The purpose of this study is to see how some teachers in primary school creates and adapts their mathematics teaching for students with special mathematical abilities. It also aims to identify opportunities and challenges that teachers see in creating a teaching adapted to these students. In this study, qualitative interviews has been done to collect data. The interviews were conducted with five teachers who all are active in the primary school. The study results show that there is great variation in how the interviewed teachers create their mathematics teaching for students with special mathematical abilities. The use of mathematics book proved to be significant for how this adaptation took place. The result also shows that the teachers’ explanations for the choice of the adaptations that they make in teaching vary. Some of the teachers stressed that the teaching they were carrying made it possible for adaptation in the normal teaching while others stressed that they made adjustments to fit the current student best. The result showed two challenges that many of the teachers saw in the creation of a teaching adapted for students with special mathematical abilities. These challenges were time and group.

Nowadays, technology plays a fundamental role in education, in general, and in mathematics education in particular. The graphing calculator has been an important technological tool in mathematics classrooms since its invention and introduction in 1985 by Casio. As graphing calculators provided so many uses, their contribution to the teaching and learning process has been investigated by many researchers who have shown the use of such technology can have a significant effect on improving mathematics teaching and learning. Investigating the impact of graphing calculators on student learning is important. It is also essential to research teachers’ perspectives on how using graphing calculators in mathematics determines how such use affects their teaching and learning. However, there are few studies on this issue. Therefore, this dissertation study may fill the gap in the literature in terms of examining high school mathematics teachers’ perspectives when they teach a precalculus course with technology integrated in the curriculum materials. In this study, I analyzed eleven teachers’ perspectives about using graphing calculator technology in a precalculus course, titled Functions, Statistics, and Trigonometry (FST). This study was a descriptive intrinsic case study in which I analyzed teachers’ perspectives about how they use graphing calculators in the FST course, specifically about their teaching and students’ learning with available graphing calculator technology. Additionally, I explored teachers' perspectives about the issues they face when using the available technology and for what topics teachers frequently used it. I used mixed methods to examine eleven mathematics teachers’ perspectives about their teaching, students’ learning, and issues that arise when they use graphing calculator technology. In the quantitative part of the study, I created an Index of Teachers’ Initial Perceived Attitude and Experience Level and an Index of Teachers’ Use of Graphing Calculators to measure teachers’ perspectives on technology use at the beginning and end of the school year, respectively. In the qualitative inquiry, I analyzed teachers’ responses to semi-structured interview questions by using thematic analysis. The results of this study showed eight of the eleven mathematics teachers’ students used graphing calculators with Computer Algebra System (CAS) capability loaned by The University of Chicago School Mathematics Project (UCSMP). Five teachers had a high initial perceived attitude and experience level and the other six teachers had a medium level. All teachers reported that helping students learn to use a symbolic manipulator was equally or less important than to use a graphing calculator. The themes (1) Teachers’ use of graphing calculators, (2) Teachers’ opinions about students’ use of graphing calculators, and (3) Teachers’ issues with graphing calculator technology were created to explain teachers’ responses to interview questions related to their graphing calculator perspectives throughout the year. Teachers typically used graphing calculators almost every day for such purposes as exploring mathematics, solving problems, and checking work. Some teachers reported the benefits of using graphing calculators in terms of instruction were focusing on the concepts and showing additional solution approaches. Teachers who wanted their students to be able to do some work without graphing calculators used no calculator tests or questions on which graphing calculators were not allowed as part of their assessment process. Teachers mentioned the need for a manual showing the steps for using graphing calculators with CAS. Teachers’ opinions about students’ use of graphing calculators included that students generally liked them. Teachers reported graphing calculators positively affected students’ learning because students were able to find the answers for problems and have better visualization opportunities. However, teachers reported some meaning was missing and students’ arithmetic skills were negatively affected because of the presence of graphing calculators. Additionally, five teachers indicated their students relied on the graphing calculators too much. The most common issue teachers had relative to graphing calculator technology was the liability issue of the graphing calculators sent by UCSMP for students to loan. Teachers were responsible for those loaned graphing calculators. Additionally, cheating, using features that minimized the mathematics, and not being familiar with the type of graphing calculators loaned from UCSMP were other issues teachers reported. Teachers’ graphing calculator use was demonstrated based on the index of teachers’ use of graphing calculators. Seven teachers were high in terms of their use of graphing calculators at the end of the school year and four teachers had a medium use of graphing calculators. For implications of this study, mathematics teacher educators can use the results to improve professional development programs for teachers. They might create workshops based on teachers’ perspectives and their initial perceived attitude and experience level. Additionally, textbook developers can create more exploration activities with graphing calculators, especially with CAS.

