This study investigates how Saudi mathematics teachers develop their understanding of classroom dialogue through a 'reform orientated' professional development programme modelled as a Community of Practice (Wenger 1998). It hypothesizes that Saudi Arabia provides an interesting context for research on teachers' professional development due the recent introduction of a 'reform orientated' primary mathematics curriculum which emphasizes a more active, dialogic role for students. This contrasts with the teacher-dominated, transmissionist pedagogy, which is widely recognized to be dominant in Saudi classrooms, thus creating a contradictory and conflicted context in which to conduct research on professional development. Therefore, this thesis reports on an evaluative case study of the aforementioned teacher professional development programme (TDP) which I instigated over a 10 week period in Saudi school based in Tabuk, North West SA. This TDP operated a cyclical design whereby discussion workshops reflected on video episodes of the teachers' classroom practice, which then produced new teaching strategies to try out in practice and then reflect on in future workshops. The purpose of researching this TDP is to establish how a community of practice on professional learning can be made to work in the SA context and the associated impact on teachers' identity development. The findings highlight how teacher development, as an issue of 'practice-and-identity' (Wenger 1998), occurred through the teachers' and my own participation in the TDP, which enabled them/us to implement new meanings and teaching strategies for developing the quality of dialogue in their classrooms. The findings also highlight how the 'landscape of practice' in which the TDP was situated generated meanings and contradictions which were negotiated by the teachers and myself as the workshops progressed. Such meanings were also important in mediating the teachers' developing identity as teachers but also in other domains of their life (e.g. as parents). The study concludes that the contradictions embedded in the SA context offer potential developmentally, in that they appear to motivate professional development (rather than hinder it). This makes a useful additional to the international literature in this field which is dominated by research situated in western contexts.

This study is situated at a time of political and educational change, whereby a need for improvement in the provision of mathematics education in British primary schools is identified. Undertaken from a phenomenographic perspective, it focuses on mathematical perceptions of student primary teachers (SPTs) as they embark upon Initial Teacher Training (ITT), and considers the potential influence of mathematical perceptions upon their ITT learning and future teaching. Research suggests negative perceptions of mathematics amongst adults, Higher Education students, teachers and student teachers, but the range of variation of mathematical perceptions of SPTs at the outset of ITT has not been previously examined. A phenomenographic study, conducted with thirty-seven SPTs due to begin lIT, led to the development of four qualitatively different ways in which SPTs perceive mathematics. The hierarchical variation is examined in relation to pedagogical associations via a conceptual framework bas~d on a non-dualist perspective of mathematics being constituted of a learner's relational understanding through experience. Potential implications for SPTs' development within ITT are explored and recommendations made regarding how these might be addressed. Whilst lTT provision is an obvious factor in students' development, this research is based on a premise of learners taking responsibility for their own development, especially with regard to intangible and often unconsciously held perceptions. The study offers insight into the range of perceptions SPTs may hold and its association with pedagogy, in order to both raise awareness and to provide a framework for reflection in SPTs' formation of personal philosophy of mathematics upon which to plan learning goals for ITT and associated aspirations for their practice as primaty mathematics teachers.

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This study investigates the impacts of a Thinking Skills based pedagogy upon pupils’ experiences of Maths, focusing upon three aspects: progress; self-concept; and the development of metacognition. Literature relating to Thinking Skills suggests that it can have significant impact, with the open nature of tasks and focus upon collaboration providing an alternative to more traditional, de-personalised forms of teaching. The implemented approach ensured increased opportunities for pupils to work collaboratively within mixed-attaining groups. This was combined with a shift from teacher to pupil-led talk, and the use of questions to probe thinking. Key strategies included a visual metaphor to encourage pupils to articulate problem solving strategies and pupils’ involvement in formulating learning goals. The research originates in challenges identified from my own primary classroom and was undertaken between September 2011 and July 2013. It details the shared experiences, of myself, as teacher-researcher, and my pupils - a cohort of 37 Upper Key Stage Two pupils. I have adopted an ‘action inquiry’ approach, which combines elements of action research and case-study. Research employed mixed methods, including the use of progress and attainment data; a measure of self-concept; and pupil views templates to chart development in pupils’ metacognition. This was further supplemented by two embedded case studies following individual children within the focus cohort. Results show a positive impact, but a complex one. Key findings include an increase in the proportion of pupils making better than expected progress; a positive shift in pupils’ selfconcept; and pupils’ increased focus upon discussions about learning, suggesting the development of metacognition. Overarching these conclusions has been a gradual change in my understanding of the nature of a Thinking Skills approach, becoming synonymous with my beliefs surrounding education in general. In short, Thinking Skills has become my philosophy for education.

