Lärare som undervisar i matematik förväntas kunna mer avancerad matematik än vad de undervisar om. Men formell matematikkunskap anses inte vara tillräckligt för att lärare ska kunna undervisa så att ämnesinnehållet blir begripligt för eleverna, de behöver även pedagogical content knowledge (PCK). Begreppet belyser en speciell form av ämneskunskap för undervisning och skiljer sig från den matematikkunskap som används av andra välutbildade vuxna. Det har föreslagits att olika arrangemang av kollegialt och praktikbaserat lärande kan utveckla lärares PCK. Ett exempel på ett sådant arrangemang är learning study. Den här avhandlingen handlar om den kunskap om lärande och undervisning i matematik som studiens lärare utvecklar då de deltar i learning studies och utforskar sin praktik utifrån ett variationsteoretiskt perspektiv. Det yttersta syftet med en learning study är att utveckla elevernas lärande om specifika lärandeobjekt, genom att undersöka vad som kan vara kritiskt för elevernas lärande. I ett samarbetsprojekt med fyra högstadielärare genomfördes två learning studies i matematik, under ett år. Lärargruppen undersökte vad eleverna behöver lära för att de ska förstå i) varför en kvot kan vara större än talet i täljaren och ii) olika representationer av konstanterna k och m i räta linjens ekvation. Under learning study-arrangemangets olika steg samlades studiens empiri in och denna består av filmade lektioner, inspelade möten där lärargruppen planerade och analyserade undervisning och elevers lärande, skriftliga elevtest samt elevintervjuer. Studien har en variationsteoretisk utgångspunkt, vilket innebär att lärande förklaras ske när en person ser något på ett nytt och mer kvalitativt sätt, genom att personen urskiljer aspekter som han/hon inte tidigare har urskilt. Studien visar de två lärandeobjektens kritiska aspekter samt hur de kritiska aspekterna gradvis förändrades och specificerades. Förändringen var ett resultat av att lärargruppen fick syn på avgörande detaljer om på vilket sätt eleverna förstod ämnesinnehållet samt hur skilda sätt att förstå kunde användas i undervisningen för att utveckla elevernas lärande. Där av titeln att få syn på avgörande skillnader. Denna form av utvecklad kunskap om lärandeobjektet kan ses som ett bidrag om PCK och vad det kan vara. / It is a common view that teachers need more than formal content knowledge to teach and to make the content comprehensible to others. They also need pedagogical content knowledge, or PCK (Shulman, 1986). It has been suggested that different teacher collaboration approaches may support teachers’ development of PCK (Chapman, 2013, Davis & Renert, 2014; Steele & Rogers, 2012). This thesis aims to provide insights into the kind of knowledge about teaching and learning mathematics that teachers develop through their participation in a specific collaboration approach called learning study. Four teachers of mathematics and their 74 students (aged 15−16 years) participated in two learning studies over the course of one year. The foremost aim of a learning study is to enhance student learning about specific objects of learning and to identify what is critical for the students’ learning (Marton & Tsui, 2004). The objects of learningin the two learning studies were to understand that dividing with a denominator between 0 and 1 gives a quotient larger than the numerator and to understand different representations of the constants b and m in the equation of the straight line. During the two learning studies data were collected from 8 video-recorded lessons, 2 written student tests, student interviews, and 14 audio-recorded sessions in which the teachers and I (PhD student) planned, analysed and revised teaching and student learning. The analysis was based on variation theory (Marton & Tsui, 2004) and focused on what participants considered to be critical aspects of the objects of learning and on the components embedded in that knowledge. The result shows the identified critical aspects of the two objects of learning and, furthermore, how the teachers’ knowledge about those critical aspects gradually changed and became more refined and specified in relation to their students’ understanding. The thesis provides an insight into the value of the teachers’ enhanced knowledge of the object of learning, in relation to how PCK can be understood.