This doctoral research was concerned with the role of language and its implications for the learning, teaching and assessment of mathematics for children aged 4-9 years. Earlier research by the author had established language and assessment as bridges enabling learning although they had the potential to increase the divide between teacher and learner. Reflection raised the question on how children achieved in mathematics despite potential difficulties with language and assessment. Review of the literature concluded that resources and sociocultural norms were also bridges between learner and teacher. A model was established of the relationships and processes between all perceived variables that provided an external, theoretical structure to be evaluated against structuralist, pragmatic and integrational linguistic approaches and empirical outcomes. The overarching approaches adopted were institutional ethnography and case study. An appropriate methodology was devised whereby sophisticated ICT equipment captured all visual and speech events during classroom interactions. Frequency analysis at word level, content analysis at utterance level and discourse analysis at total speech level triangulated with content analysis of interviews and evaluation of documentation completed the empirical research. Data analysis revealed five registers of children’s talk. Evidence suggested that the peer-peer ‘conditioned talk’ used in focused group work was the most effective for learning as it enabled them to discern the small steps in the inferential leaps in discourse made by their teachers, work out problems together, inform their peers, share findings and reinforce each others’ learning. Learners’ language showed aspects of structural, pragmatic and integrational linguistics, confirming a conclusion of the literature review that the various linguistic approaches discussed should be used to support and not exclude each other. The contribution made to knowledge is the ethnomethodology provided by the model, ICT resource and the five registers of talk revealed by the linguistic approach to discourse analysis. Teachers would be able to understand nuances of language used by their pupils and acquire essential skills and tools to put into effect the personalised learning agenda. Peer-peer observation of teachers would be an appropriate platform for the observation of the different registers used by learners, the resources that generate those registers, and their most effective use to close the gap between natural language and the subject specific language of mathematics.

Bakgrund Alla elever i årskurs ett till tre har fått utökad tid för matematikundervisning från och med läsåret 2013-2014. I arbetet belyses den utökade tiden utifrån lärares perspektiv. Syfte Syftet är att visa på hur åtta lärare beskriver att de använder den utökade undervisningstiden i matematik.  Hur beskriver lärarna den utökade matematikundervisningen?  Har den utökade tiden lett fram till några förändringar i lärarnas undervisning, om i så fall på vilket sätt?  Vad är kvalitet i matematikundervisning enligt lärarna? Metod Kvalitativ metod med semi-strukturerad intervju som redskap för datainsamling. Resultat Undersökningen visar att undervisningen inte har påverkats mycket av den utökade tiden. De flesta lärarna uttrycker dock att det är bra med mer tid, de behöver inte stressa fram längre. Kvalitet i undervisningen får man bland annat genom mer planeringstid, tid för reflektion enskilt och med kollegor, uttrycker lärarna. Ramarna styr vilken undervisning som levereras. / Background All students in grade one through three have been given extended time for mathematics education from the academic year 2013-2014. The work highlights the extended time from the teacher's perspective. Purpose The purpose is to see how eight teachers describe their use of the extended educational time in mathematics. How do the teachers describe the extended mathematics teaching? Have the extended period led to any changes in their teaching, if so, how? What is quality in mathematics teaching according to the teachers? Method The method is a qualitative method with semi-structured interview for data collection. Results The survey shows that the teaching has not been affected much by the extended time. Most teachers express, however, that it is good to have more time, they don´t need to feel stressed anymore. According to the teachers quality in teaching is obstained through more time for planning and reflection alone or with other colleagues. The teaching is determined by the framework.

