Title 
Mathematics Education: Yesterday, Today and Tomorrow. Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia
V. Steinle, L. Ball & C. Bardini (Eds.)



Content 
Contents


Preface 
PREFACE


List of Reviewers 
MERGA 36 Reviewers


Keynote Address 
Bringing research on students' understanding into the classroom through formative assessment
Kaye Stacey

Problem finding, problem posing, problem solving: Mathematics education research  Yesterday, today, tomorrow
Gloria Stillman

The mathematical brain and numeracy
Brian Butterworth

Working at the intersection of research and practice: A perspective on the study and improvement of mathematics lessons
Yoshinori Shimizu


Practical Implication Award 
Changes in students' notation when fractions exceed onewhole
Peter Gould


Symposium 
Achievements and challenges encountered by classroom teachers involved in a research project: A reflection
Sue Allmond and Karen Huntly

Building relationships between stakeholders and researchers: People, persistence and passion
Rhonda Horne & Katie Makar

Coaching Preservice Teachers for Teaching Mathematics: The Views of Students
Robin Averill, Michael Drake & Roger Harvey

Creating Communities of Inquiry Through Lesson Study
Wanty Widjaja

Crosscountry Comparisons of Student Sense Making: The Development of a Mathematics Processing Framework
Tom Lowrie

FineTuning in a Design Experiment
Ho, Foo Him, Toh, Pee Choon & Toh, Tin Lam

Four Factors to Consider in Helping Low Achievers in Mathematics
Leong, Yew Hoong, Yap, Sook Fwe, & Tay, Eng Guan

Guided inquiry as a model for curricular resources in mathematics
Christine Debritz and Rhonda Horne

Helping low achievers develop a problem solving disposition
Quek, Khiok Seng, Yap, Sook Fwe, & Tong, Cherng Luen

Implementing the Japanese ProblemSolving Lesson Structure
Susie Groves

Inquirybased learning in mathematics: Designing collaborative research with schools
Katie Makar & Shelley Dole

Learning from the implementers in a design experiment
Toh, Tin Lam, Dindyal, Jaguthsing, & Tay, Eng Guan

Learning the Work of Ambitious Mathematics Teaching
Glenda Anthony and Roberta Hunter

Mathematical Tasks and Learning Goals: Examples from Japanese Lesson Study
Brian Doig

Noticing young children's mathematical strengths and agency
Sue Dockett & Wendy Goff

Positive feelings towards the learning of mathematics for low achievers
Tong, Cheurng Luen, Leong, Yew Hoong, & Quek, Khiok Seng,

Preschool and school educators noticing young children's mathematics
Bob Perry

Primary Teachers' Algebraic Thinking: Example from Lesson Study.
Colleen Vale

Researchers noticing young children's mathematics
Barbara Clarke

Scaffolding Cards: A Strategy for Facilitating Groups in Problem Solving
Toh, Pee Choon, Dindyal, Jaguthsing, & Ho, Foo Him

Students' Performance on a Symmetry Task
Siew Yin Ho & Tracy Logan

The Classic Word Problem: The Influence of Direct Teaching
Tracy Logan & Siew Yin Ho

The Odd Couple: The Australian NAPLAN and Singaporean PSLE
Jane Greenlees

Using Instructional Activities to Learn the Work of Ambitious Mathematics in Preservice Teacher Education Settings
Roberta Hunter, Jodie Hunter & Glenda Anthony

Visual stimuli that prompt young children to notice their mathematical thinking: Two researchers' experiences
Amy MacDonald & Jill Cheeseman


Research Paper 
Probing Students' Numerical Misconceptions in School Algebra
Zarina Akhtar & Vicki Steinle

Mapping Students' Spoken Conceptions of Equality
Megan Anakin


Integrating iPads into Primary Mathematics Pedagogies: An Exploration of Two Teachers' Experiences
Catherine Attard

Respectful and Responsive Pedagogies for Mathematics and Statistics
Robin Averill & Megan Clarke

Using a Modified Form of Lesson Study to Develop Students' Relational Thinking in Years 4, 5 & 6
Lei Bao & Max Stephens

