Developing a Scale to Measure Content Knowledge and Pedagogy Content Knowledge of In-Service Elementary Teachers on Fractions

The main purpose of this study was to develop a scale for measuring content knowledge (CK) and pedagogy content knowledge (PCK) of in-service elementary teachers on mathematical fractions. Another aim of this study was to consider whether CK and PCK are separate from each other, or are in a single body. Therefore, a scale containing 22 items about mathematics fractions was designed and administered to 256 elementary teachers. Exploratory factor analysis indicated four factors that three of which are included in PCK, that is, instruction, task, and student, whereas CK had just one factor. Also to evaluate fitness of model, confirmatory factor analysis was used. The results revealed that CK and PCK are separate and correlated, and the scale has suitable validity and reliability to measure CK and PCK of in-service elementary teachers on mathematics fractions.     

Exploring challenges of assessing pre-service science teachers’ pedagogical content knowledge (PCK)

The purpose of this paper is to report on the challenges we faced in designing an instrument aimed at measuring pre-service science teachers’ topic-specific pedagogical content knowledge (PCK). After the instrument was conceptualised and developed, it was administered to 30 pre-service chemistry teachers. The findings suggest that the instrument can be used as a teaching tool to enhance pre-service science teachers’ topic-specific PCK along with some limitations. The discussion focuses on the implications of the aforementioned PCK assessment tool for enhancing pre-service science teachers’ topic-specific PCK and the challenges associated with measuring and enhancing pre-service science teachers’ PCK. Finally, our discussion focuses on the ways in which science-teacher educators can engage in transforming the concept of PCK and its use for research and professional development.     

Geography pre-service teachers’ pedagogical content knowledge

This paper reports on an exploratory study that investigated the pedagogical content knowledge (PCK) of four Geography pre-service teachers as they completed their final practicum of their Bachelor of Secondary Education programme. It uses Shulman’s (1986, 1987) two categories of PCK as a conceptual framework to identify the participants’ PCK of their Geography teaching. The first type of PCK is teachers’ representations of content that is pedagogically powerful for students; the second type of PCK refers to teachers’ understanding of what makes the learning of specific topics easy or difficult for students. Historically, researchers have tended to focus on the teachers’ representations component of PCK while little evidence-based research has been reported on the second category of PCK. Findings from this study show that all participants demonstrated both types of PCK. This study sheds light on the importance of teacher-educators modelling both types of PCK as both are equally important for pre-service teachers.     

A multi-year study of pre-service teachers’ literacy practices in the content areas: time epistemologies and indicators of stasis and growth

This three-year study focuses on 42 pre-service teachers’ perspectives on integrating literacy into their content area teaching. Pre-service teachers described time as an influential factor shaping their teaching practices, and, we found, that perceptions of time influenced pre-service teachers’ reported ability and willingness to plan for and enact the implementation of literacy strategies as part of content area lessons. While we noted a number of factors related to time, we were particularly drawn to three time-related factors that signified for pre-service teacher participants’ active roles and agency in how they were enacted in the classroom. Identifying temporal concerns about curriculum, learner response to literacy practices, and use of classroom time to scaffold learning allowed us to specify aspects of participants’ pedagogical content knowledge (PCK) development as well as facets of limited PCK growth. Using time as a theoretical lens to view pre-service teachers’ accounts of literacy practices, we suggest, provides insights into their PCK, specifically indicators of stasis and growth, and understanding about pre-service teacher resistance or acceptance to the infusion of literacy into content area teaching.     

