This thesis investigates nursery children's knowledge, understanding and skills in patternmaking as an aspect of early mathematical development. It presents two discrete but closely related studies, a cross-sectional and a longitudinal study. The methodology includes use of structured assessment activities using familiar play materials. Assessment focuses firstly on different aspects of pattern-making; secondly, on pattern perception; and thirdly, on wider aspects of developing cognition. The methodology includes collection of case study data in the naturalistic setting of the nursery class. The cross-sectional study, focused on knowledge, understanding and skil1s in pattern-making at 3½ and 4½ years, finds an increasing minority of children successful in repeated pattern-making and 2D spatial pattern-making but not linear symmetrical pattern-making. Few children evidence pattern perception at either age but an increasing minority evidences an emergent understanding of the word 'pattern.' The longitudinal study tracks children's development towards and within pattern-making from 3½ to 4½ years. It details development in two key aspects of pattern-making, colour and spatial organisation, through case study data. An examination of commonalities in development leads to hypothesised developmental pathways in both aspects of pattern-making. A single pathway leads towards complex colour organisation. Distinct pathways lead to basic and complex spatial organisation and to the basic elements of pattern. Pathways to 2D spatial pattern-making are more varied than pathways to repeated pattern-making. Quantitative analysis confirms key features of the pathways although some findings remain tentative. Differences in the detail of individual pathways are highlighted, as are wide differences in children's rates of development and in their interests and motivation. There are no findings of significant gender-related differences. Children's competencies in the colour organisation strand of pattern-making are significantly associated with abilities across key areas of developing cognition. Spatial organisation competencies are at first associated with a narrow range of primarily spatial abilities but this extends to include number and rhythmic abilities at 4½ years. The study confirms and extends some earlier findings, and also presents new findings. Findings lead to questioning of guidance on curriculum goals and pedagogy for the age-group. They highlight a need to acknowledge the creativity of many young children in this area of mathematics.

Learning to count is a central strand to the mathematical development area of the Foundation Stage Curriculum in England and Wales. Five teachers from five nurseries in one local education authority within West Yorkshire were recorded between December 2002 and June 2003. The main data for the study was taken from 21 number focus activities recorded between the teachers and small groups of children, aged 3-4 years. Conversation Analysis was used to determine the language and interaction involved, considering both children and teachers' contributions to counts and to what came before and after counts. The study found that the teachers were responsible for creating the conversational contexts for counting as well as being involved in the counting itself. The collaboration between teachers and children in counts included distinctive uses of intonation in ways that emphasised the status of numbers in the count sequence and the importance of the last word. Following counts, the study identified ways in which the quantitative meaning of counting could be extended or left implicit. This study depicts counting as a fully interactive activity that contrasts with the image portrayed in much of previous literature where children count independently and opportunities for teachers' participation are under-specified and implicitly passive.

Cognitive Acceleration in Mathematics Education (CAME) programmes have been used successfully for promoting the development of thinking skills in school students for the last 30 years. Given that the approach has had a tremendous impact on the thinking capabilities of participating students, this study explored the experience of using the programme with prospective primary teachers in Chile. Therefore, this study not only looked at the experience of prospective primary teachers during the CAME course as learners, but also examined how they perceived the approach from their perspective as future teachers, as well as how they could transfer the teaching strategies they observed to their future classrooms. Given the complexity of the phenomenon under study, this research used a mixed methods approach. For this reason, the impact that the CAME course had on prospective teachers’ thinking skills was not only approached by using a test that assessed the participants’ improvements in these skills, but their learning and teaching experiences were also recorded through qualitative research tools (learning journals, interviews and field notes). The main findings indicate that, at the end of the CAME course, prospective teachers not only demonstrated higher thinking levels, but also showed positive attitudinal changes towards teaching and learning in general, and towards mathematics in particular. The participants also had increased confidence in their ability to teach mathematics and to promote thinking skills in their students. In terms of the CAME methodology, prospective teachers not only found it novel and motivating, but also commented that dealing with the thinking skills topic during a university course was both unusual and very important for their professional development. This study also showed that, at the end of the CAME course, prospective teachers felt they had developed strategies that could be used in their classrooms in the future. In this context, the relevance of the study is not only that it described the impact and the positive results of the first experience of using a CAME approach with prospective teachers, but also that some of the conclusions have significant implications for the teaching of thinking skills and the training of primary school teachers.

