Educational Research and Professional Learning in Changing Times: The MARBLE Experience PDF
Preview Educational Research and Professional Learning in Changing Times: The MARBLE Experience
Educational Research and Professional Learning in Changing Times Educational Research and Professional Learning in Changing Times The MARBLE Experience Jane Watson Kim Beswick Natalie Brown University of Tasmania A C.I.P. record for this book is available from the Library of Congress. ISBN: 978-94-6091-943-5 (paperback) ISBN: 978-94-6091-944-2 (hardback) ISBN: 978-94-6091-945-9 (e-book) Published by: Sense Publishers, P.O. Box 21858, 3001 AW Rotterdam, The Netherlands https://www.sensepublishers.com/ Printed on acid-free paper All Rights Reserved © 2012 Sense Publishers No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. TABLE OF CONTENTS Preface vii Section 1: Background and the Marble Project 1. Introduction 3 2. Methodology 17 3. Teachers’ Pedagogical Content Knowledge 39 4. Student Attitude 55 5. Student Performance 61 6. Teachers’ Perspectives On The MARBLE Project 69 Section 2: Case Studies 7. Case Study 1: A Framework For Numeracy: Working Collaboratively 85 8. Case Study 2: An Inquiry Approach to Developing Mathematical Thinking and Communication 93 9. Case Study 3: Algebraic Representations of Proportional Relationships 99 10. Case Study 4: Beginning Inference in Year 7 111 11. Case Study 5: Enrichment Problem Solving for High Ability Middle School Students 121 12. Case Study 6: Decimal Division: Student Responses to “3 ÷ 0.5” 135 13. Case Study 7: Positive Experiences with Negative Numbers 145 14. Case Study 8: Placing Fractions on a Number Line 157 Section 3: Writing for Teachers 15. Proportional Reasoning in Middle School Mathematics 169 16. Developing Proportional Reasoning with Ratios: Making a Paint Chart 183 17. Estimating Tree Heights for Primary School 191 18. Estimating Tree Heights for Middle School 201 19. Beginning Inference in a Measurement Context 211 20. Exploring Variation in a Manufacturing Context: Licorice 223 21. An Inquiry about Pi as a Ratio 231 22. Measurement and Science: Activities for the Middle Years 249 Section 4: Reflections 23. Reflections 269 References 275 Appendices 287 Index 339 v PREFACE Academics in professional fields such as Education face a constant dilemma: their universities want them to publish the outcomes of their research in academic journals, whereas to be of the most value to their professions, the academics should publish in professional journals. On one hand, the academic journal publications that earn credit in high stakes evaluations by governments are likely to be read by less than a dozen teachers, if any, worldwide. On the other hand, the professional journal articles, likely to be read and to influence the practice of hundreds of workers in the field, gain no credit in the high stakes evaluations. This dilemma has been faced by the authors of this monograph for many years and as a result of our collaboration on an Australian Research Council (ARC) Linkage project, the MARBLE project, we have decided to tell our complete story in one place: in a monograph that brings together our research and our professional work. We hope to model for other researchers, perhaps beginning academics, what we believe are the essential features of applied research in the spirit of the aims of the ARC Linkage program. There is no reason why the professional work carried out with our teachers should not be reported in the same volume as the research outcomes associated with that work. This joining of research and professional outcomes is the main reason for the creation of this monograph. The secondary reason for telling our story is that professional research projects, such as the MARBLE project, take place in an evolving social milieu. The educational context within which a project begins may change rapidly and some of the premises of the original research design may no longer be valid. Such events may make it more difficult to publish outcomes in prestigious international journals but nevertheless the stories need to be told in order that a realistic picture is portrayed about what happens in the field of social science. The project, “Providing the Mathematical Foundation for an Innovative Australia within Reform-based Learning Environments,” or MARBLE, was officially funded from 2005 to 2007, with interactions with teachers beginning in July, 2005. The collection of data continued into 2008 and the analysis and reporting of data into 2011. The Industry Partners for the project were the Department of Education Tasmania and the Catholic Education Office (Tasmania). Details of their participation are found in Chapter 