Pedagogical knowledge in English language teaching: A lifelong-learning, complex-system perspective

Pedagogical knowledge has been the subject of theoretical and empirical studies. However, no research has so far integrated the existing scholarship with data to develop and validate a framework for pedagogical knowledge in English language teaching informed by lifelong-learning, complex-system perspectives. In the absence of such research, we used a mixed method research design through a systematic review of the literature, semi-structured interviews with experienced teachers (N=10) and teacher educators (N=10), as well as a survey of 336 practising teachers in Iran to: (1) develop a framework for pedagogical knowledge; and (2) validate this framework by designing a self-assessment questionnaire for pedagogical knowledge. Our analyses yielded a nine-component model that included: knowledge of subject matter; knowledge of teaching; knowledge of students; knowledge of classroom management; knowledge of educational context; knowledge of democracy, equity and diversity; knowledge of tests/exams; knowledge of learning; and knowledge of (professional) self. Within this nine-factor framework, each component of pedagogical knowledge consists of a number of subcomponents. The proposed framework highlights the multidimensionality and complexity of pedagogical knowledge, and the mutually constitutive relationships among different knowledge domains.


Introduction
Despite substantial research on teaching over the past few decades, studies of teaching remain largely patchy and disjointed, leading to what Cochran-Smith and Villegas (2015: 8) have described as a 'sprawling and uneven field'. Strands of teaching and teacher education research have traditionally examined discrete elements such as pedagogical knowledge, pedagogical knowledge acquisition, pedagogical knowledge development and professional learning, often in the absence of a broader agenda that can help connect the siloed body of work in these areas of interest. Teaching and teacher education research has also been slow in utilizing the rich and growing body of scholarship that explores the complex and lifelong processes involved in learning, including in learning to teach. This has resulted in often reductionist views about what teaching, teaching knowledge and learning to teach entails.
This article synthesizes bodies of work in studies of teaching to bridge the boundaries between research on theories of learning to teach as a lifelong process and conceptualizations of pedagogical knowledge as a complex system. In so doing, we seek to fill a theoretical lacuna relating to the problem of 'construct under-examination' in teacher cognition research (Burns et al., 2015). While pedagogical knowledge has been the subject of studies, the construct still remains in need of theoretical development, analytic clarification and empirical examination (Loewenberg Ball et al., 2008). No research has so far offered an integrative account of pedagogical knowledge informed by lifelong-learning and complex-system perspectives. To address this gap, we draw on the existing literature and collected data to: (1) develop a conceptual framework for pedagogical knowledge; and (2) assess the construct validity of this framework by analysing data gathered through a survey of 336 practising teachers. Our model development and validation follow three interrelated stages. First, we conceptualize 'pedagogical knowledge' using lifelong-learning, complex-system perspectives. Then, we draw upon our conceptualization to identify the relevant literature and propose a tentative framework for pedagogical knowledge. Finally, we complement the framework with collected data and use it as a basis for model validation. Underpinning our conceptualization and model development effort is the premise that pedagogical knowledge is complex, context-responsive and evolves over time. Such an understanding helps acknowledge the fluid and ever-evolving nature of pedagogical knowledge in teaching. It also helps highlight the active, creative and constructive role that teachers play in the formation of their pedagogical knowledge through formal/informal learning opportunities, professional development and reflective practices.
A conceptualization of pedagogical knowledge along the lines that we have delineated above requires us to interrogate some of the categorical assumptions that are often made about knowledge in teacher education literature. This involves moving beyond the familiar dichotomies of knowledge as theories, knowledge as beliefs and knowledge as abilities (Woods and Çakır, 2011). Instead, pedagogical knowledge should be viewed as an integrative concept 'summarizing a large variety of cognitions, from conscious and well-balanced opinions to unconscious and unreflected intuitions' (Verloop et al., 2001: 446). This, in turn, leads to considerations of ontological, epistemological and methodological questions relating to articulated, embodied and/ or enacted forms of knowledge in teaching, and the ways in which such knowledge can be best brought together and mapped conceptually.
There are two main advantages in adopting a complex-system, lifelong-learning approach to pedagogical knowledge. First, complex-system theory and lifelonglearning perspectives can deepen our understanding of knowledge as a dynamic construct with multiple and mutually constitutive dimensions that remain in an everevolving state of becoming. Within a complex-system, lifelong-learning framework, all forms of articulated, embodied and enacted knowledge become inextricably intertwined and together constitute the totality of teachers' knowledge base. This can be particularly useful in reducing some of the existing complexities around the meaning(s) of pedagogical knowledge which, as Borg (2003) has suggested, are partly caused by the assemblage of terms and concepts in this area of teacher education research. Defined through a complex-system, lifelong-learning framework, pedagogical knowledge cross-cuts the analytical boundaries drawn among theoretical, personal and practical forms of knowledge.
