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Mathematics Education: Expanding Horizons
Edited by Jaguthsing Dindyal Lu Pien Cheng Swee Fong Ng
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Content |
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Preface |
PREFACE
Jaguthsing Dindyal, Lu Pien Cheng & Swee Fong Ng
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List of Reviewers |
MERGA 35: Reviewers and Judges
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Keynote Address |
Mathematics Education as a Multicultural Field of Research and Practice: Outcomes and Challenges
Michèle Artigue
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MERGA 2012: Where We've Been, Where We Are, and Where We're Going
M. A. ("Ken") Clements
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What Can and Should We Learn from International Studies of Mathematics Achievement?
Frederick K.S. Leung
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Practical Implication Award |
A Learning Community for Pre-service Secondary Mathematics: Learning With and From Each Other
Michael Cavanagh
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Symposium |
Are Online Quizzes an Effective Tool for Mastering Basic Algebra?
Wayne Read & Patrick Higgins
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Doing it Differently: The Ups and Downs of Peer Group Learning
Shaun Belward & Jo Balatti
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Monitoring and Analysing Attendance in First Year University Mathematics Tutorials
Patrick Higgins & Wayne Read
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Working Through the Practice Architectures of First Year University Mathematics Teaching
Jo Balatti & Shaun Belward
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Research Paper |
Exploring the Use of iPads to Engage Young Students with Mathematics
Catherine Attard & Christina Curry
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Teaching Algebra Conceptually: The Process of Bringing Research to Practitioners
Megan Anakin & Ayelet Lazarovitch
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Influences of Self-Perceived Competence in Mathematics and Positive Affect toward Mathematics on Mathematics Achievement of Adolescents in Singapore
Shaljan Areepattamannil & Berinderjeet Kaur
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Socially Response-able Mathematics Education: Lessons from Three Teachers
Bill Atweh & Kate Ala’i
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Improving First Year Mathematics Teaching Through Making Connections: An Action Research Approach
Jo Balatti & Shaun Belward
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Teaching Mathematics in a Project-Based Learning Context: Initial Teacher Knowledge and Perceived Needs
Kim Beswick, Rosemary Callingham & Tracey Muir
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Stories From the Classroom: The Developing Beliefs and Practices of Beginning Primary Mathematics Teachers
Kathy Brady
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Teacher Subject Matter Knowledge of Number Sense
Hannah Briand-Newman, Monica Wong & David Evans
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Mathematics as it Happens: Student-Centred Inquiry Learning
Chris Brough & Nigel Calder
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How Does Teacher Knowledge in Statistics Impact on Teacher Listening?
Tim Burgess
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An Experienced Teacher's Conceptual Trajectory for Problem Solving
Barbara Butterfield
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Mathematical Knowledge for Teaching of MERGA Members
Rosemary Callingham, Kim Beswick, Julie Clark, Barry Kissane, Pep Serow, & Steve Thornton
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Emotions and the Development of Statistical Literacy
Colin Carmichael
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The Effects of Creating Rich Learning Environments for Children to Measure Mass
Jill Cheeseman, Andrea McDonough & Sarah Ferguson
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Developments in Pre-service Teachers' Mathematics for Teaching of Fractions
Mohan Chinnappan, Tricia Forrester & Elise Thurtell-Hoare
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Mathematics Knowledge for Teaching: Evidence from Lesson Study
Mohan Chinnappan & Ui Hock Cheah
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Characteristics of Problem Posing of Grade 9 Students on Geometric Tasks
Puay Huat Chua & Khoon Yoong Wong
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Alternative Starting Point for Teaching Fractions
Jose Luis Cortina, Jana Visnovska & Claudia Zuniga
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Concept Cartoons as a Way to Elicit Understandings and Encourage Reasoning about Decimals in Year 7
Samone Davidson & Mike Askew
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Block Model Approach in Problem Solving: Effects on Problem Solving Performance of the Grade V Pupils in Mathematics
Niño Jose P. de Guzman & Rene R. Belecina
