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.     

Influence of Constructivist Professional Development on Chemistry Content Knowledge and Scientific Model Development

The purpose of this study was to explore the relationship between teachers’ (N = 69) participation in constructivist chemistry professional development (PD) and enhancement of content (CK) and pedagogical content knowledge (PCK) (representational thinking and conceptual change strategies) and self-efficacy (PSTE). Quantitative measures assessed CK, PCK, and PSTE. Document analysis focused on PCK. Elementary teachers gained CK, PCK, PSTE, and designed lessons to advance thinking from macroscopic to abstract models. Middle/secondary teachers gained PSTE, PCK, and introduced macroscopic models to develop understanding of previously taught abstract models. All implemented representational thinking and conceptual change strategies. Results suggest that: (1) constructivist PD meets the needs of teachers of varying CK, and (2) instruction should connect representational models with alternative conceptions, integrating radical and social constructivism.     

Development and use of a test instrument to measure biology teachers’ content knowledge (CK) and pedagogical content knowledge (PCK)

Research on teachers’ professionalism and professional development has increased in the last two decades. A main focus of this line of research has been the cognitive component of teacher professionalism, i.e., professional knowledge. Most of the previous studies on teacher knowledge—such as the Learning Mathematics for Teaching (LMT) (Hill et al. 2004), the Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students´ Mathematical Literacy (COACTIV) (Baumert et al. 2010), and the Mathematics Teaching in the 21st Century (MT21) (Schmidt et al. 2007) studies—have been conducted in the field of mathematics teachers’ pedagogical content knowledge (PCK) and content knowledge (CK). There have been few comparable studies conducted with science teachers, especially biology teachers. To fill the gap, this study examines the development and use of instruments to measure biology teachers’ CK and PCK. In particular, this study describes a method to develop reliable, objective, and valid instruments measuring teachers’ CK and PCK in four steps by the use of empirical data of students. Additionally, the study explores whether CK and PCK might be measured as separate knowledge categories by using a paper-and-pencil test. This paper presents a theoretical model that guides test development and provides steps to develop and validate the instruments. Details are also provided regarding the computation of the Rasch scale score measures for 158 biology teachers. The results indicate that the instruments measured teachers’ CK and PCK in an objective, valid, and reliable way. This suggests that the new instruments can be used in combination with classroom observations to examine teaching quality and further its relation to student learning.     

On-Site Pedagogical Content Knowledge Development

Experiences and reflection have long been regarded as a foundation for pedagogical content knowledge (PCK) development. However, little is known about how experienced teachers develop their PCK via reflection-in-action during their moment-to-moment classroom instruction. Drawing upon data sources including classroom observations, semi-structured interviews and stimulated recall interviews based on lesson videos, this study examined instances when four experienced teachers were found to invent new instructional strategies/representations on the spot during the lesson (referred to as on-site PCK development) in their first attempts at teaching a new topic. The study documented the moment-to-moment experiences of the teachers, including their reconstructed thought processes associated with these instances of on-site PCK development. An explanatory model of a three-step process comprising a stimulus, an integration process and a response was advanced to account for the on-site PCK development observed among the teachers. Three categories of stimulus that triggered on-site PCK development were identified. Factors influencing the integration process and, hence, the resulting response, included teachers’ subject matter knowledge of the new topic, their general pedagogical knowledge and their knowledge of student learning difficulties/prior knowledge related to the new topic. Implications for teacher professional development in terms of how to enhance teachers’ on-site PCK 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.     

Effects of biology teachers’ professional knowledge and cognitive activation on students’ achievement

This study examined the effects of teachers’ biology-specific dimensions of professional knowledge – pedagogical content knowledge (PCK) and content knowledge (CK) – and cognitively activating biology instruction, as a feature of instructional quality, on students’ learning. The sample comprised 39 German secondary school teachers whose lessons on the topic neurobiology were videotaped twice. Teachers’ instruction was coded with regard to cognitive activation using a rating manual. Multilevel path analysis results showed a positive significant effect of cognitive activation on students’ learning and an indirect effect of teachers’ PCK on students’ learning mediated through cognitive activation. These findings highlight the importance of PCK in preservice biology teachers’ education. Items of the rating manual may be used to provide exemplars of concrete teaching situations during university seminars for preservice teacher education or professional development initiatives for in-service teachers.     