Technology Prompts New Understandings: The Case of Equality
Caroline Bardini, Reinhard Oldenburg, Kaye Stacey & Robyn Pierce

Teacher Identity and Numeracy: Developing an Analytic Lens for Understanding Numeracy Teacher Identity
Anne Bennison & Merrilyn Goos

Translation of Data from a Reallife Context into Graphical Representations
Casandra Blagdanic & Mohan Chinnappan

Teaching Roles in TechnologyRich Teaching and Learning Environments (TRTLE's)
Jill Brown

Identification of Hierarchies of Student Learning about Percentages using Rasch Analysis
Joan Burfitt

Use of Learning Trajectories to Examine Preservice Teachers' Mathematics Knowledge for Teaching Area and Perimeter:
Barbara Butterfield, Tricia Forrester, Faye McCallum & Mohan Chinnappan

Gender Differences in Children's Mathematics Achievement: Perspectives from the Longitudinal Study of Australian Children
Colin Carmichael

Relationship Between Mathematics Anxiety and Attitude Towards Mathematics among Indian Students
Mini Chaman & Rosemary Callingham

Using Photographs and Diagrams to Test Young Children's Mass Thinking
Jill Cheeseman & Andrea McDonough

Teachers' Views of the Challenging Elements of a Task
Jill Cheeseman, Doug Clarke, Anne Roche & Karen Wilson

Posing Problems to Understand Children's Learning of Fractions
Lu Pien Cheng

Educating Boris: An Examination of Pedagogical Content Knowledge for Mathematics Teacher Educators
Helen Chick & Kim Beswick

Translating Between and Within Representations: Mathematics As Lived Experiences and Interactions
Philemon Chigeza

Productive Mathematical Noticing: What It Is and Why It Matters
Ban Heng Choy

Designing Tasks to Promote and Assess Mathematical Transfer in Primary School Children
Julie Clark, Shaileigh Page & Steve Thornton

Accelerating the Mathematics Learning of Low SocioEconomic Status Junior Secondary Students: An Early Report
Tom Cooper, David Nutchey & Edlyn Grant

Thoughts Behind the Actions: Exploring Preservice Teachers' Mathematical Content Knowledge
Leah Daniel & Josephine Balatti

Sticking With It or Doing It Quickly: What Performances Do We Encourage In Our Mathematics Learners?
Lisa Darragh

Preservice Secondary Mathematics Teachers' Reflections on Good and Bad Mathematics Teaching
Hem Dayal

When Practice Doesn't Lead to Retrieval: An Analysis of Children's Errors with Simple Addition
Celeste de Villiers & Sarah Hopkins

Making Connections Between Multiplication and Division
Ann Downton

How Heavy is my Rock? An Exploration of Students' Understanding of the Measurement of Weight
Michael Drake

How Do Adults Perceive, Analyse and Measure Slope?
Bruce Duncan & Helen Chick

Great Expectations: Teaching Mathematics in English to Indigenous Language Speaking Students
Cris EdmondsWathen

Beginning Inference in Fourth Grade: Exploring Variation in Measurement
Lyn English & Jane Watson

Scaffolding the Mathematics Learning of Lowattaining Students Through Whole Class Discussions
Sarah Ferguson

InquiryBased Argumentation in Primary Mathematics: Reflecting on Evidence
Jill FieldingWells

The Make it Count Project: NAPLAN Achievement Evaluation
Helen Forgasz, Gilah Leder & Jennifer Halliday

Students 'Holding' the Moment: Learning Mathematics in an Inquiry Mathematics Classroom
Kym Fry

Students and Real World Applications: Still a Challenging Mix
Peter Galbraith

Students Using Digital Technologies to Produce Screencasts That Support Learning in Mathematics
Linda Galligan & Carola Hobohm

Exploring the Demands and Opportunities for Numeracy in the Australian Curriculum: English
Vince Geiger, Merrilyn Goos, Shelley Dole, Helen Forgasz & Anne Bennison

Children's Mathematical Knowledge Prior to Starting School
Ann Gervasoni & Bob Perry

