Resolving the amalgam: connecting pedagogical content knowledge,content knowledge and pedagogical knowledge

ABSTRACT

This paper concludes the Special Issue (SI) ‘Probing the Amalgam: the relationship between science teachers’ content, pedagogical and pedagogical content knowledge’. We review the five papers (Sorge et al; Gess-Newsome et al; Kind; Pitjeng-Mosabala and Rollnick; and Liepertz and Bronowski) by discussing evidence these present regarding the relationships between content knowledge (CK), pedagogical knowledge (PK) and pedagogical content knowledge (PCK); the development of CK, PK and PCK in novice and experienced secondary science teachers and how CK, PK and/or PCK impact students’ learning. In conclusion, we draw these findings together in offering proposals for future research via reconsideration of Shulman’s amalgam. This includes post-hoc examination of a PCK model known as ‘the Consensus Model’ (Gess-Newsome, [2015]. A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK Summit. In A. Berry, P. J. Friedrichsen, & J. Loughran (Eds.), Re-examining Pedagogical Content Knowledge in Science Education (pp. 28–42). New York, NY: Routledge; Neumann, Kind, & Harms [2018]. Probing the amalgam: The relationship between science teachers’ content, pedagogical and pedagogical content knowledge. International Journal of Science Education, 1–15) and presentation of a novel PCK structure based on evidence from the SI studies.     

Engineering teachers' pedagogical content knowledge

The aim of the study was to discover the essential characteristics of engineering teachers' pedagogical content knowledge by studying teachers' conceptions of their students' ideas of moment. To compare the conceptions maintained by teachers with those of their students, the most common difficulties experienced by first-year engineering students in understanding the moments of forces were looked at. The data on students' conceptions were collected by means of a questionnaire. In addition, four experienced teachers were given the same questionnaire as the students and then were asked to write what they expected the students' answers to be. The students' answers and the teachers' conceptions of their students' potential answers were compared. It was found that although the teachers originally appeared to be familiar with their students' conceptions, they were rather astonished by the general pattern of the students' thinking. It is planned that the information gathered about the teachers' pedagogical content knowledge will eventually be used to improve engineering teacher training.     

Teacher pedagogical constructions: a reconfiguration of pedagogical content knowledge

A brief review of the history of pedagogical content knowledge reveals various definitions and conceptualizations of the construct, as well as some conceptual problems. A new conceptualization—teacher pedagogical constructions—is offered to address some of the problems associated with PCK. Seven assertions that comprise the new conceptualization are presented, explained and defended. These are: (1) PCK represents personal and private knowledge; (2) PCK is a collection of basic units called teacher pedagogical constructions; (3) teacher pedagogical constructions result mainly from planning, but also from the interactive and post‐active phases of teaching; (4) pedagogical constructions result from an inventive process that is influenced by the interaction of knowledge and beliefs from different categories; (5) pedagogical constructions constitute both a generalized event‐based and a story‐based kind of memory; (6) pedagogical constructions are topic specific; and (7) pedagogical constructions are (or should ideally be) labeled in multiple interesting ways that connect them to other categories and subcategories of teacher knowledge and beliefs. The proposed definition results from a reconceptualization of the nature of PCK as originally proposed, taking the results of major later studies and conceptualizations of PCK into consideration, appropriating new ideas about the structure of memory, and undertaking a reanalysis and presentation of data from a previous study. The article calls for viewing PCK as neither a subcategory of subject matter (subject matter knowledge for teaching) nor as a general generic form of knowledge. It presents a view of PCK as a collection of teacher professional constructions, as a form of knowledge that preserves the planning and wisdom of practice that the teacher acquires when repeatedly teaching a certain topic. Viewing PCK as a collection of TPCs, more precisely defining it, clarifying its relations to other knowledge and beliefs entities, and speculating about its development should facilitate future investigations of PCK.     

The development of beginning mathematics teacher pedagogical content knowledge

Recent research efforts (Schmidt et al. in The preparation gap: teacher education for middle school mathematics in six countries, MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical knowledge and pedagogical knowledge. However, identifying the nature of the mathematical knowledge and the pedagogical content knowledge (PCK) required for effective teaching remains elusive (Ball et al. in J Teacher Educ 59:389–407, 2008). Building on the initial conceptual framework of Magnusson et al. (Examining pedagogical content knowledge, Kluwer, Dordrecht, pp 95–132, 1999), we examined the PCK development for two beginning middle and secondary mathematics teachers in an alternative certification program. The PCK development of these two individuals varied due to their focus on developing particular aspects of their PCK, with one individual focusing on assessment and student understanding, and the other individual focusing on curricular knowledge. Our findings indicate that these individuals privileged particular aspects of their knowledge, leading to differences in their PCK development. This study provides insight into the specific aspects of PCK that developed through the course of actual instructional practice, providing a lens for future research in this area.     

