Title 
MERGA33  2010 Shaping the Future of Mathematics Education Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia held at John Curtin College of the Arts, Fremantle, 37 July 2010
Editors: Len Sparrow, Barry Kissane, Chris Hurst


Content 

Preface 
Preface
Len Sparrow, for the Conference Organising Committee

Using PrimarySchool Learning Environments to Teach Maths at University
David Butler


List of Reviewers 

Keynote Address 
Reform under attack  Forty Years of Working on Better Mathematics Education thrown on the Scrapheap? No Way!
Marja van den HeuvelPanhuizen

Structured Failing: Reshaping a Mathematical Future for Marginalised Learners
Robyn Jorgensen (Zevenbergen)

Technology, Research and Practice in Mathematics Education
Barry Kissane


Practical Implication Award 

Symposium 
Maths in the Kimberley Project: Evaluating the Pedagogical Model
Robyn Jorgensen (Zevenbergen) & Peter Grootenboer & Peter Sullivan & Richard Niesche

Playing with Mathematics: Play in Early Childhood as a Context for Mathematical Learning.
Janette Bobis & Eva deVries & Kate Highfield &
Robert P. Hunting & Shiree Lee & Bob Perry & Louise Thomas
& Elizabeth Warren

Problem Solving in the School Curriculum from a Design Perspective
Toh Tin Lam & Leong Yew Hoong & Jaguthsing Dindyal & Quek Khiok Seng


Research Paper 
Making Sense of Critical Mathematics Teaching
Annica Andersson

Perceived Professional Learning Needs of Numeracy Coaches
Leonie Anstey & Barbara Clarke

Students' Experiences of Mathematics During the Transition from Primary to Secondary School
Catherine Attard

Percentages: The Effect of Problem Structure, Number Complexity and Calculation Format
Wendy Baratta & Beth Price & Kaye Stacey & Vicki Steinle & Eugene Gvozdenko

Why do Disadvantaged Filipino Children Find Word Problems in English Difficult?
Debbie Bautista & Joanne Mulligan

Two Test Items to Explore High School Students' Beliefs of Sample Size when Sampling from Large Populations
Anthony Bill & Sally Henderson & John Penman

The Impact of a Developmental Framework in Number on Primary Teachers' Classroom Practice
Janette Bobis

Language Negotiation In a Multilingual Mathematics Classroom: An Analysis
Arindam Bose & Manojendu Choudhury

The "Number Proficiency Index": Establishing the Starting Point for Mathematical Instruction in High School
Phil Brockbank

Scratching Below the Surface: Mathematics through an Alternative Digital Lens?
Nigel Calder & Merilyn Taylor

Using Developmental Frameworks to Support Curriculum Outcomes
Rosemary Callingham & John Pegg

Students' Frames of Reference and Their Assessments of Interest for Statistical Literacy
Colin Carmichael

Aspects of Teachers' Knowledge for Helping Students Learn About Ratio
Helen Chick

Teachers' Extent of the Use of Particular Task Types in Mathematics and Choices Behind That Use
Doug Clarke & Anne Roche

Students as Decoders of Graphics in Mathematics
Carmel M. Diezmann & Tom Lowrie

Challenging Multiplicative Problems Can Elicit Sophisticated Strategies
Ann Downton

The Impact of Two Teachers' Use of Specific Scaffolding Practices on Lowattaining Upper Primary Students
Sarah Ferguson & Andrea McDonough

The Predominance of Procedural Knowledge in Fractions
Tricia Forrester & Mohan Chinnappan

Becoming More Numerate: The Journey of Tania
Linda Galligan

Bridging the Numeracy Gap for Students in Low SES Communities: The Power of a Whole School Approach
Ann Gervasoni & Linda Parish with Cait Upton, Teresa
Hadden, Kathie Turkenburg, Kate Bevan, Carole Livesey, Deirdre Thompson,
Melissa Croswell and Julie Southwell

Auditing the Numeracy Demands of the Middle Years Curriculum
Merrilyn Goos & Vince Geiger & Shelley Dole