Longitudinal Progress of 6yearold Students Who Participated in an "Extending Mathematical Understanding" Mathematics Intervention Program
Ann Gervasoni, Linda Parish, Carole Livesey, Melissa Croswell, Kate Bevan, Teresa Hadden & Kathie Turkenburg

Measuring Mathematics Teacher Educators' Knowledge of Technology Integrated Teaching: Instrument Development
Seyum Tekeher Getenet & Kim Beswick

Principals' Views on the Importance of Numeracy as Children Start Primary School
Wendy Goff, Sue Dockett & Bob Perry

Mathematics Education as a Practice: A Theoretical Position
Peter Grootenboer & Christine EdwardsGroves

Apps for Mathematics Learning: A Review of 'Educational' Apps from the iTunes App Store
Kate Highfield & Kristy Goodwin

What Teachers See When Watching Others Teach
Louise Hodgson

Preservice Primary Teachers' Choice of Mathematical Examples: Formative Analysis of Lesson Plan Data
Ray Huntley

Mathematical Engagement Skills
Naomi Ingram

EarlyYears Swimming: Creating Opportunities for Adding Mathematical Capital to Under 5
Robyn Jorgensen

Relationships of OutofSchoolTime Mathematics Lessons to Mathematical Literacy in Singapore and Australia
Berinderjeet Kaur & Shaljan Areepattamannil

Maths Education: Is There An App For That?
Kevin Larkin

Transactional Distance Theory (TDT): An Approach to Enhancing Knowledge and Reducing Anxiety of PreService Teachers Studying a Mathematics Education Course Online
Kevin Larkin & Romina JamiesonProctor

Foundation Content Knowledge: What Do PreService Teachers Need To Know?
Chris Linsell & Megan Anakin

Preservice Teachers' Responses for Ratio and Proportion Items
Sharyn Livy & Sandra Herbert

From Curriculum to Workplace Requirements: Do They 'Match'?
Gregor Lomas & Kelvin Mills

Primary School Teachers' Perceptions of Mathematical Reasoning
Esther YookKin Loong, Colleen Vale, Leicha Bragg & Sandra Herbert

PreService Teachers' Pedagogical Content Knowledge: Implications for teaching
Margaret Marshman & Glorianne Porter

Does an Ability to Pattern Indicate That Our Thinking is Mathematical?
Catherine McCluskey, Michael Mitchelmore & Joanne Mulligan

When a Mathematics Support Pilot Program Fails Miserably: Looking For Answers
Keith McNaught

Student Preferences in the Design of Worked Solutions in Undergraduate Mathematics
David Mendiolea

Using Semiotic Resources to Build Images When Teaching the PartWhole Model of Fractions
Paula Mildenhall

Insight into Subtraction from LargeScale Assessment Data
Patricia Morley

Helpwithmaths.com: Students' Use of Online Mathematical Resources
Tracey Muir

Tracking Structural Development Through Data Modelling in Highly Able Grade 1 Students
Joanne Mulligan, Kerry Hodge, Michael Mitchelmore & Lyn English

Young Children Talking in Mathematics: What is the Point of That?
Carol Murphy

How PreService Teachers Integrate Knowledge of Students' Difficulties in Understanding the Concept of the Arithmetic Mean Into Their Pedagogy
Theodosia Prodromou


PreService Teachers' Understanding of Measures of Centre: When the Meaning Gets Lost?
Robyn Reaburn

Students' Understanding of Conditional Probability on Entering University
Robyn Reaburn

Using Tablet PCs For Active Learning: Learning From Others' Mistakes
Daphne Robson & Dave Kennedy

Entering the 'New Frontier' of Mathematics Assessment: Designing and Trialling the PVATO (online).
Angela Rogers

Overcoming Challenges of Being an InField Mathematics Teacher in Indigenous Secondary School Classrooms
Satwant Sandhu, Gillian Kidman & Tom Cooper

What Financial Dilemmas Reveal About Students' Social and Mathematical Understanding
Carly Sawatzki

iPads: Improving Numeracy Learning in the Early Years
Peta Spencer

Classroom Culture, Challenging Mathematical Tasks and Student Persistence
Peter Sullivan, Amanda Aulert, Alli Lehmann, Brendan Hislop, Owen Shepherd & Alan Stubbs

