An Aesthetic Knowing of Mathematical Identity: Performing stories of Mathematical Identity through filmed drama A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy (PhD) in the Faculty of Humanities 10/25/2016 Kelly Pickard-Smith 69960 words School of Environment, Education and Development Table of Contents Abstract .......................................................................................................................... 8 DECLARATION .............................................................................................................. 9 COPYRIGHT STATEMENT ............................................................................................ 9 Acknowledgements ....................................................................................................... 10 Chapter 1. Finding identity and wisdom through the arts ....................................... 11 1.1 Introduction: The background, justification and focus of the thesis .................... 11 1.2 Background to the study .................................................................................... 12 1.2.1 Performing mathematically .......................................................................... 13 1.2.2 A rationale for the research: Personal and professional context .................. 17 1.2.3 A rationale for the research: A previous study on learner experience .......... 20 1.3 Framing the study contribution .......................................................................... 22 1.3.1 Definitions: ‘Performatics’ and ‘aesthetic knowing’ ...................................... 23 1.3.2 A synthesis of the thesis contribution to knowledge .................................... 25 1.4. An alternative format thesis: The Film and written content ............................... 27 1.4.1 Film component: Access and distribution. ................................................... 28 1.4.2 Written component: An overview of the chapters. ....................................... 31 PREVIEWS ................................................................................................................... 35 Chapter 2. Situating ‘Art Based Research’ (ABR) methods of ‘filmed-drama’ in mathematical identity research: A literature review. .................................................... 36 2.1 Introduction ....................................................................................................... 36 2.1.1 Review Rationale: What is already known, or claimed, about mathematical identity... ....................................................................................................................... 39 2.1.2 Literature review method............................................................................ 48 2.2. A ‘collective storying’ of mathematical identity .................................................. 50 2.3. Dramatic mathematics ...................................................................................... 59 2.3.1 “Make us go to story land”: Drama in the mathematics classroom .............. 59 2.3.2 Theatre and the mathematician................................................................... 68 2.3.3 The potential for drama as research ........................................................... 72 1 2.4. Filmic Mathematics ........................................................................................... 74 2.4.1 Film and the mathematician ........................................................................ 75 2.4.2 In-between anthropological film and research ............................................. 80 2.4.3 The potential for film as research ................................................................ 90 2.5 Conclusion: Sensing mathematical identity through filmed drama ................ 92 2.5.1 Conceptualising mathematical identity as story ........................................... 93 2.5.2 Use and potential: Filmed drama for mathematical identity research ........... 96 2.5.3 Framing the thesis: Research aims and problems ....................................... 98 Chapter 3.Conceptualising identity as a story through Bakhtin and Ricoeur. ............... 100 3.1 Introduction...................................................................................................... 100 3.2 Story ................................................................................................................ 103 3.2.1 A brief encounter: Narrative structuralism, post structuralism and phenomenological hermeneutics. ....................................................................... 103 3.2.2 Ricoeur and Bakhtin: A union .................................................................... 108 3.3 Memory ........................................................................................................... 110 3.3.1 ‘I’ as me: Understanding the self through time ........................................... 110 3.3.2 ‘I’ as we: Culture and collective storying ................................................... 114 3.4 Imagination ...................................................................................................... 119 3.4.1 Plot and narrative ...................................................................................... 119 3.4.2 Performing ‘As-If’ ...................................................................................... 122 3.5 The conceptualisation of identity in this thesis ................................................. 125 Chapter 4.Between fact and fiction: Arts Based Research (ABR) and the making of ‘Performatics’. ........................................................................................................128 4.1 Introduction...................................................................................................... 128 4.2. An ABR Epistemology .................................................................................... 130 4.2.1 Becoming an Arts Based Researcher........................................................ 135 4.3 ABR Methodology and Methods: Filmed drama. .............................................. 136 4.3.1 Drama as research: Joe Norris’ ‘Playbuilding’ as a dialogic approach ....... 139 4.3.2 Film as research: Jean Rouch’s psycho-socio observational cinema ........ 149 4.4 ABR as analysis. ............................................................................................. 158 2 4.4.1 Drama as analysis: A recap ...................................................................... 159 4.4.2 Participatory film analysis. ......................................................................... 159 4.4.3 Post production film editing in Final Cut pro 7 ........................................... 161 4.4.4 Summary of ABR as analysis .................................................................... 168 4.5 Recruitment, Access and Ethics: Problems and potential of ABR. ............. 169 4.5.1 Recruitment and access............................................................................ 169 4.6 A Consequentialist approach to Ethics: Ways of having a voice and non- anonymisation as ethical research. ....................................................................... 172 4.6.1 Co-production of data: The actor/researcher relationship .......................... 173 4.6.2 Informed consent and possible harms: Managing the researcher – participant relationship ....................................................................................... 175 4.6.3 Risk to the researcher in the field .............................................................. 178 4.6.4 Data storage ............................................................................................. 179 4.7 Conclusion: How ABR is used in this thesis..................................................... 180 MAIN FEATURE ......................................................................................................... 182 Chapter 5. ‘Performatics’: Performing stories of mathematical identity through filmed drama …………………………………………………………………………...183 REVIEW ..................................................................................................................... 188 Chapter 6. The value of ‘Performatics’ as research:Critical reflections and claims to knowledge. ........................................................................................................... 189 6.1 A portrait of the artist as an academic ............................................................. 189 6.1.1 Synthesising the original contribution and claims to knowledge ................ 190 6.2 ‘Sum Anxiety’ expresses emotions, memory and imagination as fundamental to identity.................................................................................................. .................. 196 6.2.1 The affective property of story: Plot, memory and emotions ...................... 197 6.2.2 ‘Sum Anxiety’: Film clip and discussion ..................................................... 199 6.3 ‘Tense Identity’ exemplifies the dynamism of storying. .................................... 205 6.3.1 Dialogism in ‘Performatics’ ........................................................................ 206 6.3.2 ‘Tense Identity’: Film clip and discussion .................................................. 208 3 6.4 ‘Math Therapy’ reads the body as both a sign of identity and for its dramatic intent 214 6.4.1 Sum body in the literature: The mathematical body as a site of storying