Developing science teachers' pedagogical content knowledge

This article discusses the concept of pedagogical content knowledge (PCK) within the context of science teaching. First, an attempt is made to define this concept within the tradition of research on teachers' craft knowledge and to identify possible purposes of research on PCK. From this point of view, recent research on science teaching is investigated. This investigation identifies teaching experience as the major source of PCK, whereas adequate subject-matter knowledge appears to be a prerequisite. Finally, an empirical study is presented which focuses on PCK with respect to a specific topic—that is, chemical equilibrium. The effects on teachers' PCK of participation in an in-service workshop and conducting an experimental course in classroom practice are reported. This leads to the identification of elements of PCK teachers can use to promote student understanding. It is concluded that research on topic-related PCK may complement research on student learning of specific topics. © 1998 John Wiley & Sons, Inc. J Res Sci Teach 35: 673–695, 1998.     

Enhancing pedagogical content knowledge in elementary science

In this study, five elementary teachers and a university researcher developed and implemented problem‐based learning (PBL) experiences in the context of science teaching and learning. Collaborative inquiry was adopted as a methodology, while a variety of qualitative methods were used to examine the engagement and development of teachers’ pedagogical content knowledge (PCK). A PCK model is used as a framework to examine teachers’ professional knowledge growth in areas such as orientations to teaching science, knowledge of science curriculum, knowledge of students’ understanding of science, knowledge of assessment, and knowledge of instructional strategies. Implications for how teachers may be supported when adopting instructional innovations are discussed.     

The influence of an intensive in-service workshop on pedagogical content knowledge growth among novice chemical demonstrators

This study examined the influence of an intensive chemical demonstration workshop on fostering pedagogical content knowledge growth among science teachers identified as novice chemical demonstrators. The two-week summer workshop was designed around four training elements considered important to effective teacher in-servicing: theory, modeling, practice, and feedback. Clinical interviews served to probe various aspects of novice demonstrators' pedagogical content knowledge prior to and after the workshop. The interview protocols were analyzed using the methods of taxonomic, componential, and theme analysis. Differences in pre- and postworkshop clinical interview responses suggested growth in novices' representational and adaptational repertoires for demonstrating fundamental topics in chemistry. This growth was reflected in the increased number of chemical demonstrations and demonstration variations on each of the target chemical concepts that the novice demonstrators discussed after the in-service intervention. Their interview responses also suggested an increased awareness of the complexity of several chemical demonstrations, how these complexities could interfere with learning, and how simplified variations of the chemical demonstrations could promote science concept understanding. The research findings suggest that science teachers' pedagogical content knowledge in chemistry can be enhanced through intensive, short-term in-service programs.     

Emotional ecology: The intersection of emotional knowledge and pedagogical content knowledge in teaching

The purpose of this paper is to offer some theoretical as well as empirical examples that describe the interrelations between pedagogical content knowledge (PCK) and emotional knowledge in teaching and learning. The argument put forward is that there is a need to expand current conceptions of PCK and acknowledge the role of emotional knowledge. It is shown how a teacher's emotional knowledge about teaching and learning is an inextricable part of the ecosystem of teacher knowledge; this is called emotional ecology. Our research shows that the construct of emotional ecology occurs on different planes as there are different types of emotional knowledge that are aspects of PCK. The implications for pre-service and in-service teacher development are discussed.     

Probing the amalgam: the relationship between science teachers’ content,pedagogical and pedagogical content knowledge

ABSTRACT

This Special Issue aims to present evidence about the relationships between content knowledge (CK), pedagogical knowledge (PK) and pedagogical content knowledge (PCK); the development of these types of knowledge in novice and experienced secondary science teachers; and how CK, PK and/or PCK impact students’ learning. Since Shulman’s introduction of PCK as the feature that distinguishes the teacher from the content expert, researchers have attempted to understand, delineate, assess and/or develop the construct in pre- and in-service teachers. Accordingly, empirical findings are presented that permit further discussion. Outcomes permit post-hoc examination of a recent, collectively described, ‘consensus’ model of PCK, identifying strengths and potential issues. As we will illustrate, the relationship between CK, PK and PCK is central to this; that is, probing the hypothesis of pedagogical content knowledge as an ‘amalgam’ of content and pedagogical knowledge.     

Measuring teachers' pedagogical content knowledge in primary technology education

Pedagogical content knowledge is found to be a crucial part of the knowledge base for teaching. Studies in the field of primary technology education showed that this domain of teacher knowledge is related to pupils' increased learning, motivation, and interest. The common methods to investigate teachers' pedagogical content knowledge are often complicated, and time and labour consuming. Hence, a challenge in measuring teachers' pedagogical content knowledge is to construct an instrument that is time and labour‐efficient, and makes it possible to investigate large sample sizes. This paper illustrates how a multiple‐choice test to measure teachers' pedagogical content knowledge in primary technology education was designed and validated. The procedure of test construction and the first results are presented. It is concluded that the systematic procedure that was followed is effective for the construction of a valid test. In addition, statistical analyses showed that test/re‐test reliability is moderate. Data collection with larger samples is needed in order to find more statistical support for the psychometric properties of the test.     

