterise PCK by its core components following the ideas of Grossman (1990), Magnusson, Krajcik, and Borko (1999), Tamir (1988) and others alike. From this systematic review of Park and Oliver (2008) four core knowledge components of PCK emerged: knowledge of students’ understanding, knowledge of instructional strategies, knowledge of assessment and knowledge of curriculum. Additionally, van Driel et al. (2014) identified two different theoretical lines of research: research establishing a body of ‘knowledge for teachers’ and research recognising the importance of contextual factors investigating ‘knowledge of teachers’ (see also Fenstermacher, 1994). Research focusing on PCK as a knowledge base has mostly utilised paper-and-pencil tests (Baumert et al., 2010; Großschedl, Harms, Kleickmann, & Glowinski, 2015; Hill et al., 2005; Jin, Shin, Johnson, Kim, & Anderson, 2015; Jüttner et al., 2013). Research emphasising the relevance of PCK for instructional practice in specific classrooms for specific students to teach a specific topic has typically employed more qualitative approaches (Chan & Yung, 2015; Friedrichsen et al., 2009; Mthethwa-Kunene, Onwu, & de Villiers, 2015; Nilsson & Vikström, 2015; van Driel, Jong, & Verloop, 2002). The fundamentally different approaches to define and investigate PCK still endorse its relevance to construct high-quality instruction, but also hinder the process of building a coherent understanding of the construct (Park & Suh, 2015).

Over the past 30 years, research on professional knowledge focused extensively on PCK, while general pedagogical knowledge or psychological–pedagogical knowledge has just recently been investigated (König, Blömeke, Paine, Schmidt, & Hsieh, 2011; Voss, Kunter, & Baumert, 2011). Besides a large amount of research on general teaching strategies or methods of effective classroom management (e.g. Doyle, 1986; Good & Brophy, 2007) teachers use (see the discussion on ‘knowledge of teachers’ above), researchers struggled to conceptualise the knowledge base PK (as the ‘knowledge for teachers’). König et al. (2011) argue that the main problem of conceptualising general PK is the different ‘cultural perspectives on the objectives of schooling and on the role of teachers’. The components of PK should not be subject specific but still relevant for the instruction of, for example, science teachers. After reviewing the existing literature (König et al., 2011; Voss et al., 2011) as well as state documents (KMK, 2004) and a Delphi study with experts in education (Lohse-Bossenz, Kunina-Habenicht, & Kunter, 2013), Hohenstein, Kleickmann, Zimmermann, Köller, and Möller (2017) identified four main components of PK: (1) general teaching principles, (2) learning, development and motivation, (3) classroom management and (4) adequate assessment strategies. Especially, classroom management is a central component for PK and part of most conceptualisations (Grossman, 1990; König et al., 2011; Shulman, 1986; Voss et al., 2011). The recently developed instruments already show promising results for a further investigation of this important component of professional knowledge (Großschedl et al., 2015; König et al., 2011; Voss et al., 2011).

Summarising, three components of a teachers’ professional knowledge – CK, PCK and PK – have been proposed as a prerequisite for successful teaching (Shulman, 1986, 1987). In particular, previous research on PCK has suffered from a lack of a consensus definition. In 2012, a summit was held to discuss the different perspectives on PCK in previous research (Carlson, Stokes, Helms, Gess-Newsome, & Gardner, 2015). The summit led to the introduction of the model of teacher professional knowledge and skill (Gess-Newsome, 2015). This model merges several different ideas previously combined under the notion of PCK and also provides a structure of the three knowledge bases. According to the model, PCK is based on generic teacher professional knowledge bases (TPKB) such as CK and PK. However, the necessary knowledge for teachers to teach a specific topic occurs on the topic level (Veal & MaKinster, 1999) and is therefore referred to as topic-specific professional knowledge (TSPK). Both these different knowledge bases present public knowledge that is formed through best practice and research (Gess-Newsome, 2015). It is this TSPK that represents the PCK as the ‘knowledge for teachers’ (van Driel et al., 2014) that pre-service teachers should acquire during teacher education programmes. The actual resources teachers use in order to facilitate students’ learning in the classroom context and thus represent the ‘knowledge of teachers’ are characterised as personal PCK and PCK/Skill. The model points out that the development of personal PCK and PCK/Skill first requires the accumulation of TSPK (Gess-Newsome, 2015). It seems that the different types of PCK correspond to differences in the kind of PCK that teachers hold in at different stages of their professional career. In the early stages of a teachers’ professional career (i.e. in teacher education), they obtain CK and PK as well as TSPK as individual components of their professional knowledge. Furthermore, CK and PK are expected to support the accumulation of TSPK during that phase. With increasing experience, teachers develop personal PCK and PCK/Skill relevant for instructional practice as an amalgam of the individual components of professional knowledge, while their beliefs and orientations act as an amplifier or filter (Gess-Newsome, 2015). The fundamental role of TSPK as the basis of the development of teachers’ personal PCK and PCK/Skill necessitates a close inspection of the TSPK pre-service teachers acquire during teacher education programmes in order to gain a deeper understanding of its dependence on CK and PK and to make the development of pre-service teachers’ professional knowledge tangible.

Development of professional knowledge

Grossman (1990) distinguishes three different sources for the development of professional knowledge: (1) the apprenticeship of observation as a student, (2) teacher education and (3) professional experiences. The development of all three components of professional knowledge is fuelled from these three sources. Kleickmann et al. (2013) further classify the sources for development of professional knowledge based on their level of formalisation and intentional construction in formal, informal and non-formal learning opportunities. A teacher’s own school education (i.e. the apprenticeship of observation as a student) can be understood as a formal learning opportunity for CK and informal learning in terms of (personal) PCK and PK through observing the own teacher. In school, future teachers acquire CK, which serves as a basis for the further development of CK (Sadler & Tai, 2001). As to PCK and PK, teachers tend to rely on instructional strategies or misconceptions they themselves experienced in school (Lortie, 1975). Non-formal learning, however, refers to learning opportunities outside of educational settings.