Teachers' Decisions About Mathematics Tasks When Planning
Peter Sullivan, David Clarke, Doug Clarke & Anne Roche

Students Understanding of Everyday English and Kimberley Kriol in Mathematics Classroom
Kaye Treacy

PCK and Average
Jane Watson & Rosemary Callingham

The Influence of Mathematical Beliefs on LowAchieving Adult Learners
Damon Whitten

High Performance, Confidence and Disinclination to Explore: A Case Study
Gaye Williams

Mature Age PreService Teachers' Mathematics Anxiety and Factors Impacting on University Retention
Sue Wilson

Mathematics Networks and Curriculum Concepts
Geoff Woolcott

PreService Teachers' Concept Image for Circle and Ellipse
Vince Wright

Constructing a Frame of Cube: Connecting 3D Shapes with Direction, Location and Movement
Andy Yeh

Teachers' Perspectives Regarding the Decline in Boys' Participation in PostCompulsory Rigorous Mathematics Subjects
Michael Easey


Short Communication (abstract only) 
"Am I a Maths Type of Person": Responses of Top Stream Year 8 Students
Gavin Little
As part of a longitudinal study on mathematics
identity formation and senior subject selection, responses from five top
streamed classes of Year 8 students, to the openended question "Am I
a maths type of person?"have been thematically analysed through
examination of key words. Consideration is given to the type of
mathematical identity these top streamed students are constructing and
how this is related to their intended mathematics pathway in Years 11
and 12.

"Teacher's Dilemma" In Using The Internet As A Mathematical Resource In Multilingual Settings
Sitti Maesuri Patahuddin
Indonesian government policy stipulating English
as the language of mathematics instruction has created dilemmas for
mathematics teachers since they are themselves not proficient in English
communication, or with the English mathematics register. The question
thus arose as to how mathematics online learning resources (in English)
could support the development of learners'"English Maths" proficiency. Would the language in which mathematical ideas are
communicated deny learners access to mathematics learning and
constrain teachers' capacity to develop rich mathematical talk? Both
questions will be discussed through critical incidents from video data
analysis of one teacher, teaching fractions in a secondary school.

Accelerated Learning in Mathematics
Fiona Fox & Komathi KolandaiMatchett
What is acceleration and how do we achieve it?
Effective classroom pedagogy occurs in classrooms where the teacher has
evidence of accelerating the progress of priority group learners.
Accelerated Learning in Mathematics (ALiM) is a national intervention
introduced in New Zealand in 2010 aimed at accelerating the learning of
those students below and wellbelow national expectations. It focuses on
the expertise within the school to evaluate the effectiveness of
current practices that support accelerated mathematics learning and to
closely monitor the impact of a 10 15 week intervention for a small
group of students. The attention is on supporting teachers and schools
to inquire into how an effective teacher provides a short and intensive
supplementary programme alongside their classroom programme to
accelerate progress. The key themes for teaching are accelerated
learning; pedagogical response to individual learning strengths and
needs; carefully designed mathematics task in response to identity,
language and culture; genuine engagement with parents and family;
collaborative inquiry; and high levels of teacher reflective practice.
In this round table presentation we will present findings from schools
who participated in this intervention in 2012. We will examine the main
focus for teaching these students and the impact this intervention had
on the rest of the school. We will look at how these schools engaged the
parent/family and what effect this had on the rate of acceleration.
Finally we will analyse to what extent the teachers were engaged into
inquiring into their own teaching practice and to what extent this
impacted on the learning of the students.

How Is "Teaching As Inquiry" Impacted By CrossGrouping In Mathematics?
Rosemary Golds
The New Zealand Curriculum advocates a reflective
strategy termed "teaching as inquiry", which encourages teachers to
plan for their learners, then continually reflect and respond to their
learners' needs (Ministry of Education, 2007). The February 2013 ERO
report, Mathematics in Years 4 to 8: Developing a Responsive Curriculum
(Education Review Office, 2013), has questioned the ability of some
schools to be able to provide a responsive mathematics curriculum,
particularly for students who are underachieving. One of the factors
which may be having a negative impact on teacher ability to foster "teaching as inquiry" is the practice of streaming which has become
quite common in recent years in New Zealand primary school mathematics
(Years 18). This paper looks at the background of streaming in
classrooms, and explores the connections that can be made with current
research in regards to effective classroom practice for all learners of
mathematics.

