### Conference Proceedings 2005

Title |

Building Connections: Research, Theory and Practice - MERGA28 |

Content |

Table of Contents |

Preface |

Preface |

List of Reviewers |

Judges and Reviewers for MERGA28 |

Keynote Address |

Essential Complementarities: Arguing for an Integrative Approach to Research in Mathematics Classrooms |

The Impact of Mathematics Education Reform in New Zealand: Taking Children?s Views into Account |

Practical Implication Award |

Variation and Expectation as Foundations for the Chance and Data Curriculum |

Symposium |

A Mathematics Teacher Educator's Perspective of Building Connections between Research, Theory, and Practice |

Building connections: Research, Theory and Practice - A view from a Practitioner |

Building connections: Research, Theory and Practice - A View from the Profession |

Building Connections: Research, Theory, and Practice |

From the Hill to the Swamp: Combining Research and Practice |

Research Paper |

Conceptions and Tensions in Globalisation and Their Effects on Mathematics Educators |

Using Jamie's Experiences: An Investigation into Using Teachers' Stories in Pre-service Mathematics Teacher Education |

Students' Views on Using CAS in Senior Mathematics |

Rates of Change and an Iterative Conception of Quadratics |

The Role of Attention in Classroom Practice: Developing a Methodology |

Use of a Cultural Metaphor in Pre-service Mathematics Teacher Education |

Implementing Problem Solving in Mathematics Classrooms: What Support do Teachers Want? |

I Didn't Know What I Didn't Know: A Case Study of Growth in Teacher Knowledge within the Intermediate Numeracy Project |

A New Scale for Monitoring Students' Attitudes to Learning Mathematics with Technology (MTAS) |

It Depends on the Students: Influencing Teachers' Beliefs about the Ends and Means of Numeracy Teaching |

Experienced and Novice Teachers' Choice of Examples |

Teachers' Preferences and Practices Regarding Values in Teaching Mathematics and Science |

The Mathematics Talk of a Secondary School Teacher of Mathematics and Physics |

Algebraic Thinking in the Numeracy Project: Year One of a Three-Year Study |

Affordances of a Technology-Rich Teaching and Learning Environment |

'I Type What I Think and Try It': Children's Initial Approaches to Investigation Through Spreadsheets |

Primary Students' Mental Computation: Strategies and Achievement |

Developing Effective Teachers of Mathematics: Factors Contributing to Development in Mathematics Education for Primary School Teachers |

Enhancing Mathematical Understanding Through Self-assessment and Self-Regulation of Learning: The Value of Meta-Awareness |

The Value of Play to Enhance Mathematical Learning in the Middle Years of Schooling |

Early Numeracy Coordinators in Victorian Primary Schools: Components of the Role, Highlights and Challenges |

Teaching Elementary Probability: Not Leaving it to Chance |

Children's Mappings of Part-Whole Construct of Fractions |

Prospective Teacher's Representations of Multiplication |

The Evaluation of the Success in Numeracy Education Program |

Conceptual Understanding of Spatial Measurement |

Learning to Notice: One Aspect of Teachers' Content Knowledge in the Numeracy Classroom |

How Unusual is the Gender Specificity of Mathematical Test Item Types Reported for Dutch Primary School Students' |

Assessing Primary Students' Knowledge of Networks, Hierarchies and Matrices using Scenario-Based Tasks |

Pedagogy by my Standards: A Teacher's Views on Two Process Standards |

Primary and Secondary Mathematics Practice: How Different is it? |

A Mathematics Education Ghost Story: Herbartianism and School Mathematics |

Seventh-Graders' Mathematical Modelling on Completion of a Three-Year Program |

Mathematical Methods Computer Algebra System (CAS) 2004 Pilot Examinations and Links to a Broader Research Agenda |

From Arithmetic to Algebra: Novice Students' Strategies for Solving Equations |

Towards a Language-based Model of Students' Early Algebraic Understandings: Some Preliminary Findings |

Integrating ICT into Professional Practice:A Case Study of Four Mathematics Teachers |