Pre-service teachers develop their CK mostly in formal learning opportunities such as lectures (e.g. introductory physics, theoretical physics), seminars (e.g. discussing tasks from the lectures) or lab work during teacher education (Grossman, 1990; Kleickmann et al., 2013). For TSPK (e.g. introduction to physics education, lesson planning courses) and PK (e.g. introductory courses in educational science, sociology, psychology, pedagogy), several formal learning opportunities exist as well. Even though the focus of teacher education is on formal learning opportunities, pre-service teachers have the possibility to do some classroom observations and even teach their first lessons following the basic lectures. These classroom observations give the pre-service teachers the possibility to look at instructions from the perspective of a pre-service teacher and to learn from the observed teachers, thus combining formal and informal learning for TSPK and PK. Furthermore, the first own teaching experiences can provide more non-formal learning through the support of mentors and university staff members (van Driel et al., 2002). All these different pieces of teacher education contribute differently to the professional development of pre-service teachers.

In a cross-sectional sample of N = 980 mathematic pre-service, training and experienced teachers (Baumert et al., 2010; Kleickmann et al., 2013), the importance of formal learning opportunities to develop CK and TSPK was confirmed, since the development of CK and TSPK happened mostly during teacher education. Furthermore, the number of coursework has been confirmed as a significant predictor for CK and TSPK in multiple cross-sectional studies (Großschedl et al., 2015; Kleickmann et al., 2013; Riese & Reinhold, 2012). The empirical findings regarding the influence of informal and non-formal learning opportunities produce mixed results. Large-scale studies showed no significant increase in CK and TSPK with more teaching experience (Großschedl, Mahler, Kleickmann, & Harms, 2014; Kleickmann et al., 2013; Krauss, Baumert, & Blum, 2008). Smaller case studies on the contrary stressed the importance of reflective practice for the development of PCK (Park & Oliver, 2008; Schneider & Plasman, 2011; van Driel et al., 2002). These mixed results also originate from the aforementioned differences in the perception of PCK as a construct. So far, there are just a few studies investigating the development of PK. Voss et al. (2011) could show in a sample of N = 746 student teachers with little or some teaching experience that the later outperformed the teachers with no experience on their PK measure.

In summary, teacher education provides several learning opportunities for CK, TSPK and PK. Those learning opportunities can be classified in formal, informal and non-formal learning (Kleickmann et al., 2013). Formal learning opportunities are the centre of teacher education but pre-service teachers are also able to experience a combination of formal and informal learning through classroom observations or first teaching experiences. All of these learning opportunities support each of the components of the professional knowledge of pre-service teachers. In addition, the relationships of the components themselves contribute to the development of professional knowledge, because CK and PK are expected to be important factors in the evolution of TSPK. Thus, it is necessary to investigate how the structure of professional knowledge differs across different stages in teacher education as well as which learning opportunities significantly contribute to the level of each component of professional knowledge.

Research questions

The importance ascribed to teacher professional knowledge for the organisation of effective teaching is contrasted by the long-lasting lack of a consistent model. The model of teacher professional knowledge and skill recently proposed by a group of experts in research on science teacher education (Gess-Newsome, 2015; see also Berry et al., 2015) holds the potential to effectively resolve this issue and to create the foundation for research on the development of teacher professional knowledge in (university) teacher education and teacher professional development. It is the purpose of teacher education to provide learning opportunities to develop the ‘knowledge for teachers’ such as CK, PK and TSPK, which are the basis for the development of personal PCK and PCK/Skill. TSPK plays a crucial role since it is expected to be informed by the general knowledge bases such as CK and PK and also provides the resources for future personal PCK and PCK/Skill. While we expect each of the knowledge components to develop during teacher education (Kleickmann et al., 2013), we also expect the structure of the relationship among the three components of pre-service teachers’ professional knowledge to change. More specifically, throughout teacher education, the three components – CK, TSPK and PK – should become increasingly correlated. This process should be driven by a combination of formal and informal learning opportunities.

In our research, we sought to examine the structure of pre-service teachers’ professional knowledge, how it differs across different stages of teacher education and how this process depends on formal and informal learning opportunities. Accordingly, our research was guided by the following questions:

1. What is the relationship among the three components CK, TSPK and PK of pre-service physics teachers’ professional knowledge?

2. How does the relationship among the three components change over the course of teacher education?

3. To which extent does the change depend on formal and informal learning opportunities?

Method

Research context and design

To investigate the structure, the changes in the structure over the course of teacher education and predictors for the different components of professional knowledge of pre-service physics teachers, we conducted a study at 12 major institutes for science teacher education in Germany.

Teacher education in Germany is organised in two phases (Viebahn, 2003). Students aspiring to teach at a German school first complete a teacher education programme at a university. This first phase includes academic training in two subjects (e.g. physics), the respective subject educations (e.g. physics education) and educational sciences. This phase typically takes five years to complete, with a three-year Bachelor and a subsequent two-year Master programme (for details, see Neumann, Härtig, Harms, & Parchmann, 2017). The teacher education in Germany follows the same structure as studies in the sciences and its duration is comparable to other European countries such as Finland or France (see Evagorou, Dillon, Virii, & Albe, 2015) as well as Australia (Treagust, Won, Petersen, & Wynne, 2015). It is therefore different from teacher education programmes that require a bachelor’s degree to apply for a teaching license like in some states in the U.S. (Olson, Tippett, Milford, Ohana, & Clough, 2015). The second phase, the in-service training phase, is a phase of practical training at school. During this phase, trainee teachers teach a reduced number of lessons (compared to regular teachers) across a selection of topics and grades. While university teacher education focuses on developing CK, TSPK and PK as bases of pre-service teachers’ professional knowledge, the in-service training specifically aims at the development of action-oriented abilities such as personal PCK and PCK/Skills. Since the German school system historically relies on tracking, universities offer specific teacher education programmes for teaching at different tracks. Programmes entitling to teach at the highest academic track (i.e. the Gymnasium), typically involve more coursework in the subject matter (i.e. physics). These programmes cover a larger range of content areas for CK. Programmes for the less academic track, however, typically cover a subset of these content areas. This reduction is compensated by an increased amount of coursework in subject education (i.e. physics education) and general pedagogy. To secure the quality of teacher education, the Conference of the Ministers of Education and Cultural Affairs (‘Kultusministerkonferenz – KMK’) developed standards for pre-service teachers’ professional knowledge (KMK, 2004, 2008), which define a ‘common core’ for teacher education.

