Proponents of socially and culturally oriented mathematics education have argued that teaching approaches which value and connect with the learner's prior knowledge and everyday experience are more likely to promote active, meaningful, relevant and liberatory learning than approaches which rely on transmission and abstract presentation of mathematical content. In Malawi, proposals to reform the outdated secondary mathematics curriculum have been made with the aim of aligning mathematics instruction with the social and political changes in the current Malawian society. Using a case study approach, this study investigated the extent to which everyday experiences could be used as a vehicle for changing the learning and teaching of secondary mathematics in Malawi. The study was collaborative, taking place over a period of five months in severely overcrowded and poorly resourced classes in two schools. It involved three mathematics teachers in a cycle of planning and teaching mathematics lessons based on the use of everyday experiences, and observation of and reflection on these lessons, in order to document the effects of using everyday experiences on student learning and teachers' teaching practices. The data was collected through student questionnaires; classroom observations and fieldnotes; interviews and reflective meetings with teachers; and informal meetings with key education officials in Malawi. Mathematics examination results from students involved in this study and a corresponding group from the previous year were collected. A reflective and critical approach was adopted in the interpretation and discussion of the data. Teachers' participation in this study resulted in heightened awareness of their teaching roles and the value of linking school mathematics with everyday experience. The study also shows that students found mathematics interesting and important to learn despite their lack of success in it. In addition, the study documented a number of constraints to change in mathematics instruction such as teachers' focus on mathematics content and examination requirements, and students' resistance to inquiry learning. It also recorded possibilities and barriers to collaboration both between teachers and researchers, and teachers themselves. The findings of this study are timely since they could serve to inform the reform of the Malawian secondary mathematics curriculum currently being undertaken, which began without a critical examination of the classroom conditions necessary to accommodate a socio-politically relevant mathematics education.

A series of Guides to mathematical content, instructional strategies, appropriate materials and sources of further reading, in the form of booklets, was prepared for use in courses in Primary Mathematics Curriculum for undergraduate and Diploma in Education students. These booklets were intended to take the place of lectures in the course and act, when discussed in workshops, as initial input material for the course. The booklets were prepared also because there is no text currently available which is suitable for this course. Texts recommended for courses at other Colleges were examined and whilst many of them are useful, none is ideal. It is impossible to isolate the effect of the use of the Guides from the impact of the course as a whole. Actually, then, the effectiveness of the total course was assessed as it made use of these written materials. Teaching procedures for the course are described in the body of the study. Undergraduate students were tested, before and after the course, for mathematical concepts functional at the primary level, their beliefs about teaching mathematics, and their attitude towards mathematics. Twelve students were videotaped whilst presenting a number concept before and after the course and ten other students were interviewed at the conclusion of the course. A survey was sent to associates* to assess the effect of the course on each student's teaching of mathematics in the schools. Diploma in Education students undertook only the first two sets of tests because their course was very short. Analysis of the data indicates that the course, making use of these Guides in place of lectures, was effective. A significant gain in understanding was made on the test for mathematical concepts by both groups; a significant change in beliefs about teaching mathematics at the primary level was found in both groups; there was a significant gain with the undergraduate group in the ability to present a number concept; survey forms returned by associates for undergraduate students showed some increase in the use of concrete materials and the amount of mathematics taught in the second half of semester; and students who were interviewed showed that they had realized, at least, what theories and procedures were being advocated in the course. Suggestions for changes and improvements in the course are made as a result of this study.

The purpose of this study is to describe the effect of a curriculum rich in spatial reasoning activities and experiences on the ability of my fifth grade students to spatially reason. The study was conducted to examine 1) the effects of my practice of incorporating spatial reasoning lessons and activities in my fifth-grade mathematics classroom on the students' ability to spatially reason and 2) the effects of my practice of incorporating spatial reasoning lessons and activities on my students' ability to problem solve. Data were collected over a ten-week period through the use of student interviews, anecdotal records, photos of student work, student journals, pre- and posttests and a post-study survey. In this study, students demonstrated a statistically significant increase on all pre- and posttests. The student interviews, anecdotal records, photos of student work, and student journals all revealed spatial reasoning was used in mathematics problem solving. The study suggests that spatial reasoning can be taught and spatial reasoning skills can be used in problem solving.