Impact on Identity and SelfEfficacy of Primary PreService Teachers: Experiences In the Mathematics Practicum Classroom
Karen McDaid
Developing quality teachers of mathematics is a
global concern and research into mathematics teaching, early career
primary teacher identity and teacher selfefficacy often focused on
teachers' beliefs and the relationship between beliefs and teaching
practice. While some studies have looked at early career teachers and
mathematics, none have focused solely on preservice teacher beliefs
about their teaching identity as teachers of primary mathematics as it
is constructed over the duration of the practicum. The proposed
longitudinal case study aims to track the impact on selfefficacy and
identity of preservice primary teachers as they participate in their
practice teaching.

Mentoring Undergraduate Primary Education Students In The
Mathematics Classroom ? The Development Of A New Model To Help Reduce
Mathematics Anxiety
Timothy Perkins
Increasing numbers of students enrolled in
primary preservice teacher Education degrees in Australia enter
university with insufficient mathematical content knowledge (Livy &
Vale, 2011) and low confidence levels about their ability to teach and
do the mathematics required for their intended role as classroom
teachers (Wilson, 2009). Teachers need to have the knowledge and
teaching skills to improve student outcomes in the mathematics field
(Beswick, 2012). This research project explores the development of a
mentoring model aimed at increasing the confidence and competence of
preservice primary teachers by matching them with well trained, highly
capable, confident and supportive primary mathematics teachers as
mentors.

Narrative Inquiry and the Formation of Mathematics Identity
Gavin Little
Mathematics identity, as a specific type of
identity, may be considered through a variety of paradigms. If identity
is defined as a narrative, analysis of the formation of mathematics
identity may be undertaken through narrative inquiry. A narrative
approach allows the researcher to consider both personal understandings
and meanings relating to mathematics identity, in the participants' spatial and temporal location. Narrative inquiry allows the
consideration of the â€œwhy behind participants' statements and
actions, within their particular context, over a period of time.

Student Engagement in Mathematics: Switching Students On to Mathematics
Janette Bobis, Jenni Way, Judy Anderson & Maryam Khosronejad
Research indicates that students are "switchingoff" mathematics from as early as Year 5. This
presentation reports on an intervention study aimed at improving middle
year students' engagement in mathematics. Twenty middle year teachers
and their students (N=339) from seven schools were involved in a
yearlong professional development program. Student motivation and
engagement levels in mathematics were assessed prior to and at the
completion of the intervention. Comparison of student data with those
from a similar cohort not involved in the intervention indicates that it
is possible to reduce, and even reverse, the downward shift in student
engagement levels in mathematics.

Students' Preferences When Learning How To Use Advanced Calculators To Solve Mathematics Problems
Hazel Tan
In this presentation findings from part of a PhD
study on students' learning preferences and their use of advanced
calculators such as graphics calculators and CAS calculators will be
shared. Students'responses to a question asking for their preferred
method of learning how to use the calculators to solve mathematics
problems will be shared. Amongst the different methods, the highest
percentage of students indicated that they most preferred to try out the
calculator steps while receiving instructions such as observing a
demonstration, listening to an explanation, or reading the instructions.
The implications of the findings will be discussed.

The Implementation of the Patterns and Early Algebra Preschool
(PEAP) Professional Development (PD) Program in Indigenous Communities
across New South Wales
Marina Papic, Kate Highfield, Joanne Mulligan, Judith McKayTempest, Deborah Garret, Monique Mandarakas, & Elizabeth Granite
This short communication outlines a threeyear
study with 15 Aboriginal Community Children's Services across New
South Wales and the Australian Capital Territory. The project engaged
more than 60 early childhood educators and approximately 240 children
aged 4 to 5 years. Following an Early Mathematical Patterning Assessment
(Papic, in press; Papic, Mulligan, & Mitchelmore, 2011) the project
implemented an early patterning framework that developed young
children's mathematical thinking and problemsolving skills. Follow up
interviews with kindergarten teachers, supported by data from Best Start
assessments (NSW Department of Education & Training, 2009),
provides evidence of the potential impact of this program on
children's mathematics learning. A key finding is the increased
confidence and pedagogical content knowledge of early childhood
educators.