The Terminology of Mathematics Assessment
Jane Greenlees

Mathematics Teachers: Negotiating Professional and Discipline Identities
Peter Grootenboer & Julie Ballantyne

A Network Analysis of Concept Maps of Triangle Concepts
Jin Haiyue & Wong Khoon Yoong

Impact of Context and Representation on Year 10 Students' Expression of Conceptions of Rate
Sandra Herbert

Year 11 Advanced Mathematics: Hearing from Students who Buck the Trend
Kai Fai Ho

'You might say you're 9 years old but you're actually B years old because you're always getting older': Facilitating Young Students' Understanding of Variables
Jodie Hunter

Coming to 'Know' Mathematics through 'Acting, Talking and Doing' Mathematics
Roberta Hunter

The Mathematical Needs of Urban Indigenous Primary Children: A Western Australian Snapshot
Chris Hurst & Len Sparrow

Student Attitude, Student Understanding and Mathematics Anxiety
Michelle Jennison & Kim Beswick

Dispersing Mathematics Curriculum Leadership in Remote Aboriginal Communities
Robyn Jorgensen (Zevenbergen) & Richard Niesche

Upper Primary School Students' Algebraic Thinking
Natcha Kamol & Yeap Ban Har

Learning Mathematical Concepts Through Authentic Learning
Koh Noi Keng & Low Hwee Kian

A Teacher Pair Approach to Adopting Effective Numeracy Teaching Practice
Janeen Lamb & Vince Geiger

Assessment for Learning Tasks and the Peer Assessment Process
Lorraine Lauf & Shelley Dole

I liked it till Pythagoras: The Public's Views of Mathematics
Gilah C. Leder & Helen J. Forgasz

Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)
David LeighLancaster & Magdalena Les & Michael Evans

Mathematics Attitudes and Achievement of Junior College Students in Singapore
Lim Siew Yee

A 'knowledge quartet' Used to Identify a SecondYear Preservice Teacher's Primary Mathematical Content Knowledge.
Sharyn Livy

Beyond the Curriculum: The Mathematical Beliefs of Preservice Primary Teachers in Hong Kong
Wing Yee Lo & Judy Anderson

Webbased Mathematics: Student Perspectives
Esther YookKin Loong

The Relationship between the Number Sense and Problem Solving Abilities of Year 7 Students
Jemmy Louange & Jack Bana

Teachers' Perceptions of Geometry Instruction and the Learning Environment in Years 910 ESL Classrooms
Rinna K. Ly & John A. Malone

Young Children's Measurement Knowledge: Understandings about Comparison at the Commencement of Schooling
Amy MacDonald

Developing a Framework for the Selection of Picture Books to Promote Early Mathematical Development
Jennifer Marston

Professional Standards and Professional Learning: A Position Paper
Karen McDaid

CoConstructing New Classroom Practices: Professional Development Based upon the Principles of Lesson Study
Sue McDonald

Teacher Change in Response to a Professional Learning Project
Andrea McDonough & Philip Clarkson & Anne Scott

Preservice Students' Responses to Being Tested on their Primary School Mathematical Knowledge
Tamsin Meaney & Troels Lange

Computational Estimation in the Primary School: A Single Case Study of One Teacher's Involvement in a Professional Learning Intervention
Paula Mildenhall & Mark Hackling & Paul Swan

Gap Thinking in Fraction Pair Comparisons is not Whole Number Thinking: Is This What Early Equivalence Thinking Sounds Like?
Annie Mitchell & Marj Horne

Connecting the Points: Cognitive Conflict and Decimal Magnitude
Bruce Moody

A Decade of MERGA Theses
Judith A. Mousley

Using VideoStimulated Recall as a Tool for Reflecting on the Teaching of Mathematics
Tracey Muir

Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in Kindergarten
Joanne T. Mulligan & Lyn D. English & Michael C. Mitchelmore & Greg Robertson

Partial Metacognitive Blindness in Collaborative Problem Solving
Kit Ee Dawn Ng

Changing our Perspective on Space: Place Mathematics as a Human Endeavour
Kay Owens

