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Verso page
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Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia
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Content |
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Preface |
Preface, including review process
Roberta Hunter, Brenda Bicknell, Tim Burgess
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List of Reviewers |
Reviewers
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Keynote Address |
Being Mathematical, Holding Mathematics: Further Steps in Mathematical Knowledge for Teaching
Bill Barton
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Developing Pedagogies in Teacher Education to Support Novice Teachers’ Ability to Enact Ambitious Instruction
Elham Kazemi, Megan Franke, Magdalene Lampert
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Practical Implication Award |
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Symposium |
Symposium 1.1: Developing Mathematical Concepts in Australian Pre-school Settings: The Background
Judith Mousley, Bob Perry
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Symposium 1.2: Developing Mathematical Concepts in Australian Pre-school Settings: Children’s Mathematical Thinking
Marina Papic, Joanne Mulligan, Janette Bobis
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Symposium 1.3: Mathematical Thinking of Young Children Through the Eyes of Preschool Practitioners
Robert Hunting, Catherine Pearn
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Symposium 1.4: Mathematical Thinking of Preschool Children in Rural and Regional Australia: Implications for the Future
Bob Perry
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Symposium 1: Cover page: Developing Mathematical Concepts in Australian Pre-school Settings
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Symposium 2.0: Crossing Philosophical Divides to Better Understand the Complexity of the Learning Process in Mathematics
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Symposium 2.1: Uniting Psychological, Sociocultural and Poststructural Axes of Analysis to Better Understand Learning in Mathematics
Mary Klein
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Symposium 2.2: Bridging Understandings, Interest and Identity Gaps in a First Year Numeracy Subject
Kerry Smith
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Symposium 2.3: Crossing the Divide between Teacher Professionalism and National Testing in Middle School Mathematics?
Silvia Dimarco
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Symposium 2.4: Crossing Philosophical Divides: Adding Poststructuralist Insight into Building, Maintaining and Changing Teaching for Better Learning
Mary Klein
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Symposium 3.0: A New Approach to Mathematical Problem Solving in the School Curriculum
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Symposium 3.1: Reconceptualising Problem Solving in the School Curriculum
Jaguthsing Dindyal, Toh Tin Lam, Quek Khiok Seng, Leong Yew Hoong, Tay Eng Guan
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Symposium 3.2: Assessment in a Problem Solving Curriculum
Toh Tin Lam, Quek Khiok Seng, Leong Yew Hoong, Dindyal Jaguthsing, Tay Eng Guan
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Symposium 4.0: Reforming Mathematical Pedagogy in Remote Indigenous Context
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Symposium 4.1: Rich Mathematical Tasks in the Maths in the Kimberley (MITK)
Peter Grootenboer
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Symposium 4.2: Cooperative Learning Environments
Robyn Jorgensen (Zevenbergen)
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Symposium 4.3: The Use of Home Language in the Mathematics Classroom
Richard Niesche
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Symposium 4.4: Describing Teacher Actions After Student Learning from Rich Experiences
Peter Sullivan
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Symposium 5.0: Task Types and Mathematics Learning
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Symposium 5.1: The Task Types and Mathematics Learning Research Project
Helen O'Shea, Irit Peled
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Symposium 5.2: Using Tasks Involving Models, Tools and Representations: Insights from a Middle Years Mathematics Project
Barbara Clarke
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Symposium 5.3: Opportunities and Challenges for Teachers and Students Provided by Tasks Built Around “Real” Contexts
Doug Clarke, Anne Roche
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Symposium 5.4: Constraints and Opportunities When Using Content-specific Open-ended tasks
Peter Sullivan
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Symposium3.3: Teacher Preparation for a Problem Solving Curriculum
Leong Yew Hoong, Toh Tin Lam, Quek Khiok Seng, Jaguthsing Dindyal, Tay Eng Guan
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Research Paper |
Issues in bridging between senior secondary and first year university mathematics
Michael Jennings
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Students’ Perceptions of the Impacts of Parents, Teachers and Teaching upon their Anxiety about the Learning of Fractions
Michelle Jennison, Kim Beswick
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Insights into the Beliefs and Practices of Teachers in a Remote Indigenous Context
Robyn Jorgensen (Zevenbergen), Peter Grootenboer, Richard Niesche
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Innovative Problem Solving and Students' Mathematics Attitudes
Karoline Afamasaga-Fuata'i
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“My Favourite Subject is Maths. For Some Reason No-one Really Agrees With Me”: What Year 6 Students Say About Mathematics
Catherine Attard
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Re-focussing Research Agendas
Andy Begg
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Guessing Answers to Pass a 5-item True False Test: Solving a Binomial Problem Three Different Ways
Anthony Bill, Jane Watson, Peter Gayton
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Concept Maps: Implications for the Teaching of Function for Secondary School Students
Jill P Brown
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Students’ Recollections of Participating in Collective Argumentation When Doing Mathematics
Raymond Brown, Brooke Reeves
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Changing Teachers’ Classroom Practice through Developmental Assessment: Constraints, Concerns and Unintended Impacts
Rosemary Callingham, John Pegg, Teresa Wright
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The Development and Validation of the Students’ Self-efficacy for Statistical Literacy Scale
Colin Carmichael, Ian Hay
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Gender Differences in Middle School Students’ Interests in a Statistical Literacy Context
Colin Carmichael, Ian Hay
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Group Metacognition During Mathematical Problem Solving
Christina Chalmers
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Challenging Mathematical Conversations
Jill Cheeseman
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Teaching the Distributive Law: Is Fruit Salad Still on the Menu?
