University of Plymouth PEARL https://pearl.plymouth.ac.uk 04 University of Plymouth Research Theses 01 Research Theses Main Collection 2019 Oral Story: A pedagogical tool encouraging children's mathematical thinking. McGrath, Caroline http://hdl.handle.net/10026.1/13717 University of Plymouth All content in PEARL is protected by copyright law. Author manuscripts are made available in accordance with publisher policies. Please cite only the published version using the details provided on the item record or document. In the absence of an open licence (e.g. Creative Commons), permissions for further reuse of content should be sought from the publisher or author. Copyright statement: This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the author's prior consent. 1 ____________________________________________________ ORAL STORY: A PEDAGOGICAL TOOL ENCOURAGING CHILDREN’S MATHEMATICAL THINKING. by CAROLINE McGRATH A thesis submitted to Plymouth University in partial fulfilment for the degree of DOCTOR OF PHILOSOPHY Plymouth Institute of Education December 2018 2 Author’s Declaration At no time during the registration for the degree of Doctor of Philosophy has the author been registered for any other University award without prior agreement of the Doctoral College Quality Sub-Committee. Work submitted for this research degree at the University of Plymouth has not formed part of any other degree either at the University of Plymouth or at another establishment. Publications: McGrath, C. (2015) ‘Mathematical Storyteller Kings and Queens: an alternative pedagogical choice to facilitate mathematical thinking and understand children’s mathematical capabilities’, in Chinn, S. (ED.) The International Handbook for Mathematical Difficulties and Dyscalculia. Oxon: Routledge. McGrath, C. (2014) Teaching Mathematics through Story: A Creative approach for the early years. Oxon: Routledge. McGrath, C. (2014) 'Rich Story Possibilities’, Early Years Educator, 15(10), pp.28-30. McGrath, C. (2012) 'A forest full of maths’, Early Years Educator, 14(6), pp.20- 24. McGrath, C. (2012) 'From posing to solving’, Early Years Educator, 14 (4), pp.24-26. McGrath, C. (2011) 'The motion of numerals', Early Years Educator, 13 (8), pp.24-26. McGrath, C. (2010) Supporting Early Mathematical Development: Practical Approaches to Play-Based Learning (Oxon: Routledge). Word count of main body of thesis: 85, 668 words. Signed: Caroline McGrath Date: 14 December 2018 3 Caroline McGrath Oral Story: A pedagogical tool encouraging children’s mathematical thinking. Abstract This thesis is an exploration of how oral story can be used as a pedagogical tool by educators in a state infant school, to encourage children’s mathematical thinking. Two research questions are framed as follows: In using oral story as a pedagogical approach for mathematical thinking, what characterises the nature of the interaction between teachers and children and the role of children as mathematical storytellers? How can such narratives be documented? It starts by identifying the Vygotskian principles of instruction that are of importance to the practice of teaching young children. Data are generated by means of interviews, discussions, classroom observations and written reflections, which progressively focus the study. In particular, the way in which oral story allows playful conjecturing about mathematical possibilities using the question ‘what if?’ is examined. The practice of two reception class teachers is analysed and differences are shown between their mathematical epistemologies and implementation of the early years curriculum, using oral story as a teaching strategy. The contribution to knowledge made by the thesis is represented by several features. First, it lies in the detail of the exploration of the interaction between teachers and children, illuminating innovative ideas about the nature of such interaction in the context of using oral story as a pedagogical tool with whole classes and smaller groups of young children. Though oral story has been examined in previous studies, these tend to have relied on retelling a story with mathematical themes rather than constructing a story with children which allows new connections to be made. Second, the study’s findings relate specifically to children taking the role as mathematical storytellers and again, though complementing other studies, it extends our understanding of the way in which storytelling allows children to experience mathematical thinking. Third, in addition to new knowledge in the field of early years mathematics, it develops a novel way of documenting children’s mathematical narrative, making use of video of children’s storytelling to stimulate reflection on this by children, teachers and parents. 4 Acknowledgements Though the content of this thesis is, ultimately, my own responsibility, its completion pays tribute to the help and support of other people. First, I thank my supervisors, Dr Nicholas Pratt and Dr Ulrike Hohmann, each of whom has played a major part in supporting and guiding me over the course of my work and who have, together, formed an excellent and complementary team. Second, I thank students and colleagues who I have worked alongside over the past years, and the children, parents and staff at the school where the research was conducted, who helped me to create this imaginative project. Finally, all those completing a PhD rely on the kindness and support from families and friends. Thanks therefore to my family and friends, who all supported me in their own ways. 5 Contents List of Figures .......................................................................................... p.7 List of Tables ............................................................................................. p.7 Chapter One Introduction ............................................................................................... p.8 Chapter Two Mathematics and policy: possibilities for oral story ............................ p.37 Chapter Three Teaching and learning: a sociocultural theory of development ......... p.83 Chapter Four Methodology and research design ...................................................... p.146 Chapter Five Generating and analysing rich data .................................................... p.182 Chapter Six How oral story supports children’s mathematical thinking .............. p.218 Chapter Seven The practice of oral mathematical story: policy-in-use ..................... p.261 Chapter Eight Concluding discussion ........................................................................ p.313 References............................................................................................. p.330 Appendices............................................................................................ p.343 6 List of Figures Figure 1: Inner and outer pentagons. Taken from Koshy, V. (2001) Teaching mathematics to able children ...................................................... p.40 Figure 2: Research components represented using Crotty (1998).......... p.160 List of Tables Table 2.1: Early Years curriculum and Casey’s mathematical model ........ p.69 Table 2.2: National Curriculum and Casey’s mathematical model ............. p.74 Table 3: Vygotskian instructional principles and oral storytelling………...p.138 Table 4.1: Approaches taken to ensure validity in this research .............. p.166 Table 4.2: Detail of participant involvement ............................................. p.172 Table 5.1: Oral mathematical story activity over an academic year ......... p.183 Table 5.2: Extract of interview with coding ............................................... p.193 Table 5.3: Characterisation of oral mathematical story ........................... p.201 Table 5.4: Initial challenges and concerns .............................................. p.208 Table 7.1: Educator epistemology: policy-in-use...................................... p.272 Table 7.2: Oral mathematical storytelling as a pedagogic tool ................. p.300 7 Chapter One Introduction This chapter provides a rationale as to why I have chosen to carry out research in this area and in doing so offers a justification for the overarching research theme: how oral mathematical story as a pedagogical tool encourages children’s mathematical thinking. There are two research questions which are framed as follows. In using oral story as a pedagogical approach for mathematical thinking, what characterises the nature of the interaction between teachers and children and the role of children as mathematical storytellers? How can such narratives be documented? The theoretical ideas informing the background to this work and the types of evidence I will use to answer the research question are outlined. Further, I provide an overview of the study and highlight the complexities of the constructs which support this empirical work. The research evidence which supports this work involves observations of children participating as listeners and tellers of mathematical stories and playing with story-related materials (see photographs, Appendix 1). All names are pseudonyms and the project was guided by an ethics protocol which was approved by the awarding university’s ethics committee (Appendix 2). This research project takes an interpretive approach with constructionism