Thesis (M. Ed. (Curriculum Studies)) -- University of Limpopo, 2020 / The purpose of this study was to explore the Pedagogical Content Knowledge (PCK) of Intermediate Phase teachers in the teaching of decimal fractions to Grade 6 learners. The study followed a qualitative research approach whereby a case study design was adopted. Three Grade 6 teachers were selected using a purposive sampling strategy to form part of the study. Shulman‟s (1986) Theory of Teacher Knowledge was used to guide the entire study. Data were collected through lesson observations, semi-structured interviews and document analysis. Data were analysed and interpreted using the Argyris, Putman and Smith‟s Ladder of Inference. The study established that Grade 6 teachers lacked PCK in the teaching of decimal fractions. Teachers lacked confidence in the teaching of decimals. The analysis of data also revealed that teachers‟ knowledge of decimal fractions was poor, and that teachers experienced challenges in teaching decimal fractions. Generally, decimal fractions were found to be difficult for teachers to teach. This led to the conclusion that teachers lack Pedagogical Content Knowledge in the teaching of decimal fractions. These findings, though not generalizable to a wider population, provide useful information for further research and insights of what Grade 6 mathematics teachers may be experiencing in their classrooms. The findings may help teachers improve their teaching. They also have implications for teacher-education institutions as they may restructure their teaching programmes, both for pre-service and in-service teachers.

Doctor of Philosophy / Department of Educational Leadership / Royce Ann Collins / In an era of increasing demand for a limited budget, more universities are turning to adjunct faculty to fill the need and to address the student load. Adjunct faculty members are hired for their content knowledge and close association to the business world and industry. This study was conducted to investigate whether a relationship exists between (a) technological pedagogical content knowledge (TPACK); (b) pedagogical training; and (c) personal technology; and to determine which variables have the greatest influence in the willingness of adjunct faculty at a Midwestern higher education institution to choose and integrate digital technology into curriculum and expand to the discussion of TPACK into graduate level education. TPACK is both a framework and an instrument to measure the level of integration of the primary components of the TPACK framework. TPACK is a term that describes what a teacher must know to integrate technology effectively into curriculum or teacher practices and represents the combination of teacher content knowledge, pedagogical knowledge and technology knowledge as interrelated. TPACK allows educators to consider what knowledge is required to integrate technology into teaching and how they might develop that knowledge within themselves. The study was conducted with a sample (n=30) of adjunct faculty members from two extension campuses from a Midwestern, Tier 1 university. The data revealed significant relationships between pedagogical training and selection of appropriate technology, and between personal technology use and selection of appropriate technology. The data also revealed that TPACK was a significant predictor; however, the subdomains of TPACK masked the true impact because of the high presence of covariance.

This thesis focuses on how school textbooks and teachers present models of chemical bonding in upper secondary schools in Sweden. In science, as well as in science education, models play a central role, but research has shown that they often are difficult for students to understand. In science education, models are presented to students mainly through textbooks and teachers, and textbooks influence teachers’ teaching. The aim of this thesis was to investigate how textbooks and teachers present models of chemical bonding with respect to students’ difficulties in understanding. To analyze representations of models, an analytical framework based on research reports of students’ difficulties in understanding related to models in general and chemical bonding in particular was developed. The chapters of chemical bonding in five chemistry textbooks were analyzed. Further, ten Chemistry teachers’ lesson plans about chemical bonding and semi-structured interviews with the teachers concerning their teaching were analyzed. This analysis concerned teachers pedagogical content knowledge (PCK) of teaching chemical bonding, with focus on knowledge of students’ difficulties in understanding and teaching strategies that take these difficulties into account. The results show that the teachers could specify examples of students’ learning difficulties, but the teaching strategies to promote the students’ understanding were limited. This indicates a deficient interaction between knowledge of difficulties in understanding and teaching strategies, two essential components of teachers’ PCK. Further, the models of chemical bonding represented in the textbooks and by the teachers might cause students’ difficulties in understanding. This indicates a gap between research of students’ difficulties in understanding and teaching practices as well as textbooks’ development. Further, the teachers’ representations of models were strongly influenced by the textbooks. Implications for textbooks’ authors, pre-service as well as in-service teachers are addressed. / <p>Papper 2 "Upper secondary teachers knowledge..." ingick i lic.uppsatsen som manuskript med titeln: "Swedish upper secondary teachers’ pedagogical content knowledge to teach chemical bonding". Nu publicerad. </p>