Helen Chick
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Mathematics Education, Language, and Culture: Ponderings From a Different Geographic Context
Marta Civil
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Institutional Gaps in Mathematics Education Research Procedures Between a Developed and Developing Country
Ernest Kofi Davis, Wee Tiong Seah, Alan J. Bishop
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Developing Year 5 Students’ Understanding of Density: Implications for Mathematics Teaching
Shelley Dole, Doug Clarke, Tony Wright, Geoff Hilton
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It Seems to Matters Not Whether it is Partitive or Quotitive Division When Solving One Step Division Problems
Ann Downton
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Developing Conceptual Place Value: Instructional Design for Intensive Intervention
David Ellemor-Collins, Robert (Bob) Wright
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I, You and It: Pronouns and Students’ Understanding of Introductory Algebra
Judith Falle
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Teachers' Use of Mathematics Tasks: The Impact on the Mathematics Learning and Affective Responses of Low-attaining Upper Primary Students
Sarah Ferguson
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Textbook Dilemmas
Tricia Forrester
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The Master, Servant, Partner, Extension-of-self Framework in Individual, Small Group and Whole Class Contexts
Vince Geiger
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Investigating the Professional Learning and Development of Mathematics Teacher Educators: A Theoretical Discussion and Research Agenda
Merrilyn Goos
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Revealing Conceptions of Rate of Change
Sandra Herbert, Robyn Pierce
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Competencies, Skills and Assessment
Tomas Hojgaard
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Success for Underachievers: How Do They Get It?
Marilyn Holmes, Sandi Tait-McCutcheon
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Teachers’ Perspectives on the Transition from Secondary to Tertiary Mathematics Education
Ye Yoon Hong, Suzanne Kerr, Sergiy Klymchuk, Johanna McHardy, Priscilla Murphy, Sue Spencer, Mike Thomas, Peter Watson
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Developing a Productive Discourse Community in the Mathematics Classroom
Jodie Hunter
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Exploring Whether Multiple Intelligences Facilitate ‘Valuing and Working With Difference’ within Mathematics Classrooms
Fiona Jackson, Raymond Brown
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Identifying Effective Leadership Practices for Implementing a New Mathematics Curriculum in Taipei
Brandon Kao, Peter Hudson
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Being Numerate for Teaching: The Indivisibility of Learning Landscape, Participation and Practice
Mary Klein, Kerry Smith
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Leading Change in Mathematics: The Queensland Mathematics Syllabus
Janeen Lamb, Gayle Spry
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Publishing in Mathematics Education: A Matter of Gender?
Gilah C. Leder, Helen J. Forgasz
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Enhancement of Fractions from Playing a Game
Ya Ling Lee
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A Hierarchy of Strategies for Solving Linear Equations
Chris Linsell
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Using Web-Based Mathematical Interactive Exercises and Exploratory Investigations: The Possibilities and Pitfalls
Esther Yook-Kin Loong
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Young Children’s Explorations of Average in an Inquiry Classroom
Katie Makar, Debra McPhee
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Achieving in Mathematics Contested Spaces and Voices
Colleen McMurchy-Pilkington, Hannah Bartholomew
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The Option of Selecting Higher-level Mathematics Courses: Transitional Tensions
Greg McPhan, John Pegg
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There are More Than Part-Whole Strategies at Work in Understanding Non-Equal-Parts Fraction-Area-Models
Annie Mitchell, Marj Horne
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Evolving Mathematics Classroom Assessment Cultures
Rohani Mohamad
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Numeracy Test Item Readability During Transition from Pre-School to School
Judith A. Mousley
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At Home With Numeracy: Empowering Parents to be Active Participants in their Child’s Numeracy Development
Tracey Muir
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Teacher Perception and Motivational Style
Hannah Newman, Jenni Way
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Applying Mathematical Knowledge in a Design-Based Interdisciplinary Project
Kit Ee Dawn Ng, Gloria Stillman
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A Professional Learning Tool to Help Stimulate Mathematics Teachers to Reflect on their Pedagogical Practice
Richard O'Donovan
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Relative Values of Curriculum Topics in Undergraduate Mathematics in an Integrated Technology Environment
Greg Oates
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Analogical Reasoning Errors in Mathematics at Junior College Level
Wai-Kit Alwyn Pang, Jaguthsing Dindyal
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Highlighting the Similarities and Differences of the Mathematical Knowledge and Strategies of Year 4 Students
Catherine Pearn
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Reconceptualising Agency in a Senior Mathematics Classroom
Trevor Redmond, Joanne Sheehy
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Scaffolding for Learning Equation Solving
