South Africa is the first country in the world to offer Mathematical Literacy as a school subject. This subject was introduced in 2006 as an alternative to Mathematics in the Further Education and Training band. The purpose of this subject is to provide learners with an awareness and understanding of the role that mathematics plays in the modern world, but also with opportunities to engage in real-life problems in different contexts. A problem is the beliefs some people in and outside the classroom have regarding this subject such as teachers believing ML is the dumping ground for mathematics underperformers (Mbekwa, 2007). Another problem is the belief of some principals that any nonmathematics teacher can teach ML. In practice there is Mathematics teachers who teach ML in the same way that they teach Mathematics; non-Mathematics teachers who in many cases lack the necessary mathematical content knowledge and skills to teach ML competently; and Mathematics teachers who adapted their practices to teach ML using different approaches than those required for teaching Mathematics. Limited in-depth research has been done on the ML teachers, what they believe and what knowledge is required to teach this subject effectively and proficiently. The purpose of this study is to investigate the way in which ML is taught in a limited number of classrooms with the view to exploring the relationship between ML teachers’ knowledge and beliefs and their instructional practices. According to Artzt, Armour-Thomas and Curcio (2008) the instructional practice of the teacher plays out in the classroom where teachers’ goals, knowledge and beliefs serve as the driving force behind their instructional efforts to guide and mentor learners in their search for knowledge. To accomplish this aim, an in-depth case study was conducted to explore the nature of teachers’ knowledge and beliefs about ML as manifested in their instructional practices. A qualitative research approach was used in which observations and interviews served as data collection techniques enabling me to interpret the reality as I became part of the lives of the teachers. My study revealed that there is a dynamic but complex relationship between ML teachers’ knowledge and beliefs and their instructional practices. The teachers’ knowledge, but not their stated beliefs were reflected in their instructional practices. Conversely, in one case, the teacher’s instructional practice also had a positive influence on her knowledge and beliefs. It was further revealed that mathematics teacher training and teaching experience played a significant role in the productivity of the teachers’ practices. The findings suggest that although mathematical content knowledge is required to develop PCK, it is teaching experience that plays a crucial role in the development of teachers’ PCK. Although the study’s results cannot be generalised due to the small sample, I believe that the findings concerning the value of teachers’ knowledge and the contradictions between their stated beliefs and practices could possibly contribute to teacher training. Curriculum decision-makers should realise that the teaching of ML requires specially trained, competent, dedicated teachers who value the subject. This exploratory study concludes with recommendations for further research. / Thesis (PhD)--University of Pretoria, 2011. / Science, Mathematics and Technology Education / unrestricted

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The concept of pedagogical content knowledge (PCK) provides a framework for understanding the professional demands of secondary-school teachers in facilitating student learning. Teachers develop their PCK both formally in preservice and inservice education and informally with their colleagues. Teacher leaders, such as the secondary-school department chairs, can work with colleagues to promote professional growth. The purpose of this study was to understand how secondary-school department chairs understood PCK and perceived their role in promoting the PCK growth of their department colleagues. A qualitative research design using in-depth, semi-structured interviews involved 15 participants from one school district in the southeast of the U.S. Data analysis used Eisner’s (1998) four-part approach to criticism—description, interpretation, evaluation, and thematics—as the overall framework, with Hatch’s (2002) typological analysis facilitating the description and interpretation phases. The two dimensions of description and interpretation occurred simultaneously, with six typologies organizing the discussion; how participants understood and defined PCK; knowledge of context within PCK; participants’ understanding of the importance of content knowledge; growth of the teacher; development of PCK in professional learning communities; and department chair leadership in developing PCK. The evaluation dimension revealed that these chairs did indeed work with their colleagues in developing PCK that, in turn, facilitated student learning. Three major themes based on the data were developed: experienced teachers in leadership positions possess key elements of PCK; department chairs can lead as teachers; and teacher leaders bring their tacit PCK into the explicit. Implications for leadership include the need for district and school-based administrators to support the role that department chairpersons play in the professional growth of their colleagues, to provide developmental opportunities for teachers designed to focus on PCK and how PCK furthers student learning and to take advantage of the leadership offered by department chairs in promoting teachers’ professional growth. Further study might examine how department chairs work directly with their colleagues to develop PCK, how such development of PCK operates in contexts with different demographics than those of the present study, and how department chairs at different points in their careers assist their colleagues in their PCK growth.

