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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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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

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.