The following study aims to examine the special mathematical knowledge needed in order to teach mathematics. Furthermore, the study attempts to explore how teachers’ views on the knowledge needed in order to teach mathematics affects their student’s opportunities to develop their conceptual understanding. Qualitative and quantitative empirical data was attained by observations and complementary interviews. A total of three teachers, all working at the same school, was observed and interviewed. The study used Ball, Thames & Phelps (2008) practice-based theory of mathematical knowledge for teaching, MKT, as its theoretical framework when analyzing the empirical data. The result of the observations displays that math teachers tend to use common content knowledge far more than specialized content knowledge during their lessons. The outcome of this also study reveals that there is a tendency among teachers to interfuse mathematical concepts with terminology. Conceptual understanding is equated with the use of correct terminology. The students are not exposed to the underlying ideas of the mathematical concepts. The study also concludes that there seems to be a sectioning between the mathematical content taught in grade 4-6 from the rest of the content being taught in elementary school, with a low number of connections being made between mathematical topics and concepts included in the curriculum.

The math achievement of American students had been stagnant or falling since 2007, according to both national and international measures (NAEP, TIMSS, PISA). While the Common Core State Standards were partially a response to sinking levels of American math proficiency, those standards require a much greater depth of conceptual understanding of mathematics for teachers than previous standards, yet more than half of fifth- through eighth-grade math teachers are not certified to teach math. The federal government and school districts spend millions of dollars on teacher professional development, but little evidence shows what kind of professional development might be the most beneficial for math teachers. This study measured the impact of math content-based professional development on middle school math teachers. Findings suggest that the participating teachers’ content knowledge about ratios and proportional reasoning increased slightly during the study. Exit surveys indicated that the most recent PD session would have an impact on their teaching practice, although the impact would mostly be related to their pedagogy. However, there was little change in teachers’ self-efficacy toward teaching mathematics. As research indicates, content knowledge in math is connected to student achievement, the implication of which is that middle school math teachers can increase their content knowledge through professional development. Given that access to higher-level math courses is critical to college success, and the foundation for those higher-level math courses begins in middle school, it is imperative that all students and their teachers are supported to be successful in math.

This study investigated the pedagogical content knowledge supposedly held by two FET mathematics teachers from Mpumalanga Province as they taught quadratic functions in grade 11 classes. The criterion for selecting the two teachers was that they had consistently produced good results (overall pass rate of 80% or more) in the grade 12 mathematics examinations of the National Senior Certificate for the past three years or more and thus, they were classed as effective. The two teachers prepared and taught lessons on quadratic functions in grade 11 whilst they were being observed. The study focused on teacher knowledge base as exemplified in the teachers’ pedagogical content knowledge (PCK). Three elements of PCK were investigated; namely; (i) knowledge of the subject matter; (ii) knowledge of teaching strategies and (iii) knowledge of learners’ conceptions. Qualitative research approach using the case study research method was used to collect qualitative data on the pedagogical content knowledge of the two teachers through lesson observations, lesson plan analysis and interviews. Analysis of the results suggests that the two teachers have adequate subject matter knowledge but have limited knowledge on the aspects of teaching strategies and knowledge of learners’ pre-conceptions and misconceptions on the topics of quadratic functions that they taught. The study recommends that teachers be exposed to workshops that deal specifically with the various topic specific teaching strategies and knowledge of learners’ pre-conception and misconceptions on the topic of quadratic functions. / Dissertation (MEd)--University of Pretoria, 2012. / Science, Mathematics and Technology Education / unrestricted

This South African study investigated a sample of Grade 4 to 7 Natural Sciences teachers’ attitudes towards botany and botany teaching and these teachers’ botany Pedagogical Content Knowledge (PCK). It explored whether a relationship exists between teachers’ attitudes towards botany teaching and their PCK. The study provides an overview of international and South African literature and research on the underrepresentation of botany and the teaching of botany in Natural Sciences classes. Throughout the study insight is provided on the universal problems of plant blindness and negative attitudes towards botany and botany teaching in the Natural Sciences classroom. Data were collected during teachers’ interviews, class observations and analyses of lesson plan documents. The results indicated that most teachers harbour negative attitudes towards botany and botany teaching. There are various reasons for this negativity such as past experiences in botany training, zoochauvinism and plant blindness. The Pedagogical Content Knowledge of teachers in this study was insufficient. It was found that teachers’ attitudes towards botany teaching influence their PCK and teachers’ PCK can, in turn, influence teacher attitudes towards botany, which can affect the teachers’ ways of teaching. This study confirms that problems of plant blindness, zoochauvinism and negativity towards botany and botany teaching that occur elsewhere in the world are also prevalent among South African teachers. This confirmation casts doubts on Natural Sciences teachers’ botany PCK. This study adds to the literature on botany teaching and PCK in the South African context / Dissertation (MEd)--University of Pretoria, 2014. / tm2015 / Science, Mathematics and Technology Education / MEd / Unrestricted

