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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Denna studie syftar till att undersöka vilka metoder samhällskunskapslärare på gymnasiet tillämpar för att främja framgångsrik undervisning i samhällskunskapsämnet. Ämnet samhällskunskap är tvärvetenskapligt till sin karaktär och utgår från flera samhällsvetenskapliga discipliner (Skolverket, 2022). Därför har samhällskunskapsundervisningen ett variationsrikt innehåll där lärares professionella friutrymme att tolka läro- och kursplaner kan ta fasta på olika metoder och innehåll som framgångsrikt främjar lärande. Det teoretiska ramverket Pedagogical Content Knowledge (PCK) är därför applicerat på föreliggande studie för att analysera hur samhällskunskapslärare använder sin pedagogiska ämneskunskap för att undervisa framgångsrikt i samhällskunskap. Genom en kvalitativ metod i användandet av semistrukturerade intervjuer intervjuas tio legitimerade samhällskunskapslärare utifrån deras perspektiv på framgångsrik samhällskunskapsundervisning. Det erhållna datamaterialet analyseras därefter genom en kvalitativ innehållsanalys där tematiska kategorier från lärarnas svar frambringas. Resultatet visar att framgångsrik samhällskunskapsundervisning präglas av flera faktorer som exempelvis engagemang, egna intressen i kombination med djupa ämneskunskaper, verklighetsanknytning, variation samt autentiska lärandesituationer. / This study aims to investigate what methods social studies teachers in upper secondary school implement to promote successful teaching in the social studies subject. The subject of social studies is interdisciplinary in its character and draws on several social science disciplines (Swedish National Agency for Education, 2022). Therefore, social studies teaching has a varied content where teachers' professional autonomy in interpreting curricula and syllabi can embrace different methods and content that successfully promote learning. The theoretical framework Pedagogical Content Knowledge (PCK) is therefore applied to the present study to analyze how social studies teachers use their pedagogical content knowledge to teach successfully in social studies. Through a qualitative method using semi-structured interviews, ten licensed social studies teachers are interviewed from their perspective on successful social studies teaching. The data obtained is then analyzed through a qualitative content analysis in which thematic categories from the teachers' responses are derived. The results show that successful social studies teaching is characterized by several factors such as commitment, own interests in combination with deep subject knowledge, connection to reality, variation, and authentic learning situations.

Doctor of Philosophy / Curriculum and Instruction Programs / David S. Allen / Margaret G. Shroyer / Ongoing, effective professional development is viewed as an essential mechanism for eliciting change in teachers’ knowledge and practice in support of enacting the vision of NCTM’s Principles and Standards of School Mathematics. This case study of the Infinite Mathematics Project, a Title IIB MSP professional development initiative, seeks to provide a qualitative examination of the characteristics and strategies used in the project and their impact on teacher learning and practice. The project embodied many features and strategies of effective professional development such as: mathematics content focus; sustained over time; reform activities (e.g., lesson study, teacher collaboration); active learning opportunities (e.g., implementing an action plan; developing differentiated instruction activities for a mathematics classroom); coherence with NCTM and state standards; and collective participation by IHE facilitators and participant K-12 teachers from partner districts. The findings reveal teachers gained both content knowledge (knowledge about mathematics, substantive knowledge of mathematics, pedagogical content knowledge, and curricular knowledge) and pedagogical knowledge (knowledge about strategies for differentiating instruction in a mathematics classroom, for supporting students’ reading in the content area, for fostering the development of number sense, for implementing standards-based teaching, and for critically analyzing teaching). The study also provides some evidence that the project had an impact on teaching practice. In addition, an implication of the study suggests the positive impact of Title IIB MSP partnership requirements.

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.

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.