No description available.

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.

This study examines the teaching and early learning of addition in primary classrooms. The relationship between teaching and learning is examined at the level of classroom interaction, in the completion of mathematical tasks. The mathematics lessons of two classes in each of two schools were observed over a period of six months, involving four teachers and the 4, 5 and 6 year old children in their classes. The mathematical focus of the study was the learning of addition, one of the first formal mathematical concepts taught in school. This formed a basis for exploring the factors involved in the teaching of mathematics to young children, and their learning. The methodology is qualitative, with participant observation the main method of data collection. Detailed fieldnotes were taken of all mathematics lessons observed; short unstructured interviews with teachers were carried out before and after the lessons. The children's understanding of number concepts and addition was assessed at both the beginning and the end of the observation period. The data was analysed using a grounded theory approach, which produced patterns of recurring variables. Analysis of these variables, influenced by the theoretical perspectives of the researcher, provided analytical pictures of teaching and learning, from which the findings emerged. The study highlights the complexity of the classroom for teachers and young children, where curriculum considerations, understanding of the mathematics concepts, social interaction and integration into the community of the classroom, vie for attention. It indicates that children are more likely to make sense of mathematics when the number curriculum is taught with a view to its complexity, rather than broken down into simple steps; the problems young children have learning to use mathematical symbols; and that the use of story is important in helping especially the youngest children understand mathematics. This was a small scale study, but provides a 'thick description' of teaching and early learning of addition, which can form a basis for future studies. Key Words: addition, early mathematical development, primary school, constructivism, socio-cultural theory, situated cognition, symbols, real world scripts, narrative.

This thesis examines students’ experiences of learning to teach mathematics as they complete a primary Postgraduate Certificate in Education to gain qualified teacher status. The research data are drawn from students’ accounts of learning to teach mathematics, which include email communications during their studies and interviews with eight students at the end of the course. Analysis is informed by post-structuralist feminist understandings of discourse, power and knowledge. These tools are used to explore the complexities of learning to teach, the ways in which beginning teachers are ‘produced’, what counts as mathematics and the effects of power relations within pedagogical encounters. I use a reflexive approach to methodology, acknowledging the ways in which my own subjectivity permeates the enquiry, and the ways in which power permeates the research process. The study found performances of gender in students’ accounts of their experiences of the course, both on campus and in schools. Dominant discourses of teaching and mathematics create tensions for students and act as a form of control and categorisation as they strive to be recognised as legitimate mathematics teachers. It is argued that students’ subjectivities are shaped by discursive practices and peer and pedagogical relationships in the context of the course and that students are constituted as mathematical subjects often in inequitable ways. They are both powerful and powerless in different instances as they take up competing discourses, positioning themselves and their peers in shifting locations. Some students are silenced, categorised and marginalised within discourses of mathematics. Most report complying with the established practices of the school and class teacher and focused on the struggle to achieve legitimacy as successful student teachers. They 2 demonstrate both compliance with and resistance to dominant discourses as they are caught between the tensions and inconsistencies of competing and conflicting discourses. A key implication of this study is that teachers, teacher educators and student teachers need opportunities to explore their own gendered subjectivities as learners and teachers and to acknowledge that learning to teach mathematics is not solely a cognitive endeavour but one deeply located in social relations and contexts. Within teacher education more spaces need to be opened up to enable student teachers to embody themselves as mathematics subjects and primary teachers differently.