Daphne Robson, Walt Abell, Therese Boustead
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Making Sense of Partitive and Quotitive Division: A Snapshot of Teachers’ Pedagogical Content Knowledge
Anne Roche, Doug Clarke
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Lesson Study: An Effective School-Based Teacher Professional Learning Model for Teachers of Mathematics
Peter Sanders
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The Development of Fraction Ideas Among Students with Disabilities
Rebecca Seah
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Investigating Students’ Numerical Misconceptions in Algebra
Vicki Steinle, Eugene Gvozdenko, Beth Price, Kaye Stacey, Robyn Pierce
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Probing Some Key Junctures in Relational Thinking: A Study of Year 6 and Year 7 Students from Australia and China
Max Stephens, Wang Xu
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Softly, Softly: Curriculum Change in Applications and Modelling in the Senior Secondary Curriculum in Queensland
Gloria Stillman, Peter Galbraith
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Investigating Feelings towards Mathematics among Chinese Kindergarten Children
Huayu Sun
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Development of an Instrument for Ways of Using Graphics Calculators: Preliminary Findings
Hazel Tan
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Multimodal Use of Semiotic Resources in the Construction of Antiderivative
Michael O. J. Thomas, Caroline Yoon, Tommy Dreyfus
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Learning About Building Mathematics Instruction from Students’ Reasoning: A Professional Development Study
Jana Visnovska, Paul Cobb
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Exploring the Identity of a Pre-Service Teacher: Communal Processes During the Practicum
Margaret Walshaw
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Probing Teachers’ Pedagogical Content Knowledge in Statistics: “How will Tom get to school tomorrow?”
Jane Watson, Rosemary Callingham, Erica Nathan
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Reflection in Self-Assessed Online Discussion
Jenni Way
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Counting On 2008: Diagnostic and Remedial Mathematics Program for Middle Years Students
Allan White
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Growth of Pre-service Teachers’ Knowledge and Teaching Ideas About Decimals and Fractions: The Case of Vivi
Wanty Widjaja, Kaye Stacey
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Engaged to Learn Pedagogy: Theoretically Identified Optimism Building Situations
Gaye Williams
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“Better You Than Me”: Mathematics Anxiety and Bibliotherapy in Primary Teacher Professional Learning
Sue Wilson
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What Did My Students Do When They Did Their Homework Last Weekend?
Regina M.F. Wong, Michael J. Lawson
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Modelling the Height of the Antiderivative
Caroline Yoon, Tommy Dreyfus, Michael O. J. Thomas
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The "Back to Basics" Dilemma for Middle School Mathematics Teachers
Shirley Yates
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Concepts, Connections and Commitment: Locating Mathematics in a Typical School Day
Fiona McDiarmid, Ruth Pritchard
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Teaching Multi-digit Multiplication using Array-based Materials
Jenny Young-Loveridge, Judith Mills
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Linear Algebra Snapshots through APOS and Embodied, Symbolic and Formal Worlds of Mathematical Thinking
Sepideh Stewart, Mike Thomas
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Short Communication (abstract only) |
A Narrative Study on the Use of Computer Software and Hands-on Activities in Developing Young Children’s Mathematical Minds
Po Wah Chan, Tse Lok Tin
(Poster) The study is a collaborative effort
between a teacher educator and three preschool practitioners. It adopted
a narrative approach and yielded a ‘practical’ experience bearing
direct relevant as well as significance value to preschool teacher
educator and practitioners in the teaching and learning of math for
young children. Examples of how children learn mathematical concepts
through the use of computer software and hands-on activities will be
showed in the poster.
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Applying a Systems Approach to Understanding Children’s Performance in System Assessments
Patricia Morley
Large-scale assessments such as NAPLAN
(Australia) provide a wealth of data about the mathematical
understanding and achievement of students. However, measurement is only
the first step in the implementation of systems aimed at achieving
improvement. This paper presents a framework for analysis of NAPLAN data
from the perspective informed by the systems approach. Rather than ask
how well the children perform, the exploratory analysis presented here
focuses on identifying the obstacles to children’s success.
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Brain-burn, Swirling Numbers, an Evil Textbook: Accessing Students’ Beliefs About Maths Through Their Drawings
Catherine Solomon, Alison Gilmore, John Hannah, Mick Grimley
Approximately 200 students from two focus schools
were asked to draw ‘what maths or doing maths means to you’. This task
was used to augment information from a larger study of students’ beliefs
about mathematics, collected from questionnaires containing likert-type
questions and open-ended questions requiring written responses; 848
year 5 and 6 students, aged between 9 and 11, from 17 New Zealand
primary schools completed the questionnaire. The concern was that not
all students of this age are able to express their beliefs through a
method reliant on their literacy skills. The results showed marked
differences between the tasks.