Pedagogical knowledge: A complex-system, lifelong-learning perspective Discussions of teaching underwent a substantial shift during the late 1970s and early 1980s. This period marks the end of what is referred to as the process-product paradigm of research on teaching. With their root in positivism and behavioural psychology (Johnson, 2009), process-product studies helped capture observable dimensions of teaching. However, these studies failed to account for the judgements, reasonings and decision-making processes that teachers undertake in their practices. The inadequacy to explain the hidden and cognitive aspects of teaching ultimately led to the demise of the process-product research. Studies of teaching took a socio-cognitive turn and brought issues of context and cognition to the centre stage of teaching research. Subsequently, teachers came to be viewed as 'active, thinking decision-makers who make instructional decisions by drawing on complex practically-oriented, personalized, and context-sensitive networks of knowledge, thoughts, and beliefs' that evolve over time (Borg, 2003: 81). Walberg's (1977) notion of teachers' mental lives marks a shift in thinking about teaching as a dynamic process of reasoning and decision-making. Within the emerging line of research, one area that became the subject of theoretical and empirical studies was teachers' knowledge base. Interest in understanding what constitutes knowledge in teaching, which threads through teacher education research until now, has given rise to numerous terms, each highlighting a particular dimension of teachers' knowledge. Among the multiplicity of terms, one can refer to practical knowledge (Elbaz, 1983), personal practical knowledge (Clandinin, 1986;Golombek, 1998), pedagogical content knowledge (Shulman, 1986), pedagogical maxims (Richards, 1996) and more recently pedagogical knowledge base (Gatbonton, 2000;Mullock, 2006).
Despite the growing body of scholarship on pedagogical knowledge, part of the limitations of existing research in teaching to date is the way in which pedagogical knowledge is conceptualized either as a discrete construct with clear-cut boundaries or as a finished product that remains uniform across time, space and social context. This is partly due to outcome-orientated and universal tendencies in conceptualizations of knowledge. In the absence of an integrative approach that examines how teachers' personal biographies may interact with the institutional, social, cultural and political factors to mediate their knowledge, we find Buehl and Fives's (2016) definition of 'epistemic cognition' in teacher learning and praxis a more conducive way of looking at pedagogical knowledge and its development. Epistemic cognition is a processorientated way of thinking about teacher learning and knowledge, and considers a variety of factors, including the task at hand, teachers' domain of experience, prior knowledge and existing beliefs, alongside practical experiences.
Understanding teachers' cognitions, Burns et al. (2015: 597) maintain, 'as situated, dynamic, mediated, and inherently complex, shifts us toward a complex, chaotic systems ontology'. Complexity theory has been increasingly drawn upon in education literature to provide a more nuanced explanation of the interplay between various factors impacting on teachers' work and the interactive cognitions that emerge from working in a diversity of contexts. Kiss (2012) maintains that complex systems have characteristics such as sensitivity to initial conditioning, unpredictability, nested structures, non-hierarchic network systems, use of feedback loops and self-organization. A complex-system approach has been used to highlight teacher cognition as dynamic and co-adaptive systems (Feryok, 2010) that are contingent upon interactions between belief systems, context and practices (Zheng, 2013(Zheng, , 2015 and that mediate teacher learning and professional development (Opfer and Pedder, 2011).
A second, and related, limitation of current conceptualizations is the way in which pedagogical knowledge is often perceived as a construct that remains uniform across the life-course. This is reflected in research that provides snapshots of knowledge with little attention to the processes of knowledge development. More recently, there has been greater acknowledgment of the multilevel and multidimensional nature of teacher learning, which involves cognitive, emotional and motivational aspects of learning to teach spread across teachers' personal and professional lives (Korthagen, 2017). Schwille et al. (2007) use the term 'continuum of teacher learning' to highlight the lifelong processes of learning to teach. Continuum of teacher learning implies a concern not only with formal teacher preparation, induction and professional development, but also with other informal influences on how and what teachers learn.
The learning journey towards becoming a teacher starts with what Lortie (1975) describes as apprenticeship of observation, which refers to the influences on teachers' perceptions of effective pedagogies from their own years of schooling as students. Apprenticeship of observation is complemented by formal pre-service education that offers opportunities for structured learning believed to contribute to the acquisition of conceptual-theoretical knowledge about teaching (Watzke, 2007). Other phases in the continuum of teacher learning include induction and/or placement and continuing professional development opportunities, which are looser in arrangement and that can occur in less formal and structured ways through communities of practice, everyday interactions with colleagues and/or via reflective practices that help revisit long-held assumptions and beliefs.
The multiplicity of sources that contribute to teachers' learning prompts our attention to the ongoing and open-ended processes by which teachers develop their individual, self-directed modes of learning in response to the particularities of their life situations (Su et al., 2018). It is within this broad spectrum of lifelong learning to teach that teachers, as active and reflective practitioners, build their interactive cognition and develop, amend and revisit their pedagogical knowledge. Conceptualizations of pedagogical knowledge, therefore, need to account for the evidence base that points to the complexities and dynamics of pedagogical knowledge and the multilevel and multidimensional processes of learning to teach.

