This thesis investigates the impact of a mandatory primary mathematics teaching reform on teaching and achievement in the context of Seychelles. The reform was implemented in 2006 as a strategy initially to improve mathematics teaching and ultimately the pupils’ achievements. The Mathematics Lesson Structure (MLS) reform aimed to encourage a more coherent structure to mathematics lessons, provide variations in pupils’ learning experiences, and facilitate school-based teacher learning. The thesis focuses on the outcomes of the reform. Taking this reform as a case study, the thesis explores systemic policy reform in a small developing state. The research employed a mixed methods design for data collection. A questionnaire was administered to a group of teachers involved in the teaching of mathematics in primary schools (n = 219). Four schools were selected for in-depth fieldwork. In each of the four schools, a six-teacher focus group interview was carried out, and samples of lessons, amounting to 22 lessons, were observed. A focus group interview was held with a group of 8 mathematics subject leaders. Additional interviews were conducted with 2 education officers who worked with teachers in schools. Secondary data were drawn from two projects: Improving Pupils’ Achievements in Mathematics or DPAM, and Southern African Consortium for Monitoring Educational Quality or SACMEQ. Pupils sample size for the SACMEQ II, III and IP AM data files were n = 1484, n = 1480, and n = 1080 respectively. The IP AM data also consisted of teacher questionnaires and interview responses. The results indicate that the reform was beneficial to the teachers and the subject leaders in a number of ways. The teachers overwhelmingly liked the reform but lesson observation data show that they were not necessarily complying as they reported. The teachers overwhelmingly liked the reform but lesson observation data show that they were not necessarily complying as they reported. Observation data also show that the lessons deviated from the contemporary vision of what mathematics lessons should look like. Teachers’ accounts of their experiences suggest that the primary schools were challenging sites for pedagogical reform. Data about the pupils’ achievements show no progress in performance from 2006 to 2007 but an improvement in 2009. The use of MLS reduces variability in pupils’ performances. These results have implications for in-service teacher education, pedagogical reform, and policy implementation in small developing states.

Children with math difficulties do not have as much support as children with reading difficulties (Fuchs, Seethaler, Powell, Fuchs, Hamlett, & Fletcher, 2008) yet a difficulty in mathematics has the potential to impair a person's daily activities and should be treated seriously by researchers, policy makers and teachers. The ability to recall number facts appears to be fundamental deficit for children (Butterworth, 2005, p.4S8) and interventions using drill and strategic instruction show that these methods are both effective and necessary to improve children's number fact recall. A number of types of tutoring have been used in the D.K. to support mathematics ability including teacher, peer and volunteer tutoring. Volunteer tutoring is a promising method of supporting children with reading difficulties, however there is limited research on its effectiveness for children with mathematics difficulties. Learn-a-Long Math is a volunteer tutoring programme designed using the existing evidence on the most effective methods to support children with mathematics difficulties, This thesis gives a detailed account of its design and evaluation. The programme aimed to improve fact recall and calculation ability of seven and eight year old children. It was evaluated using a randomised controlled trial and process evaluation. The RCT revealed that there was a significant effect of the intervention on the math fluency (ES = .23) and calculation ability of children (ES = .52) however there was 1).0 significant effect of the intervention on the children's attitudes to math. The process evaluation explored the impact and implementation of the programme. It showed that there were benefits for the children; tutors and schools who participated in the evaluation. The findings suggested that there is potential for volunteer tutoring programmes to support children's mathematics achievement at a young age, particularly when they use a combination of drill techniques and strategic instruction.

This thesis investigates how discourses of mathematical-ability are produced and reproduced by pupils and teachers in the primary classroom and the impacts of these on teaching and learning. Building on a literature base suggesting the often negative and self-fulfilling outcomes of ability labelling and grouping, the thesis embeds this literature strongly in primary mathematics, exploring why these practices not only continue, but form the basis of much Government and school organisational policy. -- Utilising a critical realist meta-theory, the thesis draws pragmatically from multiple traditions. Data were collected from approximately 300 pupils and 14 teachers in two primary schools. Individual and group-interviews and classroom observations explored pupils’ and teachers’ productions of their own and others’ mathematical-ability, with pupil questionnaires and attainment tests used to examine the extent to which these impact on pupil attainment and learning in mathematics. -- The thesis finds that discourses of ability are pervasive, embedded in all aspects of teaching and learning in primary mathematics, and resistant to change. Pupils and teachers are fairly consistent in their understanding of mathematical-ability; this is thought of as a stable, innate quality connected to intelligence and genetics or else conceptualised in terms of, and muddled with, assessment outcomes. Assessment, labelling and inequitable ability practices create pupils from an early age as mathematically able or not, whilst setting places the focus on the mathematics, effectively ignoring the whole-child, raising many of the concerns about setting in secondary mathematics in a primary context. Many teachers recognise the inequity in the practices they engage in, yet reproduce the inequitable practices they experienced.