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Development and Validation of Mathematical Thinking Assessment Framework
Tee Yong Hwa, Chap Sam Lim
The study aims to develop and validate
Mathematical Thinking Assessment (MaTA) framework. It involved a total
of 7 classes of 16 years old students and their mathematics teachers
from Malaysia. The MaTA is implemented in the school context to assess
students’ mathematical thinking: the performance assessment is
administered to elicit students’ thinking processes during
problem-solving; the Metacognition Rating Scale is used to specify
students’ awareness while working on problems; the Mathematical
Dispositions Rating Scale is used to indicate students’ disposition
towards learning of mathematics whereas the Mathematical Thinking
Scoring Rubric is used to score and grade students’ mathematical
thinking according to the domains defined in this study.
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Diagnostic Assessment of Mathematics in Schools
Majeda Awawdeh
(Poster)
The poster illustrates two programs in numeracy assessment: the
International Competitions and Assessments for Schools (ICAS) and the
Early Literacy and Numeracy Assessment (ELNA). ICAS is a 40-item
assessment of mathematics skills and content for Year 3-12 students
which allows horizontal and vertical equating of student performance.
ELNA is an online diagnostic computer-adaptive assessment program that
assesses literacy and numeracy skills and knowledge for Pre-school-Year 2
students. Strands tested in numeracy are number, space and measurement,
and patterns. ELNA enables individualised assessment and eliminates the
‘ceiling effect’. ICAS and ELNA provide an interesting research area in
mathematics education.
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Enactments of Instructional Leadership of Mathematics in Primary Schools
Joanna Higgins, Linda Bonne
School-based instructional leadership of
professional development initiatives is important to embedding high
quality instructional practices, so that students’ mathematics
achievement is enhanced. By looking beyond designated leadership
positions it may be possible to explicate alternative enactments of
leadership in primary schools as they are played out in the school
setting, with a specific focus on setting up school structures that
support mathematics teaching. This paper uses a backward mapping
strategy to explore ways of conceptualising instructional leadership in
primary mathematics, as well as identifying school support structures
that enable teachers to advance towards a vision of high quality
mathematics instruction.
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Fine Tuning the Teaching Methods Used for Second Year University Mathematics Based on Student Perceptions about Mathematics
Leng Leng Lim, David Thiel, Jeung-Hwan Doh, Debra Bernhardt
Each year a new cohort of 240 students undertakes
the challenge of second year mathematics. The student feedback from one
year is often a reversal of that received about the course run in
previous years. The 2009 class was surveyed on their attitudes to
mathematics at both the beginning and the end of the course. This paper
reports changes in teaching methods implemented in response to the first
survey, changes in student perceptions about mathematics and on the
student feedback compared to previous years. From this data, some
conclusions are made about how students’ best learn.
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First Year Pre-service Teachers’ Patterns of Responses to a Mathematical Skills and Knowledge Test
Sharyn Livy
The aim of this study was to gain a better
understanding of the misconceptions and ways in which pre-service
teachers responded to a mathematical skills and knowledge test during
their first year of the Bachelor of Education. Two hundred and ninety
seven pre-service teachers’ results were collected. This paper will
explore the answer of one question identified as difficult for nearly
90% of the cohort.
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From Foot to Shoe Project
Lai Ha Freda Yuen
(Poster) This poster discusses a project about
feet, undertaken by the class of children ranging in 4 to 5 years in a
kindergarten of Hong Kong. Throughout this project, the children studied
parts of leg, measured and compared their feet, found out the relation
between the size of their feet and shoes, and experimented with making
their own shoes. The article documents the children’s work through
photographs, and provides the teachers’ reflections.
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Historical Evolution and Student Perspectives on Large Numbers
Mala Nataraj
The importance of a consideration of large
numbers in primary and early secondary school should not be
underestimated. A study of history of India (and of the Maya) reveals
that contemplation of large numbers provided the impetus for a
construction of place value number system. While today’s students do not
have to create a number system they do need to understand its structure
in order to develop number sense and operations and to progress to
algebra. This can perhaps be done more quickly by contemplating on large
numbers. This study examined and categorised Year 9 students’ responses
to a questionnaire on large numbers. The results suggest that many
students show competence in naming and using large numbers and some are
in the process of thinking beyond their curriculum level.
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Inquiring into Preservice Secondary School Teachers’ Generalisation Strategies in a Quadratic Generalising Task
Boon Liang Chua, Celia Hoyles
This paper reports how a group of prospective
secondary school teachers in Singapore solved a quadratic generalising
task. The findings show that the teachers were capable of deriving
multiple equivalent expressions for the task. Three approaches were used
to work out the rule: numerical, figural and pragmatic, with the last
two being more predominant. It was also found that the same expression
could be obtained from different visual representations, and conversely,
the same visual representation could also produce different
expressions.
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Instrumental Genesis as a Theoretical Framework to Examine Probability Simulations
Anthony Bill
Within a larger study of a Year 9 class
investigating sample size students examined explicitly the legitimacy of
the data generated by a Fathom die simulation. Instrumental genesis -
the process where students adopt a tool as their own - is an established
analytical framework used with computer algebra systems (CAS), and this
framework has potential application in electronic probability
simulations. In addition to a examination of students adopting the
simulation's procedures and features, any reservations students have
regarding the legitimacy of the data generated may act as a potential
impediment to learning. More recently instrumental genesis has been
extended to acknowledge the role of the teacher and the classroom
environment through a process defined as instrumental orchestration.