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Constructing and Consolidating Mathematical Entities in the Context of Whole-Class Discussion
Thérèse Dooley
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Male Students' Perspectives Concerning the Relevance of Mathematics - Pilot Study Findings
Michael Easey, Elizabeth Warren & Vince Geiger
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Spatial Metaphors of the Number Line
Cris Edmonds-Wathen
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Reinventing the Wheel: Historical Perspectives on Theories for Interpreting Discourse Patterns in Mathematics Classrooms
Nerida F. Ellerton, Pongchawee Vaiyavutjamai & M. A. (Ken) Clements
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Young Children's Metarepresentational Competence in Data Modelling
Lyn English
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Challenges in Responding to Scaffolding Opportunities in the Mathematics Classroom
Sarah Ferguson
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Using Classroom Episodes to Foster Prospective Teachers' Didactical Knowledge: Issues for Teacher Education
Rosa Tomás Ferreira, Luís Menezes & Maria Helena Martinho
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Interpreting Graphs: Students Developing an Understanding of Covariation
Noleine Fitzallen
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Young Pedestrians' Gendering of Mathematics: Australia and Spain
Helen Forgasz, Gilah Leder & Inés Ma Gómez-Chacón
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The Progress of Grade 1 Students Who Participated in an Extending Mathematical Understanding Intervention Program
Ann Gervasoni, Linda Parish, Teresa Hadden, Carole Livesey, Kate Bevan, Melissa Croswell & Kathie Turkenburg
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Auditing the Numeracy Demands of the Australian Curriculum
Merrilyn Goos, Shelley Dole & Vince Geiger
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Gesture Types for Functions
Sandra Herbert
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Evaluating Middle Years Students' Proportional Reasoning
Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn Goos & Mia O'Brien
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Singapore Students' Performance on Australian and Singapore Assessment Items
Siew Yin Ho & Tom Lowrie
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Developing Teacher Understanding of Early Algebraic Concepts Using Lesson Study
Jodie Hunter
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Designing Opportunities for Prospective Teachers to Facilitate Mathematics Discussions in Classrooms
Roberta Hunter & Glenda Anthony
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Professional Learning for Teaching Assistants and its Effect on Classroom Roles
Chris Hurst & Len Sparrow
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Curriculum Leadership: Reforming and Reshaping Successful Practice in Remote and Regional Indigenous Education
Robyn Jorgensen (Zevenbergen)
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Digital Games for Learning Mathematics: Possibilities and Limitations
Robyn Jorgensen (Zevenbergen) & Tom Lowrie
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Influences of Metacognitive and Self-Regulated Learning Strategies for Reading on Mathematical Literacy of Adolescents in Australia and Singapore
Berinderjeet Kaur & Shaljan Areepattamannil
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Identifying Stages in a Learning Hierarchy for Use in Formative Assessment - the Example of Line Graphs.
Kaye Stacey, Beth Price & Vicki Steinle
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Get Into Vocational Education (GIVE): Motivating Underperforming Students
Gillian Kidman, Tom Cooper & David Nutchey
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Mathematical Proficiency and the Sustainability of Participation: A New Ball Game through a Poststructuralist Lens
Mary Klein
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Developing a Culture of Collaboration
Janeen Lamb & Jana Visnovska
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K-2 Make it Count Students' Views of Mathematics
Gilah Leder & Helen Forgasz
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Variation and Mathematics Pedagogy
Allen Leung
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Supporting Secondary Novices' Efforts to Implement Student- and Discourse-Centred Pedagogical Practices
Gary Lewis
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The Hammer-and-Nail Phenomenon in Mathematics Education
Kien H. Lim
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Impulsive-Analytic Disposition in Mathematical Problem Solving: A Survey and a Mathematics Test
Kien H. Lim & Amy Wagler
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Teaching Algebra Conceptually: Student Achievement
Chris Linsell, Lynn Tozer, Megan Anakin, Anna Cox, Rachel Jones, Eric McAuslan, Donna Smith & Garry Turner
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Does Knowing More Advanced Mathematics Ensure Effectiveness of Working Towards Demonstrating Specialised Mathematical Content Knowledge of Second-Year Pre-Service Teachers?