An Instructional Strategy to Introduce Pedagogical Content Knowledge Using Venn Diagrams

This paper describes the use of a three-circle Venn diagram as a vehicle for introducing pre-service elementary teachers to pedagogical content knowledge (PCK). Each circle of the diagram represents pedagogy, content and context individually. The overlap of any two circles represents the interaction between the circles. For example, the overlap of pedagogy and context relates to the ways that each of these general topics influences the other. The overlap of all three circles represents a complete lesson that is an integration of the three major components of PCK. The Venn diagram is an easily remembered graphic illustration of PCK that can be useful in planning lessons. The use of this graphic organizer in a science capstone course required of all pre-service elementary teachers is described.     

Pedagogical content knowledge of French as a foreign language: differences between pre-service and in-service teachers

Pedagogical content knowledge (PCK) is an important predictor of educational quality. PCK develops from various sources, such as teaching experience. Studies investigating the effects of teaching experience on PCK development mainly focus on the question whether experienced teachers differ from novices in the amount of PCK. In a mixed methods study, we study both quantitative and qualitative differences between pre-service and in-service teachers’ PCK. Total scores on a paper-and-pencil instrument are used as a measure of French PCK. To analyse the participants’ PCK in a qualitative way, answers are coded in four categories and the prevalence of answers in each category is compared between groups. Furthermore, the nature of answers is studied. No differences on our quantitative PCK measure are observed. The qualitative analysis shows that in-service teachers have more difficulties with conceptual knowledge, while showing more practical knowledge of students’ understanding than pre-service teachers.     

专业英文之学科教学知能模式建构

以改善大专专业英文教师的专业素养为目的,旨在了解EFL环境下,大专教师专业英文PCK内涵,目的在于建立专业英文教学的PCK模型。此模型之贡献在于提供一个典范,使想成为教授专业英文的教师有个教学上参考的依据,协助教师发现并发展有效专业英文教学所需的PCK,提升教师的专业素养。研究计划预期可获得之研究成果,有利于强化国内外有关专业英文PCK研究的认知,和国内外有关专业英文PCK教师自我评估认知。     

Interaction Between Science Teaching Orientation and Pedagogical Content Knowledge Components

The purpose of this case study is to delve into the complexities of how preservice science teachers’ science teaching orientations, viewed as an interrelated set of beliefs, interact with the other components of pedagogical content knowledge (PCK). Eight preservice science teachers participated in the study. Qualitative data were collected in the form of content representation, responses to an open-ended instrument, and semi-structured interviews. Preservice teachers’ orientation and PCK were analyzed deductively. Constant comparison analysis of how their orientation interacted with other PCK components revealed three major themes: (1) one’s purpose for science teaching determines the PCK component(s) with which it interacts, (2) a teacher’s beliefs about the nature of science do not directly interact with his/her PCK, unless those beliefs relate directly to the purposes of teaching science, and (3) beliefs about science teaching and learning mostly interact with knowledge of instructional strategies. Implications for science teacher education and research are discussed.     

TELPS: A method for analysing mathematics pre-service teachers' Pedagogical Content Knowledge

A pre-service teacher's Pedagogical Content Knowledge (PCK) and their personal constructs of teaching develop throughout their teacher education program. PCK integrates generic pedagogical knowledge, mathematical teaching methodology and knowledge of the discipline of mathematics and this paper reports on a survey that can be used to assess a pre-service teacher's PCK. TELPS (Teacher Education Lesson Plan Survey) was developed to determine the PCK of pre-service teachers during their teacher education program. TELPS is shown to analyse pre-service teachers' PCK with some indication that the pre-service teacher's development of PCK can be observed.     