The overall aim of this study was to explore children's conceptions of zero. To determine whether children have more problems understanding and using zero than other single digit numbers and, if so, to investigate why these problems might arise. The focus areas of this exploration were: (a) Zero as a number and its relationship to other numbers (b) The zero number facts (c) The empty set (d) The language of zero. Initial data was gained using questionnaire returns from 100 children, aged 10-11 years, in five UK primary schools. More detailed fieldwork was undertaken using task-interviews conducted with 136 children, aged 3 to 11, in one of these schools. The children's explanations for their answers, correct or not, and the analysis of their reasoning provided some unexpected results. With regard to the children involved in this research this study concludes that a child's conception of zero consists of a series of generally accepted notions such as zero being a number, zero being worth nothing and zero being found in the number order, next to one. These generally accepted notions are subject to diversity of thought and an individual child's diversity of thought did result in high profile consequences. These were the ignoring of zero; the formation of a personal zero rule(s); children's understanding of nothing as nothingness and the startling reaction of many young children (aged 3 to 5) to the empty set. The research highlights and contributes new knowledge to an, as-yet, uncharted area of investigation that of children's conceptions of zero. As a consequence the findings are discussed in terms of their implications to primary mathematics education.

Pedagogical content knowledge was first introduced by Shulman (1986). This concept is in relation to the ability of teachers to transform the content knowledge they possess into a pedagogical form, adapted to suit the needs and abilities of the children. This study examined the ways in which primary trainees following two different routes into qualified teacher status developed confidence in mathematical pedagogical content knowledge. A case study approach was adopted focusing on trainees from a Primary SCITT (School-centred initial teacher training) and EBITT (Employment based initial teacher training) Partnership. This process explored key aspects of the training year and the perceived overall impact on the development of trainees' confidence levels in the pedagogical content knowledge aspect of mathematics. Lines of enquiry were identified related to research on the ways in which trainees learn. This included an examination of the impact of the practical experience of teaching; feedback from observations; observations of good practice; discussions with mentors and other professionals; centre-based training; discussions with peers, and previous experiences of mathematics. The trainees' perceptions of the impact of these aspects were gained through a mixed method approach and included: hard copy questionnaires, group interviews, observations of training sessions, and scrutiny of written lesson observation reports. Additional perspectives were also gained through the surveying of mentors working with the trainees and also an interview with the mathematics core tutor. Findings highlighted the importance of: reflective practice; the development of an understanding of progression in children's learning; centre-based training; the support structure within the school environment, and the teaching' experience within a second school setting. The relationship between theoretical and practical learning has been examined in detail and this highlighted the symbiotic relationship which exists between the two - concluding that both play an important role in advancing trainee teachers' confidence in mathematical pedagogical understanding.

Using a qualitative, exploratory, microgenetic research design, this research study examines the strategies that children who had only been taught the part-whole fraction sub-construct used for finding the fraction associated with solving partitive quotient problems over a sequence of tasks. Additionally, a key feature of the Pirie-Kieren theory for growth of mathematical understanding, which has not been previously extended empirically, is elaborated. Nine Year 5 children, who engaged in eight individual task-based interviews, over a six-week period, provide the data for this study. The research found that the research participants used four strategies for finding the fraction related to solving the partitive quotient problems. Further to this, one strategy appeared to resemble the conceptualisation for the part-whole relation. This finding suggests that previous part-whole learning impacts partitive quotient development. Another key contribution of this research is that it shows several ways in which part-whole knowledge impacted children's partitive quotient development. Regarding the theoretical contribution made by the current study, one of the significant findings challenges one aspect of the current Pirie-Kieren model, and therefore, an amendment to the existing model is proposed. An implication of this study for teachers of mathematics is that there should be a greater focus on the concept of a unit when teaching the different fraction sub-construct contexts. In addition, to help learners grow in their understanding of mathematical concepts, it is suggested that there is an increased emphasis on assisting them to develop robust and thorough ideas of concepts when working in local contexts.

