### Conference Proceedings 2003

Title |

Content |

Preface |

A Tribute to the Research Work of Dr. Glendon Lean |

Preface |

List of Reviewers |

Keynote Address |

Opportunities to Learn Mathematics |

The TIMSS 1999 Video Study and its Relevance to Australian Mathematics Education Research, Innovation, Networking, and Opportunities |

Working Together to Enhance Australian Aboriginal Students' Mathematics Learning |

Practical Implication Award |

Using Case Stories as a Tool for Listening More and Telling Less in Mathematics Teacher Education |

Symposium |

Identifying and Overcoming Barriers to Mathematics Learning |

Perceptions of Barriers to Numeracy |

Teachers' Perceptions of How Open-Ended Mathematics Tasks Assist in Overcoming Barriers to Learning |

The Potential of Open-Ended Mathematics Tasks for Overcoming Barriers to Learning |

Research Paper |

Students' Knowledge of Rates: A Case for a Foundation Year Program in South Africa |

Investigating the Concerns of Preservice Secondary Mathematics Teachers Through Critical Incident Reflective Journals |

Developing Prospective Primary Teachers' Personal Content Knowledge of Mathematics |

Trigonometric Graph and the Real World: The Technical Students' Experience |

Ethnomathematical Ideas in the Curriculum |

Searching for Mathematical Ideas in Stone Walls |

Implementing Beliefs, Knowledge and Practices: A Beginning Teacher's StOlY |

Teachers' Choice of Tasks: A Window Into Beliefs About the Role of Problem Solving in Learning Mathematics |

Pizza for Dinner: "How Much?" or "How Many?" |

Bicultural Perspectives in a Pre-service Mathematics Education Course |

A Window Into Mathematics Communities of Practice in Australia and New Zealand |

Secondary Mathematics Teachers' Beliefs About Assessment and Factors That Influence These Beliefs |

Investigations Into the Introduction of Logarithm Tables in Victoria |

Patterns of Participation in Small-Group Collaborative Work |

Ability Grouping and the Construction of Different Types of Learner in Mathematics Classrooms |

The Mathematics Enhancement Project: Using the Concepts of Cultural Conflict, Critical Mathematics Education, and Didactic Contract |

Curriculum: Developing a Systems Theory Perspective |

Accounting for the Contextual Nature of Teachers' Beliefs in Considering Their Relationship to Practice |

Children's Perspectives on Mathematics and Game Playing |

Defining Moments in Determining a Complete Graph in a Graphing Calculator Teaching and Learning Environment |

Subject Knowledge in Pre-service Teacher Education |

A Comparison Among Three Different Approaches to Mathematics Assessment |

The Positioning of Mathematics in an Environmental Thematic Curriculum |

Transnumeration and the Art of Data Representation |

Maps That Come Alive: Numeracy Engagement Across Multimodal Texts |

Similarity and Difference in International Comparative Research in Mathematics Education |

Addressing the Challenge of Legitimate International Comparisons: Lesson Structure in Australia and the USA |

More Perspectives on the Impact of Globalisation on Mathematics Education in Higher Education in Australasia |

Windows Into Mathematics Teaching Through Data Maps |

Teaching in a Different Direction |

Designing Research on Teachers' Knowledge Development |

Hops, Steps and Jumps: Mathematical Progress in the Early Years |

Questioning Numeracy Programs for At-Risk Students In The Middle Years Of Schooling |

Secondary Students' Perceptions of Instructional Approaches: Implications for Mathematics Learning |

Designing Assessment Using the MATH Taxonomy |

Development of a Web-Based Learning Tool to Enhance Formal Deductive Thinking in Geometry |

The Victorian Curriculum and Assessment Authority (VCAA) Mathematical Methods (CAS) Pilot Study Examinations, 2002 |

On Student Observation and Student Assessment |

Mathematics as Conversation: A Model for a Mathematics Retrieval Programme Conducted With Small Groups |

Copying on a Graphics Calculator and Implications for Mathematical Understanding |

Re-visioning Curriculum: Towards Communicative Competence |

Using Mathematics Teaching Portfolios to Empower Pre-Service Primary Teachers |

Gender and Approaches to Studying Tertiary Mathematics |

From Description to Analysis in Technology Aided Teaching and Learning: A Contribution From Zone Theory |