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The electronic calculator is now invariably the device used by people in employment and everyday life to deal with complicated and tedious calculations. The aim of this dissertation is to examine the effect it may have on the secondary school mathematics curriculum and, especially, to examine its potential as a powerful teaching aid which can be used to help pupils to acquire understanding of mathematical concepts. Chapter 1 investigates the contribution the basic calculator makes as a calculating aid which should cause the teacher to reassess the place of the standard pencil and paper algorithms in the curriculum. Some of the fears associated with this innovation are also discussed. The final section emphasises the importance of knowing the idiosyncrasies of different calculators. Chapter 2 suggests, in some detail, ways in which the teacher may use the calculator to enhance the understanding of certain topics such as fractions and place value. Applications of the calculator to everyday life problems, such as compound interest, are also included as well as the possibility of more interesting and enjoyable topics being introduced into the syllabus. New methods, such as iterative procedures, are discussed and the potential of the calculator as an aid to investigations is ascerted. Chapter 3 looks at the beneficial influence of the calculator on the mathematics curriculum generally and the possible effect on the mathematical content in particular with further suggestions following on from Chapter 2. Some contentious issues are considered and it is emphasised that more must be done to encourage the effective use of the calculator and not allow it to be overshadowed by its more 'glamorous' counterpart - the microcomputer.

Since the publication of Mathematics Counts in 1982 there has been a growing interest in investigational work in the mathematics classroom. There have been many books published specifically on investigational work and the related topic of problem solving. Class texts have been pub1ished claiming to follow the suggestions of Mathematics Counts including investigationa1 work. The new examination at 16, the General Certificate of Secondary Education appears to be moving towards containing work of an investigationa1 nature. In the first chapter the nature of investigationa1 work is examined. Distinctions are drawn between problem solving and investigationa1 work. A list of characteristics of investigationa1 work is considered with a view to clarifying exactly what constitutes investigational work in mathematics. In the second chapter the role of investigational work is considered both in the curriculum as a whole and more specifically in the mathematics curriculum. Particular attention is paid to the aims and objectives of mathematics education as set out in Mathematics from 5 to 16. The third chapter considers how investigationa1 work can be introduced into the secondary school both in the short term and over a greater period of time. The next chapter examines how an investigationa1 approach is used in a recently published mathematics scheme, SMP 11 - 16. In chapter five the various roles that the micro-computer can play in investigationa1 work is examined by considering a number of computer programs. Finally the difficulties in assessment presented by investigationa1 work are compared with methods of assessment currently in practice. Several forms of assessment are suggested for investigationa1 work undertaken in timed examinations and also as coursework within the school.

This study examined how young people are engaging with and doing mathematics, independently pursuing serious mathematical study, at home away from their classrooms, communicating with like-minded peers from anywhere in the world via the Internet, using the NRICH website and the AskNRICH web-board. An intitial study using a mixed methods methodology, including a web-survey, identified the current practice of NRICH problems being undertaken at home and students' perceptions of doing mathematical problem-solving in school. Results revealed a majority of NRICH users, predominantly high-attainers, independently choosing to work on problems, only at home and alone, believing that their teachers were unaware of this. The main study used interpretive methods in an emergent research design to study AskNRICHers' interactions through analysis of some 5000 messages posted in 600 threads from three distinct but interlinked perspectives. Parallel commentaries separating the mathematics and actions in messages were constructed and subsequently coded. A prototype visualisation tool, 'a connection diagram', was developed to portray the complex networks of interactions, categorised by response type, linking participants and messages. Thus this work has resulted in the formation of a set of techniques, including some new elements, that can manage the complexities, size and nature of the task of analysing the AskNRICH web-board. The findings characterising the AskNRICH environment have led to the proposal of the concept of a Second Learning Place, a specific type of Pupil Learning Place. In the empathetic environment of the AskNRICH Second Learning Place, the AskNRICHers collaborate, cooperate and show consideration and care to each other. Analysis of teaching and learning aspects demonstrates that the AskNRICH virtual world and the AskNRICHers' behaviours strongly promote a transformational pedagogy. The AskNRICH environment provides an exemplar of posivitve use of Internet-mediated communications leading to a harmonised mathematical experience in which the AskNRICHers are 'independent but not alone'.