Sharyn Livy
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The Development of an Assessment Tool: Student Knowledge of the Concept of Place Value
Karen Major
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Projects, Puzzles and other Pedagogies: Working with Kids to Solve Local Problems
Margaret Marshman
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The Impact of a Professional Learning Intervention Designed to Enhance Year Six Students' Computational Estimation Performance
Paula Mildenhall & Mark Hackling
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An Exploration into Growing Patterns with Young Australian Indigenous Students
Jodie Miller & Elizabeth Warren
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The Four-Three-Four Model: Drawing on Partitioning, Equivalence, and Unit-Forming in a Quotient Sub-Construct Fraction Task
Annie Mitchell
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Virtual Mathematics Education: Using Second Life to Model and Reflect upon the Teaching of Mathematics
Tracey Muir
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Developing Pedagogical Strategies to Promote Structural Thinking in Early Mathematics
Joanne T. Mulligan & Michael C. Mitchelmore
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The Influence of Gender, Parents, and Background Variables on Perceived Usefulness of Mathematics among Grade 7 Students in Mozambique
Adelino Murimo
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Problem Categorisation in Ratio - A Closer Look
Norhuda Musa & John Malone
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Student Understanding of Large Numbers and Powers: The Effect of Incorporating Historical Ideas
Mala S. Nataraj & Michael O. J. Thomas
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The Concept of Generalised Number: Valuable Lessons from the History of Algebra
Mala S. Nataraj & Michael O. J. Thomas
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Mathematics Anxiety in Secondary School Students
Lay Keow Ng
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Students' Summaries of Mathematical Lectures: Comparing the Discourse of Students with the Discourse of Lectures
Magnus Österholm
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Identity and Ethnomathematics Projects in Papua New Guinea
Kay Owens
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Let's Count: Evaluation of a Pilot Early Mathematics Program in Low Socioeconomic Locations in Australia
Bob Perry, Ann Gervasoni & Sue Dockett
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Trialling a Professional Statistical Literacy Hierarchy for Teachers
Robyn Pierce, Helen Chick, Jane Watson, Michael Dalton & Magdalena Les
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The Classicist and the Frequentist Approach to Probability within a TinkerPlots2 Combinatorial Problem
Theodosia Prodromou
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Diffusion of the Mathematics Practical Paradigm in the Teaching of Problem Solving: Theory and Praxis
Khiok Seng Quek, Yew Hoong Leong, Eng Guan Tay, Tin Lam Toh & Jaguthsing Dindyal
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Coordinating Known and Unknown Quantities in a Multiplicative Context: Problem Conceptualization, Affordances and Constraints
Ajay Ramful
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Strategies Used by Students to Compare Two Data Sets
Robyn Reaburn
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Exploring Student Reflective Practice during a Mathematical Modelling Challenge
Trevor Redmond, Raymond Brown, Joanne Sheehy & Harry Kanasa
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Steps in Developing a Quality Whole Number Place Value Assessment for Years 3-6: Unmasking the "Experts"
Angela Rogers
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On Diagnosis and Intervention: Helping Students with Special Needs Learn Fraction Ideas Involving Decimal Numbers
Rebecca Seah
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Chinese Primary Students' Mathematical Task Types Preferences
Wee Tiong Seah & Anastasios (Tasos) Barkatsas
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Mathematical Modelling for Singapore Primary Classrooms: From a Teacher's Lens
Cynthia Seto, Thomas Mary Magdalene, Ng Kit Ee Dawn, Chan Chun Ming Eric & Wanty Widjaja
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Empirical Evidence for Niss' Implemented Anticipation in Mathematising Realistic Situations
Gloria Stillman & Jill P. Brown
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Supporting Teachers in Choosing and Using Challenging Mathematics Tasks
Peter Sullivan, Doug Clarke, Debbie Michaels, Angela Mornane & Anne Roche
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Insights into Ways that teachers plan their Mathematics Teaching
Peter Sullivan,David Clarke, Doug Clarke, Peter Gould, David Leigh-Lancaster & Gerard Lewis
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Students' Ways of Knowing and Learning Mathematics and Their Ways of Interacting with Advanced Calculators
Hazel Tan
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Pedagogical Content Knowledge in Mathematical Modelling Instruction
Liang Soon Tan & Keng Cheng Ang
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Developing Mathematical Knowledge through Social Justice Pedagogy with Young Adult Arab Women
Mohammed Goma Tanko & Bill Atweh
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Developing Mathematical Resilience among Aboriginal Students
Steve Thornton, Joanne Statton & Sophie Mountzouris
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Use of Practical Worksheet in Teacher Education at the Undergraduate and Postgraduate Levels
Pee Choon Toh, Tin Lam Toh, Foo Him Ho & Khiok Seng Quekq
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The Effect of Small-Group Game Play Activities on Number Sense Performance
Rashidah Vapumarican & Manu Kapur
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Average Revisited in Context
Jane Watson & Helen Chick
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Teaching for Abstraction: Collaborative Teacher Learning
Paul White, Sue Wilson & Michael Mitchelmore
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Australian Pre-Service Teachers Overseas Tour: Implications for Mathematics Teaching and Learning
Allan Leslie White
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Investigating Pre-service Teachers' Mathematics Anxiety Using the Revised Mathematics Anxiety Scale (RMARS)
Sue Wilson
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A Revolving Model of Pre-service Teacher Development in Mathematics
Susanna Wilson
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Nature of an Attitudes toward Learning Mathematics Questionnaire
Khoon Yoong Wong & Qian Chen
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Profiling Students' Capacities to Link Number and Algebra in Years 5, 6 and 7 in Nanjing, Chin
Wenbin Xu, Max Stephens & Qinqiong Zhang
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Problem Posing in Mathematical Investigation
Joseph B. W. Yeo
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Predictive Validity of Numeracy Entry Requirements for University: Pre-service Teachers' Mathematics Knowledge and Attitudes
Jenny Young-Loveridge, Brenda Bicknell & Judith Mills
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Short Communication (abstract only) |
A Longitudinal Study Preparing Preservice Teachers to Learn and Teach Mathematics with Technology
Leah A. Nillas
Current approaches in technology integration
narrowly focus on technology alone (Harris, Mishra, & Koehler,
2009). Mishra and Koehler (2006) propose integration of multiple aspects
of technology, pedagogy, and content knowledge (TPACK). This poster
presents preliminary analysis of data from a four-course sequence
(technology, curriculum, student teaching, and research) on the
preparation of preservice teachers in integrating technology. Data from
journals, curriculum, questionnaires, and sample work (projects, lesson
plans, portfolios) were content analysed (Neuendorf, 2002). The goal is
to examine the process of becoming technology integrators and the role
of a technology course, perceptions, teaching experiences, and TPACK in
that process.
