Title |
Identities, Cultures and Learning Spaces
Editors: Peter Grootenboer, Robyn Zevenbergen and Mohan Chinnappan
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Content |
Table of Contents
MERGA 2006 Conference Proceedings
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Preface |
Preface
Stephen Thornton, Peter Grootenboer, Mohan Chinnappan and Robyn Zevenbergen
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Implications of Preservice Teachers Intentions to Use Particular Learning Tasks
Anne Scott
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List of Reviewers |
Judges and Reviewers for MERGA 29
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Keynote Address |
Creating Learning Spaces
Merrilyn Goos
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New Directions for Research on Mathematical Problem Solving
Richard Lesh
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Practical Implication Award |
To heal and enthuse: Developmental bibliotherapy and pre-service primary teachers' reflections on learning and teaching mathematics
Sue Wilson and Steve Thornton
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Symposium |
Becoming a teacher of mathematics: Wenger's social theory of learning perspective
Tracey Smith
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Bringing feminist poststructuralism to bear on [mathematics] teacher education
Will Letts
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Researching Identity in Mathematics Education: The Lay of the Land
Peter Grootenboer, Tracey Smith and Tom Lowrie
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Teacher Identity from a Bourdieuian Perspective
Robyn Zevenbergen
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Research Paper |
Game Playing to Develop Mental Computation: A Case Study
Paula Asplin, Sandra Frid and Len Sparrow
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Grade12 Mathematics Teachers' Views on Curriculum Reform in New South Wales
Paul Ayres and John McCormick
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Pedagogical Content Knowledge for Teaching Primary Mathematics: A Case Study of Two Teachers
Monica Baker and Helen Chick
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Teachers' Confidence and Beliefs and their Students' Attitudes to Mathematics
Kim Beswick, Jane Watson and Natalie Brown
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Investigating Parental Roles of Mathematically Gifted Students
Brenda Bicknell
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Authentic Learning in a Year 8 Classroom
Kathy Blum
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Reform-Oriented Teaching Practices and the Influence of School Context
Janette Bobis and Judy Anderson
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Transforming Practice: Using Collective Argumentation to bring about Teacher Change in a Year 7 Mathematics Classroom
Raymond Brown and Peter Renshaw
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Identifying At-Risk Students: Is it Possible in a Tertiary Preparation Course for Adults'
Colin Carmichael, Peter Dunn and Janet Taylor
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Mathematics Teachers and Working Mathematically: Responses to Curriculum Change
Michael Cavanagh
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Examining the Changed Role of Numeracy Coordinators
Jill Cheeseman and Doug Clarke
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The Numeracy Journey: How Long Does it Take to get on Board?
Linda Cheeseman
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Probing Teachers' Pedagogical Content Knowledge: Lessons from the Case of the Subtraction Algorithm
Helen L. Chick, Thuy Pham and Monica K. Baker
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Historical Perspectives on Mathematical Elegance: To What Extent is Mathematical Beauty in the Eye of the Beholder?
Ken Clements and Nerida Ellerton
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Many Dimensions: the Complex Picture of Student Encounters with a Computer Algebra System
Mary Coupland and Kate Crawford
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The Leaving Certificate in New South Wales from 1939 to 1962
Stephen Curtis
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Primary Students' Knowledge of and Errors on Number Lines
Carmel M. Diezmann and Tom Lowrie
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The Singaporean Mathematics Curriculum: Connections to TIMSS
Jaguthsing Dindyal
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Organisational Structure for Mathematical Modelling
Katherine Doyle
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Introducing Young Children to Complex Systems through Modelling
Lyn English
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A Model of Students' Statistical Thinking and Reasoning about Graphs in an ICT Environment
Noleine Fitzallen
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Australian year 12 "Intermediate" level mathematics enrolments 2000-2004: Trends and patterns
Helen J. Forgasz
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A Justification for Mathematical Modelling Experiences in the Preparatory Classroom
Jillian Fox
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Real World Problems: Developing Principles of Design
Peter Galbraith
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Identifying Key Transition Activities for Enhanced Engagement in Mathematical Modelling
Peter Galbraith, Gloria Stillman and Jill Brown
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Standing on the Outside: A Tale of How Technology Can Engage Those Working on the Margins of a Community of Inquiry
Vince Geiger
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Living in the Gap: A Tale of Two Different Types of Researchers
Vince Geiger and Merrilyn Goos
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One-Third is Three-Quarters of One-Half
Peter Gould, Lynne Outhred and Michael Mitchelmore
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Mathematics Educators: Identity, Beliefs, Roles and Ethical Dilemmas
Peter Grootenboer
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The Role of Abstraction in Learning about Rates of Change
Ibrahim Hassan and Michael Mitchelmore
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Maori Preservice Primary Teachers' Responses to Mathematics Investigations
Ngarewa Hawera
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Issues in Teaching Mathematics to Aboriginal Students
Peter Howard and Bob Perry
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Students in a Mathematical Community of Inquiry: What do They Think?