STEAM教师学科教学知识的基本构成与建构逻辑

教师学科教学知识(PCK)的形成是STEAM教育的发展之基。STEAM教师PCK是教师面对具体的跨学科的内容主题时,所特有的将不同学科的知识和技术转化为学生易于理解的教学形式的整合性知识,具有知识范畴的跨学科性、知识来源的实践性和知识形成的融合性等特点。通过对已有PCK研究的梳理,结合STEAM教育的特征,STEAM教师PCK可分为跨学科内容知识、教学对象知识、教学情境知识和教学策略知识。在此基础上,STEAM教师PCK的建构逻辑:一是立足理论性学习为教师建构PCK打“地基”,促进公共性PCK向个体性PCK转化;二是基于经验性学习为教师建构PCK竖“框架”,推动内隐性PCK向实践性PCK转化;三是通过实践性学习为教师建构PCK添“砖瓦”,实现陈述性PCK向程序性PCK转化。     

In-Service Teachers’ Content and Pedagogical Content Knowledge in Mental Calculations with Rational Numbers

The purpose of the present study is to examine content knowledge (CK) and pedagogical content knowledge (PCK) of Greek teachers in number sense and specifically in mental calculations with rational numbers (fractions, decimals and percentages). Examined within the framework of CK were the type of strategies employed by teachers and the extent of the repertoire of these strategies, which provides an indication of their flexibility. Teachers’ CK performance in mental calculations with rational numbers was compared with the extent of their strategic repertoire as well as with the PCK they employed when teaching mental calculations with rational numbers. The data revealed that the teachers’ high CK performance in mental calculations with rational numbers is positively influenced by the existence of an extensive strategic repertoire. Furthermore, it was found that a high CK performance and an extensive strategic repertoire in mental calculations with rational numbers positively influence the PCK of mental calculations with rational numbers.     

Developing Pedagogical Content Knowledge for Teaching a New Topic: More Than Teaching Experience and Subject Matter Knowledge

Teaching experience has been identified as an important factor in pedagogical content knowledge (PCK) development. However, little is known about how experienced teachers may draw on their previous experience to facilitate their PCK development. This study examined how two experienced high school biology teachers approached the teaching of a newly introduced topic in the curriculum, polymerase chain reaction and their PCK development from the pre-lesson planning phase through the interactive phase to the post-lesson reflection phase. Multiple data sources included classroom observations, field notes, semi-structured interviews and classroom artefacts. It was found that the teachers’ previous experience informed their planning for teaching the new topic, but in qualitatively different ways. This, in turn, had a bearing on their new PCK development. Subject matter knowledge (SMK) can not only facilitate but may also hinder this development. Our findings identify two types of experienced teachers: those who can capitalise on their previous teaching experiences and SMK to develop new PCK and those who do not. The critical difference is whether in the lesson planning stage, the teacher shows the disposition to draw on a generalised mental framework that enables the teacher to capitalise on his existing SMK to develop new PCK. Helping teachers to acquire this disposition should be a focus for teacher training in light of continuous curriculum changes.     

Comparing Pre-Service Teachers’ PCK Through 9E Instructional Practice: A Case of Mathematics and Technology Pre-Service Teachers