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Alleviating Maths Anxiety through Mentoring in an Emotional Intelligence Framework
Timothy Perkins
Mathematics anxiety in pre-service primary
teachers can be described as a debilitating lack of confidence in
one's ability both to use mathematics in a functional way and to teach
mathematical content (Uusimaki & Nason, 2004). This problem is a
widespread and much researched phenomenon (Haylock, 2001; Trujillo &
Hadfield, 1999; Wilson, 2011). The use of mentoring to ameliorate maths
anxiety has also been explored, although to a lesser extent (Beswick,
Callingham, Ashman & McBain, 2011; Hudson & Hudson, 2007; Hudson
& Peard, 2006). The proposed study will incorporate elements of
Emotional Intelligence (Goleman, 1995; Salovey & Mayer, 1990) and
Communities of Practice (Lave & Wenger, 1991) to create a mentoring
system for pre-service teachers suffering from maths anxiety. Excellent
mathematics teachers who rate highly on an emotional intelligence scale
will mentor pre-service teachers in the hope of developing the
pre-service teachers' confidence to become enthusiastic and effective
mathematics educators.
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An Analysis of Students' Strategies for Area Measurement and its Curricular Implications
Jeenath Rahaman
The concept of area-measurement is particularly
challenging for students as it encompasses the two critical domains - geometry and numbers. Most students face difficulty in connecting the
visual, spatial and numerical aspects related to area- measurement. In
line with the objectives of most curriculum, the present study tries to
explore the connection between students' formal learning of
area-measurement and its applications in other contexts through task
based interviews. Analysis of results shows that students' greater
reliance on using formal procedures limits their use of own strategies.
There is a need for including contextual and visual experiences in the
curriculum.
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Classroom Goal Structure, Achievement Goals, and Achievement: A Multilevel Mediational Analysis of Longitudinal Data
Wenshu Luo & David Hogan
This longitudinal study examines the mediational
role of achievement goals between previous achievement, gender, and
classroom goal structure, on the one hand, and subsequent achievement,
on the other. Secondary students from 115 math classes in Singapore
participated in this study. Multilevel path analyses showed that at the
class level, mastery classroom goal structure predicted subsequent
performance through mastery approach goals, and classes with higher
previous achievement and with more girls had higher subsequent
performance through lower performance avoidance goals. At the student
level, previous achievement predicted mastery approach goals, which in
turn predicted subsequent achievement.
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Critical Reflection as an Important Pathway to Pre-service Teachers' Development (A Snapshot)
Kwee Gek Chua
Singapore has placed great emphasis on teacher
preparation and pre-service teachers' development. Such preparation
and development can be greatly enhanced through the mediation of both
pre-service training at the National Institute of Education and extended
classroom learning experiences in schools. Insights gleaned from the
pre-service teachers cognitive and affective contents of the weekly
reflection logs and perspectives of their experiential learning during
practicum and a retrospective analysis of the pre-service teachers' reflective thoughts on their cooperating teachers' pedagogical
practices, setting and charting their own goals and development will be
discussed.
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Developing an Intervention Program for Students at Risk Drawing on the Strengths of Successful Existing Programs
Bernadette Long
This presentation will outline a planned study of
a mathematics intervention program that draws on the successful
features of existing and previously reported programs. Currently
successful existing programs are being reviewed and the successful
characteristics identified. Based on this, a new program will be
designed. This communication will outline the proposed research approach
that aims not only to evaluate the components of the approach but also
to describe the data collection methods including cognitive and
affective outcomes of the intervention.