The study was part of the project ‘Measuring the professional knowledge of preservice mathematics and science teachers’ project’ (German acronym: KiL), which started in 2011 and covers the professional knowledge of pre-service teachers in biology, chemistry, physics and mathematics. The process of instrument development lasted throughout 2012 and involved (1) analysing national documents and curricula from different universities; (2) collection of possible items; (3) a pilot study and (4) expert ratings and think aloud. The final data collection took place during the summer term of 2013 and involved a cross-sectional sample of N = 201 pre-service physics teachers.

Instruments

Our purpose was to measure the three components of pre-service teachers’ professional knowledge to investigate the general structure and the structure at different stages of teacher education. The instrument utilised was developed specifically for this study. In the following, we elaborate on the development of the CK and TSPK tests and provide information on the PK instrument used in the study.

To ensure that the instrument assesses the full range of CK and TSPK covered during university teacher education, we defined an instrument development framework as a basis for instrument development and validation (see Figure 1). This framework was informed by our review of literature on what CK and TSPK pre-service teachers should acquire (see the respective sections in the theoretical background) and an analysis of the syllabi of 16 major German teacher education universities. This model identifies content areas (mechanics, electricity, optics, thermodynamics, solid state physics, atomic and nuclear physics, relativity and quantum mechanics) across which students are expected to develop three types of knowledge (declarative, procedural, and schematic and strategic knowledge, see Shavelson et al., 2005) about four aspects of TSPK (student cognition, instructional strategies, curriculum, and assessment; see Magnusson et al., 1999). Since we aimed to assess CK and TSPK as bases of pre-service teachers’ professional knowledge, we settled for a paper-and-pencil format including a combination of multiple-choice, assignment, true–false, short answer and open-ended items. Item authoring followed a rigorous procedure to ensure reliability and validity (for a discussion of aspects of validity, see Messick, 1995). This procedure included expert ratings, guided interviews, as well as extensive piloting of the items.

Figure 1. Model for item developing.

Instrument development and validation included a total of five steps. In the first step, we build a pool of items assessing pre-service physics teachers CK and TSPK. We began by reviewing items from existing instruments for assessing CK at the college entry level (Ding, Chabay, Sherwood, & Beichner, 2006; Haidar & Abraham, 1991; Hestenes, Wells, & Swackhamer, 1992; Maloney, O’Kuma, Hieggelke, & Van Heuvelen, 2001; Wuttiprom, Sharma, Johnston, Chitaree, & Soankwan, 2009). These items were selected and (when necessary) revised to ensure appropriate fit with the framework for CK (see Figure 1) and thus content validity. For those areas of the framework that could not be covered by existing items, new items were developed. For TSPK, all items had to be newly developed. All new items were developed either by physics researchers (in case of CK) or by physics education researchers (in case of TSPK). In order to also ensure content validity for these newly developed items, detailed guidelines for item construction were provided to the item developers. The guidelines included a detailed description of the framework (for CK or TSPK, respectively), possible item formats together with examples and a step-by-step checklist. In total, 171 CK items 166 TSPK items were collected.

In the next step of the instrument development process, a pilot study was carried out. A total of 84 CK and 79 TSPK items were selected by the authors for inclusion in the study in order to cover each topic (e.g. mechanics), the different aspects of a topic (e.g. acceleration, angular momentum, Newton’s laws) and the different types a pre-service teacher can have (declarative, procedural, schematic/strategic). The items were arranged into two test booklets and piloted with a sample of N _Pilot = 166 pre-service physics teachers from teacher education universities in Germany. To have as many items as possible tested in this step, there was no overlap of items between the booklets. The total working time for each booklet was 240 min. This included collection of additional data concerning demographics, cognitive abilities and learning opportunities. Analysis of the data revealed reliabilities of α = .71 (booklet 1) and α = .77 (booklet 2) for CK, as well as α = .62 (booklet 1) and α = .59 (booklet 2) for TSPK. The correlation between CK and TSPK was r = .41, p < .001 (booklet 1) and r = .41, p < .001 (booklet 2). In line with the theoretical framework, CK and TSPK should be positively related but distinct constructs; therefore, the medium correlation coefficients suggest good structural validity. The correlations with the term of enrolment lay between ρ = .22, p < .05 (TSPK, booklet 2) and ρ = .47, p < .001 (CK, booklet 1). The correlation with the final school grades ranged from ρ = −.19, p = .08 to ρ = −.23, p < .001. (Note: final school grades in Germany range from 4.0 to 1.0 with 1.0 being the highest possible.) These correlations suggest good external validity (again, for a detailed discussion of validity, see Messick, 1995).

The third step of instrument development consisted of an expert review of the items included in the pilot. Since the CK items mostly stemmed from established instruments, expert review was limited to one expert per item. Experts were asked to fill in a rating questionnaire for each item that included questions about item fit to the model and overall item quality. Experts were also provided with the opportunity to provide comments. The questionnaires then served as a basis for discussion amongst the experts and the authors of the study. As a result of this discussion for each item, it was decided whether it would be included as is, revised, or excluded from the study. In case of revisions, the items were revised in a joint effort by the authors and the experts. For the expert review of the 79 TSPK items, 3 science education post-docs and 5 professors with expertise in PCK research were invited for a 2-day meeting. Experts were provided with the discrimination indices and item difficulties obtained in the pilot prior to the meeting for review. During the meeting, for each item, a group consensus was reached to include the item in the instrument, revise it or remove it. These expert ratings indicated good content validity of the instrument.

In the fourth step, guided interviews were carried out to obtain information about the substantive validity of items which exhibited critical discrimination or low student solution rates in the pilot (step 2), but were suggested to be included in the instrument by the experts (step 3). During the interviews (n = 10), pre-service physics teachers were asked to identify words or phrases in the item’s formulation they did not know or understand and to describe how they solved the question. Based on this information, items were revised if possible. If not, the information was considered during the process of selecting the final items for the instrument to be utilised in this study. The fifth and last step was a final revision and subsequent selection of items for the instruments, based on the information obtained during the whole development process. The items were bundled into one booklet. This booklet included a total of 59 CK items and 39 TSPK items. Most CK items were multiple-choice items (55 items), while the final set of TSPK items included 18 open-ended items, 15 multiple-choice items, 2 true–false items, 3 matching items and 1 short answer. Appendix 1 provides two sample CK and two sample TSPK items including the coding scheme and possible answers from pre-service physics teachers.