Instructional practice plays a significant role in understanding teachers’ pedagogical content knowledge (PCK). The aim of the study reported on was to compare mathematics and technology pre-service teachers’ knowledge of PCK. The study used a case study approach of five mathematics and five technology pre-service teachers with a total of ten. Data was collected in seven public schools around Gauteng province in South Africa. The observation technique was employed in order to understand students’ classroom practice, using a video camera to capture the setting. One lesson of 45 minutes presented by each pre-service teacher, rendering a total of ten lessons, was observed. The study adapted the theoretical framework of PCK (Shulman 1987). The study scrutinised the data based on the qualitative content analysis method and found that most pre-service teachers in both mathematics and technology possess a limited knowledge of PCK. In both subjects, most of the pre-service teachers’ classroom practice did not exhibit comprehensive knowledge of the subject matter or knowledge of the learners. However, the difference is that only mathematics pre-service teachers have some knowledge of assessment. The data also indicate that “9E” instructional practice can be a valuable tool to enhance field-specific PCK within the field of mathematics and technology education subjects. Therefore, the study proposes further investigation of the “9E” instructional model that could be used as field-specific PCK within the fields of mathematics, science and technology.     

Akademisches versus schulbezogenes Fachwissen – ein differenzierteres Modell des fachspezifischen Professionswissens von angehenden Mathematiklehrkräften der Sekundarstufe

Educational research has introduced different models for the professional knowledge of (pre-service) teachers. Existing studies show major differences regarding the construct of content knowledge, which is often conceptualized based on school subject knowledge and varies with respect to academic content knowledge. The latter indicates that the question of what content knowledge teachers need has yet to be resolved. This question is particularly relevant from the perspective of teacher education at universities, since pre-service teachers for secondary schools are usually taught academic content knowledge. In this article we suggest a model of the discipline-specific teacher knowledge that includes pedagogical content knowledge (PCK) alongside two constructs of content knowledge: academic content knowledge (CK) and school-related content knowledge (SRCK). Findings from two studies for the subject area mathematics confirm that the components are empirically separable and that the three-dimensional model is superior to the two-dimensional model (CK, PCK). Moreover, the new construct SRCK holds potential for the investigation of the knowledge of pre-service teachers.     

Developing Science Pedagogical Content Knowledge Through Mentoring Elementary Teachers

Elementary teachers are typically hesitant to teach science. While a limited knowledge of science content is a reason for this, limited science pedagogical content knowledge (PCK) has emerged as another reason in recent research. This study constitutes two case studies of a professional development program for elementary teachers involving mentoring by a university professor. The mentor took the role of a critical friend in joint planning and teaching of science. The study examines the nature of the mentoring relationship and reports the type of teacher learning that occurred, with a particular focus on the teachers’ development of science PCK.

Development of Items for a Pedagogical Content Knowledge Test Based on Empirical Analysis of Pupils' Errors

In view of the lack of instruments for measuring biology teachers' pedagogical content knowledge (PCK), this article reports on a study about the development of PCK items for measuring teachers' knowledge of pupils' errors and ways for dealing with them. This study investigated 9th and 10th grade German pupils' (n?=?461) drawings in an achievement test about the knee-jerk in biology, which were analysed by using the inductive qualitative analysis of their content. The empirical data were used for the development of the items in the PCK test. The validation of the items was determined with think-aloud interviews of German secondary school teachers (n?=?5). If the item was determined, the reliability was tested by the results of German secondary school biology teachers (n?=?65) who took the PCK test. The results indicated that these items are satisfactorily reliable (Cronbach's alpha values ranged from 0.60 to 0.65). We suggest a larger sample size and American biology teachers be used in our further studies. The findings of this study about teachers' professional knowledge from the PCK test could provide new information about the influence of teachers' knowledge on their pupils' understanding of biology and their possible errors in learning biology.     

Building Pedagogical Content Knowledge within Professional Learning Communities: An approach to counteracting regional education inequality

Pedagogical Content Knowledge (PCK) and Professional Learning Community (PLC) are key notions to help understand teacher development for the benefit of student learning. Less understood is the contribution of PLC to PCK. This paper considers the Teaching and Research System in China to be a nationally institutionalised PLC for in-service teacher education. Building on quantitative analysis of a sample of 10,202 teachers, the paper concludes that participation in teaching and research activities within PLCs benefits teachers’ PCK. The paper also concludes that building PCK through the Teaching and Research System has potential to counteract regional education inequality.