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Developing Computational Fluency in Multi-Digit Multiplication: A Learning Trajectory Approach
Kristen Tripet, Janette Bobis & Jenni Way
Learning trajectories illustrate a pathway of
learning in mathematical domains. Knowing how students develop
particular mathematical knowledge informs the construction of learning
trajectories, providing a link between conceptual understanding and task
selection (Simon & Tzur, 2004). Much of the research in multi-digit
multiplication has focused on strategies used by children to solve
problems, with limited research outlining successful pathways to
developing understanding and how these apply to the classroom setting
(Bobis, 2007; Fuson, 2003). This presentation focuses on articulating a
learning trajectory for multi- digit multiplication through an
examination of relevant research. This trajectory will be the basis for
further study and investigation through a teaching experiment with Year 5
students. It is anticipated that the study will demonstrate how tasks
can be used to effectively promote the learning process.
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Developing Statistical Literacy: Student Learning and Teacher Education
Hélia Oliveira, Rosa Tomás Ferreira, Ana Henriques, João Pedro da Ponte, Carolina Carvalho, Ana Paula Canavarro & Susana Colaco
Developing students' statistical literacy is a
challenging task for practicing teachers, requiring the development of
new perspectives and professional knowledge in statistics. This project
aims to study the development of students' statistical literacy from
elementary to secondary education and is centred on two main issues: the
characterization of key aspects of students' statistical literacy,
particularly the ability to conduct statistical investigations, and the
understanding of the development of statistical and didactical knowledge
to teach this subject. The project includes teaching and teacher
education experiments, using a mixed-method approach and stressing
collaborative work amongst teachers and teacher educators.
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Do not Call on Me: Mathematics Anxiety among Students with Learning Differences
Michelle L.W. Bower & Suriza van der Sandt
Anxiety can impact the teaching and learning of
mathematics at all levels of instruction; and anxiety can affect many
types of learners. Student with diagnosed learning differences are
perceived to be more anxious about mathematics than other students. This
survey was an investigation into some of these beliefs and feelings
towards mathematics by students with diagnosed learning differences.
Among the selected students the overall levels of anxiety were lower
than expected. Student anxiety levels were reduced and statistically
significantly after taking one mathematics course; however, these
students still prefer not to engage in further mathematics applications.
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Early Childhood Mathematics: The Case of More or Less
Mohan Chinnappan & Amy Chan
Young children possess informal knowledge of
mathematics that is broad, complex and sophisticated. They engage in
significant mathematical thinking and reasoning in many contexts. This
recognition has catalysed recent reforms on the need to bring a higher
level of focus on early childhood learning, in general, and early
childhood mathematics, in particular (Malaysian Government, 2012;
Australian Government, 2011). Early quantitative reasoning begins to
develop as early as the first 2 years of life. These reasoning
demonstrate robust sensitivity to numerical information in the
environments including counting, numerosity and systems for representing
and discriminating small and large sets.
Previous studies (Geary, 1994; Clements & Sarama, 2007) have shown
that the development of numeracy skills begin before children commence
their formal schooling experiences. Two concepts that are foundational
to their ability to perform arithmetic operations are children's
ability to discriminate between the concepts of more and less. In this
exploratory study we consider pre-schoolers' (3- to 4-Year-Olds)
understanding of these twin concepts. Results show that children tend to
have more difficulties with the concept of more than less. Implications
of the results are discussed for further investigations of studies of
numeracy in early childhood mathematical thinking and numeracy.
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Examining Opportunities and Constraints in the Use of Context Based
Experiences for Engaging Indigenous Australian Students in the Learning
of Numeracy
Kate Naughtin
This communication will describe proposed
research that examines a teaching approach aimed at improving numeracy
outcomes for Indigenous Australian students. This approach uses aspects
of local Indigenous Australian culture as a context for learning
numeracy. The research will explore the effectiveness of teaching
culture in conjunction with numeracy while examining the relationship of
culture to the dimensions within numeracy. This study will also explore
the engagement of students in such context based learning experiences
and quantify the performance of students participating in this style of
learning.
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Harnessing the Power of Cloud Computing for Mathematical Modelling in Two Different Schools
Bock Boon Lim, Mei Chuen Chen, Trevor Redmond & Joanne Sheehy
This paper describes how two schools: one form
Singapore and one from Australia, harnessed the power of the emerging
Cloud Computing technology to establish a cohesive social network
amongst teachers between the two countries as they co-developed
Mathematical Modelling lesson units. Both schools adopted the
research-based Teaching for Understanding (TfU) framework as a common
language and teaching philosophy for the teachers to develop and build
the units. This project has demonstrated how the schools have
synergistically combined new technology (Cloud Computing), innovative
pedagogy (TfU) and content knowledge (Math Modelling) to enrich
students' learning experiences and enhance their understanding of the
mathematical ideas and concepts. This model of collaboration exemplifies
how schools in different parts of the world can use new technologies to
teach the 21st Century skills to students.
