This study examined the different types of mathematical errors exhibited by primary level pupils in Brunei when working with fractions. In addition, the study examined pupils' attitudes towards the learning of fractions and investigated if there were gender differences among Bruneian pupils' performances with fractions and with their attitudes towards fractions. The study was longitudinal in nature and its two phases involved a single cohort of Primary 5 pupils followed through a full year period in four government-funded primary schools in Brunei Darussalam. Pupils' mathematical errors were assessed by means of researcher-developed paper-and-pencil tests, while pupils' attitudes towards the learning of fractions were measured by means of an adapted version of attitude questionnaire that has been used previously with Bruneian pupils. Guided by six research questions, a number of statistical analyses were carried out to ensure the validity and reliability of the instruments used. These included piloting and revising the instruments, the use of Cronbach's alpha with the items in the attitude questionnaire, and the calculation of the Pearson Product Correlation Coefficient between scales of the questionnaire. The data was analysed by calculating the percentages and means of occurrences of each type of error. Paired and independent sample t-tests were carried out in order to investigate gender differences in pupils' errors and the impact of further instruction on fraction at the P6 level, while the GLM test was administered in order to investigate if there were significant change in pupils' attitudes towards fractions from the pre- to the posttests. Qualitative information obtained through pupils' interviews, field notes and lesson observations was used to support the quantitative data. / The study revealed that though pupils' achievement in the post-test improved, their performances on fraction work remained generally unsatisfactory. Many pupils in the study continued to have difficulty with the basic operations on fractions and resorted to the use of keyword strategies in dealing with word problems. Despite the pupils' unsatisfactory performance in the diagnostic tests, they generally held very positive attitudes towards the learning of fractions. No significant gender differences were observed either in pupils' performance in working with fractions tasks nor with their attitudes towards the learning of fractions. The findings of this study also highlight a number of issues for mathematics teachers to consider when dealing with fractions, and the findings also have implications for the quality of the instructional activities provided by the teachers, for the impact of language transfer in the medium of instruction - that is, from Bahasa Melayu to English at the pupils' Primary 4 level- and for the quality of the teacher training program in Brunei.

Magister Educationis - MEd / The research explores the effects of Community of Enquiry practices on the teaching and learning of Mathematics and Literacy in two local primary schools. After the 1994 elections, both the government and education system changed in South Africa. With the introduction of Outcomes Based Education (OBE), critical outcomes that emphasized thinking and collaboration became a vital part of the curriculum. Soon after, the Education system adopted the National Curriculum Statement (NCS) and thereafter the Revised National Curriculum Statement (RNCS), which maintained these outcomes. The Curriculum and Assessment Policy Statement (CAPS) was introduced to the Foundation Phase in 2012 and to the Intermediate Phase in 2013 with the Critical Outcomes, (which emphasizes thinking) now stated as the aims of CAPS. However, no guidelines are provided regarding classroom practice. The approach to teaching these aims is not made clear. Lipman’s Philosophy for Children (P4C) is one way of working towards these aims, and promoting thinking and is consistent with many of Vygotsky’s ideas. He initiated ideas about cognitive development in which he refers to the importance of dialogue in which one is able to talk and communicate with others. Vygotsky also emphasised scaffolding where the teacher provides the learner with clues and suggestions in order to develop better problem- solving techniques and thinking habits. His concept of the zone of proximal development (ZPD) refers to the individual’s ability to accomplish more or to perform a challenging task with the proper assistance. The development of language is considered important within his theory as Vygotsky believes that individuals are born only with lower mental processes and develop their thinking ability (higher mental processes) by acquiring the thinking tools developed in a particular culture, the most important of which is language. The research followed a qualitative research methodology. The study explored the perceptions of both educators and learners after an intervention based on Philosophy for Children. Qualitative data involved two group interviews with teachers, one with the Cognitive Education Co-ordinator and interviews with four focus groups of selected Grade 5 and 7 learners (12 per group) whose teachers implemented Lipman’s Community of Enquiry pedagogy in the classroom the previous year. Quantitative data included a learner self-rating scale. All the educators of the two schools, who were involved in the classroom Community of Enquiry training, were invited to participate in the study, as were selected learners from the two Grade 5 and 7 classes at each school. I made use of thematic analysis of the interview data from both learners and teachers. Themes within the interviews were identified. Themes pertaining to teacher perception of self-change, teacher perception of learner change, and learner perceptions of self change were identified. During thematic analysis, the three research sub-questions were underlined. These were: (1) What are the teachers’ perceptions of self-change? (2) What are the teachers’ perceptions of learner change? (3) What are the learners’ perceptions of self-change? The conclusion of the study was that P4C has the potential to affect the teachers professionally and to influence the learners positively in Mathematics and Literacy classrooms. Ongoing support in cognitive education is vital in order to reach the aims required for the new CAPS curriculum.