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Lead Teacher Role: Keeping the Momentum
Anne Milburn, Viv Thompson, Deb Gibbs
In New Zealand by the end of 2009 most primary
schools will have participated in Phase 1 professional development of
the Numeracy Development Project (NDP). The project is now in its 9th
year after the pilot ‘Count Me In Too’. Having self-managing schools in
numeracy is the focus of Phase 2 of the project. Therefore the
direction of support in the future will be towards maintaining quality
teaching in classrooms. As schools are working on sustainability of
good numeracy teaching and learning, the role of Lead Teacher is
becoming more critical. They have as part of their role the continuous
improvement of teacher practice. They also have a greater responsibility
in improving, monitoring and reporting progress of students.
Maintaining the momentum can be a difficult task and requires support
from principals and facilitators in order to carry out Lead Teacher
multi-layered responsibilities. Further to Deb Gibbs and Marilyn Holmes
roundtable presentation at MERGA in 2006, facilitators have continued
to explore issues around the role of Lead Teachers. Three years later,
have changes for the better taken place or has the status quo remained?
This small study focuses on how well the Lead teachers make use of the
time allowed and looks at answers to the following questions:
1.Has the perceived value of the Lead Teacher role increased over time?
2.Has the support given to Lead Teachers to carry out their role
effectively changed?
Discussion around this study will highlight implications for lead
teachers, principals and facilitators in numeracy.
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Lesson Starter Activities in New Zealand Secondary Mathematics Lessons
Liping Ding, Margaret Walshaw
The beginning of any lesson is an important event
and may take on many forms and functions. In this presentation we
reveal how three mathematics teachers began their year 9 lessons. Using
data from the New Zealand component of the Learner’s Perspective Study
(LPS) we examine the lesson event characterised as the ‘starter’. Within
all three classrooms, the starter activities typically involved
students in solving teacher-provided problems. However, closer analysis
of video and interview data from each classroom sequences of ten lessons
reveals differences in the intent, the nature, and the enactment of
student/teacher activity. We explore how particular learning
opportunities and modes of participation, both in the moment and later
in the lesson, are interwoven with the starter activity.
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Middle School Students’ Responses to Two-tier Tasks
Shajahan Haja, David Clarke
The structure of two tier testing is such that
the first tier consists of a multiple-choice question and the second
tier requires justifications for choices of answers made in the first
tier. This study aims to evaluate two-tier tasks in ‘proportion’ in
terms of students’ capacity to write and select justifications and to
examine the effect of different two-tier formats on student performance.
Twenty students each from Y7 and Y8 participated in the study in
Melbourne in March 2008. The students took eight similar tests with each
test having eight two-tier tasks. Eight students were interviewed
individually after the testing. Analysis of students’ responses revealed
that i) Y7 and Y8 students were able to select and write justifications
to two-tier tasks, ii) Y7 and Y8 students’ success in writing or
selecting justifications varied on ‘marked answer’ and ‘select answer’
formats, and iii) Y7 and Y8 students’ justifications gave some
information about their misconceptions in proportional reasoning.
Implications for teachers looking for alternative assessment tasks
tracing students’ reasoning behind their correct and incorrect answers
are discussed.
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Models of Professional Learning in Mathematics, Science and
Technology Education: Experienced Critical Friends Rate the Impact of
Models on Teacher and Student Learning
Pamela Hammond, Doug Clarke, Ken Smith
A range of models of teacher professional
learning have been utilised within Australian schools, with varying
success. The views of 125 university-based ‘Critical Friends’ in the
Australian Schools Innovation in Science, Technology and Mathematics
(ASISTM) project were sought on the relative effectiveness of 15 models
of professional development in relation to their capacity to impact on
teacher professional learning and student learning respectively. The
findings are shared, along with recommendations to those considering
these models for future professional development programs.
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Oh Yea, But It’s Not a Real Dice
Anthony Bill
(Poster) Year 9 students compared explicitly the
fairness of three dice: a standard factory-made die, a die students
fabricated using Sculpey (TM) modelling clay, and a virtual die in a
Fathom (TM) simulation. During class discussion students developed a
fairness measure - a single statistic quantifying the fairness of the
die - calculated as the difference between the observed and the expected
frequency in 30 rolls of the die. The students pooled the fairness
measures and constructed poster-size dot plots, and the dot plots were
then used in whole-class discussion to compare the fairness of the three
dice.
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One-on-one Numeracy Intervention: A Pilot Study
Steve Thornton, Gina Galluzzo, Mary Quinane
This short presentation provides some preliminary
results of a one-on-one numeracy intervention program developed as part
of the Commonwealth Government Literacy and Numeracy Pilot Projects in
low SES schools. The intervention was modelled on a reading recover
program (Clay, 1993), using a lesson structure based on research into
how the brain learns mathematics (Sousa, 2007). Students identified as
having low numeracy levels in years 1, 4 and 8 at several Catholic
schools in the West and South of the Archdiocese of Canberra and
Goulburn were withdrawn for thirteen weeks and given on-on-one
intervention by a specially trained teacher.
