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Although Pedagogical Content Knowledge (PCK) is traditionally defined as a static quality that teachers possess and apply in practice, we conceive of PCK as constituted by a dynamic, mutually influencing process between teacher and students. This co-constructing process is expressed in real-time interaction and defined by us as Expressed Pedagogical Content Knowledge (EPCK). The aim of this study is to develop a practically usable instrument that can track the microgenetic moment-to-moment interaction that embodies EPCK, and that enables us to observe different features and levels of EPCK in the form of changes in this interaction dynamics. We were interested to know how EPCK emerges and develops on the short-term time scale of classroom interaction. After presenting a general account of complex dynamic systems based measurement of psychological constructs (e.g., PCK), we describe a coding scheme for teacher-student interactions, based on theoretical EPCK components. The instrument was applied in an empirical observation study of a visit to a mobile planetarium by a grade 3 primary school class. A principal factor analysis was used to find latent EPCK components. Results show, firstly, that the instrument was reliable. Secondly, the variables in the coding scheme were relevant in view of the underlying theory. Thirdly, over the time course of the teaching session, latent components displayed various levels of EPCK – high, low or no ECPK. Instead of being an enduring or stable property of teaching-learning interactions, EPCK is a dynamic property occurring in the form of sequences of high and low levels, and corresponding peaks in the latent factors. Notably, EPCK did not appear in the form of a continuous steady state level but occurred in the form of bursts of high-level EPCK. We conclude that our coding scheme provides an adequate method for studying pedagogical content knowledge as it self-organizes in the form of real-time activity in the classroom. Keywords: complex dynamic systems approach, teaching-learning interaction, expressed pedagogical content knowledge, out-of-school science education, observation instrument, process validity, International Journal of Complexity in Education, Vol 1, No 1 (2020)

Although Pedagogical Content Knowledge (PCK) is traditionally defined as a static quality that teachers possess and apply in practice, we conceive of PCK as constituted by a dynamic, mutually influencing process between teacher and students. This co-constructing process is expressed in real-time interaction and defined by us as Expressed Pedagogical Content Knowledge (EPCK). The aim of this study is to develop a practically usable instrument that can track the microgenetic moment-to-moment interaction that embodies EPCK, and that enables us to observe different features and levels of EPCK in the form of changes in this interaction dynamics. We were interested to know how EPCK emerges and develops on the short-term time scale of classroom interaction. After presenting a general account of complex dynamic systems based measurement of psychological constructs (e.g., PCK), we describe a coding scheme for teacher-student interactions, based on theoretical EPCK components. The instrument was applied in an empirical observation study of a visit to a mobile planetarium by a grade 3 primary school class. A principal factor analysis was used to find latent EPCK components. Results show, firstly, that the instrument was reliable. Secondly, the variables in the coding scheme were relevant in view of the underlying theory. Thirdly, over the time course of the teaching session, latent components displayed various levels of EPCK – high, low or no ECPK. Instead of being an enduring or stable property of teaching-learning interactions, EPCK is a dynamic property occurring in the form of sequences of high and low levels, and corresponding peaks in the latent factors. Notably, EPCK did not appear in the form of a continuous steady state level but occurred in the form of bursts of high-level EPCK. We conclude that our coding scheme provides an adequate method for studying pedagogical content knowledge as it self-organizes in the form of real-time activity in the classroom.

In order for out-of-school science activities that take place during school hours but outside the school context to be successful, instructors must have sufficient pedagogical content knowledge (PCK) to guarantee high-quality teaching and learning. We argue that PCK is a quality of the instructor-pupil system that is constructed in real-time interaction. When PCK is evident in real-time interaction, we define it as Expressed Pedagogical Content Knowledge (EPCK). The aim of this study is to empirically explore whether EPCK shows a systematic pattern of variation, and if so whether the pattern occurs in recurrent and temporary stable attractor states as predicted in the complex dynamic systems theory. This study concerned nine out-of-school activities in which pupils of upper primary school classes participated. A multivariate coding scheme was used to capture EPCK in real time. A principal component analysis of the time series of all the variables reduced the number of components. A cluster revealed general descriptions of the components across all cases. Cluster analyses of individual cases divided the time series into sequences, revealing High-, Low-, and Non-EPCK states. High-EPCK attractor states emerged at particular moments during activities, rather than being present all the time. Such High-EPCK attractor states were only found in a few cases, namely those where the pupils were prepared for the visit and the instructors were trained.