We used the instrument developed by Hohenstein et al. (2017) to assess the following four components of PK: Learning, Teaching, Classroom Management and General Assessment Strategies. The instrument was developed by experts of educational and psychological research in Germany. The instrument development process followed the same rigorous procedure as the development of the CK and TSPK instruments. A detailed guideline served as a base for item development (including the same item formats as for CK and TSPK), followed by an expert rating to determine if the developed items fit the construct presented in the theoretical framework. After a pilot study with about 500 pre-service teachers of all subjects at one mayor university, the authors revised and selected 64 items including multiple-choice items, true–false items, matching items, short answer and open-ended items. Appendix 1 presents two sample PK items covering the aspect of Learning and Teaching.

In addition to the assessment instruments for the three components of pre-service teachers’ professional knowledge, we administered a questionnaire to gain more insights into the demographic background of the participants such as gender and age, their previous school education and learning opportunities during their time at university (Table 1). The final grades refer to the German ‘Abiturnote’ which is composed of the grades of several subjects during the last years of the high school as well as the grades from the final exams and therefore corresponds to the Grade Point Average (GPA). The final grades represent an overall measure of the intellectual abilities of the pre-service teachers. In our analyses, we further distinguish between two different types of learning opportunities: the general structure of teacher education and the amount of classroom observation and teaching experience. On the one hand, we expect differences between pre-service teachers, who aspire to teach for the non-academic and the academic track due to the differences in content courses (Baumert et al., 2010; Riese & Reinhold, 2010). On the other hand, we also expect a gain in TSPK and PK with a greater experience in actual classroom situations (Schneider & Plasman, 2011). The participants were asked to specify the amount of time spent during general and physics classroom observations (0, 1–2, 3–6, 7–10, 11–15, 16–20, >20 h) and own general and physics teaching experiences (0, 1–2, 3–6, 7–10, >10 h).

Table 1. List of background variables.

Demographic background	Age, gender, etc.
School education	Final grades	Rated from 1.0 (excellent) to 4.0 (passed exams)
Learning opportunities	General study structure	Non-academic track vs. academic track
	Progress in the teacher education programme	Number of terms studied
	Amount of classroom observation	0–20 h of classroom observation, more than 20 h of classroom observation
	Amount of teaching experience	0–10 h of teaching experience, more than 10 h of teaching experience

Participants

Participants were recruited by local science educators in the respective lectures for pre-service teachers. A total of N = 201 pre-service physics teachers participated in the study. One participant had to be excluded from the sample due to invalid data. Thus, the final sample consisted of N = 200 pre-service physics teachers with an average age of 23.7 years (SD = 3.0 years) and 41% female participants. Most participants (71%) were enrolled in the academic track of teacher education. The median number of terms of enrolment was 6 (SD = 2.7 terms) with a range from 1 to 14 terms. In order to characterise the classroom experiences of the participants, we compared the categories chosen for the classroom observation and teaching experiences. About 33% of the participants spent more than 20 hours observing physics classrooms and 10% had more than 10 hours of own teaching experience in physics.

To be able to investigate the structure of professional knowledge across different stages of teacher education, we divided the sample of N = 200 pre-service physics teachers into two groups based on the median number of terms of enrollment. This allowed us to compare the professional knowledge of beginning to the professional knowledge of advanced pre-service teachers. With this cross-sectional design, we are not able to draw any causal conclusion on the development of the professional knowledge bases of pre-service physics teachers, but to investigate differences between different groups as a first indicator for development. We expect these groups to differ in their level of professional knowledge due to the larger amount of learning opportunities during teacher education for the advanced-level students. The median split also provides sufficient sample sizes for a multi-group comparison. However, it should be noted that participants who are relatively similar (e.g. from the 5th and 6th semester) are forced into two different groups by a median split. Since the study took place during the summer term and students usually enter the teaching education programme during the winter term, most students were enrolled either in the 2nd, 4th, 6th, 8th or 10th semester, so the typical difference in experience was one year. The group of beginning pre-service physics teachers consisted of N ₁ = 91 pre-service teachers with a mean experience of 3.2 terms (SD = 1.2 terms) and 36% were female. The second group of N ₂ = 109 advanced pre-service physics teachers studied 7.4 terms on average (SD = 2.0) and 45% of them were female. Beginning students already finished basic courses on content and general pedagogy, but only had few learning opportunities for TSPK or specialised CK. The later terms of teacher education focus more on that special CK and have a strong emphasise on TSPK.

Data collection and analysis

The study lasted 4 hours with two 15 minutes breaks. In a first block, participants had to answer questions regarding the demographic background, motivation, attitudes towards the teaching profession and additional information of attended learning opportunities. To avoid item position effects, two different booklets were randomly assigned. In booklet A, the next section consisted of items regarding CK until the first break. Then, the TSPK items followed until the next break and at the end, the PK items were presented. In version B, the CK and PK parts were interchanged. For the analysis, students’ answers were coded into a data file. Multiple-choice items were scored full credit (1 point) or no credit (0 points), true–false and assignment items were scored as partial credit (1 point per correct answer/assignment) and short answer and open-ended items were scored as partial credit (typically 0, 1 or 2 points depending on the item). In order to obtain information about the reliability of the scoring for short answer and open-ended items, a random subset of 50 booklets (i.e. 25% of the sample) were scored by a second rater. The interrater-reliability by means of Cohen’s kappa shows good to very good agreement between both raters (ϰ_CK = .84, ϰ_TSPK = .73).