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Primary Students' Mindset, Mathematics Self-efficacy, and Mathematics Achievement: Investigating the Relationships
Linda Bonne
A student's mathematics achievement can be
promoted or obstructed by their beliefs about intelligence in general
(mindset), and about their own mathematical capability in particular
(mathematics self-efficacy). Ways of investigating the effects of a
mindset intervention and a mathematics self-efficacy intervention, and
how these effects might be associated with changes in students'
mathematics achievement, will be discussed. An exploratory study with
Year 4-5 students and their teachers, drawing on design research
methodology and including quantitative and qualitative methods, will be
described. A case will be argued for extending our understanding of New
Zealand students' self-beliefs in relation to mathematics.
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Streaming for Mathematics in Victorian Secondary Schools
Helen Forgasz, Hazel Tan
Streaming (or ability grouping) for mathematics
is a hotly debated and contentious issue. In this paper, data are
presented from 44 Victorian secondary teachers who responded to an
online survey. The aims of the study were to explore the extent to which
streaming is implemented in Victorian post-primary schools, and to
examine teachers views on the policies adopted in their schools. The
findings indicated that streaming is widespread, even at grade 7, and
that most teachers supported the policies in place. In supporting their
views, various limitations to the streaming practices were also
identified.
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Students’ Performance on Two Task Structures: Two Case Studies
Shajahan Haja, David Clarke
This paper reports the effect of task structure
on two Y7 students’ performance in a pre-post testing situation. The
tests consisted equal number of ‘tasks with confidence level’ and ‘tasks
with safety-net’ structures. Two cases were analysed: i) one girl’s
performance in eight weeks gap, and ii) one boy’s performance in two
weeks gap. The boy’s performance was consistent and showed little effect
from task structure. The girl’s performance seemed significantly
affected showing progress in safety-net tasks which could be attributed
to teacher’s feedback. Task structures uncovered different patterns of
girl’s reasoning between the tests which was confirmed in interview.
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Teachers’ Perceptions Towards School-based Assessment: The Malaysian Context
Tee Yong Hwa, Chap Sam Lim
The over emphasis of examination results has
created phenomenon where teachers teach-to-test and students learn by
rote such as memorizing all the facts without really know how to apply
the knowledge and skills in the real life context. In order to reduce
the focus on examination results, the Blueprint of Education Development
suggested that students’ assessment should be measure through
school-based grading system which is holistic in nature. In Malaysia
context, there is yet available a well-established school-based
mathematics assessment framework to be used by the school teachers.
Hence, this study aims to develop and validate a framework for
Mathematical Thinking Assessment (MaTA). However, prior to this, we see
the importance of seeking teachers’ perceptions about school- based
assessment. Hence, this paper discusses the interview analysis of 18
mathematics teachers from six secondary schools on the issues and
possible challenges faced for the implementation of school-based
assessment for mathematics. The results show that the lack of exposure,
availability of assessment guidelines, preference to current traditional
assessment, time constraint, students’ mathematical ability and English
language proficiency; are the main concerns of the participating
teachers in this study.
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Teaching Algebra Using a Multifaceted Variable Approach: What Do Year 7 Students Understand about Variables?
Salma Tahir, Mike Mitchelmore, Michael Cavanagh
Student difficulties in learning algebra can
arise from the diverse meanings assigned to variables. We propose
teaching different aspects of variables (unknown, generalised number and
function) in parallel with each other using real contexts and call this
a multifaceted variable approach. We are investigating whether learning
about variables using a multifaceted variable approach before moving on
to symbol manipulations can reduce student misconceptions regarding
variables and improve their algebra learning outcomes. This paper
reports results from student interviews administered after the algebra
teaching intervention. Results indicate that students of the
experimental classes showed fewer misconceptions regarding variables
than comparison classes and they were able to recognise that variables
can have multiple values.
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Thai Students’ Perceptions of Cooperative Learning in the Mathematics Classroom
Tippawan Nuntrakune
Thai education is moving toward student-centred
learning. However, Thai students have had little experience with
cooperative learning strategies. This qualitative study reports on Thai
students’ perceptions about their engagement in cooperative learning in
mathematics classrooms. The study found that Grade 4 students utilised
four different but complementary processes (peer tutoring, peer
relationships, peer assessment and group role) to facilitate their
cooperative group work learning. These findings indicated that the
alternative teacher preparation workshops need to provide additional
workshops to improve the implementation of peer relationships, peer
assessment and group role.
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The Development of SAPP: Self-Analysis Professional Portfolio
Anne Scott, Philip Clarkson, Andrea McDonough
This paper proposes a new technique for data
collection in classroom studies. The approach adopted is to regard
teachers as a co-researcher and give them the decisions of what and when
to collect data by using hand held video cameras in the classroom.
Coupled with the data collection is an emphasis on the teachers
following through a process that enables them to self critique their
data and consider whether they have changed their practice. Pitfalls and
successes in our first attempts at using this technique are documented.