Jodie Hunter
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Structuring the Talk Towards Mathematical Inquiry
Roberta Hunter
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The Development of a Community of Practice and its Connection with Mentoring in Low Socio-Economic Secondary Schools in New Zealand
Barbara Kensington-Miller
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What to Leave Out When Preservice Mathematics Education goes from Four Years to One: A Poststructural Account
Mary Klein
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Catering for Individual Differences: Lessons Learnt from the Australian Mathematics Competition
Gilah C. Leder
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Departing from the Traditional Long Division Algorithm: An Experimental Study
Issic Leung, Regina Wong and Wai-sum Pang
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In the Hands of the Learner: The Impact of Self-Assessment on Teacher Education
Sandi Tait-McCutcheon and Brenda Sherley
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Emerging Issues in the Investigation of the Construct of Partitive Quotient
Lucas McGee, Lisa Kervin and Mohan Chinnappan
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What does Effective Teaching for Numeracy Look Like? The Design of an Observation Schedule
Tracey Muir
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Improving Early Numeracy Through a Pattern and Structure Mathematics Awareness Program (PASMAP)
Joanne Mulligan, Marina Papic, Anne Prescott and Mike Mitchelmore
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Building Powerful Understanding by Connecting Informal and Formal Knowledge
Trish O'Toole
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'Is that right?': Asking questions and appealing for help in mathematics
Angela Page
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Using the Internet in Teaching Mathematics in Primary School
Sitti Maesuri Patahuddin and Shelley Dole
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Linking Powerful Mathematical Ideas and Developmental Learning Outcomes in Early Childhood Mathematics
Bob Perry, Sue Dockett, Elspeth Harley and Nicole Hentschke
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The Notion of Carried-Number, between the History of Calculating Instruments and Arithmetic
Caroline Poisard
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An Investigation of Pre-service Secondary Mathematics Teachers? Beliefs as They Begin Their Teacher Training
Anne Prescott and Michael Cavanagh
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Promoting Change in Teacher Practices: Investigating Factors which Contribute to Sustainability
Ruth Pritchard and Fiona McDiarmid
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The VideoPaper: Issues in Implementation of a Multimedia Tool for Professional Self-Dialogue and Communication in Mathematics Education
Robin Rider and Robert Hunting
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Mathematical teacher professional development incorporating an external critical friend
Pauline Rogers
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Unpacking the Rules of Class Discussion: Young Children Learning Mathematics within a Community of Inquiry
Abigail Sawyer
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Self-Study Through Narrative Inquiry: Fostering Identity in Mathematics Teacher Education
Tracey Smith
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Describing and Exploring the Power of Relational Thinking
Max Stephens
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Student Thinking about Eigenvalues and Eigenvectors: Formal, Symbolic and Embodied Notions
Sepideh Stewart and Michael O. J. Thomas
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Developing Guidelines for Teachers Helping Students Experiencing Difficulty in Learning Mathematics
Peter Sullivan, Judy Mousley and Robyn Zevenbergen
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Moving into Third Space: High School Students' Funds of Knowledge in the Mathematics Classroom
Steve Thornton
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Equity and Technology: A Case Study
Colleen Vale
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Scaffolding Numeracy: Pre-service Teachers' Perspective
Irina Verenikina and Mohan Chinnappan
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Classroom Arrangements That Benefit Students
Margaret Walshaw and Glenda Anthony
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Supporting Learning in Early Algebra: A Model of Professional Learning
Elizabeth Warren
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Teacher Professional Development in Patterns and Algebra: Being Sensitive to a Teacher's Zone of Proximal Development
Elizabeth Warren, Tom Cooper and Janeen Lamb
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Teachers' Knowledge of their Students as Learners and How to Intervene
Jane Watson, Kim Beswick and Natalie Brown
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Spreadsheets in Year 5 Chance and Data: A Professional Development Experience
Anne Williams
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Student-Engineered 'Space to Think'
Gaye Williams
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Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model
Asmamaw Yimer and Nerida F. Ellerton
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Students' Perspectives on the Nature of Mathematics
Jenny Young-Loveridge, Merilyn Taylor, Sashi Sharma and Ngarewa Hawera
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Using ICTs to Support Numeracy Learning Across Diverse Settings
Robyn Zevenbergen and Steve Lerman
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Short Communication (abstract only) |
Breaking the Cycle: Maths Anxiety and Pre-service Primary Student Teachers
Gillian Frankcom
This paper describes part of a study which
involved 29 third year pre-service student teachers answering Maths
Anxiety and Maths Self-efficacy questionnaires and questions regarding
previous and current mathematical experiences. Results indicate that
previous depth of mathematics learning is not a factor in the level of
Maths Anxiety and neither is the level of success in current mathematics
teacher education courses, and that Maths Anxiety is highly correlated
with Maths Self-efficacy.