The implementation of a new curriculum is a challenging issue to educators in many countries. In this country training for an implementation of a curriculum is done in one week and it takes a form of one a size fits all. The study investigated how I transform my content knowledge when teaching a new topic in the new curriculum. The aim of this study was to carry a self- study of how I transformed my content knowledge when teaching energy resources and its uses to make it comprehensible to learners. The following research question guided the study:  How did my PCK develop as I developed the broad content of the energy resources and its uses into focused, teachable and comprehensible content?  How did my planning and reflecting on practice change as I participated in the process of planning, developing and implementing the lesson plans? When teachers teach, they draw upon knowledge of their subject matter, general pedagogy as well as context. This could be improved by the contribution of the concept of pedagogical content knowledge where content and pedagogy are blended. Therefore, for this study I have chosen PCK as a theoretical framework because I will be looking at how my content knowledge can be transformed into content knowledge for teaching. The study employed a qualitative research, which uses multiple realities that are socially constructed through collective and individual definitions of the situations. It is a self –study focusing on my own teaching and intending to improve my practice as a teacher. The focus is myself teaching two grade 11 classes in a township school. Khumalo M. iv Data was collected in a form of concept maps, reflective journals, lesson plan and CoRE s and PaPeRs. CoRes and PaPe-Rs were used to capture and portray my PCK. The methodological tools used to document and portray my Pedagogical Content Knowledge when teaching energy and resources, used representations called Content Representation (CoRe) and Pedagogical and Professional – experience Repertoires (PaP-eRs). The CoRe elaborated on my construction of content, which framed the topic and each Pa-PeR, was a narrative derived from the classroom observations and the journal. Findings in this study indicate that using the CoRe and PaPeR as a tool to portray PCK helps in the development of content knowledge. Some elements of PCK could be identified and the implementation of developed lessons led to insight into my teaching. Learners participated more freely and develop confidence when home language was used. I gained confidence using the CoRe to develop lessons.

The South African government that was elected in 1994 made tremendous changes in the Education system. The new government came up with the new curriculum for Basic Education (grade R- 12). The new curriculum had new topics in physical science. This made me as a teacher doubt whether I would be able to teach new topics. During my time as a student, I was not taught mining at school or college. As a result, I decided to do a self study in order to investigate how I would learn gold mining as a topic in order for me to be able to teach it to my learners. My study involved studying my own teaching practice while learning and also finding out the key things that made me understand the content knowledge involved in the topic of gold mining. The self study was done in order to ensure that I understood the content knowledge and how best to teach it to the learners. I used a collaboration team, reflective journal, group interviews classroom observation and learners’ responses to collect data. The participants were my grade 11 learners and myself. My data was analysed using a PCK model, CoRes and PaPeRs. I had to learn the content knowledge and transform it to make it understandable to learners. I designed lessons using the prior knowledge of learners and integrating Physical Science and Geography. Lessons did not go as smoothly as I had expected. Learners wanted some of their existing knowledge to be included. The classroom activities depended entirely on the relationship between the teacher and learners. I carried out my study bearing in mind that implementation of the new curriculum depends not only on classroom interactions (DoE, 2002) but most importantly on the content knowledge that the teacher has and how it is transformed. Learners taught me to understand gold mining from the geographical point of view as well from the scientific point of view. From the beginning of the study they were really excited and were looking forward to new things. Using the learners’ science prior knowledge helped me design lessons that allowed me to learn to be a facilitator.

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.

Innehållet i förskolans läroplan medför att de som arbetar med den behöver kunskaper inom många olika ämnesområden. Syftet med studien var därför att få mer kunskap om pedagogers egenupplevda ämnes- och ämnesdidaktiska kunskaper, utifrån angivna mål och riktlinjer i Läroplan för förskolan. Till det användes webbenkät som metod. Efter bearbetning omfattade studiens material 160 webbenkätsvar. Ämnet som då skattades högst var språk/kommunikation och ämnet som skattades lägst var fysik. I tillägg till det framkom att drygt 50 av respondenterna, vid planerade pedagogiska aktiviteter, använde sig av olika didaktiska strategier beroende på hur de skattade sin ämneskunskap. Till skillnad från högt skattade ämnen tenderade de nämligen att, vid arbete med lågt skattade ämnen, förbise samspel och att ha barns intresse/behov som utgångspunkter i verksamheten.

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