An investigation of the relationship of beliefs,values and technological pedagogical content knowledge among teachers

ABSTRACT

The purpose of this study was to investigate the relationship among student-centred beliefs, technology value beliefs and technological pedagogical content knowledge (TPACK) in junior high school mathematics teachers. A survey was administered to 408 teachers in Taiwan. Regression analysis results showed that teachers’ student-centred beliefs and technology values were significantly correlated with TPACK. MANOVA results found that teachers with high student-centred pedagogical beliefs may not have high technology values, and teachers with lower student-centred pedagogical beliefs may not have lower TPACK. Implications for professional development and suggestions regarding teachers’ beliefs and TPACK are discussed.     

Content knowledge and pedagogical content knowledge in Taiwanese and German mathematics teachers

In comparing content knowledge (CK) and pedagogical content knowledge (PCK) of Taiwanese and German inservice mathematics teachers, the present study examines whether the two-dimensional structure of teachers' subject matter knowledge is cross-culturally invariant and whether differences in teacher education and in teacher selection are reflected in teachers' subject matter knowledge. The results confirm that CK and PCK represent two distinct, but correlated dimensions, even in teachers from completely different backgrounds. Taiwanese inservice teachers showed considerably higher CK and also higher PCK scores than German teachers. Teacher education and teacher selection should be considered important levers for reform in mathematics education.     

Perceptions of technological,pedagogical and content knowledge (TPACK) among pre-service teachers in Estonia

Most countries stress that preparing quality teachers for twenty-first century students is an essential task for teacher training institutions. Besides the skills for how to teach subjects effectively, teachers should also know how to integrate digital technology into their teaching. Several studies have been done based on the TPACK framework. Some of these studies use this framework for specific subject domains. In this study a generally applicable instrument for measuring TPACK was created. The aim of the paper was to validate the created instrument and to find out how pre-service teachers perceive their technological, pedagogical and content knowledge regarding the TPACK framework in Estonia, in a technologically highly developed country where technology is broadly used in general education. Conducting factor analysis all items with technology merged into one factor meaning that young generation perceives technology already integrated with content and pedagogy. The results indicate that pre-service teachers lack pedagogical knowledge, but they perceive that they are good at integrating technology into their teaching. Differences in perceptions were also found according to gender, age and curricula.     

Preservice elementary teachers' views of pedagogical and mathematical content knowledge

In broad terms, this study describes preservice elementary teachers' beliefs, conceptions, and practices during the mathematics methods course and teaching practica of a teacher education program. In particular, the study employs qualitative data to investigate preservice teachers' views of mathematical and pedagogical content knowledge. The study reveals symbiotic relationships between their views of content knowledge and their instructional actions which remain problematic. With unwavering beliefs and practices, and without reconceptualizing their roles as future elementary teachers, at the end of the semester the preservice teachers emerge as poor duplicators of mathematics methods instead of initiators of learning.     

Terry's Learning: some limitations of Shulman's pedagogical content knowledge

This exploratory article seeks to map out some possible practical limitations of Shulman's notion of pedagogical content knowledge and the associated concept of pedagogical reasoning. Interview extracts are used to illustrate the argument that the views and prior knowledge of a trainee teacher of mathematics may subtly shape what is learned in the context of training. It is suggested that representations of mathematics and mathematics teaching, originating in the trainee's own learning, might be concomitant with the development of a particular style of pedagogical reasoning which then determines the type of pedagogical content knowledge that is acquired. Shulman's framework is useful for understanding the trainee's learning, but insufficient to cover a broader range of pedagogical knowledge that might be deemed desirable in the trained teacher. It is suggested that a wider framework, extending pedagogical content knowledge to incorporate alternative forms of teaching, is needed.     

Revisiting the Translation of Nature of Science Understandings into Instructional Practice: Teachers' nature of science pedagogical content knowledge

This study (a) assessed the influence of an integrated nature of science (NOS) instructional intervention on inservice secondary science teachers' understandings, retention of those understandings, and their NOS instructional planning and practices; and (b) examined factors that mediated the translation of teachers' NOS understandings into practice. Nineteen teachers participated in an intensive, 6-week NOS course, which concluded with teachers developing plans to address NOS in their classrooms. Next, 6 participants were observed as they implemented their instructional plans. Data sources included pretest, posttest, and delayed-test NOS assessments, classroom observations, and several teacher-generated artifacts. The NOS course was effective in helping teachers develop informed NOS conceptions and retain those understandings 5 months after its conclusion. Teachers met with challenges and successes as they attempted to address NOS instructionally. The translation of NOS conceptions into practice was primarily mediated by the very nature of teachers' newly acquired NOS understandings, which were situated within the science contents, contexts, and experiences in which they were developed (i.e. the NOS course); thus, limiting participants' abilities to transfer their understandings into novel contexts and contents. The results helped build a model of the sources of science teachers' pedagogical content knowledge for teaching about NOS in content-rich contexts.