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Developing Identity as a Mathematical Thinker
Kay Owens
The argument in this paper is that identity as a
mathematical thinker develops through self-directed learning within a
supportive community of practice. This paper discusses how identity as a
mathematical problem solver and investigator develops through
selfregulation. This development is illustrated by considering students
undertaking a mathematics and technology subject in a primary teacher
education degree. It shows how students set goals, plan, organise,
self-evaluate, record keep and structure their learning environment to
achieve self-regulation. The role of the tutorial group and technology
is also important in establishing their identity as a mathematical
problem solver and investigator.
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Engagement of Boys in Middle School Mathematics
Beth Southwell and Catherine Attard
Following a concern for the engagement of boys in
a NSW Year 6 classroom, action research was undertaken to explore the
effect of the use of computer technology and the change in role of the
teacher from a giver of knowledge to a facilitator, on the motivation
and engagement of the boys in the class. Data were obtained from a
number of sources, including a Motivation Scale, focus group
discussions, observations, student reflective logs and a teacher diary.
Initial results indicated that while boys responded enthusiastically to
the challenge of manipulating data using the Tinkerplots software and
developing their own questions and research topics, there was no
indication that they preferred to use technology.
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Frameworks: Climbing Aids or Entrapments?
Vince Wright and Jenny Young-Loveridge
This paper reported the influence of the Numeracy
Development Projects (NDP) in revision of the number strand of the New
Zealand mathematics curriculum. It documented how four types of teaching
and learning research frameworks were synthesised to provide evidence
for validity of the number framework and associated pedagogies.
Examination of students' responses across number domains showed
consistency and suggested a general growth path. Strategy stage norms to
set expected levels of achievement were described and challenges posed
for mathematics teaching and learning.
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If You Don't Listen to the Teacher, You Won?t Know What to Do
Pamela Perger
Everyone has beliefs about how learning should
take place and what the best practices are to enable this to happen.
Although it is believed that students' beliefs about 'best
practice' will mirror those of their teachers, and change as they change
teachers (Kershner & Pointon, 2000; Kloosterman, Raymond, &
Emenaker, 1996) the importance of listening to the 'students voice' is
becoming recognised (McCullum, Hargreaves & Gipp, 2000). This paper
reports on one aspect of a larger study that explored Pasifika student
achievement in mathematics at Year 7. What is it that these students
consider 'best practice' in learning mathematics? Do their beliefs truly
mirror those of their teacher?
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Inaccurate Mental Computation: Identifying Flawed Thinking
Ann M. Heirdsfield and Janeen T. Lamb
This paper reports on a study of five, Year 2
students' strategy choice, flexibility and accuracy when answering 20
addition and subtraction mental computation questions. All
five students were identified as being inaccurate. However, two students
employed a range of calculation strategies while the other three
students remained inflexible in their strategy choice, choosing low
order strategies. Individual interviews were conducted to identify these
aspects of calculation. Two conceptual flowcharts developed by
Heirdsfield (2001b) were utilised to identify factors and relationships
between factors that impact on mental computation. Use of these
flowcharts provides an avenue for identification of the breakdown in the
structures thereby providing an understanding of where the child is
operating and how they may be moved forward.