Abstract Teaching of music, especially instrumental music, has rarely been the interest of researchers. This thesis explores the music teaching of a well known Finnish piano teacher and artist Matti Raekallio, describing his practical knowledge and theoretical tenets and their formation during the different phases in his life. The practical knowledge of a music teacher is experiential knowledge that takes shape in practical situations. It shows especially in the teaching-related interactions of music lessons. The teacher's practical knowledge manifests in his practical theory, which guides his teaching and includes his notions of the human being, learning and knowledge. The research tasks developed in the course of the research process and can be defined as follows: 1. What kind of shape do the elements of Raekallio's practical theory take in his life story? 2. What kind of teaching strategies and styles does he use in his piano lessons? 3. What kind of teaching stories are told in piano lessons? 4. How do the teacher and his students tell about their mutual relationships and their relations to music? The teaching of instrumental music is also approached from the viewpoint of the master–apprentice tradition it is usually connected with. And in addition to the actual research questions, the way in which this tradition is told in this research is also considered. The study is based on a narrative approach. Most of the data was collected by observing Raekallio's piano lessons and by interviewing both him and his students. This data was then analysed using content analysis and narrative methods of analysis. The results of this study broaden our conception of a music teacher's work. The teacher uses versatile teaching strategies, both verbal and nonverbal. Raekallio's teaching style includes his way of speaking, of being present and of giving feedback during his piano lessons. The exploration of teaching styles proved to be a fruitful starting point in the research of the moral dimension of music teaching. Examining teaching stories opened up the socialising significance that teaching has; through these stories future pianists and piano teachers are narrated into their cultural environment. These teaching stories show the teacher's pedagogical content knowledge as narrative knowing. With the help of narrative knowing, the teacher ties together knowledge that makes possible the production of a music performance, starting from notes and ending in a musical performance. The findings reinforce our conceptions of the teacher's significance in the teaching of instrumental music. In the stories of both students and the teacher, the significance of the teacher was clear during the different stages of development as a musician and especially during the stage of professional studies as a guide into the culture and practices of the field. The concepts and theory of educational sciences proved necessary and handy tools even in the research of music teaching. To popularise or model the contextual thinking of teaching related to the teaching of music, more descriptive research in the field is needed as well as descriptions of various everyday teaching events, the teaching of students of different ages, etc. The future challenges that this research points out include research of the narrative character of teachers' knowledge in general. How do teachers use storytelling in teaching, into what kind of stories are the things to be taught woven? / Tiivistelmä Soitonopetus on ollut harvoin tutkijoiden mielenkiinnon kohteena. Tässä työssä tarkastellaan tunnetun suomalaisen pianopedagogin ja -taiteilijan Matti Raekallion soitonopetusta, kuvaten hänen praktista tietoaan ja teoriaansa sekä sen muotoutumista elämän eri vaiheiden aikana. Soitonopettajan praktinen tieto on opettajan kokemuksellista tietoa, joka syntyy käytännön tilanteissa ja joka näkyy oppitunneilla etenkin opetuksen vuorovaikutustilanteissa. Opettajan praktinen tieto manifestoituu opettajan praktisessa teoriassa, joka ohjaa hänen opetustaan ja johon kuuluvat hänen käsityksensä ihmisestä, oppimisesta ja tiedosta. Tutkimustehtävät muotoutuivat prosessin aikana seuraaviksi: 1. Millaiseksi Raekallion praktisen teorian ainekset muotoutuvat hänen elämäntarinassaan? 2. Millaisia opetusstrategioita ja -tyylejä soittotunneilla käytetään? 3. Millaisia opetustarinoita soittotunneilla kerrotaan? 