Mathematics Into the Picture
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Deakin Research Online This is the unpublished version: Gough, John 2011, Research as … explorations of theories and methodologies of research. Available from Deakin Research Online: http://hdl.handle.net/10536/DRO/DU:30041228 Reproduced with the kind permission of the copyright owner. Copyright : John Gough This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Australia License. Attribution is to John Gough. Research as … explorations of theories and methodologies of research by John Gough is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Australia License. Research As … Explorations of Theories and Methodologies of Research John Gough Deakin University Faculty of Arts & Education (with co-author contributions from some others) A draft eBook on the topic of Educational Research, for teachers, student- teachers, educators, and researchers Contents Preface .................................................................................................................................................. 6 Turning School Investigations into Valuable Research..................................................... 7 Action research is critical practice .................................................................................. 7 Linking action research with experimental approaches ......................................... 9 Implementing curriculum change – a typical example ......................................... 10 'Experiments' in education .............................................................................................. 11 'Learning' and the need to measure change ............................................................. 12 Is this learning 'enhanced' or 'ordinary' learning?................................................. 13 Spatial skills in using computer graphics software................................................ 15 Recognising the limits of the research ........................................................................ 15 Is this research really 'valid'? ......................................................................................... 16 Collecting research data from teachers and students ........................................... 17 How clear is my learning theory? ................................................................................. 18 Contrasting software for spatial learning .................................................................. 19 When people know they are part of an experiment .............................................. 20 Assessment of student understanding ........................................................................ 21 Writing conclusions ............................................................................................................ 22 References .............................................................................................................................. 23 Ethics in Action Research: A Conversation .................................................................... 25 Teaching as a Research Methodology: An Outline of a Process and Case Studies From Teacher Education ............................................................................................................ 33 Introduction .......................................................................................................................... 33 The Everyday Challenges for Teachers to Conduct Research ............................ 34 Telling it Like it is ................................................................................................................ 35 From Descriptive Case Study to Action Research ................................................... 35 From Teaching to Research ............................................................................................. 39 Teaching (and Research) as Problem Solving .......................................................... 40 Case Study 1: Conceptual Analysis and Identification of Process — Diagnosis of Spelling Errors ................................................................................................................. 41 Case Study 2: Teaching in an Era of Changing Computer Software ................. 43 Conclusions, for the Time Being .................................................................................... 44 References and Further Reading ................................................................................... 44 Curriculum Development as Research ................................................................................. 47 Curriculum Development That is NOT Research .................................................... 47 When Curriculum Development CAN be Regarded as Research ...................... 47 The Ambiguity of Words — “Authentic Assessment”, Anyone? ........................ 48 How New is New? And How Could We Know? ........................................................ 49 “Numeracy” is New, and Means …? .............................................................................. 50 Curriculum as a Concept or Topic for Research ...................................................... 52 Curriculum Development (Research) Is Needed Where Curriculum Changes .................................................................................................................................................... 52 Curriculum Development: A Mini-Case Study — “Exemplary Assessment” 53 What is exemplary assessment in or for a particular context? ......................... 54 Conclusion(s)? ...................................................................................................................... 58 References .............................................................................................................................. 59 Exploring constructivism(s): the gaps between philosophy, psychology, praxis and common sense(s). ................................................................................................................ 62 How I Do My Research ...................................................................................................... 62 What I am Researching (Some of It …) — The (My) Background .................... 63 Bringing Mathematics into the Picture ....................................................................... 64 Focussing on Constructivism and its Origins ........................................................... 65 Constructivism and Mathematics-Education — Helpful Technical Terms ... 66 Constructivism Across the Curriculum? Or Language? ........................................ 69 Constructivism and Science Education — Another Country? ............................ 70 What About 'Constructivist Teaching'?....................................................................... 74 Concluding...? ........................................................................................................................ 76 References .............................................................................................................................. 76 Notes and Activities for the Presentation of the Symposium Paper: Exploring constructivism(s): the gaps between philosophy, psychology, praxis and common sense(s). ............................................................................................................................................ 79 A Collection of Questions and Activities for the Symposium Paper: Exploring constructivism(s): the gaps between philosophy, psychology, praxis and common sense(s). .................................................................................................................... 82 Devil's Advocacy as Critical Research Methodology: Spatial Thinking as a Case Study .................................................................................................................................................. 85 Introduction: What is Devil's Advocacy? .................................................................... 85 A Devil's Advocate is a Jargon-Buster ......................................................................... 87 Critical Fatigue and the Chimerical Drive for Novelty—Post-… What? ......... 88 Active Learning — Sounds Good, But Could That be Right? ............................... 89 Oh Brave New Computer-Crazy World — 'New'? Different? ............................. 90 Students Really Learn By Really Doing Projects — Really? ................................ 93 The Great Piagetian Breakthrough — Are Children Really Like That? .......... 94 Pictures Also Need a Devil's Advocate ........................................................................ 96 Theories of Spatial Thinking: A Case Study ............................................................... 97 Piagetian Disciples — van Hiele's Developmental Theory of Geometric Learning .................................................................................................................................. 99 Krutetskii and Two Forms of Mathematical Thinking: Analytic-verbal and Spatial .................................................................................................................................... 103 Conclusions(?) .................................................................................................................... 105 References ...........................................................................................................................