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iMPaCT-Math: Programming as a Means to Motivate Exploration of Foundational Algebraic Concepts
Kien H. Lim, Eric Freudenthal, Art Duval & Amy Wagler
iMPaCT-Math is a project involving the
development and implementation of a set of learning modules for
high-school algebra students to make connections across multiple
representations: (a) statements in a program, (b) computational process;
(c) graphical output, and (d) underlying mathematical concepts. These
programming-related activities provide an experiential-visual context
for students to engage in mathematical thinking and reinforce
foundational concepts like Cartesian coordinates and slopes. Results of
pilot-testing of activities in the first three modules (coordinate
system, variables, and linear equations) will be shared and professional
development for algebra teachers on classroom implementation will be
discussed during our presentation.
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Investigating the Interrelationships Between Teachers' Pedagogical
Content Knowledge and Student Achievement Within Vocational High School
Context
Vesife Hatısaru
Students who attend vocational education are less
motivated, have reluctance towards learning (Sahin & Fındık,
2008), do not like academic subjects (Lewis, 2000), encounter problems
with mathematics (Green, 1998; Lewis, 2000; Scarpello, 2005), and
compared to other secondary students, they are usually less successful
in mathematics (Bottom & Korcheck, 1989; Berberoğlu & Kalender, 2005). The knowledge of teachers who teach in vocational high schools,
therefore, matters in raising student achievement (Bottoms &
Presson, 2000). The present study deals with teachers' pedagogical
content knowledge and its impact on student achievement.
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[email protected]: A Project around an On-line Problem Solving Mathematical Competition in Portugal
Susana Carreira, Hélia Jacinto, Jaime Silva, Juan Rodriguez,Nélia Amado, Nuno Amaral, Rosa Tomas Ferreira, Sandra Nobre, Isa Martins & Silva Reis
The [email protected] Project intends to study
mathematical problem solving in a context that goes beyond the
classroom. The research field involves inclusive web-based mathematical
problem solving competitions aimed at middle graders (children aged 10
to 14 years-old). In this poster we address two main strands of the
project: students’ creativity in mathematical problem solving, and the
impact of digital technologies in students' approaches when solving
problems and communicating results. We provide a brief theoretical
support and a short analysis of some empirical data. We also give a
summary of the research developments and data gathering for the several
questions addressed.
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Seeing is Believing: Building Mathematical Knowledge for Teaching Through Demonstration Lessons
Louise Hodgson
The focus of this presentation is to outline an
approach to research that aims to explore the potential of demonstration
lessons as a model for teacher learning. The intent of the lessons is
to allow teachers to observe the process of planning, teaching, and
assessment within the context of real time classrooms. The sessions for
teachers involve the preparation of lesson plans, demonstration
teaching, and subsequent interrogation. The data collection will include
interviews, observations and surveys and will seek to explore and
describe the relationship between demonstration lessons and teacher
learning.
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Teachers' Perceptions of Student Engagement and Disengagement in Mathematics
Karen Skilling, Janette Bobis, Andrew Martin, Judy Anderson & Jenni Way
Teachers' perceptions of their students',
including whether they perceive them to be engaged or not, influences
the teaching strategies they adopt, their responses to students and the
efforts they make in the classroom (Hadrè, Davis & Sullivan, 2008).
It is therefore important to explore the nature of those perceptions.
This study explores teachers' perceptions of Year 7 students' engagement and disengagement in mathematics. Thirty-one Year 7
mathematics teachers from ten high schools located in the Sydney
metropolitan region were interviewed as part of a larger project
investigating student motivation, engagement and achievement in
mathematics. Interviews reveal the sources from which teachers' ('accurate' and 'inaccurate') perceptions of student engagement
are based and the usefulness of conceptualising such perceptions as a spectrum' of engagement to disengagement.
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The Use of Open-Ended Tasks as an Instructional and Assessment Tool
Kum Fong Foo, Leng Low, Yen Ping Pang, Wai Leng Lye & Cherng Ginn Kenneth Lui
Open-ended mathematical tasks have the potential
to not only engage students in constructive thinking but also hels them
make connections to mathematical concepts they have learnt. A high
quality open-ended task does not necessarily imply that the students
will engage cognitively in higher order thinking to solve the task.
Teachers play a crucial role in mediating the learning process in the
implementation of such tasks. A guiding framework to characterise the
varied degree of "openness" of the mathematical tasks is developed
to ease teachers into the facilitator's role. Rubrics are designed to
provide feedback both to both the teachers and students for effective
task implementation.
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Transforming Children's Mathematical and Scientific Development: A Longitudinal Study
Joanne Mulligan, Lyn English, Michael Mitchelmore & Nathan Crevensten
A 3-year longitudinal study integrates a
pedagogical approach focused on patterns and structural relationships in
mathematics to science learning through novel experiences in data
modelling and problem solving. Students are engaged in an innovative
program, usually withdrawn in small groups and taught by the research
team in collaboration with the teacher on a weekly basis for a 2-year
period. The study tracks three cohorts of students, initially involved
in a related study1 when in Kindergarten, through to Grades 2, 3 and 4.