Mathematics Teachers: A Study of Life Inside School and Beyond |

Master, Servant, Partner and Extension of Self: A Finer grained View of this Taxonomy |

The Growth of Schematic Thinking about Derivative |

The Role of Online Discussion in Building a Community of Practice for Beginning Teachers of Secondary Mathematics |

Year 6 Students' Methods of Comparing the Size of Fractions |

Reflections on Teaching Mathematics in an Exam-Driven School: An Autoethnography |

How do we Provide Tasks for Children to Explore the Definitions of Quadrilaterals? |

Mental Computation: The Benefits of Informed Teacher Instruction |

Discourse as a Catalyst for Facilitating Practitioner Research |

Potential of Technology and a Familiar Context to Enhance Students' Concept of Rate of Change |

The Effects of Number Knowledge at School Entry on Subsequent Number Development: A Five-year Longitudinal Study |

Reforming Communication in the Classroom: One Teacher's Journey of Change |

Mentoring Mathematics Teachers in Low Socio-Economic Secondary Schools in New Zealand |

The Contested Notion of Sustainability: Possibility or Pipe Dream for Numeracy Reforms in New Zealand |

Students' Use of Context Knowledge in Interpreting Data |

Language Factors that affect Mathematics Teaching and Learning of Pasifika Students |

How Primary Pre-service Teachers Perceive Mathematics Teacher Educators' Practice: A Case Study |

Establishing a Numeracy Culture in a Distance Education Learning Environment: A Case Study |

Formalising the Role of Indigenous Counting Systems in Teaching the Formal English Arithmetic Strategies Through Local Vernaculars: An Example From Papua New Guinea |

Does Mathematics Education in Australia Devalue Indigenous Culture? Indigenous Perspectives and non-Indigenous Reflections |

Professional Development as a Catalyst for Changes in Beliefs and Practice: Perspectives from the Early Numeracy Research Project |

Growth of Teacher Knowledge within an On-line Collaborative Learning Environment |

The Use of Algebra in Senior High School Students' Justifications |

Measuring Fractions |

What Does Mathematics Understanding Look Like? |

Where Did I Go Wrong? Students' Success at Various Stages of the Problem-Solving Process |

Understanding Students' Reasoning While Comparing Expressions |

Regional Differences in the Professional Development Needs and Preferences of Teachers of Primary Mathematics |

Mathematics and the Construction of Feminine Gender Identity |

Do Teachers Change Their Practices While Participating in a Lesson Study? |

Teachers' Development of Substantive Communication about Mathematics |

Preschoolers' Mathematical Patterning |

The Effect of Money as a Context on the Mental Computation Performance of Students in Years 3, 5, 7 and 9 |

Mathematical Beliefs and Achievement of Pre-service Primary Teachers |

Student Misconceptions about Projectile Motion |

Subject Matter Knowledge: Mathematical Errors and Misconceptions of Beginning Pre-Service Teachers |

Education for Early Mathematical Literacy: More Than Maths Know-How |

Preservice Teachers' Intentions to Provide Good Examples and Help Children Replicate Them |

Understanding the Role of Assumptions in Mathematical Modeling: Analysis of Lessons with Emphasis on 'the awareness of assumptions' |

Exploring Pre-service Teachers' Reasoning about Variability: Implications for Research |

Building a Methodology for the Comparison and Evaluation of Middle-Years Mathematics Textbooks |

Assessing Multiple Objectives with a Single Task in Statistics |

Relative Risk Analysis of Educational Data |

Concerns Relating to the CAS Use at University Level |

The Integration of Mathematics and Music in the Primary School Classroom |

Interactive Whole Class Teaching and Interactive White Boards |

Children's Views of their Teacher's Role in Helping them Learn Mathematics |

Students' Attempts to Solve Two Elementary Quadratic Equations: A Study in Three Nations |

Glimpses of Generative Practice: Constructing Pre-service Teachers' Learning in Partnership |

Challenging Task-driven Pedagogies of Mathematics |

Patterns Supporting the Development of Early Algebraic Thinking |

An Indigenous Perspective on Mathematics Contextualisation in a Pre-school: From Safety to Empowerment |