Exploring the Development of Pre-Service Science Elementary Teachers’ Pedagogical Content Knowledge

This paper explores how a group of pre-service elementary science student teachers came to understand the development of their Pedagogical Content Knowledge (PCK) over the course of a semester??s study in a science methods course. At the start of the semester, PCK was introduced to them as an academic construct and as a conceptual tool that they could use to plan for, and assess, the development of their professional knowledge and practice as beginning science teachers. All participants were provided with a tool known as a CoRe (Content Representation) and the manner in which they worked with the CoRe was such that it supported them in planning for and assessing their own learning about teaching elementary science through a focus on the development of their PCK. Through analysis of data derived from the application of a CoRe based methodology (modified and adapted for this study) to the teaching of the science topic of Air, participants?? reasons for, confidence in, and perceived meaningfulness of their learning about science teaching could be examined. In so doing, the nature of participants?? PCK development over time was made explicit. The results illustrate real possibilities for ways of enhancing student teachers?? ongoing professional learning in teacher preparation and offer a window into how the nature of PCK in pre-service education might be better understood and developed.     

Teaching teachers to teach Boris: a framework for mathematics teacher educator pedagogical content knowledge

The notion of pedagogical content knowledge (PCK) was posited in the context of school teaching and the knowledge used by teachers teaching school students. It has been examined for a number of discipline areas, notably mathematics. There are, however, other teaching contexts, including those of teacher educators, whose students are pre-service teachers (PSTs). The content these teacher educators teach is not subject discipline knowledge (or not solely), but the PCK for teaching a subject discipline. What knowledge do teacher educators use as they teach PCK? This paper presents a framework for the PCK required of mathematics teacher educators as they work to develop PSTs’ PCK for teaching mathematics. The framework builds on existing research into PCK and categorises aspects of the work of teacher education. The framework’s usefulness is examined by studying the PCK used by the first author in building PSTs’ understanding of mathematics teacher PCK.     

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.     

Analysing teachers’ translation of sustainability using a PCK framework

In order to teach about sustainability, teachers need to be able to translate their personal understanding of this concept into their pedagogy in ways that make it accessible to their learners. This translation process is known as pedagogical content knowledge (PCK). This study investigated the way that two teachers translated their understanding of sustainability into their pedagogy and the effects of this translation on children’s learning (n?=?18). Two interpretive case studies were constructed. Data were generated using interviews and documents. Two frameworks were used to analyse the data. One was a definition of sustainability and the other a model of PCK expressed as pedagogical context knowledge (PCxK) that consisted of four components. The findings showed that the translation of sustainability was a complex interaction of three of the PCxK components with some use of the fourth. Some children developed an understanding of sustainability but only two were able to link their understanding with the scientific concepts taught resulting in ‘diffused learning’. Also, these findings suggest that while the PCxK model used to analyse the translation process had a degree of precision and heuristic power, further refinement is needed in order for this model to explicate teachers’ PCK.     

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.     

Pre-Service Elementary Teachers'' Perceptions of Factors in an Holistic Methods Course Influencing their Confidence in Teaching Science

Lack of confidence towards science is a major factor in the avoidance of teaching science at elementary school. This paper reports the results of a survey that asked 28 pre-service elementary teachers what they believed contributed to their confidence towards science and the teaching of science during a second year science unit where an holistic teaching/learning approach was taken. The holistic nature of the unit was based on a model that considered six major factors to be important influences on the confidence of the pre-service teacher. Using median values, and ranking from the most to least important factor influencing their confidence, the pre-service teachers identified practicum, teacher educator, pedagogical content knowledge, learning environment, assessment and reflection. Factors within pedagogical content knowledge, ranked from most to least important, were science pedagogy, science activities, children's views of science, science content knowledge and investigating scientifically. The wide variability in responses highlighted that no single factor was perceived to be a major contributor to the pre-service teachers' confidence, but rather a balanced mix was necessary. Implications for pre-service elementary science education units are discussed.     