This study investigates to what extent educators’ pedagogical content knowledge affects learners’ achievement in quadratic functions. The components of pedagogical content knowledge (PCK) examined are: (i) mathematical content knowledge (MCK), (ii) knowledge of learners’ conceptions, and misconceptions, and (iii) knowledge of strategies. The participants were seventeen mathematics educators and ten learners from each educator’s class. The sample of educators was a convenient sample, while the sample of learners was selected by means of random sampling. A mixed method design was used to execute the study. Data about educators’ MCK, and knowledge of learners’ misconceptions were collected by means of a questionnaire. An interview was used to gather data about educators’ knowledge of strategies. Data on learners’ achievements and misconceptions was collected by means of a questionnaire. Descriptive statistics were used to describe the effect of each component of the educators’ PCK on learners’ achievements. The result indicates that the achievement of learners who are taught by educators who have strong PCK is higher than the achievement of learners who are taught by educators who have weak PCK. / Mathematical Sciences / M. Ed. (Mathematics Education)

Despite the growing importance of science and technology in society, school students consider these subjects irrelevant and hard to learn. Teachers must therefore know how to teach science in ways that enhance students’ understanding and interest. This thesis explores various aspects of the teaching and learning of chemical bonding, an important topic in school chemistry that is primarily taught using models. Research has shown that students find chemical bonding difficult to understand, and that the use of models in science education contributes to this difficulty. I therefore investigated teachers’ knowledge of how to teach chemical bonding and ways of developing it to improve students’ understanding. To this end, I analysed chemistry textbooks and teachers’ lesson plans, and conducted semi-structured interviews with teachers about their teaching of chemical bonding. This revealed that the representations of chemical bonding used in textbooks and by teachers can cause students difficulties. The teachers were generally unaware of how these representations might affect students’ understanding, implying that their pedagogical content knowledge (PCK) could be improved. To explore ways of incorporating research findings into teaching practice and developing teachers’ PCK, I conducted a learning study in which three secondary science teachers together explored and reflected on their own teaching practice. CoRe, a method for creating detailed descriptions of what, how, and why specific content is taught, was used to enhance the reflections and make the teachers’ PCK explicit. As a result, the teachers developed their representations of chemical bonding, became more aware of students’ understanding, and were better able to motivate their actions and choices of content and strategies. This thesis shows how professional development can bridge the gap between research and teaching practice, and how teachers’ PCK can be developed to improve students’ understanding. / Many complex real-world phenomena can only be understood using models that make the abstract visible and provide explanations, predictions, descriptions, or simplifications. However, research has shown that students have difficulties understanding models used in science education in general, and particularly chemical bonding models. This thesis examines various aspects of the teaching and learning of chemical bonding, and its presentation in textbooks and by teachers. It is shown that the representations used by teachers and in textbooks can cause students to have difficulties in understanding, which teachers were generally unaware of. Teachers rarely justify their choices specifically to overcome students’ difficulties, suggesting that their knowledge of how to teach chemical bonding could be improved. A learning study in which teachers collaboratively explored and reflected on their own teaching practice significantly improved their presentation of chemical bonding, their awareness of students’ understanding, and their ability to justify their choices. Overall, this work shows that there is a gap between research and teaching practice, and that effective ways of incorporating research results into teaching practice are needed to improve teaching and learning in chemistry.

Doctor of Philosophy / Curriculum and Instruction Programs / David S. Allen / This study examined pedagogical content knowledge (PCK) and Mathematics knowledge for teaching (MKT) from a perspective that blends existing definitions, questions, and methodologies into a unique method of collecting and analyzing data. Many studies on MKT have been done using qualitative methodology, usually with the researcher interviewing or testing individual teachers and analyzing that data using qualitative methods. A smaller number of studies have attempted to measure MKT using a quantitative approach, often times involving paper pencil tests with multiple choice and some open ended questions. Current research is also heavily weighted towards pre-service elementary teachers in the area of MKT for division by fractions (Depaepe et al, 2013). Although it may be true many pre-service elementary teachers have difficulties with division by fractions (Li & Kulm, 2008; Ma, 1999; Tirosh, 2000), we do not know if these problems persist for in-service elementary teachers or with secondary teachers at any stage. This study used a survey created by the researcher as a synthesis of existing questions from research on MKT with regards to division by fractions. This survey was delivered through an online format. The qualitative data in this research was then coded into quantitative data using a rubric developed by the researcher producing MKT scores that could be analyzed using statistical methods and generalized to a larger population. This study examined the Mathematical Knowledge for Teaching held by elementary, middle, and secondary in-service teachers in the domain of division by fractions. In particular this research asked if there was a relationship between the educational background, training, and experience of teachers and their MKT. Multiple analysis including independent t-tests, independent one-way ANOVAs, and Multiple regression analyses revealed that Middle school teachers and teaching at a middle school were significant predictors of increased MKT scores when compared with other groups of teachers. The type of teaching license, the type of degree held, total experience, and grade level experience were all found to have no significant relationship to MKT scores.