This thesis examines number sense in primary mathematics. I begin by presenting literature to demonstrate how a cognitive definition of number sense, dominates understandings of mathematical development. I argue that this has influenced fixed-ability practices in mathematics (e.g. Boaler, 1997; Marks, 2014) presenting number-sense as a natural ability. I outline the political landscape and explore data which demonstrates that mathematics education systematically disadvantages some people (Zevenbergen, 2001). After reviewing mathematics learning from a range of theoretical perspectives, I demonstrate a gap in the literature: a sociological exploration of number sense in primary school and illustrate the need to examine school structures and their implications for equitable outcomes for all children. To address this gap I have employed Bourdieusian tools of habitus, field and capital, to explore number sense development. Through ethnographic methods in Year 4 classrooms, I examine how number sense positions children in the field of primary mathematics. This research was undertaken during the first year of statutory implementation of the National Curriculum (DfE, 2013) allowing insight into the lived experiences of children at this time. My findings show that facts, fluency and flexibility are key ways children demonstrate their number sense. Through rapid recall of facts children are seen by their teachers, peers and themselves as ‘able’ at mathematics, leading to explicit reproduction of social class, as these facts are usually learned at home. Similarly, a demand for fluency has led to a focus on procedural accuracy with calculation. Based on this, children are sorted into ability groups magnifying infinitesimally small differences between them (Bourdieu, 1986). Finally, children demonstrate flexibility through different calculation strategies; however, lessons usually rehearse single methods, hiding this key mathematical practice. Each aspect of number sense differentiates children, advantaging those with middle-class habitus and therefore reproducing educational inequalities.

The thesis investigates the role a calculator can play in the developing number knowledge of three girls and three boys as part of their mathematics program, during their first two years at primary school. Random sampling was used initially to select six girls and six boys from the twenty-four children entering a 1993 prep class. These twelve children were interviewed on entrance to school and based on the performance of the twelve children on the initial interview, a girl and a boy were chosen from the higher, middle and lower achievers to take part in the full study. The class teachers involved were previously participants in the ‘Calculators in Primary Mathematics’ research program and were committed to the use of calculators in their mathematics program. A case study approach using qualitative methods within the activity theory framework is used to collect relevant data and information, an analysis of five interviews with each child and observations of the children in forty-one classroom lessons provides comprehensive data on the children's developing number knowledge during the two years. The analysis questionnaires establishes each teacher's perceptions of the children's number learning at the beginning and end of each year, compares teacher expectations with children's actual performance for the year and compares curriculum expectations with children's actual performance. A teacher interview established reasons for changes in teaching style; teacher expectations; children's number learning; and was used to confirm my research findings. An activity theory framework provides an appropriate means of co-coordinating perspectives within this research to enable a description of the child's number learning within a social environment. This framework allows for highlighting the mediation offered by the calculator supporting the children's number learning in the classroom. Levels of children's developing number knowledge reached when working with a calculator and as a result of calculator use are mapped against the levels recommended in ‘Mathematics in the National Curriculum’ (National Curriculum Council, December 1988), and the Curriculum and Standards Framework: Mathematics (Board of Studies 2000). Findings from this comparison illustrate that the six children's performance in number was enhanced when using a calculator and indicate that on-going development and understanding of number concepts occurred at levels of performance at least two years in advance of curriculum recommendations for the first two years of school.

No description available.

The subject of the diploma thesis is the creation of study material relating the subject of theory of dividing for students trained to be teachers at primary school. In the first part of the thesis I am concentrating on theory of mentioned problem. The main target of the thesis in the second part is the collection of exercises for the students. In the third part of these I am checking the level of knowledge in the subject of divisions in natural numbers with ten years old autistics student that I take care during school instruction. The results of these tests are mentioned in the thesis.

No description available.

Homework in mathematics is a well-debated subject and can affect young children’s everyday life. This paper aims to investigate teachers' decisions regarding mathematics homework using the question “Which factors influence teachers in using homework in mathematics?” through an analysis of the existing research. The basis of the study consists of twelve articles and materials from different parts of the world. Results showed that many factors can impact the decision and how much is different from one teacher to another. Parents' view of homework and their influence on their children's learning in mathematics is something that emerged significant in the use of homework. The role of equality in the discussion of homework is also something that emerged as noticeable as all students have different prerequisites. The findings in our study showed that homework in mathematics do not have a negative impact on students´ academic achievement as long as the homework consists of a moderate amount. One of our most significant findings of this paper concluded that homework should be adapted to every individual and their needs, which teachers have to consider. Our professional development has increased by this study, as a result of a better understanding of the research area.