4. Millaiseksi opettaja ja opiskelijat kertovat suhteensa toisiinsa ja musiikkiin? Tarkastelen soitonopetusta myös siihen liitetyn mestari–kisälli-perinteen näkökulmasta ja varsinaisten tutkimustehtävien lisäksi pohdin, millaiseksi mestari–kisälli-perinne voidaan kertoa tämän tutkimuksen perusteella. Tutkimus on lähestymistavaltaan narratiivinen. Päätutkimusaineiston keräsin havainnoimalla Raekallion pitämiä soittotunteja sekä haastattelemalla häntä ja hänen oppilaitaan. Aineiston analysoin sisällönanalyysia ja narratiivisen tutkimuksen analyysitapoja käyttäen. Tutkimustulokset laajentavat käsitystämme soitonopettajan työstä. Opettaja käyttää monipuolisia opetusstrategioita, niin verbaalisia kuin nonverbaalisia. Raekallion opetustyylissä tulivat esille hänen puhetapansa sekä hänen tapansa olla läsnä soittotunneilla ja antaa palautetta. Opetustyylin tutkiminen näyttää olevan hedelmällinen lähtökohta opettajan työn moraalisen ulottuvuuden tutkimiseksi myös soitonopettajan työssä. Opetustarinoiden tutkiminen avaa opetuksen sosiaalistavaa merkitystä, sillä niiden kautta tulevat pianistit ja soitonopettajat kerrotaan kulttuuriseen yhteisöönsä. Niissä näkyy opettajan niin sanottu pedagoginen sisältötieto narratiivisena tietämisenä, jonka avulla opettaja sitoo yhteen tiedon, joka mahdollistaa kappaleen työstämisen nuottikuvasta alkaen aina kappaleen esitykseen saakka. Tutkimus vahvistaa käsityksiämme opettajan merkityksestä soitonopetuksessa. Opettajan ja oppilaiden kertomuksissa näkyi selvästi opettajan merkitys soittajataipaleen eri vaiheissa ja erityisesti ammattivaiheen opinnoissa johdattamassa alan kulttuuriin ja käytänteisiin. Tutkimuksessa käytetty kasvatustieteen käsitteistö ja teoria on osoittautunut tarpeelliseksi ja toimivaksi työkaluksi myös soitonopetuksen tutkimuksessa. Soitonopetukseen liittyvän opetustilanneajattelun yleistämiseksi tai mallintamiseksi tarvitaan lisää alan kuvailevaa tutkimusta ja kuvauksia erilaisista arkipäivän opetustapahtumista ja esimerkiksi eri-ikäisten opettamisesta. Tutkimuksen jatkohaasteena nähdään yleisestikin opettajan tiedon narratiivisen luonteen tutkiminen. Miten opettajat käyttävät kertomista opetuksessaan, esimerkiksi millaisiin tarinoihin opetettavat asiat kerrotaan?

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.

The teaching of abstract concepts requires higher cognitive thinking skills and thus presents a challenge for most subjects in the curriculum, in particular, science subjects. Teachers often complain that they struggle to develop higher cognitive skills in learners in such topics. As a result, learners fail to understand science concepts and then complain that science is boring and hence lose interest in the subject. The main reason for this study was to investigate how Grade 7 Natural Science teachers mediate the learning of abstract topics, in particular, atoms and molecules which are regarded as the building blocks in chemistry. This study further sought to develop a teaching unit of work on atoms, molecules and the Periodic Table in partnership with the participating teachers, in order to help improve teaching and learning of the topic. The study is located within an interpretive paradigm. Within this paradigm, a qualitative case study approach was adopted whereby two Grade 7 Natural Science teachers in the Khomas Region were the research participants. This approach enabled me to seek for answers beyond the obvious classroom experiences by using document analysis, semi-structured interviews and classroom observation (which were video-taped and transcribed). The theoretical frameworks underpinning this study focused on mediation of learning and social constructivism as expounded by Vygotsky, in conjunction with Shulman’s pedagogical content knowledge. Hence, emphasis was placed on the teaching strategies used by teachers, such as elicitation of prior knowledge during the lessons, language used, interaction of learners and ways how teachers deal with the challenges faced by them in the mediation of learning. An inductive analysis to discover patterns and themes was applied during the data analysis process. The themes were further turned into analytical statements to interpret the data. The validation process was achieved by using a variety of data gathering techniques. I watched the videotaped lessons with the observed teachers and I made use of member checking in the form of stimulated recall interviews and transcripts of the interviews. Thus, a summary of discussions were given back to the respondents to verify their responses and check for any misinterpretations. Different chapters of my study were given to colleagues to read through as a means of the validation process. Herein lies the importance of a critical friend in qualitative research. The findings of the study revealed that concepts of high cognitive demand should not be oversimplified when introduced to learners, as learners might find it difficult to define and conceptualise concepts as they do not have proper insights into the concepts. The findings further illuminated that teachers should develop a strong subject content knowledge as well as pedagogical content knowledge to have the best strategies in place to mediate learning of this topic. The study concludes, with Phase 2, that the exposure of and cooperation between teachers plays an indispensable role in their professional development. Essentially, this enables teachers to make use of different teaching styles as they scaffold learners in the process of making sense of, in particular, abstract science concepts. Finally, this study recommends that teachers need to engage in on-going professional development opportunities and be equipped with suitable learning support and other necessary physical resources, as a way of motivation and to be in a position to deal with all the many challenges they have to face during the mediation of learning.