Despite established literature regarding mathematics difficulties to be of higher prevalence than literacy difficulties, research into factors influencing the development of mathematics is far less comprehensive, especially in young children.While various domain-general abilities (including working memory, attention, inhibition and visual-spatial skills) are suggested to influence mathematics achievement, these should be considered within the context of additional number domain-specific approaches.There is a lack of consensus around the key skills which are of most predictive value for later maths success, and further focus is needed to specifically understand the most important factors in preschool children. A comprehensive narrative literature review was completed to contextualise this under-researched subject area and aimed to highlight the need for early identification of atypical (as a result of better understanding typical) mathematics development.The importance of both symbolic and non-symbolic number . representation in determining later maths achievements is acknowledged and the extent to which specific deficits in these skills can be identified in preschool children is debated along with their potential to predict later mathematics achievements. A Systematic Review to specifically appraise recent studies which investigate the relevance of domain-specific predictors of mathematics before the age of six sought to support the need for early identification of key factors in early maths learning. This informed an exploratory, quantitative study which combined domain-specific and domain-general variables not previously studied together.These were considered in a local population sample of 88 preschool children in order to identify interrelationships between skills, and key predictors for maths achievement in early primary school. Results indicated a close relationship between non-symbolic and symbolic processes in preschool, and highlighted that symbolic skills along with a number of domain general and environmental factors were predictive of maths attainment after a one year follow up. Implications for future research directions, and professional practice for teachers and Educational Psychologists are considered.

This thesis explores girls’ perceptions of mathematics and how they make sense of their mathematical identity. It seeks to understand the characterisations girls make of mathematics and mathematicians, shedding light upon their positioning as mathematicians. This is important because there remains a tendency for able females to rate themselves lower than males of a similar attainment, and be less likely to continue into post-compulsory study of mathematics. This research followed an interpretive paradigm, taking a grounded, case-based approach and using a mosaic of qualitative methods. Fourteen girls from a school in the south-east of England aged 8-9 at the start of the study took part in the research over 15 months. The data collected comprised scrapbooks, concept maps, relationship wheels, drawings, digital photographs, metaphors, group and individual interviews. Data were analysed using open and focused coding, sensitising concepts and constant comparison to arrive at key categories and themes. The main conclusions of the study are that time taken to explore the diversity of girls’ perceptions of themselves as mathematicians provides a powerful insight into their identity formation. Many girls struggled to articulate the purpose of mathematics dominant in their vision of what it meant to be a mathematician. Whilst they recognised a rich variety of authentic mathematical activity at home, this was overwhelmed by number, calculation, speed and processes, with mathematics recognised as desk-bound and isolating. They made sense of their mathematical identity through their characterisations of mathematics alongside interactions and comparisons with others. The girls in the study took a high degree of responsibility for their own development, believing they could improve with ever-greater effort. However, this led to the need for a buffer zone, allowing teachers, family and friends to support the individual in continuing to grow and protecting them from mathematical harm. This research recommends the provision of safe spaces for mathematical exploration in terms of time, space and collaboration, connecting mathematical study with application and interest, reframing mathematics as a social endeavour and sharing responsibility with girls for their mathematical development. Finally, it suggests the value of practitioners paying close attention to girls’ evolving mathematical identities.

This mixed methods research involved an original exploration of the views of a small group of children in years one and two, regarding their perceptions of maths and themselves as mathematicians. The views of their teachers were also gathered for additional information. Of particular interest was an evaluation of the effects of a Key Stage One maths intervention, devised by an Educational Psychology Service (EPS), on the pupils' views and their approach to maths. The research was approached from a pragmatic epistemological position which allowed for the flexibility of using a combination of both qualitative and quantitative methods. Social Cognitive theory provided a relevant theoretical background for the research. Within this, the concept of self-efficacy (Bandura, 1977,1986) provides a useful framework to aid understanding of the factors which affect learning. Previous research has shown that self-efficacy influences academic motivation, learning, and achievement (e. g. Bandura, 1997). The main emphasis was on the qualitative aspect of the research. This involved the use of semi-structured interviews with the pupils and their teachers which were undertaken before and after the pupils had been involved in the maths intervention group. The data derived from these interviews was then analysed using thematic analysis, following the recommendations specified by Braun and Clarke (2006). Quantitative scaling questions about their views of maths were also carried out with the pupils, before and after they had taken part in the maths intervention. Additional visual resources were provided to facilitate the pupils' responses. Findings from the thematic analysis of the qualitative data indicated that following the intervention, the pupils' perceptions of maths and themselves as mathematicians were more positive. Teachers also perceived an increase in the pupils' confidence and understanding of basic maths skills after the intervention. Statistical analysis of the quantitative data using a Wilcoxon test, revealed a statistical significance in changes between pre and post intervention responses. The limitations and further implications for the research regarding EP practice and the importance of pupils' perceptions for learning in maths are considered.

No description available.