To address our research questions, we utilised a structural equation modelling (SEM) approach (Kline, 1998). All analyses were performed using the free software R and the lavaan-package (Beaujean, 2014; Rosseel, 2012). SEMs are a class of statistical models that allow testing theoretical models with empirical data. The theoretical constructs are represented through latent factors, which are responsible for covariation of indicator variables (Beaujean, 2014). We used the sum scores of the different aspects of CK (e.g. mechanics, electromagnetism), TSPK (e.g. knowledge of students’ cognitions, knowledge of instruction) and PK (e.g. classroom management, general aspects of assessment) as indicator variables. The first series of SEMs were calculated to determine the structure of pre-service teachers’ professional knowledge. We specified a unidimensional model, three two-dimensional and a three-dimensional model of professional knowledge. We then compared the fit indices of the different models to investigate the extent to which the three components of pre-service teachers’ professional knowledge indeed represent distinct constructs. In a second step, we separated the sample by the median number of terms to form a group of beginning pre-service physics teachers and another group of advanced pre-service physics teachers. To compare the structure of professional knowledge between these two groups, we had to ensure measurement invariance to see if the instrument works the same in both groups and no construct bias is present (Kline, 1998). To do so, we stepwise increased the number of restrictions in both groups and compared the fit indices of the different models (Beaujean, 2014). The baseline model implies configural invariance, which assumes that the same indicator variables affect the same latent factors. The model of weak measurement invariance additionally restricts the loadings of the indicator variables to be equal across groups. The model of strong invariance also restricts the intercepts to be equal across group and thus assuming that the means of the indicators are equal in both groups, while the latent means still can vary between both groups. Strong measurement invariance is necessary to compare latent means and correlations between groups (Beaujean, 2014). The last step of invariance is strict invariance, which also sets constraints to the error variances in both groups. If one model indicates non-invariance, it is possible to free single parameters to establish partial measurement invariance. When the measurement invariance is established, a comparison of the correlation between the dimensions of professional knowledge across the two different stages of teacher education is possible. In a last step, we specified additional models to gather information on which exogenous variables are responsible for differences in the endogenous latent variables identified in the prior analysis. We computed stepwise models with the information of demographic background, school education and learning opportunities in teacher education such as the number of terms and classroom experiences as exogenous manifest variables. To reduce the number of predictors, we only used the topic-specific classroom experiences for CK and TSPK and the general classroom experiences for PK. To evaluate the model fit, we used the comparative fit index (CFI), which should be above .90, the root-mean-square error of approximation (RSMEA) and the standardised root-mean-square residual (SRMR) (Hu & Bentler, 1998). While a value of RMSEA < .05 indicates a good model fit, Brown and Cudeck (1992) argue that RMSEA < .08 is still sufficient. The SRMR should not extend .08 to a great expense in addition to that (Hu & Bentler, 1998). To compare different models, we also used the χ ² difference test and the Bayesian information criterion (BIC).

Results

In this section, we present our results following our three research questions regarding the structure of pre-service teachers’ professional knowledge, the changes in the structure across different stages of teacher education and potential predictors for differences in the three components of professional knowledge. All three scales show adequate to good reliability (α _CK = .84, α _TSPK = .71, α _PK = .87). Table 2 gives a brief overview of the different subscales we utilised to specify the latent variables, the number of aggregated variables, their means and standard deviation (standardised with the maximum possible scores of the subscales).

Table 2. Number of items, standardised means and standard deviation of indicator variables.

Component	Sub-dimension	Number of items	Mean	Standard deviation
CK α CK = .84	Mechanics	9	.53	.17
	Electromagnetism	8	.50	.19
	Optics	8	.43	.22
	Thermodynamics	8	.52	.22
	Solid state physics	7	.50	.23
	Atomic and nuclear physics	7	.51	.22
	Relativity	5	.45	.23
	Quantum mechanics	7	.42	.25
TSPK α TSPK = .71	Knowledge of students’ cognition	12	.59	.15
	Knowledge of instructional strategies	11	.42	.18
	Knowledge of curriculum	8	.45	.16
	Knowledge of assessment	8	.37	.21
PK α PK = .87	Teaching	14	.62	.11
	Learning	19	.49	.10
	Classroom Management	21	.54	.17
	General Assessment Strategies	13	.43	.21

We used the indicator variables from Table 2 to specify the different models with the different dimensions, which can be found in Table 3. The unidimensional model M1 with all indicators explained by one latent factor shows poor model fit since none of the model fit indices reaches the cut-off criteria (χ ²[₁₀₄] = 287.80, p < .001; CFI = .782, RMSEA = .094, SRMR = .086). The three different two-dimensional models M2a–M2c have as one latent factor one of the components of pre-service teachers’ professional knowledge and another latent factor comprised of a combined factor of the remaining two components of professional knowledge. These models show a better fit than the unidimensional model. However, none of the three models meets the cut-off criteria of CFI < .90 and therefore represents the data well enough. Model M3 with the theoretical expected structure of three latent factors CK, TSPK and PK fits the data relatively well (χ ²[₁₀₁] = 187.22, p < .001; CFI = .898, RMSEA = .065, SRMR = .067) and has the lowest BIC of the tested models. We therefore assume that the professional knowledge of pre-service physics teachers has the three-dimensional structure proposed in our theoretical framework. The final model M3 is displayed in Figure 2 with standardised path coefficients.

Figure 2. Three-dimensional model of professional knowledge with standardised path coefficients and latent correlations.

Table 3. Model fit indices for different latent factor models of professional knowledge.

Model	χ ^2	df	CFI	RMSEA	SRMR	BIC
M1 – unidimensional	287.80***	104	.782	.094	.086	13,785
M2a – CK&TSPK + PK	231.03***	103	.848	.079	.077	13,734
M2b – CK&PK + TSPK	279.44***	103	.791	.093	.086	13,782
M2c – CK + TSPK&PK	213.29***	103	.869	.073	.075	13,715
M3 – CK + TSPK + PK	187.22***	101	.898	.065	.067	13,700

Note: ***p < .001, CFI: comparative fit index, RMSEA: root-mean-square error of approximation, SRMR: standardised root-mean-square residual, BIC: Bayesian information criterion.

The three dimensions of pre-service teachers’ professional knowledge also share a significant amount of variance. The latent correlation between PK and TSPK with r _PK–TSPK = .81, p < .001 and between CK and TSPK with r _CK–TSPK = .78, p < .001 are both equally high. The correlation between CK and PK is also moderately high with r _CK–PK = .54, p < .001. The three dimensions are therefore closely related but still empirically separable. Furthermore, the close relationships of CK and TSPK as well as PK and TSPK support the assumptions that TSPK is indeed an amalgam of both components.

To investigate differences in the three-dimensional structure across different stages of teacher education, we divided our sample into a group of beginning pre-service physics teachers and another group of advanced pre-service physics teachers. To compare structural differences in both groups, we first need to establish measurement invariance to ensure the comparability of our measurement instrument. Table 4 contains the summary of the different levels of measurement invariance with stepwise increasing constraints across both groups. The configural invariance model (χ ²[₂₀₂] = 276.20, p < .001; CFI = .904, RMSEA = .061, SRMR = .078) as well as the model for weak invariance with fixed loadings (χ ²[₂₁₅] = 292.52, p < .001; CFI = .899, RMSEA = .060, SRMR = .086) both indicate a good model fit across the groups. The BIC of the weak invariance model is also lower than the configural invariance model and the χ ² difference test also implies weak measurement invariance (Δχ ² = 16.32, Δdf = 13, p = .23).