We are currently witnessing an increase of international interest in mathematics education, fueled partly by the growing concerns of students’ declining results, but also by changed perceptions of what mathematics students should master. In response, many initiatives have appeared in order to move away from traditional to more inquiry based approaches to teaching. Though several small-scale studies have contributed much to our understanding on how to support teachers in this work, there is still a lack of research conducted on a larger scale. Therefore, the aim of this thesis is to add to our knowledge of how to support instructional improvement at scale. This is done by focusing on two common approaches to support mathematics teachers’ development of reform based practices: teacher professional development [PD] programs and curriculum materials. The thesis builds on four papers which are all connected to a project aiming at improving the mathematics instruction in a large Swedish municipality. The project includes a PD-program for almost 400 elementary teachers and the mathematics curriculum materials that teachers are using play a central role in the program. The first two papers focus on curriculum materials either by using surveys to compare teachers’ views of the support offered in the materials and their reported mathematics instruction, or by conducting textbook analyses to characterize how some commonly used materials communicate about, for example, goals of lessons. The results demonstrate that teachers using different materials experience different levels of support from them and also show variations in their reported instruction. These differences are further reflected in the textbook analyses which show that the materials offer teachers various support, for example regarding how they communicate about goals. The last two papers focus on teacher PD-programs either by comparing the effects of two programs on student achievement, or by using surveys to examine teachers’ views of one of the programs and its impact on their reported instruction. The results indicate that the two PD-programs have affected students’ achievement in different ways, demonstrating both decline and improvement. Even within the programs differences are revealed between students at the primary and secondary levels. These variations are further present in the teacher surveys, where the results show differences between teachers from different grade-levels. By drawing on the literature review and the results of the papers, the thesis ends with a discussion of possible elaborations of a widely used core conceptual framework for studying teacher PD.

In 1981 the author submitted that "many of the (then) more recent school syllabuses remain disjointed and give expression still to a school mathematics course as step-by-step progression through a list of disparate topics". The position has not changed. It is not yet generally accepted that there can no longer be an accepted body of mathematical knowledge that needs to be taught. The rapid development of new technology and the introduction of the microcomputer should enable the 'modern' mathematics of the early 1960's to enhance the mathematical experiences of pupils in a practical and comprehensible way and prompt a new style of teaching and learning mathematics. There is, however, a fundamental core of mathematics which must inevitably find a place in the school mathematics curriculum. In Part I of the thesis the emphasis is on a method of presentation of certain key topics which illustrate the basic pattern of a group structure. Former complications at school level of putting plane geometry on a logical footing have to be avoided. The use of complex numbers highlights significant and sometimes rather difficult geometrical ideas. In Part 11 the author attempts to show how some of these ideas may be presented to extend the basic pattern to that of linear algebra. The work culminates in Part III with the use of linear complex algebra to present more vividly the symmetries of the Platonic solids. The author anticipates the realistic presentation of the aesthetic side of 3-dimensional geometry and takes a look at its possible presentation through the medium of the microcomputer. At this early stage of the development of the ideas to be discussed, there can be no formal testing of the results by quantitative analysis. Evaluation of the viability of the proposals will be qualitative and the comments of 'critical academic friends' will be included. The originality demanded of a piece of research goes beyond the exposition. Here it will consist of new insights into ideas appropriate to senior pupils in schools and a rewriting of existing material often thought to be beyond their scope. The work is supported by suggested lesson sequences, transcripts of recorded presentations, and examples of students' work. Subsequent development must face the question of assessment and evaluation at sixth-form level of the proposed new style of teaching mathematics. The author makes some suggestions in the concluding chapter.

It is the purpose of this study to review in brief the changes that have taken place since the turn of the century in content of mathematical studies in the high school and to examine theoretically the significance of such changes.

This study investigates the teaching and learning of mathematics in four rural schools in the Eastern Cape Province of South Africa. The study is set against the backdrop of Curriculum 2005 (C2005) - an outcome based curriculum reform initiative that has been introduced to all South African schools. The objective of the study is to investigate the teaching and learning practices of four rural teachers of mathematics in this complex reform milieu. The following broad research question guides this study: "How do teachers interpret and implement the new mathematics curriculum in terms of a political perspective (how teachers and learners are connected to the curriculum); a socio cultural perspective (what adjustments the teacher makes to accommodate the learners' circumstances); and a practical perspective (how the teacher implements the goals of C2001?" The South African situation provides a unique and particularly challenging context for teaching and learning and curriculum reform. It is understood that schools differ - and therefore curriculum issues cannot be solved through general pronouncements but rather viewed from a multiplicity of perspectives. In this thesis, I examine the teaching and learning of mathematics in four rural classrooms in the Eastern Cape. By way of honouring the contextual complexity of the situation, 1 have adopted a multiple perspectives approach to analysing what goes on in these four classrooms. I use a political perspective to help understand how power operates in the curriculum process. / I employ a socio cultural perspective to examine how the curriculum process attends to the local circumstances of teachers and learners. A practical perspective is used to examine how the curriculum is implemented in a technical sense. This constructivist interpretive study employs the techniques of case study and narrative inquiry to study the curriculum practices of four teachers. Multiple methods - including interviews, participant observation and video recording - were used to gather data. Narrative accounts of the teaching and learning of mathematics were constructed and then analysed using the three perspectives. The study concludes that the curriculum can be interpreted at different levels formal, perceived, operational and experiential - and each level can be analysed in terms of the political, socio cultural and practical. Bringing these three perspectives together is a challenging, but necessary task in order to understand and act upon the complexities of educational reform in rural South African classrooms.