I denna uppsats studeras förekomsten av värden i geometrikapitel i läromedel för gymnasieskolans Matematik A. En metod baserad på innehållsanalys som använts i en tidigare studie om förekomst av värden i algebrakapitel har vidareutvecklats. Sammanlagt 955 uppgifter i geometrikapitlen i fem olika läroböcker har analyserats. Resultatet visar på en skillnad mellan intentionerna i gymnasieskolans styrdokument och det utrymme olika värden ges. Även skillnader mellan det utrymme studerade läromedel ger åt olika värden har påvisats.

This research was undertaken to determine the influence of a video class system on the strategic teaching and learning of school mathematics. A literature investigation served as a frame of reference for the planning, execution and assessment of the empirical investigation. Some of the approaches which have the greatest influence on the learning of school mathematics, namely the behaviourist, cognitive and constructivist approaches, are described and, where necessary, critically assessed. Factors which influence the learning of school mathematics are discussed in an interrelated manner and are used to identify the features of the strategic learning of school mathematics. It is then attempted to determine how teaching should take place to enable the strategic learning of school mathematics. To reach this objective, different approaches to the teaching of mathematics are discussed, based on approaches to the learning of mathematics, and the influence of these on the teaching of school mathematics is determined, based on the literature investigation. Different factors which influence the teaching of mathematics are identified and used to describe the characteristics of the effective teacher, who teaches mathematics for the strategic learning of the subject. The empirical investigation involved a quantitative as well as a qualitative investigation. In the quantitative investigation an actual experimental design with a pre-test and post-tests was used. Video recordings were made with one experimental group (video recording class) and delivered (played back) with another experimental group (video delivery class). The control group received conventional mathematics teaching. A quantitative field investigation was undertaken by means of an adapted LASSI-HS to establish the influence of the video class system used in the investigation on the study and learning strategies of the learners. In this way the influence on the strategic learning of mathematics could be determined. At the same time the influence of the video class system on the mathematics performance of the learners was established, in order to determine the extent of success of the use of the video class system. A qualitative investigation by means of an observation schedule, together with the analysis of video recordings of mathematics lessons, was used to determine the influence of the video class system on the teaching of mathematics. The video class system did not have a negative or a positive influence on the performance of either the video recording classes, the video delivery classes or the control classes of the schools who participated in the research. Neither did the video class system have a positive or a negative influence on the use of learning and study strategies (concerning mathematics) of the different class groups who participated in the research. That means that the video class system did not negatively influence strategic learning in learners who may use it. / Thesis (Ph.D. (Education))--Potchefstroom University for Christian Higher Education, 2003

Cooperative learning has emerged to be a preferred teaching-learning model in South Africa since the inception of Curriculum 2005 (C2005) emphasising Outcomes-based education (OBE). However, the documented success rate of cooperative learning in mathematics was experienced in small group sizes (emanating h m small class size) of about five learners. This study, therefore, aims at affording mathematics teachers and learners of crowded classes an opportunity to effectively use cooperative learning, namely the Hour-glass model in mathematics lessons. The prevalence of crowded classes in the majority of South African schools seems to inhibit the effectiveness of cooperative learning in mathematics. The big cooperative group size of about eight learners in South African context results in very complex lines of communication between learners. The teacher spends more time trying to manage off-task behaviour of learners instead of engaging them in active participation in the learning of mathematics. The combined quantitative and qualitative research methods were used. For the former, the study orientation in mathematics (SOM) questionnaire and the mathematics academic achievement test were used to collect data with regard to the influence of the Hour-glass model on the learners' learning skills in mathematics, and on the mathematics academic achievement respectively. A specific true experimental design, namely, the Solomon Four-group design, was used because of a large sample size (n > 500), and its credited ability to control the sources of threats to internal validity. For the latter the lesson observation and interviews were conducted to collect information about the influence of the Hour-glass model on learners' social skills during cooperative learning in mathematics. The groups that received the treatment (i.e. Hour-glass model) achieved higher scores of practical significance in mathematics academic achievement test than the groups that did not receive the treatment The Hour-glass model also yielded positive social skills among learners during mathematics learning. The teachers who applied the Hour-glass model revealed that they coped easier with crowded mathematics classes when using cooperative small groups. However, the Hour-glass model did not significantly influence learners' learning skills in mathematics. Certain logistical and administrative limitations emerged with regard to the implementation of the Hour-glass model in the usual school setting. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2004.