2. Over the time of the project the Partner Investigators from the Department of Education were Tich Ferencz and Denise Neal. From the Catholic Education Office they were Louise Hodgson and Marcus Bucher. All four of these people were involved in planning and delivering the professional learning to teachers and made valuable contributions to the project. The authors were the Chief Investigators of the project and we would like to acknowledge the colleagues who provided assistance and support over the years since 2005. In the early years of the project, Annette Salter, Karen Wilson, Scott Taylor, and Helen Boughton were our Research Assistants. Jane Skalicky vii PREFACE suggested the name MARBLE for the project and collaborated on some of our professional publications. From 2007 to 2010, Suzie Wright, was our main support and contributed significantly to many of the publications that are the basis for chapters in this monograph. Noleine Fitzallen was the Australian Postgraduate Award Industry (APAI) Scholarship holder in the project and assisted in many of the professional learning sessions. Judith Deans was our Administrative Assistant, organising data entry and typing many manuscripts, as well as organising this monograph. Our colleague Rosemary Callingham provided significant input to the Rasch analyses that were carried out as part of the project. To all of these people we express our gratitude as a large project such as this requires a genuine team effort, which we certainly had. Key Curriculum Press in the United States, although not an official Industry Partner in the project, provided its software, TinkerPlots: Dynamic Data Exploration (Konold & Miller, 2005), to every school in the project. The project then provided each school with a copy of the accompanying book and data sets, Digging into Data with TinkerPlots: Data Analysis for Middle School Students (Brodesky, Doherty, & Stoddard, 2008). As a result of this collaboration, the authors and other members of the Mathematics Education team at the University of Tasmania produced an Australian version of the accompanying book, Digging into Australian Data with TinkerPlots: Data Analysis for Middle School Students (Watson, Beswick, Brown, Callingham, Muir, & Wright, 2011). Summary of Content The chapters of the monograph are presented in four sections. The first includes the research aspects of the project including background (Chapter 1), methodology (Chapter 2), teachers’ pedagogical content knowledge (Chapter 3), student attitude (Chapter 4), student performance (Chapter 5), and teacher feedback (Chapter 6). Section 2 contains reports of seven case studies that were carried out as part of the MARBLE project. These case studies were based in individual schools and included work related to developing a school curriculum (Chapter 7), implementing a problem solving program (Chapter 8), teaching algebra meaningfully (Chapter 9), beginning inference with Year 7 (Chapter 10), extension problem solving for high ability primary students (Chapter 11), considering student solutions to a particular problem (Chapter 12), teaching negative numbers (Chapter 13), and working with fractions (Chapter 14). As the project directly led to the publication of papers for the profession, these are included in the third section. Topics include the big ideas of middle school mathematics (Chapter 15), proportions from mixing paint (Chapter 16), estimating tree heights for primary (Chapter 17) and secondary (Chapter 18) classrooms, informal inference and measurement (Chapter 19), licorice production and statistics (Chapter 20), pi as a ratio (Chapter 21), and measurement and science (Chapter 22). The final section contains a chapter with the reflections of the authors on the project. We envisage that this monograph will be a supplementary text for honours, masters, and professional doctorate courses where the aim is to provide a range of viii PREFACE experience for educators related to research, professional learning, and classroom teaching. Although the project was based in Australia, we are aware that similar conditions in relation to the school curriculum, the teachers and students, and the constantly changing educational environment exist in other western countries. We hope that the sharing of outcomes will benefit educators and teachers in this wider realm. Further we intend that the descriptions of our professional learning contexts will inspire others to use similar themes in their work with teachers. The ultimate aim of our endeavours, through our research and professional work with teachers, is improved learning outcomes in mathematics for students. ix
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