In addition, two new cohorts of mathematically able students are being
tracked from Kindergarten to Grade 2.
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Translation of Word Problems by Year 6 Lower Ability Students: An Action Research Project
Min Chern Lim & Kai Kow Joseph Yeo
Although there is general endorsement among
mathematics educators and researchers on the significance of
translations in mathematical comprehension, there is substantial
evidence that students struggle to accurately translate verbal, tabular,
graphical and algebraic representations of mathematical relations
(Gagatsis & Shiakalli, 2004; Galbraith & Haines, 2000; Porzio,
1999; Wollman, 1983). This action research set out to investigate the
effects of using translation on raising the understanding of word
problems involving fractions among Year 6 lower ability students. The "Fast Food Approach" (FFA) was designed by integrating elements from
Polya's four stages of problem solving (1957) and The Problem Wheel
(Lee, 2008) with the intent of providing a structure to enhance
students' ability to translate in order to better "understand the
(word) problem". The study employed a single- group pre-test and
post-test design involving an intact Year 6 class of lower ability
students from a primary school in Singapore. The findings indicated that
FFA may be used to enhance the process of problem solving, as well as
improve students' attitude towards and self-confidence in mathematics
and problem-solving abilities.
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Using Students' Algebraic Thinking to Support Teacher Learning
Shikha Takker
This paper reports a preliminary study aimed to
utilise the potential of students' thinking and learning to support
teacher learning. The paper begins with a review of research on algebra
teaching and learning with the objective of identifying and analysing
tasks that relate research on students' algebraic thinking with the
practice of teaching. It then discusses a task based on students'
algebraic thinking developed and tried with a cohort of middle school
teachers from Mumbai. Insights from the study and its implications for
continuous teacher professional development are discussed.
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Poster (abstract only) |
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Round Table (abstract only) |
Developing Self-Regulated Teacher Learners to Improve Student Outcomes in Mathematics
Janette Bobis, Jenni Way & Judy Anderson
Student disengagement in mathematics in the
middle years and the related issues of underachievement and lower
participation rates in higher levels of mathematics have been linked to
teachers'understanding of mathematical content and their pedagogy
(Ryan & Williams, 2007). Research has identified the on-going
learning of teachers as key not only to improving their own knowledge,
but also valued student outcomes (Timperley, Wilson, Barrar & Fung,
2007).
The round table will begin by outlining the theoretical underpinnings of
a professional learning program, Empowering Teachers of Mathematics
(ETM) and its two complementary foci: its impact on teachers (knowledge,
beliefs, practices and ability to self-direct their learning); and the
measurement of student outcomes (engagement and achievement). The
session will provide an opportunity for international colleagues to
discuss issues affecting the (a) sustainable growth of teacher
mathematical content and pedagogical content knowledge; (b) the
engagement of middle-years students in mathematics; and (c) how self-
directed learning in teachers can be supported in a program of
professional learning.
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Models and Modelling for the Future
Lyn D. English, Richard Lesh, Kit Ee Dawn Ng & Gloria Stillman
The terms, models and modelling, have been used
variously in the literature, including in reference to solving word
problems, conducting mathematical simulations, creating representations
of problem situations (e.g., constructing explanations of natural
phenomena), and creating internal, psychological representations while
solving a particular problem.
This proposed roundtable session will focus on the models and modelling
perspective first initiated by Richard Lesh. From this perspective,
models may be viewed as conceptual systems or tools comprising
operations, rules and relationships that can describe, explain,
construct, or modify an experience or a complex series of experiences.
Modelling involves the crossing of disciplinary boundaries, with an
emphasis on the structure of ideas, connected forms of knowledge, and
the adaptation of complex ideas to new contexts (English, in press;
Hamilton, Lesh, Lester, & Brilleslyper, 2008).
The roundtable will begin with a review of the models and modelling
perspective and will then be open to discussion on issues including (but
not confined to):
1. Models and modelling in different nations, including sharing and
collaboration;
2. The role of task context (including interdisciplinary themes) and
task design;
3. The nature of the mathematical ideas and processes embedded in
modelling
problems;
4. Transfer of learning (e.g., from model-eliciting activities to model
exploration and model adaptation activities);
5. Models and modelling with young children;
6. Across-grade sharing of modelling products (e.g., grades 2 and 7
students sharing
their solutions to a given modelling problem);
7. Towards the future: advancing models and modelling.
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Professional Conversations among Mathematics Educators
Rosemary Callingham, Kim Beswick, Helen Chick, Julie Clark, Merrilyn Goos, Barry Kissane, Pep Serow, & Steve Thornton
The development of survey questions to address
aspects of Pedagogical Content Knowledge (PCK) in mathematics for an
Australian Teaching and Learning Council project led to intense dialogue
and challenging discussion among the project team. Using the questions
developed as a prompt, similar opportunities were provided to
mathematics educators within the project team's participating
institutions. These sessions had very positive feedback. MERGA members
are invited to participate in a similar experience in this round table,
and to reflect upon this approach for useful professional learning.