Procedure
Initial conceptualization is an important step in model development and helps set the parameters for the later stages (Jakeman et al., 2006). We therefore used the conceptual definition of knowledge delineated above as the starting point for developing a tentative framework that can map out the complex interconnections between different dimensions of the construct. We derived our definition of pedagogical knowledge from earlier work that points not only to the bodies of knowledge 'about the act of teaching, including goals, procedures, and strategies that form the basis for what teachers do in classroom' (Mullock, 2006: 48), but also to the accumulated knowledge about content, culture and political context (Akbari and Dadvand, 2014). The standard procedure for model development follows from conceptualization to the review of the literature (Dörnyei, 2003). To this end, we examined existing studies of pedagogical knowledge. Given that some aspects of pedagogical knowledge are specific to learning areas, we focused on the literature review on English language teaching. This was done by searching the archives of the education databases of ERIC, EBSCO, SAGE and Education Research Complete. The multidisciplinary databases of ScienceDirect and ProQuest, as well as the major academic journals, were also searched to ensure relevant studies were included in our literature review.
Eligibility criteria included both conceptual and empirical studies of teaching knowledge in the broader field of teacher education, and within the subfield of English language teaching. Inclusion criteria also included peer-reviewed articles, reports, policy documents, books and book chapters that were written in English on the topic. The following terms were used in the database search: 'pedagogical/teaching knowledge', 'knowledge base', 'teacher expertise', 'teacher cognition', 'pedagogical beliefs', 'teaching beliefs', 'teaching expertise', 'teaching effectiveness', 'lifelong learning in teaching', and 'complex system in teaching'. The broad initial inclusion criteria allowed for identifying a relatively large number of studies. A subsequent exclusion criterion was applied to remove studies that were either 'incomplete', followed 'ambiguous methodologies' or had little 'content relevance'. This led to a shortlist of 236 publications that dealt specifically with different dimensions of knowledge in teaching.
In the next step, the identified studies were analysed to map out the area(s) of pedagogical knowledge. These knowledge areas were then used to draw conceptual boundaries among the key domains of pedagogical knowledge. These conceptual boundaries later became the basis of a tentative ten-component framework. Within this tentative framework (see Table 1), each component of pedagogical knowledge contained a set of subcomponents that together constituted separate, yet interdependent, domains of pedagogical knowledge, including: knowledge of subject matter; knowledge of culture and cultural differences; knowledge of students; knowledge of learning; knowledge of teaching; knowledge of tests/exams; knowledge of classroom management; knowledge of educational context; knowledge of democracy, equity and diversity; and knowledge of professional self. Qualitative data were collected in an effort to review, complement and consolidate the structure of the initial framework. We conducted semi-structured interviews with two groups of participants: ten experienced English teachers and ten subject matter experts (SMEs). These two participant groups were deemed suitable for their expert opinion and evaluative reflections on the initial conceptualization. First, ten experienced English language teachers, teaching in two private language institutes across Tehran, Iran, were invited to take part in semi-structured, reflective interviews using convenient sampling technique. These participants, seven males and three females, had a range of teaching experience from 5 to 12 years, and all had graduate degrees in English teaching. Ten SMEs were also invited to participate, using snowball sampling technique. These were university lecturers and teacher educators with the main responsibility of delivering undergraduate/graduate coursework and supervising practicum in teacher education programmes. Of these participants, six were male and four were female, with 4 to 11 years of teaching experience from four universities and institutes of higher education that provide master's of English language teaching in Tehran. Both experienced English teachers and SMEs were invited to take part in the study, and were informed about the aims of the research before participating in the interviews.
The semi-structured interviews with the experienced teachers and the SMEs lasted between 32 and 97 minutes. The interviews: (1) probed into the participants' perspectives regarding important areas of pedagogical knowledge for teachers; and (2) elicited their reflective feedback on the initial conceptualization of pedagogical knowledge. The interviews were transcribed and analysed to identify any additions to the components and subcomponents of knowledge. The analysis of the teachers' data pointed to six components of knowledge: knowledge of content, knowledge of teaching, knowledge of learning, knowledge of classroom management, knowledge of students, and knowledge of culture. The interview data from the SMEs pointed to seven components: knowledge of content, knowledge of teaching, knowledge of learning, knowledge of classroom management, knowledge of students, knowledge of culture, and knowledge of context. In both cases, each component of knowledge consisted of a number of subcomponents, summarized in Table 2. In the last stage of the model development phase, the components and subcomponents of pedagogical knowledge that emerged from the analyses of the interview data were triangulated with those of the tentative framework developed from the literature. Overall, this triangulation confirmed the structure of the initial model, but did not add any new elements to the framework. Therefore, we proceeded to model validation using the framework of pedagogical knowledge that had emerged from the review of the literature.