Experiences of Learning and Teaching Mathematics: Using Activity Theory to Understand Tensions in Practice
Shaileigh Page & Julie Clarke

Facilitating the Development of Proportional Reasoning through Teaching Ratio
Linda Parish

An Ethnographic Intervention using the Five Characteristics of Effective Teacher Professional Development
Sitti Maesuri Patahuddin

Exploring the Relationship between Mathematical Modelling and Classroom Discourse
Trevor Redmond & Joanne Sheehy & Raymond Brown

Assessing the Number Knowledge of Children in the First and Second Grade of an Indonesian School
Rumi Rumiati & Robert (Bob) Wright

Enactivism and Figural Apprehension in the Context of Pattern Generalisation
Duncan Samson

Mathematics Registers in Indigenous Languages: Experiences from South Africa
Marc Schafer

Using Concept Cartoons to Access Student Beliefs about Preferred Approaches to Mathematics Learning and Teaching
Matthew Sexton

How to Build Powerful Learning Trajectories for Relational Thinking in the Primary School Years
Max Stephens & Dian Armanto

Students' Opinions about Characteristics of Their Desired Mathematics Lessons
Peter Sullivan & Doug Clarke & Helen O'Shea

The Multifaceted Variable Approach: Selection of Method in Solving Simple Linear Equations
Salma Tahir & Michael Cavanagh

Interactive Whiteboards and all that Jazz: Analysing Classroom Activity with Interactive Technologies
Howard Tanner & Sonia Jones & Gary Beauchamp & Steve Kennewell

One on One Numeracy Intervention: A Pilot Project in Low SES Communities
Steve Thornton & Gina Galluzzo & Mary Quinane & Debbie Taylor

Critical Moments in Learning Mathematics: First Year Preservice Primary Teachers' Perspectives
Stephen Tobias & Penelope Serow & Martin Schmude

Now I'm teaching the children: Changing from Assessment of Learning to Assessment for Learning in Fiji
Kaye Treacy & Poniparte Tiko Fiji & Sarita Harish & Prabha Nairn

Student Centred Approaches: Teachers' Learning and Practice
Colleen Vale & Mary Weaven & Anne Davies & Neil Hooley

Utilising Year Three NAPLAN Results to Improve Queensland Teachers' Mathematical Pedagogical Content Knowledge
Eduarda van Klinken

Documenting the Learning of Teacher Communities Across Changes in their Membership
Jana Visnovska

The Researcher's Self in Research: Confronting Issues about Knowing and Understanding Others
Margaret Walshaw

Indigenous Children's Ability to Pattern as They Enter Kindergarten/Preprep Settings: An Exploratory Study
Elizabeth Warren & Jodie Miller

Biased Sampling and PCK: The Case of the Marijuana Problem
Jane M. Watson & Erica L. Nathan

Student Change Associated with Professional Learning in Mathematics
Jane Watson & Natalie Brown & Kim Beswick & Rosemary Callingham & Suzie Wright

Counting On in the Middle Years
Allan Leslie White

Modelling the Cooling of Coffee: Insights From a Preliminary Study in Indonesia
Wanty Widjaja

Abstracting by Constructing and Revising a 'Partially Correct Construct': A Case Study
Gaye Williams

Preservice Teachers Constructing Positive Mathematical Identities: Positing a Grounded Theory Approach
Sue Wilson

'I always feel more confident when I know where things are going': How do Preservice Teachers Engage with Mathematics Curriculum Documentation?
Sue Wilson & Jane McChesney

Algebraic Thinking: A Problem Solving Approach
Will Windsor

Equivalent Fractions: Developing a Pathway of Students' Acquisition of Knowledge and Understanding
Monica Wong

Three Primary School Students' Cognition about 3D Rotation in a Virtual Reality Learning Environment
Andy Yeh

Socioeconomic Background, Senior Secondary Mathematics, and Postsecondary Pathways
Eng Yeoh & David LeighLancaster

Two Decades of Mathematics Education Reform in New Zealand: What Impact on the Attitudes of Teacher Education Students?
Jenny YoungLoveridge

