Shulamit_Kapon_16Dec2013.pdf

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ON THE EPISTEMIC NATURE OF PEDAGOGICALCONTENT KNOWLEDGE

Shulamit Kapon

University of Haifa

Abstract: This paper presents a theoretical examination of teachers' cognition involved inintegrating new practices to the instruction of science. It reviews studies of PedagogicalContent Knowledge (PCK) and Technological Pedagogical Content Knowledge (TPCK) andquestions their applicability in conceptualizing teachers' knowledge at the individualcognitive level. It argues that while categorical models of teachers' knowledge are productivefor acknowledging and assessing specialized knowledge for teaching, they are still far fromfully describing teachers' complex coordination of knowledge. Informed by the Knowledge inPieces epistemological perspective (diSessa, 1993) it is suggested that teachers knowledgecould be more productively modeled as a dynamic complex system in which PCK (or TPCK)reflects an evolving state of a complex system instead of a dichotomist category ofknowledge.

Keywords: pedagogical content knowledge, knowledge in pieces, online teaching

INTRODUCTIONHow well do prevalent categorical conceptualizations of teachers' knowledge account for thecoordination and development of specialized knowledge for teaching during actual practice?This question is particularly crucial when considering the large-scale integration ofeducational technologies in the instruction of science. K 12 online learning programs are

becoming widespread (Barbour, 2009; Powell & Patrick, 2006) . Information communicationtechnologies (ICT) contain no inherent specific instructional functions, and many of the pre-designed online curricular materials are not necessarily fully designed for the instructionalfunctions a teacher might implement at a given moment. Take for example a physics teacherwho teaches a fully online class. Consider the possible ways in which this teacher might usean available technology and online instructional resources by redesigning and transformingthem in moment-to-moment activity aimed at achieving a local particular instructional goal.This teacher draws upon and coordinates various types of knowledge such as previousinstructional experiences, content knowledge, familiarity with the class as a group and thestudents as individuals, knowledge about the available technology, available curricula,

alternative instructional schemes, etc.The complex coordination described above is sometimes carried out over a microgenetic timescale as the teacher cognizes, explores and responds to the students reactions, with the localinstructional goal in mind. It also has a developmental aspect. A teachers first efforts atemploying a particular online-instruction scheme probably differ from her uses of thisscheme as a skilled online teacher. Thus the form and function of the instructional actionemployed by a teacher change over time and with accumulated experience.

How well do prevalent categorical theoretical conceptualizations of teachers' knowledgeaccount for this coordination? This paper argues that they are still far from achieving thisgoal. It questions the productivity of conceptualizing teachers' knowledge at the individual

cognitive level as compartmentalized into categories and subcategories, and suggests analternative perspective.


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CATEGORICAL MODELS OF TEACHERS' KNOWLEDGELee Shulman's influential work reframed the study of teachers knowledge in ways thatattend to the role of content in teaching, and represent the specialized understanding ofcontent that is unique to the profession of teaching. Shulman (1986, 1987) defined seven

categories of knowledge for teaching, and argued that the category that is most likely todistinguish the content specialist from the pedagogue is the category of Pedagogical ContentKnowledge (PCK). He described PCK as ways of representing and formulating the subjectthat make it comprehensible to others (1986, p. 9). Since its introduction in 1986, PCK has

become widely employed in the context of teacher education. Many studies have highlightedthe central role of PCK in teachers' practice and in teacher education. However, someeducational researchers (Ball, Thames, & Phelps, 2008; Borko & Putnam, 1996; Friedrichsen,Driel, & Abell, 2011; Gess-Newsome, 1999; Lee, Brown, Luft, & Roehrig, 2007; Magnusson, Krajcik, & Borko, 1999; Marks, 1990; Schoenfeld, 2006) have also argued thatan understanding of the nature of PCK; namely, a clear unambiguous definition of its scope,structure and function, is needed both theoretically and empirically. Some of the researchers

cited above (Ball et al., 2008; Hill, Ball, & Schilling, 2008; Magnusson et al., 1999; Park &Chen, 2012; Tsamir & Tirosh, 2008) suggested parsing Shulmans PCK and CK (contentknowledge) or SMK (subject matter knowledge) categories into further subcategories.However there is no consensus on the list of these subcategories, their definitions,hierarchical structure or empirical differentiation.