Table 4. Model fit indices for different levels of measurement invariance between beginning and advanced pre-service physics teachers.

Model	χ ^2	df	CFI	RMSEA	SRMR	BIC
Configural invariance	276.19***	202	.904	.061	.078	13,955
Weak invariance	292.52***	215	.899	.060	.086	13,903
Strong invariance	319.93***	228	.881	.063	.090	13,861
Partial strong invariance	306.63***	226	.895	.060	.088	13,859
Partial strict invariance	324.20***	242	.893	.058	.092	13,791

Note: ***p < .001, CFI: comparative fit index; RMSEA: root-mean-square error of approximation; SRMR: standardised root-mean-square residual; BIC: Bayesian information criterion.

The model for strong invariance with loadings and intercepts restricted between groups fails the CFI-cut-off value of .90 and also the χ ² difference test favours the weak measurement invariance model (Δχ ² = 27.41, Δdf = 13, p = .01). This result indicates significant differences in the means of the sub-dimensions between the groups. Therefore, we compared the differences of the means of the sub-dimensions between beginning and advanced pre-service physics teachers. We recognised big differences on the optics sub-dimension (M ₁ = 2.77, M ₂ = 3.95, d = .70) and on the solid state physics sub-dimension (M ₁ = 2.93, M ₂ = 4.02, d = .72). We allowed the intercepts of these two indicator variables to vary freely between the two groups to establish partial strong measurement invariance (χ ²[₂₂₆] = 306.63, p < .001; CFI = .895, RMSEA = .060, SRMR = .088). This led to an improvement of model indices and the χ ² difference test favours partial strong invariance (Δχ ² = 14.12, Δdf = 11, p = .23). The model of partial strict invariance with varying intercepts of the optics and solid state physics indicators but fixed error variances across the two groups shows acceptable model fit (χ ²[₂₄₂] = 324.20, p < .001; CFI = .893, RMSEA = .058, SRMR = .092), the lowest BIC of all models and an improvement in the χ ² difference test as well (Δχ ² = 17.57, Δdf = 16, p = .35). In summary, it was possible to ensure strict measurement invariance between beginning and advanced pre-service physics teachers, except for differences between the intercepts of the optics and solid state physics subtests. This enables a comparison of the means and correlations between the latent factors of the two groups to gain insight into the differences in the structure of the three components of professional knowledge across different stages of teacher education.

First, the group of advanced pre-service teachers shows higher means on all three latent factors (CK: .56, TSPK: .64, PK: .37) in comparison to the beginning pre-service teachers. Thus, the group comparison not only considers different stages of teacher education but different groups of ability. Second, the correlations among the three latent factors are shown for both groups in Table 5. While we found a high correlation between CK and TSPK and PK and TSPK in the overall model (Figure 2), we see a remarkable shift between beginning and advanced pre-service physics teachers. The correlation of CK and TSPK in the beginner group increases from .60, p < .01 to a high value of .89, p < .001 in the advanced pre-service teachers group. We also observe the reverse effect with the correlation of PK and TSPK. Both components are strongly connected in the beginner group with a correlation of .94, p < .001, which decreases to a still important but smaller correlation of .69, p < .001 for more experienced pre-service physics teachers. While the TSPK of beginning pre-service teachers is closely related to PK, more advanced pre-service students integrate CK and TSPK more and more.

Table 5. Latent correlation matrix among the three different dimensions of professional knowledge for beginning and advanced pre-service physics teachers.

	Beginning pre-service teachers			Advanced pre-service teachers
	CK	TSPK	PK	CK	TSPK	PK
CK	–			–
TSPK	.60**	–		.89***	–
PK	.57**	.94***	–	.47**	.69***	–

Note. ***p < .001, **p < .01.

To answer our third research question, we specified several different exogenous manifest variables, which might be responsible for differences in the latent constructs. We expected that the personal background such as gender and final school grades as well as the general structure of teacher education and specific formal, informal and non-formal learning opportunities affect the three components of pre-service teachers’ professional knowledge. A summary of the regression models can be found in Table 6. The sample size for this analyses consists of N = 199 participants due to one invalid final school grade. In a first step, we used the demographic and school background data to predict CK, TSPK and PK. For all three models, the final school grades become highly significant (β _CK = −.54, β _TSPK = −.41, β _PK = −.35, all at p < .001 level). Despite the fact that male pre-service teachers show higher CK (β = .21, p < .01), gender has no significant influence on TSPK or PK. The first regression model already accounted for a significant amount of variance especially for the latent CK variable ($R_{\mathrm{CK}}^2=.32$) but also for TSPK ($R_{\mathrm{PCK}}^2=.17$) and CK ($R_{\mathrm{PK}}^2=.14$). In a second step, we controlled for two different learning opportunities in teacher education: number of terms and whether pre-service physics teachers aspired to teach at the non-academic or academic track. The influence of gender on CK and of the final school grades on all three latent factors remain nearly the same. The number of terms has a significant impact for all three latent variables (β _CK = .37, p < .001; β _TSPK = .30, p < .001 and β _PK = .24, p < .01). However, the general study structure of non-academic track and academic track pre-service teachers has no significant influence on TSPK and PK and only a small significant influence on the level of CK (β _CK = .14, p = .044). Including the amount of experience in teacher education via the number of terms raises the explained variance for all three constructs ($R_{CK}^2=.49,R_{\mathrm{TSPK}}^2=.26,R_{\mathrm{PK}}^2=.19$ ). The third and final model included variables that controlled for the amount of classroom observation and own teaching experiences. While we expected that CK and TSPK should be influenced through topic-specific experiences, for PK, all teaching experiences should support the knowledge acquisition. Participants differed in all three knowledge bases if they had more than 20 hours of physics-related or general classroom observations (β _CK = .14, p = .041; β _TSPK = .16, p = .041 and β _PK = .17, p = .020). It is also important to note that by controlling the number of terms in teacher education the teaching experience showed no significant effect on the three latent constructs. The final regression model of pre-service physics is able to explain an important amount of pre-service physics teachers’ CK ($R_{\mathrm{CK}}^2=.51$), TSPK ($R_{\mathrm{TSPK}}^2=.31$) and PK ($R_{\mathrm{PK}}^2=.23$). Concluding the analysis, we were able to identify different sources for development of pre-service teachers’ professional knowledge in the final school grades, the number of terms and the amount of classroom observation.