The influence of the mathematics class on middle school students' interest for statistical literacy.
Colin Carmichael

Walking the Talk: Translation of Mathematical Content Knowledge to Practice
BARBARA BUTTERFIELD & MOHAN CHINNAPPAN


Short Communication (abstract only) 
A Survey of Instructional Leaders in Primary Schools: Emerging Patterns in Numeracy Leadership
Joanna Higgins & Linda Bonne
One component of an ongoing New Zealand study
investigating instructional leadership in numeracy, an online survey,
was completed by 44 primary school leaders  numeracy lead teachers,
principals, deputy and assistant principals, and syndicate/team leaders.
Patterns identified in an analysis of the responses showed that
numeracy lead teachers often had a multiplicity of roles, and suggested
that numeracy lead teachers who were also a member of the management
team had greater influence than those who were not. Implications for the
future leadership of numeracy will be discussed.

Aboriginal Independent Community Schools Numeracy Strategy
Daniel Pinchas & Renae Small & Rebecca Youdale & Shirley Riley & Kaye Treacy
The Aboriginal Independent Community Schools
(AICS) Numeracy Strategy is a DEEWR funded action research project
providing support to independent Indigenous community schools in Western
Australia. Over the next two years, the Strategy will work towards
making significant improvements in Indigenous students' understanding
and skills in numeracy. The project uses a cycle of discovering what
students know, focusing on the mathematics they need to learn and
implementing effective pedagogy.
Consultants will make regular visits to the schools, working shoulder to
shoulder with teachers, Aboriginal Education Workers, and principals.
Professional development workshops will be run within schools and at
conferences, with resources being developed to support the
implementation of the Strategy. Progress will be monitored using
standardised assessment and classroom based assessment tasks.

An Alternative Pathway to University Mathematics
Nicholas Crouch
The University of Adelaide's Maths Learning
Service offers a bridging course as an alternative pathway to
university. This selfpaced course is for some students a form of
distance education. The course appears to be unique in Australia because
of the selfpaced nature, with students able to take as much or little
time as they require, and the fact that students are not graded but
rather only progress once a certain level of understanding is achieved.
This communication will discuss the experience of teaching in this mode
and the effectiveness of the individual feedback on learning.

Calculator Technologies and Females' Mathematics Learning: A Pilot Study
Janelle Hill
The relationship between females' attitudes to
calculator technology and their achievement and participation in
higherlevel secondary school mathematics was investigated in this small
pilot study. The sample comprised nine females who had recently
completed secondary schooling. Most believed that technologies such as
graphics and Computer Algebra System calculators were obstacles to
higherlevel mathematics learning and did not enable them to gain a
better understanding of mathematical concepts. Several indicated that
mathematics was not particularly useful or relevant for them except as a
vehicle to university entry. More research is needed to determine the
representativeness and significance of these findings.

Elementary Students' Understanding of Variable: The Role of Problem Type and Representation
J. Matt Switzer
Research has found marked differences in student
performance with various algebraic problems (e.g., word problems, word
equations, equations) (Koedinger & Nathan, 2004). In addition,
research has shown that students' understanding of variable is fragile
(Booth, 1984; Carraher, Schielmann, & Brizuela, 2001; Stacey,
1989). Often, the teacher/researcher's introduction of literal symbols
assumes that students make connections between their informal
symbolisations and formal conventional symbolisations (Kaput, 2008).
This crosssectional research project explores the influence of problem
type and variable representation for United States Grade 4 & 6
students as they transition from informal representations of variables
to formal conventional representations.

Lesson Study as Research and Professional Development for Practitioners
Jodie Hunter
Lesson study is a professional development
process whereupon teachers collectively and systematically examine their
own practice in order to improve their teaching (Fernandez &
Yoshida, 2004; Stigler & Hiebert, 1999). The focus of this report is
on how involvement in a lesson study cycle focused on primary
mathematics lessons supported teachers to develop reflective practice.
It will outline teacher perspectives of their experiences in the project
and examine how their reflective skills and investigation into their
classroom practices developed. Conclusions will be drawn of the factors
which facilitate or inhibit lesson study as a process of professional
development and research.

