This study examines how formal mathematics can be taught in the Swedish secondary school with its new curriculum for mathematics. The study examines what a teaching material in formal mathematics corresponding to the initial content of the course Mathematics 1c could look like, and whether formal mathematics can be taught to high school students. The survey was conducted with second year students from the science programme. The majority of these students studied the course Mathematics D. The students described themselves as not being motivated towards mathematics. The results show that the content of the curriculum can be presented with formal mathematics. This both in terms of requirements for content and students being able to comprehend this content. The curriculum also requires that this type of mathematics is introduced in the course Mathematics 1c. The results also show that students are open towards and want more formal mathematics in their ordinary education. They initially felt it was strange because they had never encountered this type of mathematics before, but some students found the formal mathematics to be easier than the mathematics ordinarily presented in class. The study finds no reason to postpone the meeting with the formal mathematics to university level. Students’ commitment to proof and their comprehention of content suggests that formal mathematics can be introduced in high school courses. This study thus concludes that the new secondary school course Mathematics 1c can be formalised and therefore makes possible a renewed mathematics education. / Denna studie undersöker hur formell matematik kan undervisas i den nya svenska gymnasieskolan med dess nya ämnesplan för matematik. I studien undersöks hur ett undervisningsmaterial i formell matematik motsvarande det inledandeinnehållet i kursen Matematik 1c kan se ut och huruvida denna matematik kan undervisas med gymnasieelever. Undersökningen genomfördes med elever från det naturvetenskapliga programmets andra årskurs. Majoriteten av dessa elever läste då kursen Matematik D. Eleverna beskrev sig själva som ej motiverade i matematik. Resultatet visar att innehållet i ämnesplanen kan presenteras med formell matematik. Detta både med avseende ämnesplanens krav på innehåll och atteleverna kan förstå innehållet. Ämnesplanen kräver dessutom att denna typ av matematik tas upp som en del av innehållet i kursen Matematik 1c. Resultatet visar också att eleverna är öppna för och vill ha mer formell matematik i undervisningen. De tyckte att det kändes ovant eftersom att de aldrig tidigare stött på denna typ av matematik, men vissa elever fann formell matematik som enklare än matematiken som normalt presenteras på lektionerna. Studien finner ingen anledning till att skjuta upp mötet med formell matematik till universitetsnivå. Elevernas engagemang för bevis och tillgodogörandet av innehållet talar också för att formell matematik kan introduceras i gymnasiekurserna. Studiens slutsats är således att nya gymnasieskolans kurs Matematik 1c kan formaliseras och öppna för en förnyad matematikundervisning.

The study explores Mathematics educators’ use of students’ out-of-school experiences in the teaching of Transformation Geometry. This thesis focuses on an analysis of the extent to which students’ out-of-school experiences are reflected in the actual teaching, textbook tasks and national examination items set and other resources used. Teachers’ teaching practices are expected to support students’ learning of concepts in mathematics. Freudenthal (1991) argues that students develop their mathematical understanding by working from contexts that make sense to them, contexts that are grounded in realistic settings. ZIMSEC Examiners Reports (2010; 2011) reveal a low student performance in the topic of Transformation Geometry in Zimbabwe, yet, the topic has a close relationship with the environment in which students live (Purpura, Baroody & Lonigan, 2013). Thus, the main purpose of the study is to explore Mathematics teachers’ use of students’ out-of-school experiences in the teaching of Transformation Geometry at secondary school level. The investigation encompassed; (a) teacher perceptions about transformation geometry concepts that have a close link with students’ out-of-school experiences, (b) how teachers are teaching transformation geometry in Zimbabwe’s rural secondary schools, (c) the extent to which students’ out-of-school experiences are incorporated in Transformation Geometry tasks, and (d) the extent to which transformation geometry, as reflected in the official textbooks and suggested teaching models, is linked to students’ out-of-school experiences. Consistent with the interpretive qualitative research paradigm the transcendental phenomenology was used as the research design. Semi-structured interviews, Lesson observations, document analysis and a test were used as data gathering instruments. Data analysis, mainly for qualitative data, involved coding and categorising emerging themes from the different data sources. The key epistemological assumption was derived from the notion that knowing reality is through understanding the experiences of others found in a phenomenon of interest (Yuksel & Yildirim, 2015). In this study, the phenomenon of interest was the teaching of Transformation Geometry in rural secondary schools. In the same light, it meant observing teachers teaching the topic of Transformation Geometry, listening to their perceptions about the topic during interviews, and considering how they plan for their teaching as well as how students are assessed in transformation geometry. The research site included 3 selected rural secondary schools; one Mission boarding high school, a Council run secondary school and a Government rural day secondary school. Purposive sampling technique was used carefully to come up with 3 different types of schools in a typical rural Zimbabwe. Purposive sampling technique was also used to choose the teacher participants, whereas learners who sat for the test were randomly selected from the ordinary level classes. The main criterion for including teacher participants was if they were currently teaching an Ordinary Level Mathematics class and had gained more experience in teaching Transformation Geometry. In total, six teachers and forty-five students were selected to participate in the study. Results from the study reveal that some teachers have limited knowledge on transformation geometry concepts embedded in students’ out-of-school experience. Using Freudenthal’s (1968) RME Model to judge their effectiveness in teaching, the implication is teaching and learning would fail to utilise contexts familiar with the students and hence can hardly promote mastery of transformation geometry concepts. Data results also reveal some disconnect between teaching practices as espoused in curriculum documents and actual teaching practice. Although policy stipulates that concepts must be developed starting from concrete situations and moving to the abstract concepts, teachers seem to prefer starting with the formal Mathematics, giving students definitions and procedures for carrying out the different geometric transformations. On the other hand, tasks in Transformation Geometry both at school level and the national examinations focus on testing learner’s ability to define and use procedures for performing specific transformations at the expense of testing for real understanding of concepts. In view of these findings the study recommends the revision of the school Mathematics curriculum emphasising pre-service programmes for teacher professional knowledge to be built on features of contemporary learning theory, such as RME theory. Such as a revision can include the need to plan instruction so that students build models and representations rather than apply already developed ones. / Curriculum and Instructional Studies / D. Ed. (Curriculum Studies)