In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.

This thesis focuses on four different aspects of history teachers’ comprehensive understanding of the school subject history. More specifically, the aim is to study the comprehension of the subject as perceived by individual history teachers. Special emphasis is placed on identifying the concepts of the field of history that are central to the teachers’ understanding of the school subject history.           The first aspect studied is the teachers’ biographical changes. In a life history perspective it seems as if the teachers’ subject conception changes from an unproblematic and tentative approach to a more complex and confident understanding of the subject. The second aspect treated is the rationale behind their grasp of the purpose and content of the subject. Three major positions are identified, namely educational (bildung) orientation, critical orientation, and identity orientation.           The third aspect studied is the teachers’ interpretation of a curriculum new to them. The teachers placed the curriculum in the field of tension between an education policy position, emphasizing more precise knowledge, on the one hand, and a history science position, emphasizing concepts of historical consciousness. The fourth aspect studied is five different conceptual tools displayed in the teachers’ remarks on having completed the teaching of a new course. These are termed ‘history as narrative’, ‘history as time-space’, ‘history as explanation’, ‘history as perspective taking’, and ‘history as skills’           At the general level the study shows not only that subject conception is of importance to the teachers’ understanding of their obligation as teachers of history but also how it is formed and constantly transformed by many different factors. In this process it is clear that the concepts used by the teachers, although variously defined, can be seen as specific to the school subject history and essential to the construction of history as a school subject. / Baksidestex: Vad är syftet med skolämnet historia? Vad ska skolämnet historia innehålla? Det här är en doktorsavhandling där fokus sätts på lärares förståelse av skolämnet historia. Mer precist avgränsas syftet till att undersöka ämnesförståelsen hos nu verksamma historielärare. Särskild vikt läggs vid att identifiera centrala begrepp i lärarnas ämnesförståelse. Undersökningen bygger både på enkäter och intervjuer och tar sin utgångspunkt i fyra olika aspekter av historielärarnas ämnesförståelse som redovisas i separata studier. Den första aspekten är ämnesbiografisk och tar fasta på de faktorer lärarna menar har påverkat utvecklingen av deras ämnesförståelse. Den andra aspekten har sitt fokus på lärarnas förståelse av historieämnets övergripande syfte och innehåll. Den tredje aspekten handlar om hur lärarna tolkar inriktningen och innehållet i den nya ämnesplan som infördes i gymnasieskolan 2011. Den avslutande aspekten fokuserar på de ämnesredskap som blir synliga i de utsagor lärarna gör om innehållet i gymnasieskolans kurs Historia 1b.

South Africa has a unique cultural, historical, socio-economic and linguistic contextual complexity that influences the implementation the intended curriculum and educational policies. The contextual complexity continues to result in Science teachers entering into the teaching profession with a wide spread diversity in background and qualifications. The secondary data analysis used a concurrent mixed methods approach (QUAL + quan) to explore the interconnection between teacher characteristics, classroom practices and learner achievement in Physical Science. The primary sample consisted of 18 schools that were stratified by district and quintile. From the available data, nineteen Grade 12 Physical Science teachers with varying levels of qualifications and experience were analysed. A combination of qualitative and quantitative instruments, specifically, Science teacher questionnaires, Science lesson observations and Science teacher interviews, were explored. The data was analysed quantitatively using descriptive statistics, frequency tables and Pearson correlation coefficients. The qualitative data involved content analysis and the presentation of case studies and the themes that emerged. Significant Pearson correlations indicate a positive relationship between years of related experience and pass rates and also pointed to an interconnection between professional qualifications, related experience and learner achievement. Differences in teacher characteristics were also indicators of competency in content knowledge and ultimately influenced classroom practices. Four case studies are offered in an attempt to provide in-depth descriptions of the teacher characteristics and practices for Grade 12 Physical Science teachers in Gauteng. Recommendations for future research, teacher training and policy implementation are presented. The diversity in teacher characteristics, particularly in Physical Science classrooms, influences the classroom practices that teachers select in their day-to-day teaching and impacts learner outcomes in terms of achievement. / Dissertation (MEd)--University of Pretoria, 2013. / gm2014 / Science, Mathematics and Technology Education / unrestricted

This study is concerned with how competent mathematics teachers develop pedagogical content knowledge (PCK) in statistics teaching. Pedagogical content knowledge was used as the theoretical framework that guided the research and data collection. The study’s methodology consisted of two phases. In the first phase, the six identified mathematics teachers undertook a conceptual knowledge written exercise. The result of this exercise was used to select the best four performing teachers for the second phase of the study. The second phase consisted mainly of lesson observations, interviews, written documents in the form of completed questionnaires, written diaries or reports, document analysis designed to produce rich detailed descriptions of participating teachers’ PCK in the context of teaching statistics concepts at school level. The concept mapping exercise was used to indirectly assess participating teachers’ content knowledge and their conceptions of the nature of school statistics and how it is to be taught. The qualitative data obtained were analysed to try to determine individual teachers’ content knowledge of school statistics, related pedagogical knowledge, knowledge of learners’ conceptions in statistics teaching, knowledge of learners’ learning difficulties as well as how they developed their PCK in statistics teaching. The analysis was done based on iterative coding and categorisation of responses and observations made to identify themes, patterns, and gaps, in school statistics teaching. Commonalities and differences if any, in the PCK profiles of the four participating teachers were also analysed and determined. The results of the study showed that overall, individual teachers develop their PCK in school statistics teaching by: (a) formally developing their knowledge of the subject matter in a formal undergraduate educational programme, as well as subject matter content knowledge during classroom practice; (b) using varied topic-specific instructional skills such as graphical construction skills in teaching statistical graphs; (c) using diagnostic techniques (oral questioning and pre-activity, class discussions and questioning) and a review of previous lessons to introduce lessons, and to determine learners’ preconceptions in statistics teaching ; (d) Using teaching strategies that can help to identify learners’ learning difficulties as well as intervention to address the difficulties; (e) continually updating their knowledge of school statistics by attending content knowledge workshops and other teacher development programmes designed to improve content knowledge and practice. / Thesis (PhD)--University of Pretoria, 2012. / Science, Mathematics and Technology Education / unrestricted

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.

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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>

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.