Model validation
A self-assessment questionnaire was developed in order to examine the construct validity of the framework. The questionnaire was piloted with a random sample of 40 teachers from two private language institutes in Tehran who were invited to participate in the research. Once the reliability of the questionnaire was established (Cronbach alpha coefficient: 0.91), we distributed 600 questionnaires to a random sample of practising English language teachers at different institutes, schools, and centres of higher education in Tehran and four other provinces across the country. Both face-to-face methods and emails were used to invite participants. The participants were informed of the purpose of the study, the right to voluntary participation and possible withdrawal, as well as the confidentiality/anonymity of their responses. Of the 600 invited participants, 382 filled out and returned the questionnaire (a return rate of 64 per cent). Upon initial inspection, 46 questionnaires were discarded because they either had missing items or incomplete information. This left 336 questionnaires for model validation. Our model validation framework included three phases of exploratory data analysis (EDA), confirmatory data analysis (CDA) and model evaluation (Figure 1).

Figure 1: Three stages of EDA, CDA and model evaluation used in model validation
The SMEs were also consulted during the model validation phase. This helped us examine the conceptual integrity of the model at each stage of the analyses. Figure 2 shows the iterative process that was used during model validation.

Figure 2: Iterative process of model validation
Prior to any analyses, Statistical Package for Social Sciences (SPSS, Version 17) was used to conduct reliability analysis on the 336 questionnaires (Cronbach's alpha coefficient: 0.84). Descriptive statistics did not indicate abnormality in the mean, standard deviation, and normality of distribution of the data. Then, cluster analysis and group identification analyses were conducted on the data to identify subgroups for the subsequent model exploration and confirmation. Ward's minimum variance method pointed to five groups with no outliers. The data, then, were grouped into five clusters using the K-means refinement. One-way analysis of variance (ANOVA) confirmed the reliability of data clustering showing significant mean difference among the clusters (p<0.05). After data clustering, we divided the dataset into exploratory and confirmatory data with the ratio of 2:1 (Sharma, 1996): 236 participants with equal representation from the five clusters were assigned to the exploratory dataset, and the remaining participants became the confirmatory dataset.