A Teacher-Researcher Perspective on CAS in Senior Secondary Mathematics |

What Students Say: Analysis of Structured Survey Data in Relation to Technology and Mathematics Learning |

Difficulties Children Face When Learning to Count |

Student Perspectives on Equation: Constructing the Mathematical Object |

Learning to Teach Mathematics With Technology: A Study of Beliefs-In-Context |

Facilitating Affective Change With Preservice Primary Teachers |

Mental Computation: Refining the Cognitive Frameworks |

Designing a Discussion: Teacher as Designer |

Mathematics in Indigenous Contexts: A Case Study |

Constructing and Using a Personal Numeracy Teaching Model in a Classroom Setting |

Percentages: A Foundation for Supporting Students' Understanding of Decimals |

The Development of Multiplicative Thinking in Young Children |

Julia's Journey: Teacher Research in the Primary Mathematics Classroom |

Achievement Self-Rating and the Gender Stereotyping of Mathematics |

Australian Secondary School Teachers' Use of the Internet for Mathematics |

Teaching Mathematics Using the Internet |

Posing Problems in ICT-Based Contexts |

Monitoring Standards in Education: Mathematics 2002 Assessment |

Tensions and Possibilities: Indigenous Parents Doing Mathematics Curriculum Development |

Count Me In Too and the Basic Skills Test in New South Wales |

Shaping Practice: Worksheets as Social Artefacts |

First Graders' Use of Structure in Visual Memory and Unitising Area Tasks |

Re-visioning Curriculum: Shifting the Metaphor From Science to Jazz |

Individualization of Knowledge Representation in Teacher Education in Mathematics |

Organising and Representing Grouped Data |

A Whole School Approach to the Provision of Mathematics for Low-Achieving Girls in a Secondary School |

Interactive Animation Provides a Vehicle for Exploring Students' Understandings of Derivatives |

Is it Better to Burn Out or to Rust? |

Links Between Beliefs of Pre-Service Teachers About Literacy and Numeracy Learning |

High School Students' Interpretation of Tables and Graphs: Some Findings From Fiji |

Identifying Effective Scaffolding Practices Through Structured Peer Observation and Review |

Gambling Behaviour and Understanding of Probability Concepts Among University Students |

Probing Whole Number Dominance With Fractions |

Metacognitive Intervention in a Cognitive-apprenticeship-computer-based Environment |

A Model of Early Number Development |

Gender and Attitudes to Computer Use in Junior Secondary Mathematics |

Year 8 Students' Reasoning in a Cabri Environment |

Sociomathematical Worlds: Investigating Children's Developing Relationships With Mathematics |

Number Combinations and Arithmetic Structure: Implications for Early Algebra |

Inference From a Pictograph: Statistical Literacy in Action |

Predicting Dice Outcomes: The Dilemma of Expectation Versus Variation |

The Development of Children's Reasoning Strategies in Probability Tasks |

Lesson Study: A Model of Professional Development for Teachers of Mathematics in Years 7 to 12 |

Associations Between Student Pursuit of Novel Mathematical Ideas and Resilience |

Assessing Generalisation of Advanced Multiplicative Strategies |

Changes in Teachers' Perceptions of Technology in Mathematics |

The Perspectives of Two Children who Participated in the Advanced Numeracy Project |

Mathematical Errors in Fractions: A Case of Bruneian Primary 5 Pupils |

Numeracy in New Times: Implications for Youth, Work and Employment |

Reforming Mathematics Education: A Case Study Within the Context of New Times |

Teachers' Conceptions of School Algebra and its Teaching: Preliminary Findings from a Study in Colombia |

Short Communication (abstract only) |

A Student's Strategies in Deriving Quartic Modelling Functions Using Rates of Changes This paper reports findings from a research study which examined students' strategies for deriving modelling functions from numerical patterns with rates of changes in contrast to the equation-graph matching approach prevalent in schools. Students involved were final year mathematics undergraduate students some of whom were practicing teachers of mathematics or were intending to teach. Students had already examined the cases of linear, quadratic, cubic and some exponential functions and were requested to extend their projects to quartics, other exponential functions and a trigonometric or logarithmic function. This paper presents and discusses the data from the quartic project of one of the 8 students involved in the study. |

