Table Of ContentEducational 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)
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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
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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
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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
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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.
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