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The Effect of Real-life Context in Learning Complex Concepts in Mathematics: A Cognitive Load Perspective
Majeda Awawdeh
A controlled randomized experiment was conducted
to examine the hypothesis that by using real-life cover stories from
learners' real-life to explain fractions, the new concepts could be more
readily assimilated into existing knowledge held in long-term memory
compared to the more traditional geometric contexts. Grade 5 students
(n=32) from a Sydney public school participated in this study. A 2x2
ANOVA with repeated measures was used to analyse the results. The result
supported the hypothesis.
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The Impact of the Secondary Numeracy Project on Mathematics Teaching in Senior Secondary Schools
Roger Harvey
This paper explores the impact of the project on
the teaching of mathematics in senior secondary classrooms. The
Secondary Numeracy Project provides professional development for
secondary mathematics teachers. Schools opting into the project
participate in school based in-service development of their mathematics
teaching team. The specific focus of the Secondary Numeracy Project is
on enhancing the teaching of mathematics to students in their first two
years of secondary school. The impact on pedagogy in the senior
secondary school mathematic resulting from the project, as reported by
mathematics teachers who participated in the project, will be discussed.
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The MAaCAS Project - Mathematical Applications and Computer Algebra Systems
Vincent Geiger
(Poster) This poster outlines a study that aimed
to investigate the potential of Computer Algebra Systems (CAS) to
enhance the processes associated with mathematical modelling and
application tasks. Data for the study was drawn from a one year study of
five different secondary school classrooms. Analysis of the data
revealed that there were significant differences in the uptake of CAS
technology and of the use of applications of mathematics between
schools. Implementation of technology rich approaches to mathematical
modelling varied from classroms where students engaged in complex rich
tasks to those where use of applications of mathematics was limited.
This poster also highlights the affordances and constraints experienced
by teachers in implementing new approaches to learning/teaching
mathematical modelling through the use of technology.
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The Times (Tables): They Are a Changing
Brenda Sherley, Sandi Tait-McCutcheon
The teaching and learning of basic facts is a
topic of perennial interest and significance to teachers, teacher
educators, and the mathematics education community. This study builds
on to a prior study of basic facts teaching and learning in New Zealand
by examining in detail the practice of one teacher as she reflects on
her teaching and learning programme. From this study the authors seek
to advance knowledge and lead to the provision of advice for teachers
and researchers.
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Towards Mathematically Significant Classrooms: A Video Study
Steve Thornton, Kathryn Moyle
This presentation provides some preliminary
results of the use of videos as a vehicle for reflection and planning
with pre-service secondary teachers. A lesson was developed to
illustrate the elements of a framework that we term ‘mathematically
significant classrooms’, consisting of tasks (Watson & Mason, 2007),
norms (Yackel & Cobb, 1996) and conversations (Chapman, 1993).
Students’ responses to the framework, including their use of it in
planning lessons during professional experience, will be discussed. The
framework provides a robust framework through which teachers can reflect
on the intellectual quality of a mathematics classroom (Gore, Griffiths
& Ladwig, 2004).
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Using Collective Argumentation to Teach Mathematics
Margaret Marshman
This study explores how Collective Argumentation
has given the students in a middle-school mathematics classroom a
framework which allows them participate in mathematical discussions to
develop the skills and desire to think, reason and work mathematically,
where personal understandings can be expressed, re-considered, shared
and co-authored. This has led to students sharing the authority and
promoted student engagement
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Using the Model Method to Solve Simple Word Problems
Suat Khoh Lim-Teo, Bee Kwang Poh
In Singapore primary schools, an approach of
representing relationships between quantities using blocks, called the
model method, is used to solve word problems. While very useful for
difficult problems at upper primary grades, this method is taught at
primary two for solving simple one- or two-step problems. A research
study was designed to find out whether beginning primary three pupils
would prefer to use the method or other methods for simple word
problems. The pupils’ ability to handle the component parts of the
method and the difficulties encountered were also investigated. This
presentation will describe the findings of this study.
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Whose Mathematics?
Judy Bailey
With the release of the New Zealand Curriculum
document (2007) we, as two pre-service teacher educators, formalised our
ongoing conversations about the nature of mathematics. A literature
review is being undertaken as part of these conversations. This reveals a
wide variety of explicitly made and implicit conceptions of
mathematics. Of particular interest is Barton's description of NUC
(near-universal conventional) mathematics and the suggestion that
'mathematics could have taken many forms, the forms and preferences of
NUC-mathematics were not inevitable; they are the result of a particular
historical trajectory that includes many social influences, including
language' (2008, p. 24). Implications for mathematics in the NZC, and
our work as pre-service teacher educators are being considered.
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‘It Just Feels Different!’ Engaging Students in Mathematics Using Virtual Grand Prix Racing
Angela Jones, Ruth Pritchard
This project involved a teacher examining her use
of an interactive mathematics program with a class of 13-14 year old
boys to promote engagement in mathematics. Students identified a variety
of mathematical concepts implicit in the learning experience, and
described ways in which it presented opportunities to encounter, apply
or develop these ideas. It provides an example of how the affordances of
such software can be accessed by teachers developing new approaches to
teaching through in-depth professional development. The teacher’s
heightened awareness allowed her to capitalise on the novel context to
promote increased opportunities for learning and participation in
mathematics.