Statistical Literacy over a Decade |

Teaching Percentage as a Multiplicative Relationship |

'I am really not alone in this anxiety': Bibliotherapy and Pre-service Primary Teachers' Self-image as Mathematicians |

Language Appropriate for the New Zealand Numeracy Project |

Results of a Teaching Experiment to Foster the Conceptual Understanding of Multiplication Based on Children's Literature |

Prioritising the Voice of Researched: Using Photographs to Elicit Mathematical Thinking of Participants |

The Victorian Curriculum and Assessment Authority (VCAA) Mathematical Methods Computer Algebra System (CAS) Pilot Study Examinations 2003 |

"Open your textbooks to page blah, blah, blah": "So I just blocked off!" |

Student Expectations of Studying Mathematics at University |

High School Students' Understanding of Samples and Sampling Variability: Implications for Teaching and Research |

Short Communication (abstract only) |

"My Mom Thinks I Should be an Engineer': Parental influences and Girls on Track for Math-Related Careers Despite increasing girl retention in advanced high school mathematics programs, female college entrants disproportionately avoid math-related IT majors (National Academy of Engineering, 2002; National Research Council, 2001). Girls on Track (Berenson, 2004; Berenson, Vouk, & Robinson, 2002; Howe & Berenson, 2003), a longitudinal multi-institutional intervention program, works to increase middle-grade girls' interest in math-related careers. Project data shows that parental influence is a key factor in the girls' success in school mathematics and in their career choice. We identify four major roles of parents: Providing learning infrastructure such as books, software and tutoring, Being a role model and providing access to other community role models, Managing time and tasks, Emotional support and encouragement |

An Investigation of the Selection Process of Mathematically Gifted Students In Korea, the gifted education appears to gain much popularity lately that it has become a 'hot issue' in the education circle. Unusual enthusiasm of Korean parents for education led them to take their children to a reputable centre for gifted education programs, which enormously increases the demand for gifted education. Gifted education programs were primarily operated by gifted education centres run by universities. Now many elementary and secondary schools have started launching gifted educational programs because government's policies encourage gifted education. At this juncture where gifted education has been rampantly expanding without thorough planning, it is necessary to review the gifted education form a reflective perspective. Gifted education is mainly implemented following three: selection, education and evaluation for reselection. In this paper, the issues of selection and evaluation for reselection will be touched upon from a critical point of view. The aim of this paper is to investigate mainly problems for the selection and reselection of mathematically gifted students. Inappropriate and appropriate problems and examples of student answers will be presented. |

Graphs, Transformations, Rates of Change and Quadratic Context Variations This paper presents a case study of a student who developed quadratic schemes by solving a contextual problem during a teaching experiment. Mary reflectively abstracted patterns from graphical transformations, critical points, rates of change and equations representing variations of a base context whilst interacting and negotiating meanings with the researcher. A multi-representational software assisted Mary in verifying/justifying her conjectures. Findings include Mary's schemes to characterize quadratic covariations. The student-researcher interactions fostered the development and consolidation of Mary's quadratics conceptions. |

Mathematical Problem-Solving Frameworks of Different Mathematics-Anxiety Levels Students This paper explores the problem-solving frameworks of 621 Secondary 2 students (13 to 14 years old). These students were asked to complete in writing the statement 'When I am given a mathematics problem to solve, this is what I do...'. The data were coded under the four phases of problem solving which were arrived at from a preliminary analysis of the data. The four phases: Understand / Represent the Problem (U), Find a Way to Solve the Problem (F), Solve the Problem (S), and Check the Solution (C) were noted. Secondary 2 students were found to rely on individual problem-solving frameworks to guide them when solving problems. The frameworks of different mathematics-anxiety students were similar, brief and specific in nature. |