Preservice Primary Teachers' Ability to Communicate Mathematics Concepts Effectively
Chua Kwee Gek
Process, one of the important components to
attain the aim of the Singapore Mathematics curriculum, is often given
less emphasis as its mastery seem less tangible in an assessment
context. This paper describes a preliminary study to determine Singapore
preservice teachers' ability to articulate mathematics concepts
succinctly. The findings show that they were not able to communicate
their teaching ideas and concepts effectively. Effective mathematics
communication skills using accurate mathematics language and various
strategies were then integrated into their pedagogy module so as to
equip them better with the necessary repertoire of knowledge and skills
for effective mathematics teaching.

Preparing a New Generation of High School Mathematics Teachers
Joanne E. Goodell
In 2005, the National Academy of Sciences and
National Academy of Engineering together commissioned the report "Rising Above the Gathering Storm" (Committee on Prospering in the
Global Economy of the 21st Century, 2007). The report recommended the
UTeach teacher preparation program at the University of Texas at Austin
as one that should be scaled up across the nation to address the
declining population of high school mathematics teachers. Cleveland
State University is now one of 20 universities replicating UTeach, and
will accept first year students in August 2010. In this session, I will
outline the major differences between this program and traditional
programs, and discuss issues I have dealt with during the
preimplementation phase.

Primary Students' Theories of Intelligence, Mathematics SelfEfficacy and Achievement: Analysis of the Initial Data
Linda Bonne
In preparation for the collection of baseline
data for doctoral research, two assessment instruments  one for
students, the other for teachers  were trialled in 2009. At the start
of 2010, the final student questionnaire was completed by Year 3 to 6
students in seven schools to gauge their implicit theories of
intelligence and their mathematics selfefficacy. Data from a separate
assessment of the students'mathematics achievement were also
collected (n = 364). The students' teachers (n = 24) completed a
questionnaire to identify their theories of intelligence and
selfefficacy for teaching mathematics. Initial findings will be
presented.

Singaporean Senior Secondary Students' Ways of Using Graphics Calculators
Hazel Tan
This presentation provides some preliminary
findings from a large scale survey of 964 Singaporean Senior Secondary
mathematics students regarding the use of graphics calculators. Based on
Geiger's (2005) framework of four metaphors for technology use â€“
Master, Servant, Partner and Extension of Self â€“ an instrument was
developed (Tan, 2009). It was administered as part of a PhD study on
students' learning preferences and their ways of learning and using
graphics calculators. The findings are compared to those in the pilot
study presented at MERGA 32 (Tan, 2009). The relationship between
students' use of calculators and their mathematics self ratings are
discussed.

Teaching and Learning in an Interactive Multimedia ELearning Environment
Sharon London & Mike Mitchelmore & Michael Cavanagh &
This project investigated how teachers used the
HOTmaths learning system in laptop learning environments. It took place
in 8 Year 9 classes at three Catholic secondary metropolitan NSW
schools. Each school used laptops in a different configuration, and
selected teachers in two schools were provided with extensive
professional development. Data on the implementation were collected via
classroom observations, interviews with teachers, and pre and
posttesting using the ACER PATMaths test. The results indicated
significant improvements in student performance of the intervention
groups as compared with the nonintervention groups.

The Effectiveness of a Dynamic Professional Development Model Using an Online Mathematics Learning System
Sharon London & Joanne Mulligan & Michael Cavanagh & Matthew Bower
This study will evaluate the effectiveness of an
online professional development model using communication pathways
developed for a webbased mathematics learning system. Upper primary
teachers from Catholic and government schools in NSW and Victoria will
engage in a fourstage online professional development program employing
webconferencing software (Adobe Connect). Professional development
will focus on new pedagogies using technology, and promote collaborative
reflection and analysis of teaching and learning. Data sources will
include digital recordings of a representative sample of lessons,
transcripts of PD sessions, data generated by the online mathematics
learning system, online surveys completed by students and teachers, and
online interviews with teachers.