The developmental process of PCK is another open question. Shulman and colleagues(Wilson, Shulman, & Richert, 1987) suggested that PCK emerges and grows as teacherstransform their content knowledge for the purposes of teaching. The general transformativenature of PCK has been embraced at different levels by many researchers (see for examplethe collection of studies in Gess-Newsome & Lederman, 1999) . Yet there are hardly anystudies that examine in detail how this transformation takes place. One possible reason is thatthe researchers who have paid the most attention to PCK are primarily interested indetermining what teachers need to know in order to teach effectively and how this knowledgecan be assessed.

Empirical evidence shows that teachers knowledge is much more fragmented, intuitive andcontext- sensitive than categorical models of teachers knowledge suggest. Researchers whohave examined t eachers instructional actions have documented idiosyncratic and topic -specific integration of components (e.g., Grossman, 1990; Park & Chen, 2012) , whereasresearchers who asked teachers to think about different specific teaching contexts found thatteachers express contradictory pedagogical views in different contexts (Eley, 2006; Kali,Goodyear, & Markauskaite, 2011; Kane, Sandretto, & Heath, 2002; Postareff, Katajavuori,Lindblom-Ylanne, & Trigwell, 2008) . Hence, modeling teachers knowledge as neatly parsedcategories might be instrumental for the purpose of establishing external standards andassessment; however, it is unlikely that this is how this knowledge is organized andconstructed in teachers minds (Borko & Putnam, 1996; Gess-Newsome, 1999) .

The increasing role of technology in education has added additional complexity to the notionof PCK (Borko, Whitcomb, & Liston, 2009) . Several lines of research have aimed toconceptualize the knowledge that instructors and designers of technology-rich learningenvironments draw on. A widely investigated strand is Technological Pedagogical ContentKnowle dge (TPCK) (AACTE, 2008; Angeli & Valanides, 2009; Archambault & Crippen,2009; Koehler & Mishra, 2005; Koehler, Mishra, & Yahya, 2007; Mishra & Koehler, 2006;

Schmidt et al., 2009) which makes explicit reference to PCK. Koehler and Mishra (e.g.,Koehler & Mishra, 2005; Koehler, Mishra, Hershey, & Peruski, 2004; Koehler et al., 2007;


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Mishra & Koehler, 2006) conceptualized TPCK as an extension of the concept ofPedagogical Content Knowledge (Shulman, 1986, 1987) . They suggested that the integrationof technology into the process of education adds an additional core category to Shulmansframework. Hence, TPCK is a subcategory of knowledge that reflects the intersection ofthree core categori es of teachers knowledge: technological knowledge (TK), pedagogical

knowledge (PK), and content knowledge (CK).The general idea of specialized knowledge for teaching specific content with technology iscertainly compelling. However, the TPCK model has been criticized on theoretical grounds.Graham (2011) pointed out that it is not clear whether the development of TPCK should beconceptualized as transformative or integrative, an ambiguity that has been highlighted byother scholars as well (Archambault & Barnett, 2010; Archambault & Crippen, 2009) . Angeliand Valanides (2009) argued that although teachers epistemic beliefs and values aboutteaching and learning influence how they reason about their disciplinary instruction, they arenot represented in the TPCK model. In particular, teachers epistemic beliefs and values have

been dealt with in some categorical models of PCK, although this subcategory has not been

developed or described in detail at the individual processing level (e.g., Carlsen, 1999; Magnusson et al., 1999; Park & Chen, 2012) .