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Humanities, School of Education, 2012 / Reflection about lessons delivered is a practice widely encouraged in teaching. Reasoning, particularly about transformation of subject matter knowledge of lessons yet to be taught, is an internal process and a speciality evident largely in expert teachers. The study investigates the feasibility of fast-tracking its development in pre-service chemistry teachers. It focuses on developing this specialty within a specific topic, as a theoretical construct called Topic Specific PCK (TSPCK). Five knowledge components of TSPCK are identified as the enablers that transform subject matter knowledge. The components are: (1) students’ prior knowledge, (2) curricular Saliency, (3) what is difficult to teach (4) representations, including powerful analogies, and (5) conceptual teaching strategies. These components are identified, with reference to literature, as aspects specific to the subject matter knowledge of the teacher and useful in its teachability. A new tool to measure the quality of TSPCK is developed. The procedure for developing the tool consists of the following steps: (i) confirming the characteristics of the test items fitting the Topic Specific PCK construct, (ii) production of test items, (iii) judgment of items, (iv) construction of the instrument (v) piloting and (vi) validation of the instrument. Care is taken to ensure presentation of multiple evidence and discussions, addressing the interpretive and arguments as requirements for showing validity of the construct measured by the instrument. The Topic Specific PCK tool is validated with a group of 20 practicing teachers. The tool is scored, using a rubric corresponding to the five components with each being rated on a four point scale, from 1 (Limited) to 4 (Exemplary). The analysis of the generated scores is done using the Rasch statistical model (Winstep, version 3.72.3). The reliability indices as indicated by person reliability and item reliability are found to be high at 0.86 at 0.91, respectively. The persons and item scores reflect measures well inside the conventionally acceptable range of -2 and +2. A further indicator of validity of the tool is the empirically calculated hierarchy of test items’ order of difficulty, found similar to the theoretically predicted pattern for the teacher group. Based on the above analysis and findings, I regard the tool as valid and reliable. My research design is based on mixed-methods research (MM). The research strategy takes the form of a case study. The study is located in a methodology class for final year physical science pre-service teachers. They formed an experimental group (N=16) for this study. I delivered an intervention, targeting understanding of transformation of Chemical Equilibrium concepts, using the above listed five knowledge components. I collected data through a combination of tools, including the newly designed Topic Specific PCK tool in Chemical Equilibrium, an Achievement tool and a science teacher Belief tool. Both the Achievement and the Belief tools were adapted from existing tools, and were thus considered tried and validated. The findings suggest that the quality of Topic Specific PCK in chemical equilibrium may be improved in pre-service teachers by the explicit discussion of the knowledge enabling its transformation. They also suggest that, in the process of discussing aspects of subject matter knowledge related to its transformation, pre-service teachers improve their conceptual understanding of chemical equilibrium. Both these improvements were not affected by the shift or lack of shift in teacher beliefs from teacher-centred towards student-centred practices. I acknowledge the small size of the sample as a practical limitation to the generalization of the statistical findings in this study. I suggest that emphasis be placed on the trends displayed, as they are similar to those obtained from the multiple sources of the qualitative component of the study. Finally, I recommend that the development of PCK in pre-service teachers be considered in a topic by topic manner. I urge that the teaching of chemistry topics be explicitly organized in a format in which pre-service teachers would be expected to reason about them, and particularly transform them for teaching.

Thesis advisor: Joseph J. Pedulla / There is considerable evidence that new teachers are ill prepared for classroom practice, including self-reported evidence collected from teachers (e.g., Levine, 2006), and statistical evidence for differences in the achievement of students with new versus more experienced teachers (Rivkin, Hanushek, and Kain, 2005). In light of the challenges encountered by new teachers (e.g., Levine, 2006), this study examined the value of different forms of teacher knowledge for teachers with different levels of experience. In particular, this study investigated the interactive relationship between teaching experience and teacher content knowledge, and student achievement in mathematics and science. In New York City, Boyd et al. (2009) linked practice-focused teacher preparation to student mathematics achievement in the first year of teaching and teacher content preparation to achievement in the second. However, other studies demonstrated interactions between teaching experience and content knowledge with different interpretations (e.g., Kukla-Acevedo, 2009; Monk, 1994). At the same time, this study examined the interactive relationship between teaching experience and teachers' pedagogical content knowledge, and student achievement. Extant models of teacher career development (Huberman, 1989; National Research Council, 2010) and how teacher education affects student achievement (e.g., Desimone, 2009) offered theoretical grounding for the study. With nationally representative samples of fourth and eighth grade U.S. students--participants in the 2011 Trends in International Mathematics and Science Study--this study employed hierarchical linear modeling to address its research questions among an array of student achievement outcomes in the domains of mathematics and science. This study attempted to account for salient student, teacher, and contextual factors, and the probabilities of teachers' receipt of various teacher education "treatments" (i.e., propensity score analysis) to reduce the plausibility of selection threats to internal validity. The study found no evidence for relationships between teacher content knowledge or pedagogical content knowledge and student mathematics and science achievement in fourth and eighth grade. Furthermore, the results indicated no interactive relationships between forms of teacher knowledge and teaching experience, and student achievement in these grades/subjects. The limitations of cross-sectional, observational studies using large-scale data and directions for further research are discussed. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement, and Evaluation.