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Poster (abstract only) |
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Round Table (abstract only) |
Captivate - Video Screen Capture Technology for Data Collection
Anthony Bill
"Captivate", a product from the Adobe(TM) suite,
is a video screen capture software that records students’ actions on a
computer as a video recording. The software operates in parallel and
behind the primary software - a typical example is Microsoft(TM) Excel.
Students are aware that Captivate is running, but they soon ignore its
presence and this allows a natural recording of students’ use. The
software includes a audio recorder; if students work in pairs and are
encouraged to discuss their work the audio recording adds immensely to
the richness of the data collected. The video recordings are easily
exported to widely-used file formats such as AVI and MPEG, and this
allows the video-clip to be used independently of Captivate. The files
may then be analysed, using for example, N-Vivo, and edited, reproduced,
transmitted, and displayed as needed. Practising teachers may find
application of the software as an instructional tool. Teachers could
create short instructional video for students that they can replay
on-demand in computer laboratories. This has the potential to improve
teaching practice by liberating the teacher from some repetitive
classroom tasks. The round-table seeks to discuss other researchers’
use of screen capture technology as a data source. The presenter will
demonstrate recordings made during class and small group interviews.
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Developing Communication and Participation Patterns in Mathematics with Diverse Learners
Roberta Hunter, Glenda Anthony, Zain Thompson, Heather Howe
Current shifts in teaching and learning practices
in mathematics classrooms challenge teachers to develop mathematical
communities which offer all participants opportunities to engage in
mathematical inquiry, explanations, justification and generalisations.
The complexities and challenges to achieve this are many, particularly
with the diverse learners in our classrooms. We want to explain a
framework we have developed to explore ways teachers can constitute
classroom norms which support such dialogue. Teachers participating in
the research study will describe how they have adapted and used the
framework in their numeracy classrooms and also how they have used it as
a reflective tool to plan next possible growth areas. In this session
we seek feedback on where adjustments need to be made to meet the
explicit needs of Maori and Pasifika students in particular. Whilst
knowledge of how to develop productive communication and participation
patterns with diverse learners in New Zealand is the focus of our study
we hope that experiences from Australia and other countries will add to
the discussion.
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Successful Ways of Enhancing Achievement of Maori Students in Mainstream Settings
Honor Ronowicz, Tracey Muir
The University of Waikato Numeracy advisers will
start the round table discussion by presenting the findings from a case
note and a small research project involving teachers with significant
numbers of Maori students in their classrooms and Maori students from
schools that are working in depth in numeracy across the Waikato region.
The international evidence cited in Wendy Nielsen, Cynthia Nichol, and
Jenipher Owuor (2008) positively supports the enhancement culturally
responsive pedagogy has on student’s connection with the learning
process. In New Zealand, Best Evidence Synthesis research highlights the
importance of relationship building with Maori students to increase
engagement and raise achievement (Alton -Lee 2003). Aspects that might
be considered in this discussion include the underpinning principles of
Te Ao Maori, classroom strategies that seem to improve achievement for
Maori students, Ka Hikitia, the Ministry of Education, Maori Education
Strategy, and the work of Dr Russell Bishop et al.
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Teaching the Mathematics of Gambling to Reinforce Responsible Attitudes Towards Gambling
Robert Peard
The general acceptance afforded the national
image of Australians as gamblers have given gambling a legitimacy rare
in other countries. Concerns with the social effects of this have led
many State governments to implement programs to counteract negative
social effects. The Queensland Treasury has allocated funds for the
development of teaching resources for this purpose including the
development of the Unit presented here. In 2006 the author constructed a
Unit of work for Queensland Senior Secondary (Years 11 and 12)
Mathematics classes entitled ‘The Mathematics of Responsible Gambling’
as a consultancy to the Queensland State Government. Towards the end of
2007 the ‘Secondary Mathematics Teaching Resources Kit’ was distributed
to all secondary government schools. This paper describes the activities
of the Unit, their relationship to the Queensland Syllabus objectives,
the research upon which the Unit is based, and the current research into
the effectiveness of its implementation which began in November 2008
and will continue in Semester 1 of 2009.
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The Effect of Reform-Oriented and Other Mathematics Curricula on Students’ College Mathematics Placement Test Scores
Jon D. Davis, Jeffrey C. Shih
This study examined the college mathematics
placement exam results of 1,277 students learning from nine secondary
mathematics curricula and two Advanced Placement (AP) mathematics
programs in 25 different high schools in the United States. The results
suggest that students learning from several traditional mathematics
programs and AP Calculus significantly outperformed students learning
from the reform-oriented mathematics program, Core-Plus Mathematics
Project, on algebra manipulation and calculus readiness questions. Prior
mathematics achievement, course completion, and gender also
significantly influenced mathematics placement scores.
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