What do we know and where do we go? Formative assessment in developing student teachers’ professional learning of teaching science

In the context of teacher education, it could well be suggested that assessment activities that build on formative interactions between student teachers and teacher educators might offer new windows into better understanding teaching and learning. This paper presents findings from a study into a primary science teacher education initiative that seeks to build the foundations on which 24 primary science student teachers, through the use of formative assessment of their science teaching and learning, can begin developing their pedagogical content knowledge (PCK). In the project, formative assessment consists of activities used by teacher educators to stimulate interactions, self- and peer-assessment in order to provide insights into how student teachers develop their PCK during a semester. Content Representations (CoRes), were used as a tool to unpack the student teachers’ approach to teaching a science topic and the reasons for that approach. The results indicate that the use of CoRes, together with subsequent self-assessment and formative interactions with teacher educators and peers, do have the potential for PCK development for student teachers. The results further highlight the need for developing reliable and valid tools for capturing and assessing student teachers’ PCK in pre-service teacher education.     

Investigating the relationship between pre-service physics teachers' professional knowledge,self-concept,and interest

This study investigates the relationships between professional knowledge, self-concept, and interest of pre-service physics teachers. In order to support student learning and interest development alike, teachers need a profound professional knowledge and respective motivational orientations. Developing both professional knowledge and motivational orientations in teachers is therefore a key challenge of teacher education. Prior research has focused on the development of content knowledge (CK) and pedagogical content knowledge (PCK) within teacher education, but the role of motivational orientations such as self-concept and interest have mostly been neglected areas of study. As individuals develop domain-specific motivational orientations, they compare their achievement in an external frame to the achievement of their peers, and they compare their achievements in an internal frame across domains. The effects of these psychological processes on domain-specific motivational orientations are described by the generalized internal/external frame of reference model (GI/E model). We assessed the professional knowledge (CK and PCK) and motivational orientations (self-concept and interest) of N = 200 pre-service physics teachers from 12 teacher education institutes in Germany. To investigate the predictions of the GI/E model, we utilized structural equation modeling. In line with the GI/E model, the analysis revealed that pre-service teachers use social comparisons. Pre-service teachers with a higher CK/PCK also showed a higher CK/PCK self-concept. We also identified instances of internal comparisons as we found that a high level of CK corresponds with a lower PCK self-concept. While we could not identify the same effects from professional knowledge on interest, self-concept mediated the effects from professional knowledge on interest. The results suggest that interdependencies between professional knowledge and motivational orientation should be given more consideration in teacher education research and should also be addressed more explicitly in teacher education.     

‘Crossing’ the equals sign: insights into pre-service teachers’ understanding of linear equations

This paper reports on an exploratory study designed to determine and enhance the conceptual understanding of a group of pre-service mathematics teachers at one Irish university utilizing an established framework for understanding mathematics. 23 students on a one year Professional Diploma in Mathematics Education participated in the study, which involved the distribution of a pre- and post-test and engagement in a ten week intervention designed to enhance their subject matter knowledge (SMK) and pedagogical content knowledge (PCK). The findings highlight that although there was an improvement in overall conceptual understanding across the entire cohort at the end of the intervention, within certain mathematical topics there was a statistically insignificant improvement and many deep-rooted issues remain. In this paper we focus on the pre-service teachers’ understanding of elementary algebra, in particular, how to solve a linear equation.     

Investigating the development of prospective mathematics teachers’ pedagogical content knowledge of generalising number patterns through school practicum

The purpose of this study is to investigate the development of three prospective elementary mathematics teachers?? pedagogical content knowledge (PCK) of number patterns with its two components: (1) knowledge of students?? understanding and difficulties and (2) knowledge of topic-specific strategies and representations. For our investigation, we use Radford??s (ZDM Math Educ 40:83?C96, 2008) framework called ??architecture of algebraic pattern generalisation?? to redefine these two components of PCK in the context of patterns. A case study was conducted to explore the development of PCK through a school practicum course and to examine how observation of number pattern lessons in schools and discussions of these observation contribute to prospective teachers?? PCK. Analysis of the data indicated that observations and discussions of number pattern lessons resulted in considerable change in the way prospective teachers take into account students?? understanding of and difficulties with patterns, as well as in the way they use pattern-specific strategies such as algebraic pattern generalisation during their lessons.     

A proficiency model for pre-service physics teachers' pedagogical content knowledge (PCK)—What constitutes high-level PCK?