Classroom and Learning Factors Preferred by Year 9 Students in the Teaching and Learning of Mathematics This report describes a recent case study research which provides evidence that student learning, and student achievement can be accomplished by teachers working with a greater knowledge of student development. The key elements investigated in the study include both classroom and learning features. In particular an understanding of Kohlberg's (1963, 1973) stages of moral development is addressed. Giddens' (1984) concepts of the reflective cycle and its ability to lead to empowered action and to the uncovering of the range of choices (for the students and teacher) to act, or not to act, to make a difference to events is included. The data collected via personal observations, students' perceptions and voice, emphasized that an understanding of Kohlberg's and Giddens' work can add new dimensions to the middle years of schooling debate regarding adolescent teaching and learning. An understanding of young adolescents, especially in Year 9, requires greater knowledge of developmental and learning theories with a holistic approach to teaching and learning. |

Developing a Framework of Growth Points in Secondary Students' Understanding of Function It is widely accepted that teachers' knowledge of students' thinking in acquiring concepts and procedures in a specific mathematical domain can be a powerful tool in informing instruction. The framework of growth points in the understanding of function developed in the present study may provide such a contribution. This paper is a progress report of the development of the framework of growth points. The basis of the framework was an initial survey of the literature, which was progressively revised, using data from students in Years 8 to 10 in Victoria and The Philippines. |

How is the Motivation of the Two Year 13 Pacific Islands Mathematics Learners Shaped by their Culture? A Case Study The aim of this project is to link research to the improvement of mathematics teaching practice by investigating ways in which mathematics educators and teachers can foster Pacific Islands learners' motivation to learn mathematics. An important area to investigate is the ways in which Pacific Islands learners' motivation is shaped by their culture. A small study involving two students was conducted with the specific aim of exploring cultural influences that contributed to their motivation to learn mathematics. The factors that appeared to have the most influence on motivation were; the aspiration of students to do well so that they can help their families financially, the need to do mathematics to obtain a job, and the disparities between home and school. |

Persisting Teen/ty Confusions as an Indicator of a Specific Learning
Difficulty in Mathematics: Implications for Assessment and Instruction A specific difficulty in memorizing basic arithmetic facts has been well established as a persisting problem for students with learning difficulties in mathematics. Theories for underlying causes range from low working memory capacity to a failure to encode numbers semantically. Understanding the quantity meaning of the teen numbers is a particular difficulty for some students. This paper will present an intervention designed for a Year 2 Queensland student with persisting teen/ty confusions and a self-acknowledged difficulty in memorising the large doubles facts. Making the tens/ones structure of the teen numbers more transparent to the student provided a foundation for him to learn his large doubles to the point of fluency. |

Professional Learning in the Teaching of Area Seventeen Year 1 and Year 2 teachers participated in a professional development program focusing on the teaching of area. The teachers were offered three different levels of consultancy support. A comparison of results from the students and teachers indicates that the success of the teacher professional development, as measured by student learning and teachers' change in practice, was determined by teachers' ability to work in school-based teams, and an initial desire to improve their teaching of mathematics. The success of the program as a teacher professional development activity was not dependent on the level of consultancy support provided for teachers. |

Questions in Primary Mathematics Classrooms In this paper data gathered from teachers who participated in a professional development program designed to improve the quality of questioning in mathematics classrooms are presented. Teachers from five primary schools participated in the program. It was designed by the teachers and funded as a Quality Teacher Project. At the beginning and end of the school year, data were gathered by questionnaire about teachers' practice and, in particular, the types of questions that they used in their mathematics teaching. The types of questions that these primary teachers used when teaching mathematics are discussed. |

The Predictive Factors of Classroom Learning Environments on High School Students' Mathematics Anxiety The purpose of this research was to examine the possible associations between the perceived classroom environment of high school students in Southern California and the level of mathematics anxiety that they possess. Data were gathered using a revised version of Plake and Parker's (1982) Revised Mathematics Anxiety Ratings Scale and the What is Happening In This Classroom learning environment survey created by Fraser, McRobbie, and Fisher (1996). This research involved both quantitative and qualitative data obtained via the research instruments and interviews with those having extremely high or low math anxiety. |