Values Operating in Effective Mathematics Lessons in Singapore: Reflections from Classroom Observations
Ho Siew Yin
This presentation reports on a study that
investigated the professional and pedagogical beliefs of effective
mathematics lessons that were covalued by the teacher and students.
This study contributed data to an international pilot study that
investigated how different interpretations of effectiveness incorporate
traditional, cultural or indigenous views of mathematics education. The
conceptualisation of this study was stimulated by previous research
findings which found that students' learning of mathematical ideas
appeared to be regulated by the teachers' valuing of professional and
pedagogical beliefs (Seah, 2007; Seah & Ho, 2009). Data from photos
of "effective learning moments" taken by students during the lesson
observations in one primary school will also be presented.


Poster (abstract only) 

Round Table (abstract only) 
K10 National Mathematics Curriculum Implementation: Implications for Research and Teacher Education
Merrilyn Goos & Robyn Jorgensen & Christelle Plummer & Glenys Reid & Peter Sullivan & Gaye Williams &
The session started will start a few minutes'
reflection from panel members about issues associated with the
implementation of the K10 National Curriculum. This will be followed by
input of ideas from participants. Gaye Williams will highlight aspects
of MERGA Feedback on the Draft K10 National Curriculum as they become
pertinent to the conversations arising. The purpose of the session is to
raise awareness of issues associated with National Curriculum
implementation, and invite contributions from participants about future
directions for research and teacher education in the light of this.

Magnifying Misalignment of Student Data Across a Range of Assessment Tools to Inform Future Learning Goals
Marie Hirst & Anuja Singh
The round table discussion will begin by
presenting the findings from a small study investigating possible
misalignment of student data from three different assessment tools. It
will also look at how any misalignments impact on making overall teacher
judgements about student achievement. The three tools used in this case
study were AsTTle (Assessment Tool for Teaching and Learning), GloSS
(Global Strategy Stage Assessment) and IKAN (Knowledge Assessment for
Numeracy) some of which are widely used across New Zealand schools.
With the introduction of National Standards in New Zealand, teachers
will become more accountable when making overall teacher judgements
(OTJ). An essential aspect of OTJ is that teachers effectively select,
use and analyse different assessment tools such as those mentioned
above. The small study focuses on helping teachers understand the
misalignments within the assessment tools thus helping teachers to use
data effectively in order to set clear learning goals.
In the Round Table we hope to stimulate discussion with Australian, New
Zealand and other international colleagues about:
· How do other countries address misalignments of various assessment
tools?
· Challenges when selecting appropriate assessment tools. · Feedback and advice on how to extend this small case study further
by formulating a research question. · How to best utilise overall teacher judgement with a range of
assessment tools?

Make it Count: An Evidence Base to support Numeracy, Mathematics and Indigenous Learners
Will Morony & Caty Morris
Make it count: Numeracy, mathematics and
Indigenous learners is a national, four year project that is developing
whole school, evidence based, sustainable practices to enhance
Indigenous studentsâ€™ learning. Community engagement is key to the
project's success and various communities of practice are being built
to support the work of the project. Eight clusters of schools across
Australia are working together to build their evidence base so teachers
will know whether they are doing things better or not; so they have
certainty around what they believe, and clarity about why things have
worked (or not). Contributing to this is the emerging role of the
clusters · Critical Friends' · mathematics and/or Indigenous
education academics · who are working in collaboration with the
schools in their particular focus. Adding to the evidence base is the
overall project evaluation which includes both quantitative and
qualitative longitudinal data about change. The project staff is also
identifying direct and indirect evidence. Our challenge is to provide an
evidence base of "stuff" that works. How do we marshall the
different layers of this "stuff" into the evidence base and, at the
same time, evolve the various roles of those contributing? Do we need
something more? The aim of this round table presentation is to open up
discussions about participants' experiences and knowledge that can
maximise the evidence base from a layered, schoolbased project like
this and to inform the work of the project with new thinking, learning
and knowledge.