This study identifies proficiency levels in pre-service physics teachers' pedagogical content knowledge (PCK) and reveals how teacher education can promote transitions into higher proficiency. Teacher education plays a fundamental role in supporting pre-service teachers' PCK development. Proficiency levels are a powerful source when evaluating this PCK development because they characterize what learners are likely to be able to know on a specific level. Previous research has presented a model of proficiency levels in pre-service physics teachers' PCK; however, evidence for the model's validity is still lacking. According to the Refined Consensus Model of PCK, factors such as teachers' content knowledge (CK), their teaching experience, and their beliefs about teaching and learning science promote PCK development. Thus, understanding how and when pre-service physics teachers' CK, teaching experience, and beliefs contribute to their proficiency can bring insights into how teacher education can promote PCK development. To address this issue, N = 427 observations of pre-service physics teachers were analyzed. Utilizing the scale anchoring procedure, four different proficiency levels in pre-service physics teachers' PCK were identified. Analyzing these proficiency levels showed that lower levels can be characterized as remembering content-unspecific knowledge, whereas higher levels encompass content-specific strategies to structure and elaborate lessons. Additionally, logistic regression models revealed that pre-service physics teachers' CK is crucial for an increase in PCK proficiency. However, transitions into higher levels of PCK additionally require teaching experience and adequate beliefs about teaching and learning. Thus, our proficiency levels can be used to bring insights into how proficiency in PCK can be supported during teacher education. For example, teacher education should provide courses focusing on the science curriculum and the assessment of student learning to promote pre-service physics teachers' progression in PCK.     

Module-Phase-Dependent Development of Pedagogical Content Knowledge: Replicating a Role-Change Approach in Pre-Service Teacher Education in an Outreach Lab

Research in Science Education - How pre-service teachers (PST) develop components of pedagogical content knowledge (PCK) is an open question. Theoretically based on PCK and combined with student...     

呼唤现代教师教育学的学科建设

教师教育学是以对基础教育包括中小学和幼儿园教师职前职后一体化的教育为对象,以荟萃其认识成果、揭示其发展规律、指导其实践活动为目标,进而融科研、教学、育人于一体的专门化、应用性知识体系。应在教育学一级学科门下增设教师教育学二级学科,促进教师教育的理论研究,加强对教师教育实践的科学指导。应注重教师教育学科的组织、队伍、专业、课程与教材建设,运用历史和逻辑相结合的研究思维及形而上和形而下、思辨和经验、实证和实地等多种研究方法,对教师教育由低到高、由独立封闭到开放多元的运演轨迹及其主体与客体、目的与手段等要素进行全景式的考察,以建设科学与教学相统一的现代教师教育学科。     

Pre-service English teachers’ perceptions and practice of field experience and professional learning from expert teachers’ mentoring

Though it is well known that pre-service teachers’ field experiences are recognized as key to enhancing teaching practice, Taiwanese pre-service teachers who take ‘Teaching Methods and Materials’ in elementary school’s seven areas often complain that they lack field experience. They do not have the opportunity to experience teaching demonstrations among real elementary school students. This case study discusses 35 pre-service English teachers’ professional learning and the field experience they acquired from expert teachers in the Teaching Methods and Materials of English in the Elementary School course in Taiwan. Data in this study include: (1) observation notes, (2) lesson plans, worksheets, and teaching materials, (3) videos on teaching demonstrations, (4) conversation notes on lesson planning, (5) the class syllabus, (6) semi-structured interviews with expert teachers, and (7) participants’ reflections on their mentoring experience. Participants held positive attitudes toward the mentoring experience and their expert teachers. Because it helped them combine their knowledge of the classroom context, lesson plan content, instructional pedagogy, and their students, these 35 participants regarded teaching practice as more beneficial than observing expert teachers’ instructions and having conversation with expert teachers after teaching practice. In addition to mentored field experience, online discussions and seminars on topics are suggested for inclusion in mentoring activities.