This study was carried out to investigate how Grade 10 Life Science teachers in three schools in the Omusati region of Namibia are including Environmental Learning (EL) in terms of the curriculum policy. A qualitative approach was used to generate data through document analysis, interviews and classroom observations to investigate the application of the policy of including environmental learning in classroom curriculum practice. The research was primarily directed towards examining constraints and enabling factors in the context of the three schools that participated in the study. The study revealed that teaching strategies for the inclusion of environmental learning were not widely evident, suggesting disparities between the policy of enabling environmental education through the inclusion of environmental learning across the curriculum. It was notable that teacher knowledge and interest in environmental education influence how they include environmental learning and that assessment practices narrow the scope of environmental learning in ways that do not include critical thinking and problem solving skills. The study concludes that despite diverse constraints inhibiting inclusion, the evidence suggests that the inclusion of environmental learning in Namibia’s Life Science curriculum can enable environmental education. The above main findings are used to make recommendations toward strengthening environmental content knowledge of teachers and to improve assessment practices. It was also noted that some of the environmental learning constraints could be transformed into enablers with more teacher support and by making a better link between environmental learning theories and practices. This will involve a redirection of the curriculum documents as well as the provision of other learning support materials to support environmental learning. The study has enabled me to conclude that what is happening should be encouraged so that it continues and is strengthened although the implementation of environmental learning is not as clear as the policy had mapped out.

This study aimed to investigate how Grade 11 Biology teachers mediate learning through code-switching from English to Oshiwambo. It was triggered by my experience as a teacher when I came to observe that the majority of teachers still use the home language during their lessons though the language policy for schools in Namibia clearly states that English should be used as a medium of instruction from Grade Four onwards. The research was carried out at Happy Secondary School (pseudonym), a rural government school in Omusati Region, Namibia. It was a qualitative case study underpinned by an interpretive paradigm. The unit of analysis was the mediation of learning through codeswitching from English to Oshiwambo. Document analysis, questionnaires, interviews (semistructured, focus group, stimulated recall interviews) and lesson observations were used as data gathering techniques, to ensure adequate coverage, validity and trustworthiness of the data gathered. The study adopted Vygotsky’s social constructivism and the socio-cultural perspective in conjunction with Shulman’s Pedagogical Content Knowledge (PCK) as the theoretical frameworks. The data analysis process entailed organising data into themes from which four analytical statements were then derived in relation to the research questions. The study found that both Biology teachers and learners view code-switching as a useful tool in making learners understand the biological concepts. The study revealed that Biology teachers code-switch from English to Oshiwambo to make learners understand better, increase participation, explain concepts, elaborate, for disciplinary purposes, when giving examples of everyday knowledge events and when asking questions. The study also revealed that learners code-switch mainly for good communication, easier self-expression, due to loss of words, when unprepared to explain concepts and due to fear of making mistakes. It emerged, however, that both teachers and learners experience some challenges when codeswitching from English to Oshiwambo is used to mediate learning in Biology lessons. These include time constraints, lack of biological terms in Oshiwambo, different Oshiwambo dialects and the language policy. In addition, learners also lose the opportunity to learn English and find it difficult to answer questions in the examinations. The study revealed that Biology teachers and learners try to overcome these challenges by good lesson preparation, mini-teaching, using English/Oshindonga dictionaries or simply by adhering to the language policy.

Stoichiometry is proven to be one of the difficult topics for learners in the NSSC Physical Science syllabus due to its abstract nature. Over the years the Examiner’s reports reveal that learners' performance is very poor in this topic. In addition, learners fear the topic and have developed a negative attitude toward it. It is against this background that I decided to carry out a qualitative case study; investigating how teachers mediate the learning of stoichiometry. The study was conducted at two schools in the Oshikoto Region, Namibia and it involved two grade 11 Physical Science teachers. The study is located within the interpretive paradigm and made use of interviews, document analysis and lesson observations (which were video-taped and transcribed) followed by stimulated recall interviews to generate data. The generated data were analyzed using the inductive approach whereby themes were identified. The themes were later used to develop analytical statements in relation to my research questions and these were used to interpret the data. Moreover, the study adopted the notion of pedagogical content knowledge (PCK) proposed by Shulman (1986, 1987) as well as Vygotsky's (1978) mediation of learning and social constructivism as the theoretical frameworks. The data were validated by triangulation, member checking as well as using the stimulated recall interviews while watching the videos with each participant. The findings of the study show that teachers use several tools to mediate the learning process and this includes the use of language, learners' prior knowledge and analogies. In addition, it emerged in this study that teachers are faced with a number of challenges when mediating learning of this topic. Hence, the study recommends that teachers should develop their pedagogical content knowledge for them to effectively eliminate the challenges faced as well as to come up with the best teaching strategies which they can use to mediate learning and help learners make sense of the topic stoichiometry.