This study focuses on the effectiveness of mathematics teaching to children aged 9-10 years, applies a mixture of six methods to classroom-level data collected in England and China, correlates observable teacher behaviours with pupil mathematics performance and collects multiple perceptions that indirectly connect with the differences of teaching and learning cross-nationally. It has been found in the study that 9-to 10-year-olds (n = 343) from China outscored their English peers (n = 236) at the same age by over 20 per cent in each of two mathematics tests derived from TIMSS 2003. Structured analysis of lesson videos has revealed that Chinese mathematics teachers scored much higher than their English colleagues on an internationally validated observation instrument which focused on the quality of six dimensions of teacher behaviours. Furthermore, the quantity of teacher behaviours was also measured and the subsequent correlational analysis on pooled data indicated a positive effect of whole-class interactive teaching (r = 0.97, p < 0.01) and pupil time on task (r = 0.95, p < 0.01) and a negative impact of whole-class lecture (r = -0.91, p < 0.01), individual/group work (r=-0.81, p < 0.05) and classroom management (r = -0.77, p < 0.05) on pupils’ mathematics performance cross-nationally. Qualitative findings are connected with quantitative results to explain how teachers think, how this relates to the way they teach and how the differences of teaching result in the performance gap cross-nationally. The study replicated previous TER findings from the West across two geographically and culturally different countries, suggested possible directions for future enquiries,and recommended potential ways for practice and policy innovations.

Despite the potential positive effects of using technology with students who have difficulties in mathematics in the Kingdom of Saudi Arabia and the great efforts made by the Saudi Government to improve the education system of the nation, which has included a continuous rise in the educational budget, there still remain some obstacles for some teachers when using technology, and while some of these teachers overcome these barriers, others do not succeed in this the challenge. This study investigated the barriers that teachers face when using technology in their classroom in primary schools, and why some overcame obstacles while others did not. Semi-structured interviews and observations were used for the purpose of this research, which were undertaken with three mathematics teachers from school A which used technology, and the other three from school B, which did not use technology. The researcher observed each teacher 45 times separately, 45 minutes each time, over a period of three months. The three teachers in school A were observed during the first 45 days, and the other three were observed for another 45 days. The researcher found from the interviews’ responses of all six teachers and the consequent observations, that the head teacher’s support was the main reason behind their decision to overcome or not overcome the obstacles they face when using technology to help students with difficulties in mathematics. The principals of both schools played a crucial role in managing the challenges they faced with technology. This became evident when the head master of school A helped the teachers in overcoming the obstacles they faced when using technology by training teachers and through technical support, which reflected positively on teaching and learning mathematics, leading to a continued and enthusiastic use of technology. On the other hand, the head teacher in school B did not help or support his teachers in providing technology in school, nor help with overcoming the challenges they faced with technology, which reflected negatively on their enthusiasm to continue to overcome barriers such as the provision of technology in the school, and the lack of training and technical support, in spite of their beliefs that the technology has a positive impact on teaching and in the learning of students who have difficulties in mathematics. This study concludes with recommendations regarding future research in this area.

In this paper, the researcher describes the attitudes and opinions of a sample of primary Math teachers in Lebanon towards using technology as a tool for teaching math, investigates the importance of integrating technology into Math curriculum in terms of learning theories, and presents an exemplary integrated math lesson plan prepared by the surveyed math teachers. In particular, he discusses the learning theories underpinning integration strategies; explaining how each strategy addresses classroom needs, and how each suggests a way to integrate technology resources. 35 primary math teachers are selected on a random basis from a cluster population. The teachers are selected in a way that represents different primary grades (G1, G2, G3, G4, G5, G6, G7), different school systems, different socioeconomic areas, and geographic locations. The researcher prepares and justifies the use of a survey as an appropriate method for studying the above educational issue. Three methods of collecting data were used: documentary sources, observation, interviewing and mail questionnaires. On analzying the results, two findings emerged. First, the main use of the educational technological tools is to enhance higher order thinking skills. Upper and middle teachers rate the use of the educational technological tools to enhance higher order thinking skills higher than do the lower grade teachers. Second the use of the educational technological tools to enhance basic skills was less frequent. Lower grade teachers report using the educational technological tools for this purpose significantly more than do teachers in the middle and upper grades. The researcher refers the main use of the educational technological tools to foster higher order thinking skills to a growth in various social psychosocial and cognitive skills. The factors that contribute to these outcomes are identified: the software's instructional design and cooperation and collaboration among students. Finally, implications and recommendations for education are presented along with suggestions for further research.