This study investigated the comparison between captured and revealed Pedagogical Content Knowledge (PCK) about graphs of motion. The aim of the study was to explore PCK when captured in a written format and discussions (captured PCK) and compare it to the PCK that the same teachers revealed in practice (revealed PCK) when teaching the topic. Four Grade 10 Physical sciences teachers were purposively and conveniently selected as participants of the study. Their PCK was captured through Content Representations (CoRes) and interviews. The revealed PCK on the other hand was gathered through lesson observations. The Topic Specific Pedagogical Content Knowledge (TSPCK) model was used as the framework that guided the analysis of the two manifestations of PCK. The focus was on teachers’ competences in the TSPCK components namely; learners’ prior knowledge including misconceptions, curricular saliency, what is difficult to teach, representations including analogies, and conceptual teaching strategies. The results of this study indicated that teachers’ competences in the TSPCK components varied. This was evident in both the captured and the revealed PCK. Thus it suggested that a teacher’s level of competence in one component is not necessarily an indication of his or her competence in the other components that define PCK, and subsequently in his/her overall captured or revealed PCK. Furthermore, the study suggested that the level of competence in a component in the captured PCK is not necessarily an indication of the level of competence within that component that the teacher would reveal during lesson presentation. The level may be the same, slightly different (higher or lower) or even be drastically different in the lesson than suggested by the captured PCK. A concluding remark was then made that teachers’ captured PCK is not necessarily a true reflection of the PCK they reveal during lesson presentation and that different instruments must be used to reflect on and assess teachers’ PCK in a topic. / Dissertation (MEd)--University of Pretoria, 2017. / Science, Mathematics and Technology Education / MEd / Unrestricted

Orientador: Zulind Luzmarina Freitas / Resumo: Este estudo vincula-se à linha de pesquisa “Educação Matemática”, do Programa de Pós-Graduação em Ensino e Processos Formativos da Universidade Estadual Paulista “Júlio de Mesquita Filho”, Campus de Ilha Solteira-SP (FEIS-UNESP). A partir do pressuposto de que analisar a prática de sala de aula contribui para a formação continuada do professor, temos o objetivo de compreender o processo de formação continuada vivido por uma professora iniciante ao ministrar a disciplina de Desenho Geométrico e Geometria Descritiva. A questão norteadora do trabalho foi “Quais as contribuições da prática que vão sendo mobilizadas e incorporadas na formação de uma professora em início de carreira?” A pesquisa desenvolveu-se em ambiente natural, durante os meses de março a junho de 2018, nas aulas de Desenho Geométrico e Geometria Descritiva do Curso de Licenciatura em Matemática na FEIS-UNESP. Como eixo teórico central nos valemos dos estudos de Lee Shulman e seus seguidores e de Paulo Freire. Foram feitos registros através de gravações em vídeos/áudios e de anotações da professora em uma caderneta de campo. Os dados que deram origem ao corpus foram problematizados por meio de Análises de Conteúdo, ancoradas no estudo de Moraes (1999). Foram criadas duas Unidades de análise, a primeira intitulada de Matemática Clássica, foi dividida em duas categorias, sendo elas A Severidade da Matemática, com as subcategorias Utilização dos Conceitos Retirados dos Livros de Euclides e A demonstração Matemática... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The present study is encompassed in the research line “Mathematical Education”, from the Postgraduate Program in Teaching and Formative Processes of Sao Paulo State University “Júlio de Mesquita Filho”, at Ilha Solteira Campus (FEIS-UNESP). Based on the assumption that analyzing the teaching practice contributes to the continuing education of a professor, we aim to discuss the process of continuing education of a professor at the beginning of their career by teaching a during the majors of Geometric Design and Descriptive Geometry. The guiding question of the work was “Which are the contributions of the teaching practice that are mobilized and incorporated in the formation of a professor at the beginning of their career?” The research was developed in a natural environment, between March and June 2018, during the majors of Geometric Design and Descriptive Geometry of the Mathematics Undergraduate Course at FEIS-UNESP. As the central theoretical axis, we used the studies of Lee Shulman and his followers, and Paulo Freire. Records were made through video and audio recordings and the professor's notes in a field notebook. Data that originated the corpus were problematized through Content Analysis, anchored at Moraes‟ (1999) work. Two units of analysis were created, the first titled Classical Mathematics, was divided into two categories, namely The Severity of Mathematics, with the subcategories Use of Concepts Taken from Euclid's Books, and The Mathematical Demonstration; as the... (Complete abstract click electronic access below) / Mestre

Denna kvalitativa studie syftar till att undersöka hur samhällskunskapslärare uppfattar och tolkar det medborgarbildande uppdraget i Sverige samt hur de tar sig an och implementerar politiska kontroversiella samhällsfrågor i undervisningen, som ett led i ämnesdidaktiska överväganden. Det teoretiska ramverk som ligger till grund för denna studie utgår från att lärares didaktiska reflektioner och överväganden grundas på hur de tolkar sitt undervisningsämne och att det är en ständigt pågående och cirkulär process. Vidare har även Mouffes definition av politik samt Hess definition av kontroversiella samhällsfrågor använts för att både avgränsa och synliggöra att det krävs diskussion och motsättningar för att utveckla demokratin. Åtta samhällskunskapslärare har deltagit via semistrukturerade intervjuer och deras utsagor har bearbetats och analyserats genom tematisering. Studiens resultat visade att det medborgarbildande uppdraget tolkades som en viktig förberedelse för eleverna men visade även att det fanns skillnader mellan lärarnas förväntningar. De deltagande lärarna beskrev att samhällets komplexitet och motsättningar behöver förstås och att eleverna behöver möta detta genom diskussion och samtal för att mejsla fram väl genomtänkta och övervägda ställningstaganden, vilka blir till verktyg för att både värna om och utveckla demokratin.