Poster (abstract only) |

Round Table (abstract only) |

Collective Mathematical Understanding as Improvisation This research is concerned with the nature of the growth of mathematical understanding, and more specifically with how a group of learners can develop a collective understanding for a mathematical concept. We seek to characterise collective mathematical understanding as a creative and emergent improvisational process, through drawing on theoretical perspectives from the fields of jazz (Becker, 2000; Berliner, 1994; 1997), theatre (Sawyer 1997; 2000) and conversation (Sawyer, 2001). In considering video data, taken from an initial pilot study, we extend improvisational theory to begin to consider collective mathematical understanding as a process with a similar nature and characteristics. |

Numeracy Equipment and Year 3 Children: Bright, Shiny Stuff, or Supporting the Development of Part-whole Thinking? New Zealand teachers' use of equipment has increased as a result of their participation in the Numeracy Development Projects. However, the equipment choices of the four teachers interviewed in this study were not strongly consistent with the equipment use recommended in the NDP materials. In the teachers' reasons for equipment choices, the surface features of equipment seemed equally important as the conceptual development it can support. In contrast, the reasons given for equipment choices by the 34 Year 3 children who were interviewed were almost exclusively concerned with how the equipment might help them to solve the given problem. The children's success rates at solving the problem declined as the equipment became more structured; this paralleled the teachers' equipment choices. The ultimate goal for teacher educators must be for all teachers to have a richly connected conceptual map of numeracy, in order for teachers to be able to effectively use equipment in ways that help children to construct their own meaningful connections as they learn about number. Rather than talking about equipment as "bright, shiny stuff", teachers must have a clear focus on the role that equipment can play in the development of children's part-whole thinking. In this round table presentation the findings from this study, which was conducted during 2002 as part of a Masters thesis, will be discussed. |

Professional Development for Mathematics Education Researchers As mathematics educators, we frequently speak of the professional development needs of mathematics teachers. Many of us run professional development sessions or courses. Others of us conduct research and in our scholarly writings reflect on the implications of our findings on teacher professional development. Less often do we think about our own professional development needs. In my capacity as MERGA Vice-President (Research), I have often thought about how MERGA might assist in promoting the range of skills that mathematics education researchers might need to serve as the providers and nurturers of the next generation of researchers in our discipline, and to function as more effective and fruitful researchers whose findings are widely disseminated, highly acclaimed, and broadly implemented for the betterment of mathematics teaching and learning at all levels. I am proposing this round table session as the means to commence a discussion on what the professional needs of mathematics education researchers might be and what MERGA might do with respect to them. Some of the ideas floating around in my head include: various types of reviewing (conference papers, scholarly articles, book chapters, ARC grants), supervising higher degree students, examining theses, preparing grant applications (large/small/other), developing tenders, writing for different audiences, approaching publishers, learning about new/different research approaches/techniques, using computer software effectively for conducting research and/or analysing data, mentoring others, developing teaching/research portfolios, and promoting interviewing skills (as interviewer and/or interviewee). I'm sure there are other needs. Come and share your concerns and ideas |

Student Beliefs & Their Impact on Participation in Mathematics in the Middle School This round table discussion will focus on a proposed study of middle school children's beliefs about their participation in mathematics classrooms. In the study the motivation of students when undertaking mathematics tasks, and the influence of motivation on strategies for coping with frustration when experiencing difficulties, will be investigated. It is suspected that some students may not have established perceptions of the benefits of being competent in mathematics, nor be aware that there is potential for them to be empowered by competency. One determinant of participation in education is student perceptions of goals, and the influence that perceptions play on motivation. Students who feel in control of their lives are more likely to have opportunities for success both within schools and without (Lapadat, 1998). Dweck (2000) investigated perceptions of intelligence and contended that students may hold beliefs that inhibit their participation at school; that students can be taught that both intelligence is incremental and a mastery orientation can be taught through explicit instruction. Students of one grade six class will complete an assessment in which each task is incrementally harder to complete. Once each task is completed, they will be asked to evaluate their work. If correct they will continue to the next task. If not, they will be asked how they feel, and what teaching they require in order to continue. Various background data will be gathered to seek to identify contributing factors, and a survey adapted from Dweck's instrument will seek data on their beliefs concerning mathematical intelligence. |