Parental involvement in children’s learning plays a significant role in attainment in primary school. However, in the case of mathematics, a core subject in the primary school curriculum, research suggests that parents face a number of barriers to involvement. Following an approach informed by the sociocultural theory, this project aimed to investigate parental involvement in children’s school mathematical learning through a focus upon experiences, identity and activity. Twenty-four parent-child pairs took part in the study. The children were all aged between 7 and 11 years old and attended primary schools in the UK. Parents took part in a semi-structured episodic interview and parent-child dyads were observed completing a 20-minute simulated school mathematical activity. Data analysis consisted of four phases. Firstly, interview responses were subjected to a thematic analysis to examine parental experiences of: (1) school mathematics, (2) parent-child mathematical activity, and (3) home-school communication. Secondly, the interview transcripts were analysed using dialogical self theory to investigate mathematical identity. This concentrated on how parents constructed a mathematical ‘self’, to describe themselves, and a mathematical ‘other’, to describe their children. Thirdly, the observations of parent-child mathematical activity were analysed for mathematical goals, contingency and scaffolding. Finally, the results of the second and third phases were compared to study the relationship between identity and goals. Analysis of parental experiences extended existing academic research in a number of areas. This included parental interaction strategies, particularly propinquity, and barriers to parental involvement, for instance divergent mathematical understandings. Uniquely, in applying dialogical self theory to study mathematical identity, this research showed how the mathematical ‘self’ and ‘other’ shift spatially and chronologically through participation in sociocultural activity. Identity formation was also shown to be a reflexive process that embraced a range of diverse social influences. Mathematical goals were seen to form and shift due to the activity structure, artefacts and conventions of the task, social interaction between the dyad, and the prior experience parents and children brought to the task. Analysing parentchild school mathematical interaction in this manner provides a distinctive contribution to understanding a widespread, but poorly understood social practice. The final stage of analysis indicated that the mathematical identities parents assigned to children more closely match the goals in parent-child mathematical activity than the mathematical identities parents constructed for themselves. The original and important findings generated by this project provide distinct implications for academics, educators and others working with parents and children.

This thesis recounts my research into value and purpose in the classroom construction of mathematical activity. The research took place in a boys’ independent school where high examination expectations sustain. I am a teacher at the school; this thesis also narrates the development of a teacher-researcher identity through research. Grounded methods and cultural-historical activity theory (CHAT) were used to explore the activity of the mathematics classroom in relation to pupils’ developing mathematical capability. Pupil participants were interviewed from year 7 to year 10 and observed in lessons in order to reveal values associated with mathematical action through productive participation. Teachers were interviewed to explore the purposes they tried to convey in their lessons. By examining the actions engendered by participative, institutional and personal values I draw a picture of the object of mathematics classroom activity within established norms of order and work. Exploring the co-construction of classroom activity with CHAT revealed the persistence of systemic tensions within the stable activity. Neither pupils’ developing authority nor teachers’ awareness of these tensions impacted substantially on the roles that sustained. This stasis accompanied limits placed upon pupils’ expectations of personal transformation, and inhibited scope for the teacher to introduce aims other than examination success. I conclude that engagement with the generative potential of tensions was hampered by a restrictive focus on the high-stakes end point of compulsory mathematics education. Responsibility for this is attributed to the combination of cultural and institutional pressures which results in opportunities being placed aside and mathematical capability undeveloped. In developing a dual identity, I placed the aims and effectiveness of mathematics teaching in a wider socio-historical context, concluding that the development of mathematical authority as defined by examination curricula results in the classroom as a tool-and-result methodology, producing pupils in an enduring relationship with knowledge and knowledge construction.