Message from Student Teacher Constructed Posters This paper reports the upshot of a poster contest 'Mathematics-Language of the Universe' conducted for prospective teachers on 10.11.2002 in 'Tuticorin, India'. 20 student teachers (12 females& 8 males) from 7 colleges of education in 'India' participated in the poster contest. I designed the poster contest to meet the objective of out bringing the concept orientation of student teachers (STs) towards mathematics and to provide an opportunity to organise their thinking about mathematics in a creative way. The contest delineates the specific objectives of exposing the significance of mathematics, utility value of mathematics in daily life and social values of mathematics by way of eliciting the prospective math teacher's ideas. Philosophy in Mathematics, aesthetic beauty of Mathematics, Mathematics and art of living, Mathematics and religious tolerance are some of the themes selected by the STs. Role of Mathematics in the development of human science, Mathematical symbols and shapes used in daily life, Mathematics and aeronautics are some other concepts used by the contestants. 4 STs depicted how Mathematics promotes other subjects by choosing different personification of Mathematics such as the rising sun, tree root, the sun with planets and peacock with feathers. One contestant tried linking mathematics with the structure of chemical molecules. This contest served as a window to analyse the beliefs of future teachers about Mathematics as a subject. |

Persistent Mathematics Misperceivers: Two Case Studies In a study of 744 Western Australian Year 8 and 9 students, three different types of misperception were identified when students performed linear transformations. To examine their particular perceptual problems, nine persistent misperceivers (those who misperceived in the same way on three tests) were given one-on-one remedial instruction. Case studies of two different types of persistent misperceiver are presented here, one involving angles, the other involving reflections, to demonstrate to maths teachers what may be happening in their classrooms unbeknown to them. |

The Language of Zero: An Understanding of Place Value The acquisition of the 'language of zero' is important in the developmental progression of place value understanding. This short communication paper reveals the 'language of zero that children and teachers use in Christchurch primary school classrooms and considers educational implications of research findings from a larger study. Key international literature regarding place value development and acquisition of number are referenced. The paper is intended to invite feedback to inform subsequent studies regarding the acquisition of place value language. |

Young Children Reasoning with Tables: Toward a Model While there is more research on kids ages eight and up, less is known about young children reasoning with tables. A series of design experiments (Droujkova, In preparation, In press) led to a table reasoning model (TRM) describing children, ages three to eight, working with qualitative and numeric tables. TRM includes four components of reasoning: *Sameness/variation: what and how entities are varied or kept the same. *Action/object: ways children conceptualise entities as objects and actions. * Local/global: reasoning about neighbour cell patterns vs. thinking of rows and columns. *Coordinates/function: focus on the position of entries, or on functions forming entries. Competent work with tables requires fluent use of all components in multiple contexts. Moving toward such competency, young children exhibit a variety of reasoning patterns, often surprisingly different from adult approaches (Brizuela & Lara-Roth, 2002). For example, a beginner typically fills every cell with the same picture with no variation. Children view the 2*3 cell in the multiplication table as a product (action) of two numbers (objects), or as a doubling (action) of the number three (object). During missing cell value tasks, children search clues in row and column interactions, exhibiting global reasoning, or look at local neighbour cell patterns. In ?jigsaw? tasks of putting cut-up tables back together, children can focus on coordinates of each cell within table structures, and/or on the function used to create the cell entry. TRM helps to analyse ways children reason about tables. It is a robust tool for designing learning activities developing table reasoning. |

Poster (abstract only) |

Round Table (abstract only) |

Challenges for Mathematics Education in Pacific Island Nations in the 21st Century The purpose of the roundtable is to discuss with interested people the challenges for mathematics education faced by Pacific Island Nations. The form of the roundtable will be oral presentations and discussion rather than papers to reflect the oral style traditionally used in Pacific Island countries. The session will start with people working in these countries speaking about the problems in their particular localities with a focus on cultural, political, geographic, and economic influences on mathematics education. This will be followed by a more general discussion about the possible ways that some of these challenges might be addressed. Particular issues that are expected to be discussed include: ? the ways that members of MERGA might possibly help the Island nations; ? the possible role of research; ? the types of research that might be appropriate, and ? the involvement of non-indigenous researchers. Although research will be a major focus of discussion, other development activities are also likely to be discussed. |