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Primary Pre-service Teachers? Understanding of Place Value
Romina Jamieson-Proctor
The development of place value understanding is
an essential foundation concept that enables students to have a strong
number sense. However, place value is a common problem area experienced
by students and pre-service teachers alike. This paper reports the
results of an initial investigation of pre-service teachers?
understanding of the symmetry of the place value system. The results
suggest that pre-service teachers' mathematical content knowledge with
respect to the symmetry of the place value system is weakest for
fractions
and when they are asked to generalise their understanding to a base a
system. Overall more of the pre-service teachers had a pre- or
uni-structural understanding of the symmetry of the place value system.
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Teacher Misconceptions about Projectile Motion
Anne Prescott and Michael Mitchelmore
Student misconceptions of projectile motion in
the physics classroom are well documented, but their effect on the
teaching and learning of the mathematics of motion under gravity has not
been investigated in the mathematics classroom. An experimental unit
was designed that was intended to confront and eliminate misconceptions
in senior
mathematics secondary school students studying projectile motion as an
application of calculus to the physical world. The approach was found to
be effective, but limited by the
teacher's own misconceptions. It is also shown that teachers can
reinforce student misconceptions of motion because they cannot
understand why students have difficulty understanding it.
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The Initial Professional Development of Teachers Learning to Use a Framework for Determining Students' Strategic Thinking
Peter Hughes
Derived initially from the observation of
children's methods of counting, Mathematics Recovery and Count Me in
Too, the New Zealand Numeracy Projects have, as a starting point for the
training of teachers, the understanding and use of a strategy framework
that traces children's development in number reasoning. Research
indicated the usefulness of teachers interviewing students in their own
class, and viewing video clips of strategic reasoning across of a wide
range of ages of student. This paper outlines how interviews and the
video clips are incorporated into the initial stages of teacher
Professional Development in learning to use the strategy number
framework.
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Understanding mathematics anxiety in a New Zealand secondary classroom
Naomi Ingram
Since finishing a Masters in Mathematics
Education, I have taught mathematics concepts in industry and in a
secondary classroom, and have frequently come across able students who
have difficulty learning and achieving to their academic potential in
mathematics. These difficulties seem to stem from anxiety that the
students experience when doing mathematics.
This is case study of Year 10 students (14-15 years old) who are in the
top achievement class of an Otago secondary school. Students were chosen
for this class by the school at the beginning of Year 9 because they
demonstrated excellence in one or more fields, not necessarily
mathematics. Through mainly qualitative methods (classroom observations,
questionnaires, and individual interviews), the following is being
investigated: the mathematical identities of students in the class; the identification of maths anxiety and potential maths anxiety in
students; interventions to improve the mathematics experience of anxious and
potentially anxious students.
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Poster (abstract only) |
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Round Table (abstract only) |
Approaches for Teaching the Division of Fractions
Leyton Walker
When contemplating the division of two common
fractions, the 'invert and multiply' algorithm, does not develop
naturally from using manipulatives. (Borko; Eisenhart; Brown; Underhill;
Jones & Agard. 1992) suggest it is for this reason, that it is
unlikely that children will invent their own 'invert and multiply' algorithm. Before a student can be expected to 'invent' this algorithm,
knowledge of whole number division and basic fraction concepts,
including the notion of equivalent fractions is essential. (Sharp,
1998).
The purpose of this round table discussion is to take cognisance of the
suggestions attested to by Borko et al. and Sharp and examine the
teaching approaches adopted by
classroom teachers, as they relate to the process of division with
fractional numbers. To highlight this, six Year 7 and Year 8 teachers
were asked to solve and then describe their mathematical approaches and
processes used to calculate 2/3 รท 1/2; illustrate the meaning of the
operation and describe the means by which they would explain their
respective methods for solving problems involving the division of
fractions with their students. The opportunity to examine the use of
mathematical equipment that may be used to support and illustrate the
mathematical process of division with fractions, will also be examined
with the view to generating a conceptual representation of the meaning
of the division of fractions.
References
Borko., H; Eisenhart., M; Brown, C.A., Underhill, R., Jones, D., &
Agard, P. (1992). Learning to teach hard mathematics: do novice teachers
and their instructors give up too easily? Journal for Research in
Mathematics Education 23 194-222.