The purpose of this study was to investigate the implementation process of the present and newly introduced instructional techniques in new elementary school mathematics curriculum in sixth grade through the reports of teachers, which has been piloted in some specific schools. Moreover, it was aimed to find out the effects of several parameters on implementation, like city where school teachers are working is located, teachers&amp / #8217 / gender, teaching experience and number of students in the classroom. In addition, difficulties faced by teachers during the implementation process and teachers&amp / #8217 / general opinions about the new curriculum are examined. The sample consisted of 80 teachers working at elementary schools located in Ankara, Istanbul, Bolu and Kocaeli (Izmit). The Teacher Questionnaire was administered to participants in the 2005-2006 academic year. In order to investigate the differences in Teacher Questionnaire&amp / #8217 / s sub-scales&amp / #8217 / scores (Learning-Teaching Process, Material Usage, Evaluation Techniques) of the participants with respect to city, gender, teaching experience, academic level and number of students in classes, separate Multivariate Analysis of Variance were run. The results of this study indicated that teachers&amp / #8217 / implementation of the new methods and techniques highlighted in the curriculum can be interpreted as at high level. MANOVA tests indicated that teachers&amp / #8217 / implementation of the new methods and techniques were not affected by number of students in the classrooms, gender and teaching experience. According to the results of the study, teachers&amp / #8217 / usage of recommended educational equipments was found as at average level and MANOVA tests indicated that teachers&amp / #8217 / usage of recommended educational equipments was affected by teaching experience but not by gender and number of students in the classroom. The results of this study also showed that teachers&amp / #8217 / implementation of new evaluation techniques was at average level and MANOVA tests indicated that teachers&amp / #8217 / implementation of new evaluation techniques were not affected by gender, teaching experience and number of students in the classrooms.

In the course Discrete Deterministic Chaos, Dr. Mark Daniels introduces students to Chaos Theory and explores many topics within the field. Students prove many of the key results that are discussed in class and work through examples of each topic. Connections to the secondary mathematics curriculum are made throughout the course, and students discuss how the topics in the course could be implemented in the classroom. This paper will provide an overview of the topics covered in the course, Discrete Deterministic Chaos, and provide additional discussion on various related topics. / text

The educational system in Kuwait is intended to provide primary and secondary students with required skills in order to operate in the technical careers commonly undertaken. However, mathematics education lags significantly behind other countries in Kuwait. In the 1997 and 2008 TIMMS international studies of primary and secondary mathematics achievement, Kuwait ranked near the bottom on almost all scores. Thus, improving mathematics education in Kuwait is an issue of serious concern. This research focuses on the question of whether mathematics teaching and learning in Kuwaiti primary schools (grade 4) can be improved through the use of computer-based tools for practice drills and constructive mathematics play. An observational intervention was used in a classroom of 24 children, where students took a pre-test for mathematics achievement, then engaged in a series of exercises through the term and were retested at the end of the term. This was accompanied by a series of in-services and teacher interviews that were conducted within the school, in order to discover attitudes about mathematics teaching and learning and to train teachers in the suggested approaches and techniques. A combined qualitative and quantitative approach included analysis of test scores and interviews with teachers and students. The overall outcomes of the study did show a slight increase in mathematics achievement scores. However, more importantly it showed an improvement in children's and teacher's attitudes to mathematics learning related to the introduction of constructive play activities (derived from the Cambridge University N-RICH program and selected for students based on level of achievement) Overall, the importance of this study is that it provides pragmatic information for Kuwaiti teachers and curriculum designers on improving mathematics teaching and learning.