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Students' Conceptions of Equality
Megan Anakin, Chris Linsell & Jeffrey Smith
Don't we know enough about students' conceptions of equality already? In this round table discussion, we will
present preliminary findings from three lines of inquiry that suggests
that students' conceptions of equality are more complicated than
previous theoretical frameworks indicate. This research stems from
recent studies in New Zealand that suggest primary and intermediate
students have difficulty solving missing number problems that involve
the concept of equality. Rather than viewing students' erroneous
responses as problematic, we are probing into how students express their
conceptions of equality. We are using diverse methods to analyse
students' written, verbal, and non-verbal responses to arithmetic
missing number problems collected from different assessment contexts.
Two lines of inquiry involve extant data analysis from samples of over
400 Year 4 (8 and 9 year old) and Year 8 (12 and 13 year old) students
that participated in the National Educational Monitoring Project in
2009. In these inquiries, one involves quantitative analyses of
student's written responses and the other involves quantitative and
qualitative analyses of students' oral responses that were video
recorded in one-on-one interviews with an adult assessor. The third line
of inquiry is a prospective classroom-based study that involves
microanalysis of video recorded interactions between pairs of Year 6 (10
and 11 year old) students as they work together to solve a series of
missing number problems. Because we are proposing a more complicated
theoretical framework of students' conceptions of equality, we seek
feedback, as well as critique, about the strengths and limitations of
our diverse methods of inquiry.
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Teachers' Mathematical Knowledge and Practice
Mohan Chinnappan
The day-to-day work of teachers of mathematics is
governed by a range of factors not least their knowledge of mathematics
that is relevant to their professional work. An emerging field of
research is theorising about understandings of mathematics that teachers
need to develop in order to support practices that will optimise
mathematical learning (Ball, 2000; Ball et al., 2001; Ma, 1999). The
outcome of this stream of research has significant implications for the
interpretation of teachers' classroom practices, teachers' professional standards, teacher education programs, quality professional
development programmes, and, ultimately for arguments about
professional strength of the community teachers of mathematics. This
Round Table Discussion session will provide a forum for researchers to
share their views and findings on the following issues. Colleagues are
also invited to suggest new lines of inquiry that has the potential to
add to the current debates about teachers' mathematical knowledge and
the teaching of mathematics.
_ Teacher's understanding of subject matter knowledge from a
pedagogical perspective;
_ Mathematical Knowledge for Teaching (Ball et al, 2008);
_ Relations between courses in mathematics and practice;
_ Teachers' subject matter knowledge and representational fluency
_ Teachers' subject matter knowledge and students learning outcomes
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Teaching Mathematics Respectfully: Preparing Culturally Responsive Mathematics Teachers
Robin Averill & Megan Clark
Culturally responsive teaching is widely seen to
promote equity of access to achievement. The literature indicates that
teacher respect is essential for culturally responsive teaching.
Teachers showing respect to students has been a recurring theme in
recent New Zealand studies; one student stating that the most important
thing to teach prospective mathematics teachers was "to respect the
kids". In this round table we present findings from a study into
the nature of respect in teachers" interactions in senior secondary
school mathematics classrooms. Our study drew from mathematics
students' and teachers' perspectives of teacher practice gathered
using teacher and student questionnaires and semi-structured interviews,
and videos of twelve mathematics lessons. Participants included six
Year 12 and 13 mathematics classes and their teachers across three
multi-ethnic city schools. Findings included that mathematics teachers
show respect to students through their pedagogical practices,
professionalism, disposition, and knowing their students well. Using
students' names and providing timely and perceptive individual
assistance with mathematical tasks are examples of respectful practices.
Some differences between teachers' and students' views emerged with
students placing greater emphasis than their teachers on
professionalism and the constructive treatment of student errors. The
perceived challenges to teachers demonstrating respect included factors
relating to student behavior, curriculum content, and the diversity of
students' mathematical abilities and ethnicities. This round table
forum will begin with a short presentation of findings to initiate
discussion regarding how our mathematics teacher education practice can
promote respectful teacher behaviours and how teacher respect can
contribute to culturally responsive mathematics teaching.
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