Sharp, J. (1998). A constructed algorithm for the division of fractions.
In: The Teaching and Learning of Algorithms in School Mathematics.
Morrow, L.J. & Kenny, M.J. (editors) Reston, VA: National Council of
Teachers of Mathematics.
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Keeping it Going: Challenges in Sustaining Numeracy Practice
Deborah Gibbs and Marilyn Holmes
New Zealand, along with many other countries, has
been investigating ways of raising children's achievements in
mathematics by improving teachers? professional knowledge,
skills and confidence. The Numeracy Development Project (NDP) in New
Zealand grew out of The New South Wales Department of Education and
Training initiative 'Count Me In Too' in 2000, and was further developed
by 'research evidence about mathematics education, effective teaching,
teacher learning, effective facilitation practice, and educational
change' (Ministry of Education, 2004).
Pivotal to the success of the project are facilitators, principals and
lead teachers who work with classroom teachers to effect changes in
teaching practice. Schools participating in NDP can expect continuous
and focussed support throughout their year long professional
development. Sustaining the numeracy momentum within a school is a
difficult task and can be further complicated by the employment of
untrained numeracy teachers or provisionally registered teachers with
varying levels of understanding. During their time in the project, lead
teachers have mainly an administrative responsibility. However, in
subsequent years, it is magnified to include a complex, multi-layered
facilitation role.
This small study by Deborah Gibbs and Marilyn Holmes highlights two
challenging aspects: (a) The needs of untrained numeracy teachers as
they try to come to grips with the numeracy project as well as the
school?s mathematics programme; and (b) the complexity of the lead
teacher's responsibility in mentoring new untrained staff. Discussion
generated around this study will highlight the implications for
facilitators in numeracy and pre-service educators.
References
Ministry of Education. (2004). The Numeracy Story continued. What is
the evidence telling us? Wellington: Learning Media.
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Non-specialist teachers of mathematics: Pedagogical challenges in the Middle Years of Schooling
Barbara Tadich
This round table discussion will focus on the
efficacy, pedagogies and practice of nonspecialist teachers of
mathematics in the middle years of schooling in a regional Victorian
setting. Case study data, collected through questionnaires and
interviews of 26 junior secondary teachers with no mathematics methods
in their training, from six, rural, coeducational Victorian Government
schools, will be presented.
Current middle years' reform and initiatives such as Victorian Essential
Learning Standards (VELS) provide guidelines for effective teaching
strategies to engage young
adolescents generally. However, in order to provide expanded learning
opportunities in mathematics, teachers require professional knowledge of
their subject. Being able to present an understanding to student of big
ideas, the main branches and concepts of mathematics, and providing a
sense of their interconnections aids students to engage in mathematics.
This research project was undertaken to investigate whether
non-specialist mathematics teachers' pedagogical practices in secondary
schools were influenced by their limited training and mathematical
pedagogical knowledge. The findings indicate that lack of method
training and knowledge of pedagogical content impacts on both the
teachers and the students' mathematical engagement at junior secondary
level.
Through this round table I invite other researchers to discuss their
experiences of working with middle years mathematics teachers to seek
their input in the possible
development of further work in investigating the challenges of
non-specialist mathematics teachers in junior secondary schools and
overall student engagement in mathematics.
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The use of hand-held technology in the learning of statistical concepts
Derek Smith
Researchers and educational policymakers have
given encouragement to the use of electronic technology in the teaching
and learning of school mathematics and in the
assessment of senior mathematics and statistics courses. If used
appropriately (judiciously) is hand-held technology able to offer
secondary mathematics and statistics teachers and their students a
significantly richer mathematics learning experience? Little research
into hand-held technology and statistics has been done and during this
round table discussion, the researcher describes the use of hand-held
technology [graphical calculators] in three, N.C.E.A. Level 3,
statistics classrooms in a large co-educational urban secondary school
and the impact that they had on teacher pedagogy, student learning and
understanding of statistical concepts will be presented. The roundtable
is to discuss aspects of this study and to invite other researchers to
share their experiences in working with secondary school teachers in
statistics. The feedback provided in this round table is to assist and
inform the researcher about planning, implementing and appropriate
methodology for a more in-depth study in hand-held technology use and
statistical literacy and thinking.
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