Exploratory data analysis (EDA)
During the EDA phase, the exploratory data from the earlier clustering stage underwent principle component analysis (PCA) with varimax rotation to uncover the underlying constructs in the data (Shultz and Whitney, 2005). As a measure against multicollinearity, the determinant was calculated to be higher than 0.00001. Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy (.816) and Bartlett's test of sphericity (.000) were both significant, indicating that the data were factorable. PCA with varimax rotation on the exploratory dataset gave way to nine factors with eigenvalues greater than one. These nine factors, which had minimum item-on-factor loadings of 0.35, together accounted for 57 per cent of the variance in the data. Cattell's scree test of eigenvalues was also used to plot the number of factors supported by the data. The results confirmed the factor structure that emerged from PCA.
Consultation with SMEs confirmed the conceptual integrity of the PCA factor structure. In the emergent framework, knowledge of subject matter accounted for 17 per cent of the total variance, followed by knowledge of teaching (13 per cent). These were followed by knowledge of students (6 per cent); knowledge of classroom management (4 per cent); knowledge of educational context (4 per cent); knowledge of democracy, equity and diversity (4 per cent); knowledge of tests/exams (3 per cent); knowledge of language learning (3 per cent); and knowledge of professional self (3 per cent). It is worth noting that despite the overall correspondence of the PCA factor structure with the factor structure of the tentative model of pedagogical knowledge from the literature, there were differences between the two frameworks. First, knowledge of culture and cultural differences did not emerge as a separate factor from the EDA. The subcomponents of this knowledge all loaded on knowledge of students. In addition, knowledge of students' first language, and knowledge of first and second similarities/differences loaded on knowledge of students. Knowledge base for professional development was part of knowledge of professional self in the tentative model loaded on knowledge of teaching instead.

Confirmatory data analysis
The CDA phase started with reliability and item analysis on the emergent nine-factor framework of pedagogical knowledge from the EDA phase. Cronbach's alpha was used to estimate the variance for the factor structure that emerged from the EDA. Then, LISREL (Version 8.8) was used to conduct confirmatory factor analysis (CFA) on the confirmatory data, which helped empirically test the EDA factor structure (Sharma, 1996). During the CDA, the remaining 100 self-assessment questionnaires of the confirmatory data set underwent CFA. CFA verified the nine-factor model of pedagogical knowledge. The loadings between the indicators (subcomponents of knowledge) and the latent factors (component of knowledge), as well as the covariance among the factors, were all significant at α=0.001 (p≤0.001). However, four subcomponents of knowledge did not load on their corresponding components in the analyses. These included knowledge of English culture, knowledge of instructional management, knowledge of curriculum and its objectives, and knowledge of available teaching/learning resources. The exclusion of these subcomponents gave way to a nine-factor model with 50 items. (See Figure 3 for the final self-assessment questionnaire.) We consulted the SMEs about the conceptual integrity of the final model, especially the four items that were removed from the final framework. The SMEs still considered these four subcomponents as important constituents of language teachers' knowledge base. Our explanation for removing these subcomponents rests on our assumption that the other subcomponents of knowledge in the model already tap into the knowledge that these subcomponents addressed. With this explanation, and given the absence of sufficient empirical support for their inclusion, we removed these four items from the framework prior to the final phase of our model validation, namely the model evaluation phase.

Dear respondent,
This questionnaire aims to measure your KNOWLEDGE about English Language Teaching (ELT). Each item is, thus, designed to examine one aspect of your professional knowledge as an English teacher in relation to your performance in classroom. Please answer the questions to the best of your knowledge by checking the box that best describes your state of teaching knowledge. Your thoughtful and candid responses are greatly appreciated.
Your information and responses will be kept confidential and will be used only for research purposes. Thank you very much in advance for your time and cooperation.

