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Frame of Reference in Iwaidja: Towards a Culturally Responsive Early Years Mathematics Program

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Frame of Reference in Iwaidja: Towards a Culturally Responsive Early Years Mathematics Program Frame of Reference in Iwaidja: Towards a Culturally Responsive Early Years Mathematics Program Cris Edmonds-Wathen Bachelor of Arts (University of Melbourne) Bachelor of Arts (Honours) (University of Western Sydney) Graduate Diploma of Primary Education (Charles Darwin University) Thesis submitted in total fulfilment of the requirements for the degree of Doctor of Philosophy School of Education College of Design and Social Context RMIT University December 2012 Declaration I certify that except where due acknowledgement has been made, the work is mine alone; the work has not been submitted previously, in whole or in part, to qualify for any other academic award; the content of the thesis is the result of work which has been carried out since the official commencement date of the approved research program; any editorial work, paid or unpaid, carried out by a third party is acknowledged; and, ethics procedures and guidelines have been followed. Cris Edmonds-Wathen December 2012 Acknowledgements I’d like to thank the people at RMIT University who supported this project, especially my senior supervisor, Dianne Siemon, who trusted me as I voyaged beyond the common fields of mathematics education and focussed me as I returned. I’d also like to thank my second supervisor Jude Ocean for constructive feedback and Michael Buxton for his creative approach to university resourcing. I’d like to thank the people who helped me get started: Deb Olle, Maria Angel, Michael Christie, Nicholas Evans and Rachael Nordlinger; and all those people those people who read drafts or discussed ideas with me, including Adrielle Drury, Alex Roberts, Caitlin Newton- Broad, Ella McHenry, Emily Gray, Mary Finlay-Donley, Mary Laughren, Ruth Singer, Stephen Thornton, Therese Carr and anonymous reviewers of conference papers. I am grateful for the financial support provided by the Australian Institute of Aboriginal and Torres Strait Islander Studies, who funded the linguistic fieldwork, and by RMIT University, who awarded me an Australian Postgraduate Award scholarship and supported my attendance at conferences. I am also grateful for the support of the Top End Group School with respect to travel to and from Croker Island and of Stephanie Fielder and Adrian Fitzpatrick who provided me with accommodation at Minjilang. I also wish to acknowledge the support of the School of Education at Charles Darwin University in the final month of writing. Thanks to all the people of Minjilang who participated in the project, Charlie Mangulda, David Galak, Freddy Gabiya†, James Cooper, Joy Williams†, Khaki Marrala, Maggie Marburrunbi, Rae Girribuk†, and those who did not want their names used. Also thanks to all the children and their parents. I sincerely hope that this project will provide a benefit to the community. Thanks also to the present and past staff at Mamaruni School, particularly the teachers who participated in the project and the assistant teachers who hold up the school. This project would not have been possible without the support and collaboration of Bruch Birch. Bruce helped with everything from introductions, transcription lessons, transport, cameras and microphones, lunch and dinner, heated analytic discussions and appreciating my puns. Thanks also to Sabine Hoeng who facilitated a recording session in Darwin. The North Australia Research Unit, the ANU campus in Darwin, provided a wonderful environment in which to work and I’d like to thank the people there, particularly Nicole Everett, John Nai-Smith, Dave Williams, Kim Johnstone and Chris O’Brien. Heartfelt thanks to Rebecca Adams, Dave Newman, Tilly and Gabe for so many meals and conversations – your open door was a beacon for me many evenings, particularly in the final year. Rebecca also created the wonderful maps. Thanks to my other friends and family who put up with my lack of normal sociability during this process. Finally, I’d like to dedicate this thesis to the memory of Joy William Malwagag. Joy supported this project from the outset and worked tirelessly helping me to translate the Iwaidja recordings despite her illness. Ngawiny, I miss our fishing trips around Darwin – we were going to catch something good next time for sure. I hope I have done justice to your language and country in this thesis. v Table of Contents Declaration............................................................................................................................ iii Acknowledgements ............................................................................................................... v List of Tables ....................................................................................................................... xv List of Figures ..................................................................................................................... xvi List of Australian languages mentioned in thesis ............................................................... xix Map 1: Australian languages mentioned in thesis ............................................................... xx List of world languages mentioned in thesis ...................................................................... xxi Map 2: World languages mentioned in thesis ................................................................... xxii Abbreviations ................................................................................................................... xxiii Glossary ............................................................................................................................ xxiv Summary .......................................................................................................................... xxvii CHAPTER 1 – INTRODUCTION ................................................................ 1 1.1 BACKGROUND ............................................................................................................. 2 1.2 GOALS AND METHODOLOGY .................................................................................. 5 1.3 THESIS STRUCTURE ................................................................................................... 9 1.4 ACKNOWLEDGING AND RESPECTING CONTEXT ............................................. 10 CHAPTER 2 – LANGUAGE IN MATHEMATICS EDUCATION ........ 13 2.1 CULTURALLY RESPONSIVE MATHEMATICS EDUCATION ............................. 13 2.1.1 A Model of Culturally Responsive Education ........................................................ 14 2.1.2 Building on the Known ........................................................................................... 16 2.1.3 Case Study: Yup’ik Mathematics Program ............................................................ 18 2.1.4 Case Study: Native Hawaiian Creole ..................................................................... 18 2.1.5 Indigenous Learning Styles .................................................................................... 19 2.1.6 Conclusion to Culturally Responsive Mathematics Education .............................. 20 2.2 LEARNING THROUGH LANGUAGE ....................................................................... 21 2.2.1 Cognitive Load ....................................................................................................... 21 2.2.2 Linguistic Relativity ............................................................................................... 22 2.2.3 Examples of Linguistic Relativity in Number ........................................................ 23 2.2.4 Conclusion to Learning through Language ............................................................ 26 2.3 LANGUAGE OF INSTRUCTION AND COGNITION .............................................. 27 2.3.1 Definitions of L1 and L2 ........................................................................................ 27 2.3.2 Language Distance .................................................................................................. 28 2.3.3 Language of Instruction in Mathematics ................................................................ 29 2.3.4 Cognitive Benefits of L1 Instruction ...................................................................... 30 vii 2.3.5 Case Study: Papua New Guinea .............................................................................. 31 2.3.6 Bilingual Programs and Indigenous Teachers in Australia ..................................... 32 2.3.7 Conclusion to Language of Instruction ................................................................... 33 2.4 LANGUAGE AND IDENTITY .................................................................................... 34 2.4.1 Language and Identity in Australia ......................................................................... 34 2.4.2 Language Endangerment and Language Shift in Australia ..................................... 36 2.4.3 Case study: Māori Immersion and Revitalisation ................................................... 37 2.4.4 Language Policy in the Northern Territory ............................................................. 38 2.4.5 Conclusion to Language and Identity...................................................................... 40 2.5 TEACHING MATHEMATICS IN ENGLISH IN THE NORTHERN TERRITORY . 40 2.5.1 Indigenous Students Speaking English ................................................................... 41 2.5.2 English as a Second Language Methods and Training ........................................... 43 2.5.3 Assistant Teachers ..................................................................................................
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