Table 6. Regression models to predict differences in CK, TSPK and PK.

	CK	TSPK	PK
First step	R² = .32	R² = .17	R² = .14
Gender	.21**	.00	−.10
Final school grades	−.54***	−.41***	−.35***
Second step	R² = .49	R² = .26	R² = .19
Gender	.20**	.01	−.09
Final school Grades	−.44***	−.39***	−.33***
Number of terms	.37***	.30***	.24**
Academic track	.14*	−.04	−.04
Third step	R² = .51	R² = .29	R² = .22
Gender	.19**	.01	−.09
Final school grades	−.42***	−.37***	−.31***
Number of terms	.32***	.23*	.22**
Academic track	.13^+	−.05	−.02
>20 h of general classroom observations	–	–	.17*
>20 h of physics classroom observations	.14*	.16*	–
>10 h of general teaching experience	–	–	−.08
>10 h of physic teaching experience	−.04	.05	–

Note: ***p < .001, **p < .01, *p < .05, ⁺ p < .10; Gender: 0 – female, 1 – male; Academic track: 0 – non-academic, 1 – academic; hours of classroom observation/teaching experiences: 0 – no, 1 – yes. All variables standardised.

Discussion

It is the goal of every teacher education to provide future science teachers with the necessary tools to construct meaningful learning opportunities for students. Following the vision of Shulman (1987) and Grossman (1990), a sound professional knowledge is necessary for all teachers to obtain. There is a particular consensus amongst science education researchers that such professional knowledge includes content knowledge (CK), topic-specific professional knowledge (TSPK – also known as the ‘PCK for teachers’) and pedagogical knowledge (PK) (Gess-Newsome, 2015). However, research investigating how these three components unfold during teacher education is very rare (cf. Großschedl et al., 2015; Riese & Reinhold, 2010). In order to investigate the structure of pre-service teachers’ professional knowledge at different stages in teacher education, we developed an instrument which covers the core aspects of each dimension and also the breadth and depth of the knowledge bases necessary for teaching (Gess-Newsome, 2015). After several steps of piloting the developed items, we administered the final instrument consisting of 59 items for CK, 39 items for TSPK and 67 items for PK to a nationwide sample of N = 200 pre-service physics teachers and computed a series of structural equation models to investigate the structure, the differences of structure across different stages of teacher education and possible predictors for differences in each component of professional knowledge.

A three-dimensional model fitted the data relatively well, so that we can assume the three components of pre-service teachers’ professional knowledge to represent distinct constructs. Even though the three dimensions were separable, we found significant high latent correlations between pre-service physics teachers’ CK and TSPK (r _CK–TSPK = .78, p < .001) and between PK and TSPK (r _PK–TSPK = .81, p < .001). Our results show higher correlation than in the sample of N = 436 German pre-service physics teachers of Riese and Reinhold (2012), who found significant latent correlations of r _CK–TSPK = .68 and r _PK–TSPK = .61. However, it is difficult to compare both results since Riese and Reinhold (2012) focused solely on the topic of mechanics in assessing CK and had a strong emphasis on the use of experiments in physics instructions for TSPK. In addition to the results from the domain of physics, Großschedl et al. (2015) also report a high significant latent correlation between CK and TSPK (r _CK–TSPK = .68) but a considerable smaller correlation between PK and TSPK (r _CK–TSPK = .35) for pre-service biology teachers. Again, conceptual differences for PK might be a reason for differences. Großschedl et al. (2015) focused on the two PK aspects Learning and Teaching but did not include the central aspects of Classroom Management and General Assessment Strategies. We therefore consider our work as an extension of the existing literature by investigating the breadth of each dimension of pre-service teachers’ professional knowledge. Despite those fundamental differences in the conceptualisation of pre-service teachers’ professional knowledge bases, the similarities of the structure support the assumption of a three-dimensional model.

By dividing our sample into groups of beginning and advanced pre-service physics teachers, we found evidence that the overall structure is not stable but different at different stages of professional education. With the establishment of partial strict measurement invariance for both groups, we ensured that the instrument works the same in both groups and is therefore no cause for differences in the correlation patterns. Since the results arise from a cross-sectional comparison of groups, their composition might potentially be another reason for the observed differences in correlation. However, both groups do not differ in the distribution by gender (χ ²(1, N = 200) = 1.55, p = .21) or the final school grades (t(198) = 0.83, p = .41). Still, the median split might underestimate some of the differences between the two groups since relatively similar participants are separated into two different groups. We noted a shift in the correlation of the three dimensions from one group to the other. Beginning pre-service physics teachers show a very high latent correlation between PK and TSPK of r _PK–TSPK = .94, p < .001 which decreases to (a still high) r _PK–TSPK = .69, p < .001 for advanced pre-service physics teachers. This result aligns well with the structure of formal learning opportunities in the German teacher education system. Despite a strong focus on content courses at the beginning, pre-service teachers also visit lectures on the fundamentals of general pedagogy while the formal learning opportunities for pedagogical content knowledge are very few and usually take place much later in teacher education. Even though the reasons for this shift cannot be answered surely with our data, Friedrichsen et al. (2009) observed a similar phenomenon in her case study of four teachers without formal learning opportunities. These teachers relied heavily on their general PK when planning lessons and showed little knowledge of domain-specific PCK. Since PCK is the main source for planning and reflecting lessons (Gess-Newsome, 2015), we can observe the same pattern in our study. Pre-service teachers at the beginning of their teacher education seem to rely more on a general pedagogical understanding when answering TSPK items. Additionally, we found a similar shift in the correlation of CK and TSPK. The correlation increased from a moderate r _CK–TSPK = .60, p < .01 in the beginning pre-service teachers group to a very high r _CK–TSPK = .89, p < .001 in the advanced pre-service teachers group. Advanced pre-service teachers had more formal learning opportunities on CK and also TSPK which could lead to an increase in the integration of both components. Content knowledge is considered a prerequisite for the development of TSPK (Kind, 2009; Schneider & Plasman, 2011). Furthermore, research in mathematics showed a significant increase in the correlation of CK and TSPK with a higher level of expertise for in-service mathematics teachers (Krauss, Brunner, et al., 2008) as well. The level of TSPK of pre-service teachers therefore might first allude to general PK and with an increase in formal learning opportunities for CK to integrate this component more and more.