Utilizing OpenSource Dynamic Mathematics Software in Teaching Geometry
Mailizar
This paper discusses the differences of
students' achievement between using opensource dynamic mathematics
software (GeoGebra) and Geometer's Sketchpad in learning geometry.
There were 43 participants taken from two secondary school classes in
Indonesia. The GeoGebra group consists of 21 students, and the
Geometer's Sketchpad group consists of 22 students. The findings show
that the use dynamic mathematics software can have positive effect on
students' achievement. However, findings do not show any significant
difference between the two groups.

What Does Numeracy Mean to Teachers of Subjects Other Than Mathematics?
Elizabeth Ferme
Although there has been considerable research
into the importance of teaching numeracy and being numerate, little is
reported on how numeracy is regarded in the secondary school setting by
nonmathematics teachers. This paper reports on a preliminary study into
the prominence of numeracy in Australian curriculum documentation and
teacher perceptions of numeracy in their daily practice. Results
indicate that secondary teachers have a narrow view of numeracy and have
limited access to professional learning in that area.

Worksheets vs. Practical Activities in Mathematics in the Primary Classroom
Bilinda Offen
As a teacher educator in primary mathematics, I
am intrigued by the number of "worksheets" used; this is the
antithesis of my philosophy of how primary mathematics should be
implemented. My proposed research is informed by a study by Marcia L.
Tate (2009). My study will compare the engagement of students, concept
retention and practical application of numeracy skills of children using
worksheets to those involved in practical hands on activities.
The children will be taught using a range of activities. Their learning
behaviours will be monitored, they will be interviewed regarding their
attitudes and formative assessment will be administered.


Poster (abstract only) 
Designing a detailed instructional framework: A teaching experiment in multiplication and division
David EllemorCollins
Within a larger design research project, we
developed an instructional framework for multiplication and division, to
be refined through a teaching experiment with lowattaining primary
students. We describe the instruction at multiple scales, from the broad
organization into domains and phases, through the sequencing of small
topics, to the details of specific instructional activities. We also map
the multiple dimensions of mathematisation involved: progressions
toward larger numbers, more abstract settings, more formal notations,
more sophisticated strategies, and so on. The framework contributes to
research on arithmetic instruction; and also to our developing notions
of frameworks, learning trajectories, and instructional design.

Effects of using different types of display and rules on
preschoolers patterning recognition in Malaysia: A preliminary study
Sharifah Norul Akmar Syed Zamri & Nor Adlina Fadil
The aim of this preliminary study is to explore
the effects of using different types of display and pattern rules on
achievement in pattern recognition among preschoolers in Malaysia. A
total of one hundred and fifty six preschoolers were involved in this
study. The instrument used was adapted from Gadzichowski (2012). It
contains 25 patterns which were divided into five different groups based
on display; colour, shape, object, letter and number. Each group
comprised five different patterns with rules of increasing difficulty.
Each child was interviewed individually. A correct answer was given 1,
otherwise zero. Descriptive statistics and a two factor ANOVA for
correlated measures were conducted. Results show that the overall
achievement of the children was rather low. Children find certain rules
easier than others. The different displays had no significant impact on
the achievement of pattern recognition amongst these children.

Exploring secondary school mathematics teachers' understanding of statistical graphs
Ajeevsing Bholoa & Leena Ramkalawon
One of the most basic tasks in statistics is to
represent data graphically and this suggests that teachers need to
possess graphical competence. We explore the statistical graph
comprehension of one preservice and one inservice secondary school
mathematics teachers through a series of video recorded interviews.
Initially, both teachers claimed strong selfefficacy towards teaching
statistical graphs conceptually. However, thinking processes deployed by
them to selected statistical tasks revealed procedural knowledge rather
than the claimed conceptual knowledge. These consequences suggest that
the focus should be on developing the necessary competencies of teachers
to work with statistical graphs effectively.