As a result of two years working with the pre-service primary teachers in a College in Fiji I became aware of the difficulty many of the students were having understanding the primary school mathematics they would be required to teach. During that time I had attempted to help them overcome the difficulties by using different teaching approaches and activities but was far from satisfied with my efforts. Hence I decided to make a concerted effort to help the students by planning, implementing and partially evaluating a mathematics education unit, known as the Teaching Program for the first semester of their course. This work formed the basis of my study. For the Teaching Program I chose a constructivist teaching approach with number sense as the underlying theme. To examine the aspects of the Program I used my observations and those of the students especially ones reported in their mathematics journals. To evaluate the effectiveness of the Teaching Program I collected and analysed quantitative data from traditional testing of the class of forty students as well as data from case studies of six of the pre-service teachers in the class. To determine what features of the Teaching Program were linked to positive changes my main source of data was the case studies, especially entries from their journal writings. The findings suggested that a significant development of the cognitive aspects of the students’ number sense did occur during the time of the Teaching Program but not as much as was hoped for. As a result of the analysis of the data I came to a greater realisation of the importance of the non-cognitive aspects of number sense and the necessity for a greater consideration of them in the development of a Program. I also realise now that a major development that did occur was in my understanding of the knowledge and learning of mathematics. My ideas of a teaching paradigm of social constructivism had not guided me sufficiently to incorporate activities and procedures to develop the non-cognitive aspects. I suggest that a paradigm which extends the theory of social constructivism to give greater consideration of these aspects of learning in general, and hence numeracy and number sense in particular, was needed. As a result of this study, my introduction to the theory of enactivism appears to be giving me some direction in this search at this stage.

This thesis is about the process of becoming, or not becoming, a primary school mathematics teacher. The aim is to understand and describe the professional identity development of novice primary school mathematics teachers from the perspective of the novice teachers themselves. The study is a case study with an ethnographic direction where seven novice teachers have been followed from their graduation and two years onwards. The ethnographic direction has been used to make visible the whole process of identity development, both the individual and the social part. The empirical material in the study consists of self-recordings made by the respondents, observations and interviews. The empirical material is analysed in two different but co-operating ways. First a conceptual framework was developed and used as a lens. Second, methods inspired by grounded theory are used. The purpose of using them both is to retain the perspective of the respondents as far as possible. At the time of graduation the respondents are members in a community of reform mathematics teaching and they want to reform mathematics teaching in schools. In their visions they strive away from their own experiences of mathematics in school and practice periods. Four cases are presented closely in the thesis as they show four various routes into, and out of, the teaching profession. These four cases make visible that the respondents’ patterns of participation regarding teaching mathematics changes when they become members in new communities of practice with mathematics teaching as part of the shared repertoire. But, the four cases also make visible that the existence of such communities of practice seems to be rare and that the respondents’ different working conditions limit their possibilities of becoming members in those that exist. During the time span of this study, the respondents hardly receive any feedback for their performance as mathematics teachers. Even if they teach mathematics they don´t teach it as they would like to and they don´t think of themselves as mathematics teachers. Two years after graduation none of the respondents has developed a professional identity as primary school mathematics teacher. A primary school teacher in Sweden is a teacher of many subjects but they are the first teachers to teach our school children mathematics. For the respondents to develop a sense of themselves as a kind of primary school mathematics teacher, mathematics teaching has to become part of their teacher identities. For this to become possible, mathematics must become a part of their image of a primary school teacher as an image of a primary school mathematics teacher. Furthermore memberships in communities of practice with mathematics in the shared repertoire must be accessible, both during teacher education and after graduation. Then professional identity development as a primary school teacher would include becoming and being a teacher of mathematics.

The South African education system is under a serious strain in relation to Mathematics attainment. Only 40% of learners in SA pass the final school leaving examination and only 5% of learners manage to pass Mathematics with more than 50%, according to The Economist (2014). In a bid to solve this problem the government proposes the use of ICTs (such as computer hardware and software, tablets, and smartphones) within teaching and learning. The assumption is ICTs can be utilised to address this important challenge and “facilitate ongoing improvement of educator skills” (The National Integrated ICT Policy White Paper: The White Paper, 2016: p.8). Research shows that teachers’ perceptions regarding the use of ICTs impact on their practices (Mwendwa, 2017; Munyengabe, Yiyi, He Haiyan, & Hitimana, 2017; Alharbi, 2012; Yuan & Chun-Yi Lee, 2012). This project intends to explore six grade 6 Mathematics teachers’ perceptions about whether and how pedagogy shifts with the use ICTs in the classrooms utilising Cultural Historical Activity Theory. This research utilises interviews as a method for the collection of empirical data to describe a group of research participants’ (or teachers’) perceptions who happen to be directly interviewed. These interviews have been conducted across two no-fee paying primary schools in the Western Cape Province (WCP), in South Africa (SA). Interviews were analysed along the CHAT dimensions: object, subject, tools, rules, community and division of labour to establish whether pedagogy altered along any of these dimensions. Findings indicate that teachers think pedagogy shifts in the ICT based lessons with division of labour becoming more fluid. Findings also show that the object of the activity system grows to encompass more than mere mathematical compression but also motivation, creativity and cognitive development. Besides, teachers stated that ICT based learning could assist learners in their mathematical attainment. This project is an investigation and not an intervention study. Recommendations are also suggested in this thesis for further research such as video-taping teaching and learning of mathematic contents and concepts in both traditional and computer-based classrooms. Further study in utilising classroom observations to focus on student-student interaction in relation to ICTs is also recommended.

This thesis is pursued to the possibilities of using photography in teaching of mathematics. I have gathered enough information for condition of use photography. In the next step I followed the objectives: to analyze selected mathematics textbooks in terms of using photography according its six roles; documenting the influence of photography in exercises on their answer; creating a task with photographs that would complement the gaps in their use in didactic materials. Analysis has shown that most often use photos in textbooks is in a motivational role, that does not carry relevant information to solve a excercise. The effectiveness of using a photo is verified on several excercises, which showed a higher abundance of right answers and pointed out the need to look for the right format, motive and quality of the photograph. This excercises also confirmed grasping a decimal system by pupils through a money model. The next part of the thesis is devoted to the creation of excercises with photography in various roles, which are less common in educational materials than the motivational role. Excercises include many different activities from manipulative to creative. Activities with phootgraphs is possible to use in different teaching organizations and can be used in teaching very quickly and easily. An...