No presente trabalho foi investigado o desenvolvimento do Conhecimento Pedagógico do Conteúdo para o ensino de argumentação científica (PCKarg) de um professor de Química recém formado (PQRF). Objetivou-se investigar o desenvolvimento do PCKarg desse professor desde sua formação inicial até seu envolvimento com um professor experiente (PQ) e um grupo de quatro professoras do Ensino Fundamental I em atividades envolvendo processos de argumentação e ensino investigativo. Para isso, foi apresentado a PQRF o contexto em que quatro professoras polivalentes lecionavam \"Ciclo da água\" e \"Evaporação\" no 3º ano do Ensino FundamentaI I. Dentro desse contexto cabe destacar a influência do material didático escrito empregado pelas professoras - suas concepções acerca do ensino de Ciências e propostas de aulas experimentais - e a influência das concepções e do discurso de uma professora especialista formada em Biologia (PB) sobre a prática docente dessas professoras. Após PQ e PQRF assistirem e analisarem registros audiovisuais de aulas que ocorreram em sala de aula e no laboratório didático, eles (re)planejaram, com base no contexto das aulas, uma intervenção que tinha como objetivo engajar as professoras polivalentes em processos de argumentação e ensino investigativo. Na sequência, a intervenção foi implementada favorecendo a interação entre PQRF e as professoras de modo que esse professor vivenciasse as demandas impostas ao assumir o papel de professor-formador introduzindo as professoras na argumentação científica e no ensino investigativo. Os dados foram coletados a partir dos seguintes instrumentos - material didático escrito (empregado pelas professoras), entrevistas registradas em áudio e vídeo, realizadas separadamente com as quatro professoras polivalentes e com PQRF, registros audiovisuais das aulas a respeito de Evaporação, respostas de PQRF ao instrumento Representação de Conteúdo (CoRe) de argumentação produzido antes do planejamento, durante a interação entre PQRF e as professoras polivalentes e dois anos após o término dessa interação, registros em vídeo das intervenções e discussões em grupo, produção de texto e representações pictóricas por parte das professoras polivalentes e elaboração de mapas conceituais por PQRF. A análise do desenvolvimento do PCKarg foi feita com base no modelo de Grossman. Identificou-se que, ao longo de todo o processo, PQRF mostrou mudanças significativas em elementos da base de conhecimentos de professores e em elementos relacionados ao PCK propostos no modelo de Grossman. Sendo assim, PQRF apresentou mudanças: (i) em suas concepções acerca dos propósitos para ensinar o conteúdo específico, (ii) em seu conhecimento de estratégias instrucionais, (iii) em seu conhecimento da compreensão dos estudantes e (iv) no conhecimento do conteúdo específico. Entre os fatores que contribuíram para o desenvolvimento do PCKarg destacamos a apresentação feita por PQ e a reflexão sobre o contexto em que a intervenção iria ocorrer; a apresentação de modelos de práticas argumentativas - que se configuraram como um ponto de partida para que o ensino investigativo e a argumentação científica fossem incorporadas à prática docente de PQRF e a restrição de não fornecer respostas prontas e fomentar a argumentação científica nas professoras por meio de boas perguntas. Destacamos que esse último aspecto contribuiu, significativamente, com o desenvolvimento de um repertório de boas perguntas por meio das quais a argumentação foi favorecida, causando impacto nas concepções acerca dos propósitos para lecionar por meio da argumentação científica e no desenvolvimento do PCKarg de PQRF. / The present study investigated the development of Pedagogical Content Knowledge of scientific argumentation (PCKarg) of an early career chemistry teacher (PQRF). This study aimed to investigate the PCKarg development of this teacher since the pre-service education until his involvement with an expert teacher (PQ) and a group of four primary school teachers during activities involving argumentation process and inquiry teaching. Thus, it was presented to PQRF the context in which four primary teachers lectured water cycle and evaporation in 3rd grade of primary school. In this context we highlight the influence of the textbook employed by teachers - the conceptions of teaching science and proposals for experimental classes in it - and the influence of ideas and discourse of an Biology teacher (PB) on the teaching practice of these primary teachers. After PQ and PQRF observed and analyzed video recordings of primary teacher\' classes that occurred in the classroom and laboratory they (re)designed, based on the context of the classes, an intervention with the teachers. This intervention aimed to engage the primary teachers in argumentation processes and inquiry teaching. In sequence, the intervention was implemented in order to promote the interaction between PQRF and primary teachers so that PQRF had to deal with the demands imposed to assume the role of a teacher educator introducing teachers to scientific argumentation and the inquiry teaching. Data were collected from the following instruments - textbook (used by teachers), interviews recorded in audio and video conducted separately with the four primary teachers and PQRF, video recordings of lessons on evaporation, PQRF responses to Content Representation instrument (CoRe) of argumentation produced before the planning, during the interaction between PQRF and primary teachers and two years after the end of this interaction; text production and pictorial representations by the primary teachers and concept maps elaborated by