En stor del av unga barn spelar digitala spel på sin fritid och flera studier har visat på positiva effekter på ungas engelskaförmåga genom detta. Med tanke på dess potential för lärande vore det intressant att undersöka lärares uppfattningar om dem och hur de använder dem. Syftet med detta arbete var att undersöka på vilka sätt som lärare i engelska för lågstadiet använde digitala spel i sin engelskundervisning samt vilka utmaningar och möjligheter de ansåg fanns i detta användande. Inom ramen för studien genomfördes fem intervjuer med lärare från olika kommuner och skolor i Sverige. Intervjuernas innehåll kategoriserades genom den fenomenografiska ansatsen. Resultatet diskuterades även utifrån ramverken LTC och TPACK. Resultatet visade att alla utom en lärare använde digitala spel i engelskundervisningen i syfte att variera undervisningen eller att motivera eleverna. Bingel och elevspel.se användes mest. Utmaningar som lärarna såg med spelen var tidsåtgången, teknik som strular, en svårighet att anpassa spelen ur ett didaktiskt perspektiv samt att det skulle öka elevernas skärmtid ytterligare. Möjligheterna de såg var motivation, variation, nivåanpassning, mer självgående elever samt att spelen gjorde lärandet lustfyllt. Inställningen till digitala spel verkar bero på ålder, intresse och yrkesverksamma år, samt deras uppfattning om teknologisk och ämnesspecifik kunskap.

Des projets européens comme Eurydice, des rapports de l’OCDE présentent l'épistémologie comme un élément incontournable de professionnalisation du métier enseignant. Portés par un courant didactique nouveau, des cours d’épistémologie émergent dans l’ensemble des programmes de formation des maitres et ne se destinent donc plus exclusivement aux seuls professeurs de sciences. En Belgique francophone, ils sont introduits officiellement dans un décret sur la formation initiale des instituteurs et des régents en décembre 20001. De cette modification curriculaire, nous avons choisi d’analyser le seul cours qui en porte l’intitulé et qui est proposé à l’article 6 - initiation à la recherche, notions d’épistémologie des disciplines, préparation au travail de fin d’études. Notre étude porte sur l’appropriation de cette injonction à former des enseignants à l’épistémologie. Si la légitimité de tels cours ou d’approches n’est plus à débattre, les démarches ou enseignements demeurent nébuleux. Les concepts de nature of sciences et Pedagogical content knowledge sont alors utilisés pour appréhender, modéliser la question épistémologique dans les discours de quinze formateurs de la Fédération Wallonie-Bruxelles. / Doctorat en Sciences psychologiques et de l'éducation / info:eu-repo/semantics/nonPublished

This study investigated the relationship between teachers' pedagogical content knowledge (PCK) about electrostatics and learners' performance in the topic. Two in-service and two pre-service physical science teachers, together with their learners, agreed to participate in the study. The PCK of the teachers was viewed as two manifestations; the personal PCK, which is static in nature and the enacted PCK, which is dynamic. A content representation (CoRe) tool and lesson plans were used to collect data that reflected the personal PCK of the teachers. The data for the enacted PCK was collected using classroom observations, and video stimulated recall (VSR) interviews. A topic specific PCK model was adopted as the framework for this study. The model asserts that specific content is transformed for instruction through five components, namely; learners' prior knowledge, curricular saliency, what is difficult to teach, representations including analogies, and conceptual teaching strategies. Guided by the model, I developed two rubrics to assess and quantify the quality of the teachers' personal and enacted PCK on a four-point scale. Learners, on the other hand, wrote a test developed specifically for this study which explored their performance in the fundamental concepts chosen for this study. The performance of the learners was then related to the personal and the enacted PCK of the teachers separately. The results revealed that the personal and the enacted PCK of the teachers, as well as the performance of the learners, varied across fundamental concepts of electrostatics. The variations in the personal and enacted PCK provided empirical evidence that supports the notion that PCK has a concept specific nature. The results also showed that the performance of the learners was better related to the enacted PCK of the teachers compared to the personal PCK. These results imply that it is important to make teaching practice the centre of pre-service teacher education given the direct impact of enacted PCK on learning. Furthermore, exploring PCK at concept level reveals the strengths and weaknesses of the concepts. As such, pre-service teacher education and in-service teacher professional development may be tailored in a manner that addresses the concepts that require intervention. / Thesis (PhD)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / PhD / Unrestricted