Do High School Students Need Mathematics to Prepare for the Academic Numeracy Demands of University? High school students across Australia traditionally take at least one mathematics subject in their senior years of study. These subjects are seen as necessary for success at university and an important part of a students' well rounded education. Similarly statements are often released relating the importance of mathematics in the changing technologically based world. Yet more and more universities have removed the mathematics entry requirements from their courses and few universities list numeracy as an attribute of one of their graduates. Currently in Queensland, the majority of students planning to study at university still choose to study mathematics in their senior years, although there have been significant decreases in the number of students studying calculus inclusive mathematics courses. But will students still opt to study mathematics at all if universities do not include it as a prerequisite? This round table discussion will present preliminary results of research into the current status of mathematics entry requirements in Australian universities and the academic numeracy demands of courses for which senior mathematics is not an entry requirement. We aim to investigate, through discussion, how to determine what mathematics is required for university study, to answer the question 'What are the numeracy demands of university study?' |

Keeping it Going: Exploring Ways to Sustain Professional Development in Numeracy Numeracy has been a major focus of recent professional development initiatives for primary school teachers in many countries. Research has shown that a variety of factors contribute to a school?s ability to sustain gains after completion of professional development programmes. An exploratory action research study undertaken with five inner-city primary schools focused on identifying and providing a variety of tools to sustain effective numeracy practices. Teacher surveys, professional discussions with staff, and classroom observations informed the intervention. Numeracy facilitators/researchers worked with principals and Lead Teachers in mathematics to develop increased knowledge and understanding of issues surrounding numeracy teaching and learning. A central theme was the use of reflective practices which promoted the use of critical peers, observation, and videoing of mathematics lessons. Major issues found to be inhibiting sustainability included: leadership and staff changes within schools, a lack of school wide numeracy policies, and teachers? lack of in-depth knowledge of numeracy content and pedagogy. Interim findings suggest that teachers require further support and opportunities to experiment with, and reflect on, new ideas encountered within the professional development. Offering external support, creating a forum to address the issues, and promoting professional learning communities within the schools, enabled the schools to refocus on effective numeracy practices. Some reluctance by teachers to deprivatise or critically reflect on their practice was apparent. Round table participants are invited to contribute to a discussion of factors which may contribute to the sustainability of effective numeracy practices, to inform further research. |

Preparing for Assessments of our Research Productivity We have already entered an era of greater scrutiny of the nature and impact of our research from practitioners and we are about to receive active evaluations of our research productivity from the government and other funding agencies. First, we need to understand DEST policy developments and implications. Next, we need to understand the processes used by funding agencies in awarding grants, especially the ARC. Then we need to consider the types of projects that will have an impact on the field of education, and especially mathematics education. This roundtable will allow participants to share understandings of policy directions, especially the anticipated research assessments and the implications for our activities, it will review processes for applying for competitive grants, and it will allow discussion of implications for future mathematics education research. There will also be discussion of the MERGA research policy and consideration of whether variations or additions are needed to anticipate the forthcoming evaluative environments. |

Use of Projects in the Teaching of Statistics The aim of this round table discussion is to examine the merits of a project-based teaching approach for teaching statistics. My proposed research involves the lecturer using a project-based teaching approach that covers all of the prescribed content concepts in a statistics paper. This project would be introduced initially, and then every concept would be taught with respect to its relevance in the project analysis. The taught content would include the method of sampling, data analysis and the drawing of conclusions. Data measuring the level of reasoning in statistics along with student confidences in using statistics would be measured for students taught a similar content in two different ways. It will be hypothesised that students will display significantly greater ability to reason statistically with more confidence than those that have been taught using a traditional topic order approach with a multitude of examples. Yesilay (2000) suggested that students tend to learn more by doing a project than in any regular coursework. Murtonen & Lehtinen (2003) identified linking theory with practice as one of five difficulties experienced by education and sociology students in quantitative methods courses. It is hoped that the use of a project will enable the student to learn more effectively as it will provide a link from theory to a real world problem. Discussions will revolve around the use of a project-based teaching approach in either the assessment or delivery of a paper in statistics. Specific questions addressed will be: How have you used projects in the teaching of statistics? How effective did you find the use of these projects? |