This research examines the preparation made to enable mathematics teachers to appropriately prepare school leavers entering directly into the workforce upon graduation to handle the different branches of mathematics. The methodology was that of the interpretive qualitative paradigm. The method was that of the multi method case study and the tools included: constructed conversation; interviews; telephone calls; email; focus group; photography; video recording; participatory observation; observation and documentation. The theoretical framework was informed by components of the Engeström (2001) second generation model. The study found that while there was hardly any preparation made in the system to accommodate mathematics teachers in the appropriate preparation of students to cope with rapid changes in technology and mathematical skills in the workplace, because of on-the-job training, the newly employed were able to handle the mathematics at their workplaces. Additionally, the technological tools in use at workplaces allowed employees to handle the mathematics in work: complicated algorithms associated with mathematical operations were hidden in these technological tools. Employees were then only required to perform an operation of a push or a pull of a button (switch) to turn on or to turn off the device. Equally, mathematical knowledge at the workplace was an activity; thus there was no need for the pedagogical format required for school mathematics classes. This research is significant since this is the first of its kind in the Caribbean using components of the Engeström (2001) second generation model as its theoretical framework and for examination of the mathematics informing workplaces in Antigua and Barbuda. It has also served to bridge a gap between school teachers and employers on communication of the different branches of mathematics required in the workplaces of Antigua and Barbuda. Simultaneously it represents a new block in the wall of literature from scholars in the field of workplace mathematics since the Caribbean’s space was empty.

This research explores elements and processes involved in interpretation of media graphs. The investigation was comprised of a literature review and a collection of empirical data. The literature review revealed a lack of qualitative evidence related to the complex relationships between elements and processes which comprise the interpretation of media graphs. This study explores the interpretation of media graphs by primary student teachers who would be involved in teaching about graphing. The main study was composed of two complementary datasets: questionnaires and interviews, which allowed an interplay between qualitative and quantitative data. 218 undergraduate and PGCE student teachers from Britain and Brazil responded to a questionnaire with items related to individual details, reading background and media graph tasks. 13 volunteers gave interviews which explored three types of questions: reading the data, reading between the data and reading beyond the data. The interviews also recalled the questionnaire responses. The data analysis of the questionnaires was software based, and a micro analysis approach was developed with the data from the interviews. The analyses of data gave evidence for the discussion about the notion of critical sense in graphing. It was concluded that critical sense in interpretation of media graphs is related to the mobilisation and balance of several aspects, such as: mathematical knowledge, contextual reference, personal experience and affective exhibition. The discussion of the results might help the reflection about teaching and learning of graphing in ways that will support the development of critical sense.

Ma thèse se place dans le champ de l'histoire d'une discipline scolaire, l'arithmétique, pour les filles, dans les écoles primaires de la Somme de 1881 à 1923. Elle s'inscrit ainsi dans la lignée des travaux menés par B. Belhoste, B. Dancel, A. Chervel, R. d’Enfert, B. Poucet, et d'autres historiens des disciplines scolaires. Elle s'inscrit aussi dans la lignée de l'enseignement féminin, ouvert par F. Mayeur et poursuivi par R. Rogers. Ce type de recherches nécessite le recueil et l'analyse de sources qui mettent en lumière les différents acteurs : le maître et les élèves, mais aussi le ministère de l'instruction publique et ses représentants hiérarchiques. Aux archives départementales de la Somme, il existe de nombreuses sources manuscrites et imprimées, ce qui explique le choix de ce département comme terrain de recherche. Ma thèse s'inscrit dans la suite de mes travaux de recherche de Master 2 et porte sur la question de la scolarisation des filles dans le public et dans le privé, leurs performances, tout au long de cette période, le contenu et les finalités de l'enseignement qui leur est proposé, la question de la formation des institutrices congréganistes et laïques. Il s'agit, en mettant à jour les pratiques des maîtres et les résultats des élèves, de mesurer l'écart éventuel entre les prescriptions officielles et leur mise en œuvre. Cette étude montre que l'enseignement mathématique à l'école primaire atteint une dimension plus éducative à la fin des années vingt et que les performances des filles deviennent identiques à celles des garçons, soulignant ainsi, finalement, une certaine réussite du projet scolaire républicain dans ces deux domaines / My thesis is set in the history of one particular subject : arithmetic, taught to girls in primary schools of the Somme under the Third Republic. This way, the thesis is in line with the works led by B. Belhoste, B. Dancel, A. Chervel, R. d'Enfert, B. Poucet, and other school subjects historians. Furthermore, it is also in line with girls education, initiated by F. Mayeur and continued by R. Rogers. That kind of research requires the collection and analysis of sources dealing with the different roles evolving in a classroom : not only the teacher and the pupils but also the Public Instruction Ministry and its hierarchical representatives. At the regional archives of the Somme you can find numerous hand-written and printed sources, hence my decision to focus on this particular area. My previous works enabled me to come to a certain number of conclusions about the aim of arithmetic as well as girls' education. My thesis looks at the rest of this work and focuses on the schooling of girls in public and private schools, specifically on their performances during this time, the content and goals of the education offered to them, as well as on the education or training of both religious and secular female teachers. Speaking of the teachers' practices and the pupils' results, I intend to determine the potential gap between official instruction and their actual application. This study reveals that the teaching of mathematics in primary school reached a much more educational dimension by the end of the Twenties and that the girls' and boys' performance became equal, finally emphasizing a certain success of the Republican school project in both subjects