Worldwide the teaching and learning of mathematics pose a great challenge to mathematics teachers as learners' performance in the subject leaves much to be desired. This is particularly the case in South Africa where there was a great disparity in the development of teachers in the past. Extensive research has shown that many teachers in South Africa are under-qualified, especially in the teaching of mathematics at secondary schools. Those who are regarded as well qualified for teaching mathematics at secondary schools still experience problems in teaching certain sections of the syllabus, for example geometry, which is not offered at tertiary institutions. It is for this reason that the researcher, together with colleagues at an experimental school, joined forces to share the teaching of mathematics in what they referred to as "collaborative teaching". This work therefore involves a case study, which resulted after three teachers successfully achieved good matric results on employing this approach between 1993 and 1996. The study is based on an experimental design where both quantitative and qualitative methods were used. The aim of the study was to measure the extent to which collaboration between teachers affects the learning of mathematics in Grades 12. Two schools, the experimental school and a control school were involved. Learners from the experimental school were taught according to a collaborative approach whereas learners at the control school were taught conventionally (one teacher teaching all sections alone). This happened over a period of six months in 2001. Learners who were taught collaboratively outperformed those who were taught conventionally especially in the most problematic areas of the syllabus, namely geometry and trigonometry. The teachers who were involved in this approach, that is, collaborators, loved it to the extent that one of them applied it in another school where it improved their Grade 12 results tremendously. Learners who were taught according to this approach greatly appreciated it and wished they had been taught the same way in other subjects. This approach did not, however, significantly influence learners in their problem solving and information processing skills. In addition, one of the most serious limitations of this approach is to find a substitute for a teacher who leaves the team. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

The aim of this thesis is to ascertain how primary school teachers would like to improve their mathematics teaching. The central questions for this research are: In what ways do teachers want to improve their mathematics teaching? How do the teachers justify their statements? What main features can be distinguished out of the teachers answers? Three interviews and seven surveys have been used to collect information from a total of nine teachers, at one primary school. Teaching pupils from preschool to sixth grade. The results have been analysed, interpreted and discussed using a drama pedagogical perspective, inspired by a holistic approach to learning. In order to investigate connections between drama pedagogic and holistic perspectives on learning in the teachers’ answers, three main characteristics of drama pedagogic usage have been defined: To embody (meaning: to act and/or create); Process (meaning: learning takes time and seeks deep understanding); Play (meaning: joyful activity which involves relatively little supervision by the teacher). The results show that teachers would like to work in more practical ways, where investigative and experimental activities are more commonplace. Although not supported by all responses, a significant majority of respondents expressed belief in working methods, and reasoning about learning, with fundamental connections to a drama pedagogic and holistic perspective on learning. This thesis concludes that the teachers surveyed believe in embodiment actions as a learning medium, and that knowledge can be highlighted by the principles of process. / <p>Examensarbete nr 1 (utav totalt 2) inom lärarprogrammet med inriktning drama mot skolår 5 - 9 samt gymnasieskolan.</p>

The main objective of this study was to investigate the effect of using a suggested mathematical word-problem training programme on Primary 4 pupils' performance in mathematical word-problems. The study had a pre-post control group design. A treatment and a no-treatment group were exposed to pre-post methods of gathering data (a mathematical word-problem achievement test and a mathematical word-problem attitude scale). The treatment group was given direct and explicit training on how to solve mathematical word-problems, while the pupils of the no-treatment group received no such training; they were taught the same material they study at school. A "t" test was used to compare the means of scores of the control group pupils and those of the experimental group in the pre-post measurements. Results of the study revealed a significant improvement in the experimental group pupils' performance in mathematical word-problems because they had attended the suggested programme. Results also revealed that experimental group subjects' attitudes towards mathematical word-problems underwent an exceptional change because they had attended the suggested programme. Their attitudes towards mathematical word-problems became more positive than before. In the light of the results of the study, some recommendations were made for improving mathematics teacher training programmes, for mathematics teaching, and for further research.