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Girls' Perceptions of Mathematics

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Girls' Perceptions of Mathematics Girls’ perceptions of mathematics: an interpretive study of girls’ mathematical identities Doctorate in Education Institute of Education Catherine Foley May 2016 Acknowledgements I would like to thank my supervisors Dr Carol Fuller and Dr Natthapoj Vincent Trakulphadetkrai for their wisdom, guidance and unfailing support. To all those on ‘the corridor’ I will be forever grateful for your encouragement and endless patience. Thank you to Neil who is my rock, and to Samuel for always helping me keep things in perspective. Finally, thank you to the head teacher and teachers of the schools who made me so welcome and gave their time willingly, and most of all to the fourteen girls without whom this thesis would not exist – may you achieve everything you hope for and more. Declaration of original authorship I confirm that this is my own work and the use of all material from other sources has been properly and fully acknowledged. 2 Abstract 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. 3 Table of Contents Acknowledgements ............................................................................................................................ 2 Declaration of original authorship ..................................................................................................... 2 Abstract .............................................................................................................................................. 3 List of Tables ....................................................................................................................................... 9 List of Figures ..................................................................................................................................... 9 1 Introduction ............................................................................................................................. 11 1.1 Personal and professional background ............................................................................ 12 1.2 Introduction to the context for the study ........................................................................ 13 1.3 Overview of the research ................................................................................................. 14 1.4 Structure of the thesis ...................................................................................................... 15 2 Literature Review ..................................................................................................................... 17 2.1 Setting the context ........................................................................................................... 17 2.1.1 Why does mathematics matter? .............................................................................. 17 2.1.2 Mathematics attainment – the national and international context ........................ 18 2.1.3 The nature of mathematics ...................................................................................... 19 2.1.4 Mathematics education: purposes and curricula .................................................... 21 2.2 Mathematics as a social construct ................................................................................... 23 2.2.1 Social constructivism and sociomathematics .......................................................... 23 2.2.2 Situated learning and ethnomathematics ............................................................... 25 2.2.3 Media and culture .................................................................................................... 27 2.2.4 Mathematics in the home ........................................................................................ 28 2.2.5 Exploring perceptions of mathematics .................................................................... 30 2.2.6 Stereotype formation ............................................................................................... 32 2.3 Gender and mathematics ................................................................................................. 34 2.4 Mathematics and the affective domain ........................................................................... 38 2.4.1 Self-concept, self-efficacy and mindsets .................................................................. 39 2.4.2 Mathematical resilience ........................................................................................... 43 2.4.3 Identity formation and mathematical identity ........................................................ 44 4 2.4.4 Mathematics anxiety ................................................................................................ 46 2.5 Conclusion and research questions ................................................................................. 47 3 Methodology and methods...................................................................................................... 49 3.1 Introduction and key concepts ........................................................................................ 49 3.2 Exploring perceptions of mathematics: ontological and epistemological stance ........... 49 3.2.1 Subjectivity ............................................................................................................... 50 3.2.2 Constructionism and social constructivism .............................................................. 50 3.2.3 Interpretivism ........................................................................................................... 51 3.3 Methodological rationale and research approach ........................................................... 51 3.3.1 Constructivist grounded theory ............................................................................... 52 3.3.2 Interpretive case-based approach ........................................................................... 53 3.3.3 Listening to children: pupil voice, pupil perspectives and the Mosaic approach .... 54 3.4 Gathering data ................................................................................................................. 56 3.4.1 The pilot project ....................................................................................................... 56 3.4.2 Contextualising the case: the school and participants ............................................ 59 3.4.3 Data collection methods: building a picture ............................................................ 61 3.4.4 Timescale .................................................................................................................. 69 3.5 Working with participants ................................................................................................ 70 3.5.1 The role of the researcher: insider research and reflexivity .................................... 70 3.5.2 Children as active participants ................................................................................. 71 3.5.3 Ethical considerations .............................................................................................. 72 3.6 Analysis and interpretation .............................................................................................
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