Investigating the effect of the secondorder use of context on Mathematics literacy tasks
Felipe AlmunaSalgado & Caroline Bardini
The incorporation of contextualised tasks has
been highly recommended by reform documents and curricula. Nevertheless,
the role that task context plays in assessments is an unsolved matter
because there are arguments relate to whether it makes a task easier or
harder for students. This study represents an attempt to scrutinise to
what extent the nature of demand of the secondorder use of context may
affect students' performance on literacy tasks. It is anticipated that
this study can provide a deeper understanding of how task context
impacts students' performance, thereby contributing to the improvement
of contextualised assessments among teachers, policy makers, and
assessment writers.

Patternbased learning in Linear Algebra
Rosemarie Mohais
In the traditional Mathematics classroom, usually
a small fraction of students are able to form or recognise patterns
which are core to solving problems, however, many other students never
get as far. Patternbased learning is a new developing strategy that
aims to promote effective teaching/learning of Mathematics by enabling
all students to recognise patterns. The technique involves presentation
of the solutions to standard wellknown problems through software. Once
the student has gained experience in solving multiple problems using a
clear pattern of solution, he/she can then independently apply the
technique. In this poster, Patternbased learning is applied to Linear
Algebra.

Testing a Framework of Cognitive Ability and Student's Thinking Process in Geometric Argumentation
TsuNan Lee & Caroline Bardini
This study aims to analyse student's thinking
process in geometric argumentation from geometric examples and
counterexamples between Grade 3, 5 and 7 students in Victoria,
Australia and Taiwan. There are two experiments in this study. The first
will test and compare cognitive frameworks of geometric argumentation.
The second will analyse student's thinking process though geometric
examples. It is anticipated that this study can provide a better
understanding of thinking process in geometric activities and assist
students enhance their abilities in geometry.


Round Table (abstract only) 
Are We Bored Yet?: Raising Attainment And Maintaining Interest
Kim Beswick & Rhonda Faragher
The Australian Curriculum: Mathematics
(Australian Curriculum, Assessment and Reporting Authority, 2012), with
its specification of content for year levels, represents a break from
stage based curricula which have become the norm in Australian
educational jurisdictions in recent decades. It thus provides an
opportunity to rethink the appropriateness of developmental approaches
to mathematics teaching and the concept of readiness that underpins the
widely accepted tenet of teaching from where students are at (Anderson,
2010). Such an approach has the risk of students who fall behind their
peers remaining behind even when they make progress (Capraro, Young,
Lewis, Yetkiner, & Woods, 2009). This is exacerbated in mathematics
because of a prevailing belief that mathematics, to a greater extent
than other school subjects, is inherently hierarchical and hence must be
taught in a linear fashion that precludes access to advanced content
(e.g., algebra) until more basic topics (e.g., arithmetic) have been
mastered. A year level based mathematics curriculum has the potential to
contribute to solving at least two major problems that currently
characterise mathematics learning particularly in the middle and
secondary years of schooling. These are 1) persistent gaps in attainment
between various disadvantaged groups and a majority of their year level
peers, and 2) impoverished curriculum offerings for low attaining
students who struggle to master 'basic' content.
This Roundtable will provide a forum for discussion of these
propositions and the opportunity afforded by the implementation of the
year level based Australian Curriculum: Mathematics. Stimulus in the
form of evidence that challenges the hierarchical and linear nature of
mathematics learning will presented and ways that these ideas might
contribute to closing attainment gaps discussed.