Postgraduate tutors have an important role to play in teaching and learning in higher education. There has been substantial research conducted in this area - much of it is orientated towards improving the quality of the methods of instruction and classroom practice. Far less research has been focused on the postgraduate tutors as producers of content. This research is based on an intervention that tasked five postgraduate tutors with planning two tutorials and designing an assessment task: activities that fell outside the scope of their usual work and roles. The aim of the research is to discover more about how postgraduate tutors, who typically have extensive and expert content knowledge, but very little pedagogical knowledge, develop pedagogical content knowledge. The study tracks the decision making process and the knowledge reservoirs that the participants emphasise in their planning and design in order learn about the teaching beliefs and priorities of these novice teachers. The analysis goes on to explore the criteria for legitimation that the postgraduate tutors establish and/ or entrench. The study finds that the participants are highly sensitive to the many kinds of constraints that circulate and that they in turn re-circulated. It goes on to suggest that postgraduate tutors are likely to reproduce the regulative rules that they find in operation and the cumulative messages of what is valued in terms of student and teacher performance in a given context.

Esta pesquisa se insere na temática de conhecimento de professores. Trata-se de um estudo de caso e a coleta e o tratamento dos dados se inserem na perspectiva da pesquisa qualitativa. Nosso intuito foi o de investigar o conhecimento pedagógico de conteúdo (CPC) de uma professora de química quando esta desenvolveu o tópico \"soluções\" nas suas turmas de Ensino Médio. Objetivou-se ainda contribuir com evidências sobre o papel do conhecimento de conteúdo no CPC. Nossos dados estão baseados em questionários, planos de aula, planejamentos, CoRes, registros audiovisuais de aulas e entrevistas. Os dados foram todos transcritos e a análise dos mesmos foi baseada na categorização das manifestações do conhecimento de professores e interpretados com relação aos correspondentes domínios dos conhecimentos de professores, conforme proposto por Rollnick et al. (2008). As interações discursivas presentes nas aulas da professora foram analisados segundo a ferramenta proposta por Mortimer e Scott (2002). A triangulação desses dados permitiu inferir sobre o conhecimento pedagógico do conteúdo dessa professora e revelaram que ela possui um CPC pouco desenvolvido com relação ao conteúdo investigado, enfatizando a memorização e cálculos em detrimento de conteúdos conceituais. Nesse estudo de caso o conhecimento do conteúdo se revelou importante e afetou outros domínios de conhecimento dessa professora, gerando reflexos no desenvolvimento do seu CPC. Concluímos pela centralidade do papel desempenhado pelo conhecimento do conteúdo no desenvolvimento do CPC e consideramos o conhecimento do conteúdo como um dos componentes essenciais do CPC. / This work has a qualitative research perspective and it is a case study related to teacher knowledge. Our focus was the pedagogical content knowledge (PCK) of a chemistry teacher during the developing of the subject matter \"solution\" at high school context. The aim of this research was also provide some evidences about the role of the subject matter knowledge (SMK) in the PCK construct. Our data are based in questionnaires, classes plans, planning, CoRes, classes video recordings and interviews. Data were all transcribed and categorized by using categories related to the manifestations of teacher knowledge and interpreted in relation to the corresponding domains of teacher knowledge, as proposed by Rollnick et al. (2008). The discursive interactions observed in classroom were analyzed by using the tool proposed by Mortimer e Scott (2002). Data triangulation allowed us conclude that the PCK of this teacher is not very well developed in relation to the subject matter investigated. The teacher emphasizes procedural approaches at the expense of conceptual understanding. During this case study the role of SMK was highlighted and it influenced others domains of this teacher knowledge, reflecting in her PCK development. We concluded by the central role performed by SMK in the PCK development and we consider SMK as one of the PCK essential components.