Thus although PCK and TPCK are productive terms for acknowledging specializedknowledge f or teaching, modeling teachers knowledge at the individual cognitive level as

parsed into dichotomist categorizations fails to reflect the empirical findings cited above.Recently it has been suggested that TPCK is not a fixed category of knowledge but rather ahigher level mental model that helps teachers to integrate their prior knowledge (Krauskopf,Zahn, & Hesse, 2012) : "Teachers need not only to combine from more independentknowledge domains (TK and PK) more interrelated aspects (TPK and PCK), in order to solvefor the overall task (TPCK). Rather, with regard to the representational format, thiscombination needs also to be accompanied by a transformation into a mental modelrepresentation of elements and interrelations that can be manipulated and from whichinferences can be made" (p. 1196). Yet, this suggestion also has its theoretical limits. First,the suggested processes are unidirectional (TK+PK=>TPK, PK+CK=>PCK,TK+PK+CK=>TPCK) rather than multidirectional transformations (e.g, PCK=>CK). Everyteacher has experienced moments when her understanding of content deepened afterdesigning instruction, and during these experiences for instance PCK led to the improvementof CK. Second, the suggested mental model accounts for the dynamic attributes of teachers'knowledge but not for their stable knowledge constructs. The next section explains why, inmy view, modeling teachers knowledge as a dynamic complex system in which PCK (orTPCK) reflects an evolving state of a complex system rather than a category may come closerto describing the dynamics of teacher knowledge at the cognitive level. This paper does notdismiss the notion of mental models with regard to teachers' knowledge, but argues that theyare only one part of the complex knowledge system.

MODELING KNOWLEDGE AS A COMPLEX SYSTEMModeling the mind as a complex knowledge system and attending to the mechanisms ofchange involved in learning entails describing reasoning and understanding as involvingmany diverse knowledge elements that can be activated and used in particular contexts.Complex systems approaches to cognition have a theoretical basis in both artificialintelligence (Minsky, 1986) and in complex systems science (Jacobson & Wilensky, 2006;

Sabelli, 2006) . In the field of educational research, an influential effort to study thinking andlearning from a complex systems perspective was initiated (1993) by diSessa in an article


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presenting the empirical underpinnings of the Knowledge in Pieces (KiP) epistemological perspective (diSessa, 1993) .

The basic knowledge elements of the systemThe KiP approach to understanding individual reasoning involves identifying elements ofknowledge evident in episodes of learning at a small enough grain size so that they are notthought of as intrinsically right or wrong, but instead as productive or not for a particularcontext (diSessa, 1993, 1996; diSessa, Gillespie, & Esterly, 2004; Kapon & diSessa, 2012; Parnafes, 2007; Parnafes & diSessa, in press; B. L. Sherin, 2001) . For example, diSessa(1996) showed how a students explanation of projectile motion that might have beeninterpreted as an incorrect impetus theory misconception (McCloskey, 1983) shouldinstead be decomposed into the activation and use of several ideas that can in fact be

productive in different contexts. In the same manner, it is argued here that modeling PCK as aseparate cognitive category masks its fine structure and thus the explanation for this typicalconduct. In fact, an article (Kali et al., 2011) that reexamined two earlier studies oneducational design practices (Goodyear & Markauskaite, 2009; Ronen-Fuhrmann & Kali,2010) , as well as an empirical study that followed the learning of pre-service science teachersenrolled in a model-based physics course for potential teachers (Harlow, Bianchini, Swanson,& Dwyer, 2013) explicitly suggested that conceptualizing pedagogical knowledge asfragmented seems more in line with empirical findings than a theory-like categoricalconceptualization. Kali et al. termed the relevant basic knowledge elements "pedagogical p-

prims," thus adapting diSessa (1993) concept of phenomenological primitive (p-prim),Harlow et al. termed them "pedagogical resources" (the term "resources" was adapted fromHammer, Elby, Scherr, & Redish, 2005 interpretation of KiP) .

The development of the knowledge system

Knowledge from a KiP perspective is modeled as a complex system with loosely interactingsmall knowledge elements (KE) that are not intrinsically right or wrong. Hence, learninginvolves a progressive systemization of this system driven by mundane and accumulatedexperiences, which necessitates the reorganization and recontextualization of existing KE andthe integration of new ones; hence the path from Nave => Novice => Expert is continuousand gradual. From this point of view, concepts are not modeled as unitary elements butrather as complex knowledge systems that evolve along this path.