Model evaluation
Model evaluation was used after CFA to estimate the model's overall fit for the confirmatory dataset. Given that there is no single agreed upon criterion for model evaluation (Heubeck and Neill, 2000), heuristic measures called goodness of fit indices tests -including absolute fit, incremental fit, and parsimony fit -were conducted on the confirmatory dataset. In addition to normed chi-squared statistic, the analyses of this phase included absolute fit tests of the root mean square error of approximation (RMSEA) and the root mean square residual (RMR), incremental fit test of the nonnormed fit index (NNFI), and the parsimony fit goodness-of-fit index (PGFI), as well as the parsimonious normed fit index (PNFI).
In order to ensure that the final model adequately fits the data, the confirmatory dataset was used in model-fit analysis. As Table 3 shows, the assessment indices for absolute fit, incremental fit, and parsimony fit are all larger than the minimum cut-off values needed for appropriate model fit, that is, normed chi-squared < 2, RMSEA < 0.05, RMR ≈ 0, NNFI > 0.90, PGFI > 0.50, and PNFI > 0.50. These model-fit estimates, in turn, confirmed the validity of the model that emerged from the CDA phase of the study.

Discussion and conclusion
Learning to teach is a complex and lifelong process, so are the bodies of knowledge that teachers develop for their practices. Understanding what constitutes pedagogical knowledge, therefore, poses several ontological, epistemological and methodological questions about the nature of the thinking mind, the relationship between embodied, articulated and unarticulated forms of knowing, the ways in which personal biographies, time, space and activity interact in the ongoing (re)production of knowledge, and how one can best provide an account of pedagogical knowledge without reducing its personal and contextual complexities. The long tradition of teaching and teacher education research has tried to address these questions, albeit in a fragmented and often siloed fashion. This has resulted in a field of inquiry that houses multiple traditions, terms and labels.
In this study, we drew upon complex-system and lifelong-learning perspectives to propose and validate a conceptual framework for pedagogical knowledge focusing on the field of English language teaching. The model that emerged from our analyses explains pedagogical knowledge in terms of nine components: knowledge of subject matter; knowledge of teaching; knowledge of students; knowledge of classroom management; knowledge of educational context; knowledge of democracy, equity and diversity; knowledge of assessment/testing; knowledge of learning; and knowledge of (professional) self. Within this nine-factor framework, the components of pedagogical knowledge consist of 50 subcomponents that provide a detailed account of what each dimension of pedagogical knowledge entails.
In the absence of a validated model that can help explain pedagogical knowledge (Akbari and Dadvand, 2014), the findings of this study can have conceptual and practical implications for teaching and teacher education research. At a theoretical level, a validated model that frames pedagogical knowledge through its constitutive elements can provide more conceptual coherence to an area of teacher education research that is characterized by multiple, and at times seemingly contradictory, terms and labels. At a more practical level, such a framework can help bridge the theorypractice divide in teacher education research by offering an evidence-informed basis for a range of decisions regarding teacher admission, preparation and certification in teacher education programmes.
We should note at the end that caution needs to be exercised in interpreting and applying the findings of this study. As a complex system, pedagogical knowledge represents a dynamic and context-sensitive system of mutually constituting elements that evolve over time and in response to the particularities of teaching contexts. Therefore, the boundaries we have constructed among different components and subcomponents of pedagogical knowledge should be understood as serving an analytical-conceptual purpose. As housed within a complex system, these territories of knowledge remain fluid, without discernable beginnings or endings. Far from being a finished product, pedagogical knowledge remains in a constant state of flux throughout life, with multiple personal, institutional, social, cultural and political factors contributing to it.
This points to the context-specificity of pedagogical knowledge. What constitutes relevant or viable teaching knowledge may vary depending on the needs and circumstances that surround teachers' work within different settings. In agreeing with Burns et al. (2015), who have pointed to the impacts of socio-historical factors within the classroom on teachers' cognition, we wish to underline the importance of context, temporality and spatiality in teaching and the sorts of knowledge it requires. Therefore, we reiterate that our proposed framework is not meant as a one-size-fits-all template. Rather, it aims to further enhance our understanding of the complexities of teaching as a form of professional practice, which is guided, among other things, by significant bodies of pedagogical knowledge (Shulman, 1998).

Notes on the contributors
Babak Dadvand is a research fellow and lecturer at the Melbourne Graduate School of Education, the University of Melbourne. Babak's research is in the areas of teaching and teacher education, diversity, equity and social justice education, as well as civics and citizenship education.
Foad Behzadpoor is a lecturer at Azad University, West Tehran Branch, Iran. Foad's research focuses on teacher education, reflective teaching, second language acquisition and English for specific purposes (ESP).