PQRF. Analysis of PCK development was based on the Grossman\'s model. The elements of PCK presented in this model were used as categories to document the PCKarg development of PQRF during the in-service training. It was identified that, during the whole process, PQRF showed significant changes in elements of the knowledge base for teaching and the elements related to PCK proposed by the Grossman model. Thus, PQRF showed changes: (i) in their conceptions of the purposes to teach the specific content, (ii) in their knowledge of instructional strategies, (iii) in their knowledge of understanding of students and (iv) subject matter knowledge. Among the factors that contributed to the development of PCKarg we can highlight the presentation done by PQ and reflection of the context in which the intervention would occur; the presentation of models of argumentative practices - that is configured as a starting point for the inquiry teaching and scientific argumentation were attached to teaching practice of PQRF and the restriction of not provide ready answers and foster scientific argument in teachers through good questions. We emphasize that this later aspect contributed significantly to the development of a repertoire of good questions through which the argument was favored impacting PQRF\'s conceptions of the purposes for teaching through scientific argumentation and development of PCKarg.

Thesis (M.Ed. (Mathematics)) ---University of Limpopo, 2016 / This research explored the pedagogical content knowledge (PCK) of algebra as held by a group of senior phase teachers in Limpopo Province, South Africa. Sixty-one teachers from different districts in the province participated in this study. This qualitative study used a case study design. Data was collected using a test and content representation (CoRe) matrix. The results were analysed through analysis of narratives. The study revealed that most of the teachers could not identify the main concepts that are taught in algebra. It was discovered that some could not differentiate between algebra and arithmetic. The findings also point out that the teachers had inadequate knowledge of algebra subject matter. The participants were able to identify some of the concepts that learners were supposed to do in the next grades. The findings revealed that most of the participants did not know the importance of teaching algebra. It was revealed that most participants could not identify the learners‘ difficulties; they could not specify the procedures they followed when teaching the identified main concepts in algebra, or give reasons for using those procedures. Furthermore, they could not specify factors that influenced their teaching. However, they were able to indicate different methods they used to assess learners‘ understanding. It was concluded that these teachers had inadequate PCK of senior phase algebra. The study recommends development programmes for both subject matter knowledge and PCK for practising teachers. Keywords: pedagogical content knowledge, content representations (CoRes), algebra, senior phase mathematics teachers.

Reforms that have taken place in the South African education system since 1994 have led to changes in terms of how learning areas are taught in schools. There have been changes regarding the teaching of physical development activities in schools in recent years. Physical education as a subject was infused within life orientation (LO) as a learning area with physical development activities as one of the outcomes. The time to teach physical development activities has been reduced as other learning outcomes within LO have to be taught. This has led to situations where the teaching of physical development activities is undermined in many schools. Pressure to perform well in learning areas such as mathematics and literacy makes educators to devote less time on the teaching of physical development activities. To a larger extent, financial resources on the other hand, are being directed to other learning areas due to pressure to conform to international education standards. There is a need for school leaders to respond to new conditions of teaching. This research project deals with the leadership practices of heads of department (HODs) in the implementation of physical development activities. The study aims to investigate how HODs lead and manage the educators who teach physical development activities. Among other things, the study will focus on the HODs‟ leadership styles relevant to the teaching of physical development activities. The study will also look at challenges they experience in their departments, training needs and how they keep balance between teaching and monitoring educators who teach physical development activities. The researcher used qualitative research approach to collect information for the study. Semi-structured interviews were conducted with two HODs and four educators in two primary schools. The findings indicate that lack of experience and specialisation in the teaching of physical development activities has an influence on the HODs leadership style. More support is needed in the teaching of physical development activities in order to boost the confidence of those who are teaching this part of the learning area. Deployment of staff members to the relevant positions is one of the priority areas. An implication for schools, particularly HODs and school management teams is that the teaching of physical development activities is as important as the teaching of other learning areas. / Dissertation (MEd)--University of Pretoria, 2013. / gm2014 / Education Management and Policy Studies / unrestricted