When employing a KiP perspective, one assumes that information in the world is nottransparently available. An underlying assumption is that the knowledge system provide waysof perceiving the right and the "relevant" information , and that these knowledge constructs

develop and function as knowledge systems (diSessa, 2002; diSessa & Sherin, 1998; diSessa& Wagner, 2005; Wagner, 2006, 2010) . diSessa and Wagner (2005) and Wagner 2010discuss the notion of concept projections; namely, the assimilatory schemes with which aknower assimilates and interprets that which is available to be perceived. They argue thatconcept projections are derived from experiences. Thus good instruction involves carefullychoosing and exposing the learner to a wide variety of contexts in which the concept is used.This will allow the learner to accommodate and generate a large span of conceptual

projections, which will afford the identification of the concept in different contexts.

It is argued here that teachers' professional knowledge functions as a complex knowledgesystem which informs their perception and interpretation of incidences of learning andinstruction, and that the theoretical machinery described in the paragraphs above is applicableto this knowledge system as well. Table 1 presents an interpretation of existing findings from

previous studies on teachers' knowledge from a KiP perspective.


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Table 1

Interpreting existing findings on teachers knowledge from a KiP perspective

Research findings A knowledge system account

Experience-based instructional approaches supportsophisticated use of technology for teaching among pre-service teachers (Angeli & Valanides, 2009; Koehler &Mishra, 2005; Koehler et al., 2007; Kramarski &Michalsky, 2010)

Providing experiences from whichthe development andaccommodation of new concept

projections can be derived

CK and PCK are developed simultaneously(Kleickmann et al., 2013)

Designing instruction providesopportunities to refine existingconcept projections related tocontent

Teachers implement instructional reforms through thelens of their current practices (Cohen & Ball, 1990; Kleickmann et al., 2013)

Teachers interpret instructionalreform by activating assimilatoryschemes

The development of PCK is an ongoing continuous process throughout a teachers career (Seymour &Lehrer, 2006; M. G. Sherin, 2002)

The road from a novice to anexpert teacher is a continuousgradual path

PCK develops in relatively mundane ways (Seymour &Lehrer, 2006; M. G. Sherin, 2002)

The development of theknowledge system involves a

progressive systemization

Additional affordances of the KiP perspectiveKiP also offers additional affordances to the study of teachers knowledge. First, studies on

personal epistemologies made up of fine-grained, context-sensitive resources (diSessa, 1985; Elby, 2001, 2009; Elby & Hammer, 2001; Hammer & Elby, 2003; Louca, Elby, Hammer, &Kagey, 2004) suggest that the KiP description of particular forms of knowledge elements ina complex knowledge system might als o apply to teachers p ersonal epistemologies. Second,the inherent contextual sensitivity of KiP is advantageous when accounting for changes inteachers' knowledge during practice. Third, KiP models of the nature and dynamics ofknowledge elements, which when activated are considered as explanatory without any

questioning at the timescale of particular reasoning (i.e., this is how things are) (diSessa,1993; Kapon & diSessa, 2012) , suggest terminology that might describe teachers' decisionsthat appear to respond in a rule-governed manner to particular configurations of cues (suchas described by Calderhead (1981) ).

CONCLUSIONIt was argued here that while categorical models of teachers' knowledge are productive foracknowledging and assessing specialized knowledge for teaching, they are still far from fullydescribing teachers knowledge at the individual cognitive level. It is hypothesized here thatto account for the coordination and development of specialized knowledge for teachingduring practice, such as the complex coordination of knowledge involved in teaching adisciplinary content in a fully online classroom, it might be more productive to model


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teachers knowledge as a dynamic complex sys tem in which particular exemplars of PCK (orTPCK) reflect an evolving state of a complex system instead of dichotomist categories ofknowledge.

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