The nature of PCK

Section 3.3.1 above discussed the first process of the theoretical framework of pedagogical reasoning and action introduced by Shulman and his colleagues: comprehension, which is of high importance when analysing

teachers’ KAG. The second process of this framework, transformation, consists

of five different sub-processes: preparation, representation, selection, adaptation, and tailoring. The first sub-process, preparation, involves the critical interpretation and analysis of the instructional materials in terms of the teacher’s own understanding of the subject matter. This stage usually includes “(1) detecting and correcting errors of omission and commission in the text [also see Andrews, 1999b, 2007], and (2) the crucial processes of structuring and segmenting the material into forms better adapted to the teacher’s understanding and, in prospect, more suitable for teaching” (Shulman, 1987: 16). In the preparation stage the teacher resorts to their subject matter knowledge (in the case of grammar, their KAG) and their PCK. The second sub-process, representation, entails the identification of alternative ways of representing the content for instruction to the learners, for example, in the form of new analogies, metaphors, illustrations, activities, and examples. The third sub-process, selection, has to do with the instructional selection the teacher makes of teaching approaches and strategies, which range from lecture and demonstration to different forms of co- operative learning, Socratic dialogue, and discovery learning. For instance, a teacher teaching grammar may decide to teach a grammatical feature either deductively, inductively, or using a combination of both. The last two processes, adaptation and tailoring, refer to the fitting of the represented material to the characteristics first of the student population in general and then of specific learners in one class (e.g., conceptions, prior-knowledge, abilities, aptitudes, expectations, motivations, and attention). Representation, selection, adaptation, and tailoring are the concern particularly of the teacher’s PCK.

The last four processes of the model of pedagogical reasoning and action involve the actual performance of the teacher in the classroom and include:

instruction, evaluation, reflection, and new comprehension. The third

process in the model, instruction, entails the observable teaching practices in

the classroom and includes such pedagogical aspects as classroom management, explanations, discussions, responses, and interactions. Shulman claims that “teaching behavior [during instruction] is bound up with comprehension and transformation of understanding” and he illustrates how “the flexible and interactive teaching techniques [Colleen, a teacher in Grossman’s study] uses are simply not available to her when she does not understand the topic to be taught” (ibid.: 18). This means that it is possible to explore a teacher’s PCK and subject matter knowledge through the observation of their classroom performance, which is actually one of the data collection instruments used in my study. The fourth process, evaluation, involves the checking of students’

understanding during interactive teaching, the assessment of their performance, and the evaluation of the teacher’s own teaching practices. The fifth process,

reflection, engages the teacher in the act of “reviewing, reconstructing, re-

enacting and critically analysing [their] own and the class’s performance, and grounding explanation in evidence” (ibid.: 15). This process naturally calls for the teacher’s awareness of the instructional strategies they used (PCK) and of their subject matter and resembles the procedures followed in stimulated recall, another instrument to be used in this study. Finally, the sixth process, new comprehension, refers to the new understandings of “purposes, subject matter,

students, teaching, and self” the teacher achieves and the consolidation of these new understandings (ibid.).

In his review of the historical development of PCK, Hashweh (2005) introduces a new conceptualisation of this construct, which he now calls Teacher

Pedagogical Constructions and which he describes through seven assertions.

First, “PCK represents personal and private knowledge” (p. 274) instead of public and objective awareness. This means PCK can be explored, and thus made public, mostly by means of class observation of individual teachers and by introspective work with them such as through interviews and think-aloud protocols. My study, for instance, explores teachers’ GRPK through class observation and stimulated recall. Second, “PCK is a collection of basic units called teacher pedagogical constructions” (ibid.). Unlike subject matter knowledge, which Hashweh sees as “well organized and hierarchically ordered” (ibid.), PCK is not a single unit but is composed of a set of knowledge entities.