Finally, our regression analyses show that a considerable amount of variance in the three dimensions of pre-service teachers’ professional knowledge can be explained by background variables of the pre-service teachers and even with the addition of the number of terms and other possible influencing factors, the final school grade remains the single most important factor. Besides that, the number of terms as an indicator for formal learning opportunities led to an improvement in the prediction of CK, TSPK and PK. It should be noted that the effect of the number of terms is considerably smaller on TSPK and PK in comparison with CK. One reason might be that while the CK taught is mainly canonical at all universities in Germany, the formal learning opportunities for TSPK and PK might take place at different times with different focuses. Future longitudinal studies could provide more detailed insights when controlling for the different learning opportunities at different universities. The influence of the formal learning opportunities declined when more informal learning opportunities were included in the regression model. For general PK, pre-service teachers with more than 20 hours of general classroom observations showed significant higher scores on the latent factor. The same results can be found for CK and PCK with observations in physics classrooms. Classroom observations are part of various types of internships as part of the formal teacher education. It is usually accompanied by different observation tasks. Thus, the learning opportunity is implemented in a formal context and also provides informal learning through the observation of instructions from various teachers. However, pre-service teachers with more than 10 hours of own teaching experience had no additional significant higher professional knowledge compared to teachers with 10 hours or less teaching experience. The sole number of hours of teaching experience seems not sufficient to predict the development especially for TSPK (Friedrichsen et al., 2009). There are several moderating factors that support growth of PCK through teaching experience. Possible moderating influences are the assigned mentors (van Driel et al., 2002) and most importantly, the reflection of the experiences (Park & Oliver, 2008). Additionally, our instrument represents the professional knowledge bases of pre-service teachers and therefore is from different nature compared to the personal PCK or PCK/Skill constructs, which are expected to rely more on teaching experiences (Gess-Newsome, 2015). Future research should therefore broaden the perspective on the influence of different learning opportunities on more action-related aspects such as personal PCK and PCK/Skill.

Conclusion and implications

Our results suggest that teacher education not only needs to focus on formal learning opportunities, which are necessary for developing the CK required for an advanced understanding of TSPK, but also to attend to different types of learning opportunities like observing expert teachers. Classroom observations and reflections can support the development of all three knowledge bases and hence enable pre-service physics teachers to gain an integrated understanding on the planning and enactment of teaching. It is necessary, though, to further investigate the development of all three components and their relationship in real longitudinal settings. The professional knowledge bases are seen as an important factor in developing personal PCK and PCK/Skill (Gess-Newsome, 2015). To enable future teachers to develop a rich repertoire of planning, teaching and reflecting skills, a broad theoretical foundation in all three dimensions of professional knowledge is necessary (Shulman, 1987). The study presents important evidence that the relationship amongst the central components of pre-service teachers’ professional knowledge evolves during teacher education. Especially TSPK, the important precondition for planning, enactment and reflection of teaching changes its connotation from a more general pedagogical understanding to a content-oriented understanding. Future research needs to validate the relationship of theoretical knowledge and personal knowledge by combining multiple measurement tools. The data from paper-and-pencil tests need to be combined with additional qualitative data from actual teaching in a combined study design. It is crucial to further investigate the development of professional knowledge of pre-service physics teachers to enable them to create high-quality science instructions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Stefan Sorge http://orcid.org/0000-0001-9915-228X

Additional information

Funding

This study is a part of the ‘Measuring the professional knowledge of preservice mathematics and science teachers’ project’ (German acronym: KiL), which is funded by the Leibniz Association (Project No. SAW-2011-IPN-2) and is carried out by the Leibniz Institute for Science and Mathematics Education (IPN) in cooperation with the Psychology for Educators work group at Kiel University.

Appendix 1

Sample CK items

Mechanics

Table

Solid state physics

Table

Sample TSPK items

Knowledge of students’ understanding

Table

Table

Scoring Rubric	Sample answers
Full Credit (1): One of the following two solutions or a similar solution is provided: i) Force vector in the direction of movement; there needs to be a force ‘responsible’ for the movement, ii) Force vector in the direction of the resultant force; instinctive drawing of a parallelogram of forces.	[Force vector to the right] There must be a force acting to the right, in order to make the body move to the right. [Force vector in the direction of the resultant force] Since F2 is larger than F1, the ball will fly into this direction. [Force vector upwards] The vector sum of all forces must point in the direction of movement.
No Credit (0): No solution or a solution other than the above solution or a similar solution is provided	[Force vector pointing left] Resistance of the air. Students think in two dimensions. [No force vector] m is moving into the direction of F_2 since F_2 is larger (longer vector). [Force vector to the right]. The body is moving to the right. The direction of movement of v.

Knowledge of curriculum

Table

A spiral curriculum refers to the repeated coverage of contents at increasingly sophisticated levels of elaboration in higher grades. Electricity for example is taught in primary, middle and high school. Name electricity contents from primary, middle and high school ordered based on the idea of a spiral curriculum.

Table

Scoring Rubric	Sample answers
Full Credit (1): One of the following sequences or a similar one is provided: Conductors/Isolators (4), Ohm’s law (8), band model (12) Light bulb as appliance (4), energy transformation in the light bulb (8), efficiency of a light bulb (12) Light bulb as an element (4), ohmic resistance as an element (8), coil as an element of the electric circuit (12) Simple electric circuit (4), branched circuits (8), oscillating circuits (12) Magnets (4), magnetic field lines (8), magnetic Field, electromagnetism (12)	Grade 4: Glowing light bulb, switches; Grade 8: Current, Voltage (Variables); Grade 12: Hall Effect 4: Electric circuits; 8: Induction; 12: Electrical field 4: Metal conducts current. 8: Different metals conduct the current differently (resistance); 12: Semi-conductors 4: Electric circuits; 8: Resistors, electric components. 12: complex circuits
No Credit (0): No sequence, incomplete sequence or sequence other than the above sequences or a similar sequence is provided.	Grade 4: Units, Variables in electricity; Grade 8: conducting of experiments; Grade 12: electricity in relation to the atom 4: What conducts current?; 8: Conductors and isolators; 12: When does a substance conduct currents?

Sample PK items

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