Assessment Standards In Undergraduate Mathematics
Carmel Coady, Deborah King & Cristina Varsavsky
This roundtable will report and seek
participants' feedback on progress towards the project Developing a
shared understanding of assessment criteria and standards for
undergraduate mathematics, funded by the Office of Learning and
Teaching. The project seeks to engage the higher education mathematics
community in a conversation around assessment standards which builds
upon the Learning and Teaching Academic Standards project outcomes for
the sciences (Yates, Jones & Kelder, 2011), and their
contextualisation within the mathematics discipline. It aims to
influence assessment practices in mathematics departments, to move away
from idiosyncratic marking and grading approaches that favour procedural
mastery towards practices that measure the quality of all aspects of
student work against external anchors, ensuring comparability of
standards within and across mathematics departments. The project will
result in a reference framework and toolkit to support tertiary
educators in the development of quality assessment standards and
criteria. The project approach incorporates the four essential elements
that, according to Sadler (2009), are required to convey and apply
achievement standards: (i) exemplars of different levels of achievement
invoking the criteria relevant to the judgment made, each of them with
an (ii) explanation of how the judgment was made; a (iii) conversation
about the exemplars and their corresponding judgments to establish a
common vocabulary; and (iv) the sharing of what has been tacit
knowledge within the discipline community.

National Testing: Is it valid
Fiona McDiarmid & Deb Gibbs
The recent publication of the Trends in
International Mathematics and Science Study (TIMSS) 2011, has raised
much debate in the public and political arena in New Zealand. Analysis
of the data indicates that New Zealand students performed less well than
most developed countries, and performance of ten year olds has declined
since 2001. The question being asked is, "Why are New Zealand's
ten year olds not performing as well as those in other developed
countries?" In 2010, New Zealand introduced National Standards in
mathematics, reading and writing. The mathematics standards rely on
teachers making judgments about a student's overall learning from a
wide range of relevant evidence. Other countries such as Australia,
England and the United States of America have introduced national
testing. The notion that New Zealand students aren't practised in
taking tests in this manner has been offered as an explanation for the
decline. How does a student's prior testtaking skills and experience
impact on results in such a high stakes activity? Do international tests
like TIMSS provide an accurate measurement of a student's
mathematical understanding and ability to solve complex problems?
Should teachers be investing some time in practising the techniques for
tests of this type?
This round table forum presents a smallscale study investigating the
impact of practiced skills involved in test taking in relation to
mathematics standard data. Discussion will focus on high stakes testing
versus overall teacher judgments in assessing mathematical competence.

Students' Transition From Number To Algebra
Christina Lee & Christine Ormond
In the 21st century algebra continues to be seen
as a 'gatekeeper course' for mathematics (Rand Mathematics Study
Panel, 2003). Many future career opportunities are lost to students who
do not have a good understanding of algebra at some level. The
Australian Curriculum, in its strand Number and algebra, introduces
formal algebra to students at an earlier stage than has been the case in
most Australian states in the past. In this round table presentation we
will firstly examine some aspects of what the curriculum says about
early algebraic ideas and reasoning. We will then examine three lesson
plans designed to introduce students to foundational algebraic concepts,
also discussing some current doctoral research. This research asks:
What strategies do teachers use when teaching algebra in the transition
years, and how do these choices reflect their beliefs about mathematics
teaching and learning? Participants will have the opportunity to discuss
the results of some current research on teachers'beliefs and
practices in this area of teaching. They will also review some research
findings in current literature, and what this says about the teaching
and learning of early algebraic concepts.

Teacher Judgements in Mathematics
Christine Hardie
National Standards, introduced into New Zealand
schools in 2010, require teachers in years one to eight to make overall
teacher judgments in mathematics. This new assessment policy asks
teachers to use the standards and exemplars to make defensible and
dependable holistic judgments about whether a student is above, at,
below or well below their year standard. The centrality, complexity and
nature of teacher judgment practice in mathematics in such a policy
context need to be understood. My study drew from principals' and
teachers' perspectives about how teachers approach and make overall
teacher judgments in mathematics and was gathered using semistructured
interviews and from document analysis. Participants included four
principals and seven teachers of students in years three to six. A range
of approaches to judgment making emerged from exploring the beliefs,
understandings and judgment practices teachers adopted. Teachers
utilised both explicit and tacit knowledge in the decision making
process and valued their relationship with and knowledge of their
students, giving attention to features other than those specified in the
mathematics standards. This round table forum will begin with a short
presentation of findings to initiate discussion regarding influences
that could be considered to ensure teacher judgments in mathematics are
dependable and whether exemplars and standards are sufficient to inform
professional judgments in mathematics.