Hence the difficulty in providing a clear-cut definition in the introduction to this section. Third, “teacher pedagogical constructions result mainly from planning, but also from the interactive and post-active phases of teaching” (ibid.). When planning to teach some content, a teacher devises a plan of action which involves drawing on many sources of teacher knowledge (e.g., knowledge of subject matter, knowledge of learners, knowledge of syllabus, and knowledge of pedagogy) to reflect upon and make decisions about certain aspects like how much to teach, what ideas to prioritise and how to introduce them, anticipating and coping with student difficulties, and checking students’ understanding. The teacher then builds pedagogical constructions about the teaching of such content, which can be further developed during interactive teaching and follow-up reflection (e.g., by adding more ways of representing content knowledge to the learners). Therefore, teachers build and accumulate PCK through experience as they teach some content regularly. Not surprisingly, in his doctoral study in 1985, Hashweh found that experienced teachers planned far less than inexperienced teachers since the former were able to recall and draw on pedagogical constructions which the latter had not developed yet. Fourth, “pedagogical constructions result from an inventive process that is influenced by the interaction of knowledge and beliefs from different categories” (ibid.). This means that each new teacher‘s pedagogical construction is an original amalgam which the teacher has developed from different teacher knowledge and beliefs categories to teach some particular content. This might explain why there exist some researchers who conceive of PCK as consisting of other types of knowledge while there are some others who see PCK as a separate knowledge category. In my study, as in Hashweh’s conceptualisation, PCK is regarded as an independent construct influenced by other elements of the teacher knowledge base.

Fifth, “pedagogical constructions constitute both a generalised event- based and a story-based kind of memory” (ibid.). Through experience we develop scripts of different aspects of our lives. Just as we have ‘supermarket’ scripts which allow us to understand behaviour and events in supermarkets, teachers develop scripts in relation to the teaching of different topics which will allow them to know, for instance, how to activate learners’ previous knowledge about that topic, how to provide meaningful examples to a particular group of students, and how to use different instructional strategies to represent content knowledge to the learners. All general knowledge about specific events (e.g., teaching passive

voice) is stored in our event-based memory, which is updated every time we have a relevant new experience. This updating process, according to Schank and Abelson (1995), destroys the coherence of any particular sequence of events we may have experienced. However, when something significant occurs (e.g., a funny misunderstanding when teaching passive voice), events are stored in sequence in our story-based memory and are retrieved from memory as a unit. Story-based knowledge is developed by telling the story repeatedly either to oneself or to others. Sixth, “pedagogical constructions are topic specific” (ibid.). Each pedagogical construction is connected in the teacher’s memory structure to a particular topic the teacher uses, which is why PCK and subject matter knowledge have been often related by researchers. Each topic thus becomes a label which helps teachers remember the relevant pedagogical construction they need at a given time. My study explores the teachers’ GRPK, or what Hashweh might call ‘English grammar pedagogical construction’, and its corresponding sub-categories. Finally, “pedagogical constructions are (or should ideally be) labeled in multiple and interesting ways that connect them to other categories and subcategories of teacher knowledge and beliefs” (ibid.). Thus, teachers might be able to access the knowledge stored in their passive voice pedagogical construction (e.g., about specific mistakes students make when using passive voice) by using their knowledge of learners, or, more specifically, their knowledge of learners’ common grammatical errors. Hashweh’s conceptualisation of PCK has been included in this section because it enhances our understanding of not only the nature of PCK as an independent construct but also they way PCK is related to other types of teacher knowledge.

Recent developments in the study of teacher knowledge in the field of mathematics teaching indicate that PCK consists of three types of knowledge: knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum (Ball et al., 2008: 402-403). GRPK as understood in the present study focuses on the second type of knowledge, which Ball et al. (2008) exemplify listing the following tasks: “Teachers sequence particular content for instruction. They choose which examples to start with and which examples to use to take students deeper into the content. Teachers evaluate the instructional advantages and disadvantages of representations used to teach a specific idea and identify what different methods and procedures afford instructionally” (ibid.: 401). Though my interest is specifically on knowledge of

content and teaching, as pointed out in 3.4, other knowledge categories which interact with GRPK like knowledge of learners, knowledge of syllabus/curriculum, and knowledge of context will be explored.