Online Professional Development for Mathematics Teachers
Brooke Evans & Patricia McKenna & Don Gilmore & James Loats
Using collaborative problem solving to develop a "learning community" among mathematics teachers is an established
approach to professional development within the field (Lachance &
Confrey, 2003; Ryve, 2007). However, the question of whether an online
environment adequately facilitates the development of a learning
community among teacherlearners remains unanswered (Kim & Bonk,
2006). Any answer to that question will be partial and temporary for two
reasons. First, teachereducators can currently choose from an array of
webbased conferencing software of variable quality and capabilities.
Second, the rapid pace of innovation of educational technology creates
both opportunities and challenges for teacher educators: what some
technologies constrain today, other technologies enable tomorrow.
Despite these conditions, this roundtable discussion will focus on how
one online approach to professional development used by the faculty of
Metropolitan State College of Denver (Metro) both promoted and impeded
community building and collaborative problemsolving among a group of
elementary mathematics teachers in rural Colorado and how other schools
may be working through these issues. The growth of online mathematics
education and the need for teachers in rural schools to obtain
certification in mathematics suggest that mathematics teachereducators
can use Metro's study and the discussions at this roundtable to
structure and conduct online professional development courses in ways
that conform to the principles of reformbased instruction.

Targeted Learning: A Successful Approach
Linda Cheeseman & Bina Kachwalla & Marilyn Holmes
In 2007 â€œTargeted Learning Groups were set
up in Otago and Southland, New Zealand to support students with their
development of knowledge about numbers and to help students become
numerate flexible thinkers (Holmes & TaitMcCutcheon, 2009). Since
then many schools in New Zealand have trialled the intervention and
adapted, where appropriate, to suit the audience in their areas.
The purpose of this round table is to outline how the mathematical
intervention has been implemented in some of the low socioeconomic
schools in Auckland, New Zealand. The discussion will focus on the
impact of this intervention on student mathematical knowledge and
problem solving skills.
Data collated from sample schools have indicated that if there is a
delay in strategy learning, it is often due to a deficit in one or all
of the four knowledge domains: numeral identification, number sequence,
place value, and basic facts. In order to bridge the knowledge deficit
this intervention provides teachers, parents and teacher aides with a
structured and sequential framework of knowledge teaching.
The repetition of any learning enables students to master and retain new
knowledge (Nuthall 2002) and the consistent nature of the intervention
knowledge lessons provide a foundation for students to develop
confidence to problem solve.
This round table forum will afford an opportunity for international
colleagues to share their experiences of mathematical interventions that
have effectively raised student achievement. The discussion will be
open to support, critique and/or add to the existing intervention and to
seek further research ideas.

Teaching Mathematics for an Ethical Citizenry
Helen J Forgasz
At a recent professional development session
where I spoke, the principal, a former high school head of mathematics,
welcomed participants and reflected on the importance of mathematics for
children's futures. He spoke of the relevance of mathematics and its
power to model reality. The following exemplar was proposed: â€œImagine
you are the general of three army divisions. The first is winning
handsomely, the second is holding its ground, and the third is suffering
huge losses. You have sufficient support troops for only one division.
Where would you deploy them?â€ The answer, he said, was simple, and
based on mathematical modeling, â€œTo the winning division,
naturallyâ€. He provided a second example: â€œImagine you are charged
with placing landmines for maximum effect. How would you arrange
them?â€ Again, he claimed, mathematical modeling would enable this
decision to be easily made.
I left the session disturbed and perplexed. Both examples used to
epitomise the power of mathematics were in military contexts, and
enabling deaths (collateral damage) was not considered problematic. The
principal seemed insensitive to any conceivable wrong in what he had put
forward.
Contemporary mathematics curricula urge teachers to ensure that students
are exposed to â€œreal worldâ€ mathematics. I have no argument with
this. But, do teachers reflect on the implications of the contexts in
which the examples are set? Do they consider if there are covert
messages that reinforce stereotypes, or have moral, ethical, or
political implications? At this round table, these issues and the
research opportunities offered will be explored.
