Showing papers in "Mathematics Education Research Journal in 1999"

Head mathematics teachers’ beliefs about the learning and teaching of mathematics

Abstract: This paper reports on an investigation of teacher beliefs concerning the nature of mathematics and the learning and teaching of mathematics. The focus is on the espoused beliefs of 40 Head Mathematics Teachers in Australian secondary schools. These beliefs are compared with the espoused beliefs of classroom mathematics teachers in the same schools and with recent mathematics education reform documents from Australia and USA. A confirmatory factor analysis of responses from a specifically constructed survey identified two factors (child-centredness and transmission) which form the basis for the comparative analysis. Interviews with eight of the Head Mathematics Teachers who responded to the survey provide further detail for these comparisons. The ramifications of the similarities and differences in espoused beliefs of the different groups of teachers and the reform documents are discussed.

Secondary mathematics teachers’ knowledge of slope

Abstract: This study, conducted in the United States, investigated secondary mathematics teachers’ concept definitions, mathematical understanding, and pedagogical content knowledge of slope. Surveys were collected from 18 preservice and 21 inservice teachers; 8 teachers from each group were also interviewed. Geometric ratios dominated teachers’ concept definitions of slope. Problems involving the recognition of parameters, the interpretation of graphs, and rate of change challenged teachers’ thinking. Teachers’ descriptions of classroom instruction included physical situations more often than functional situations. Results suggest that mathematics teacher education programs need to specifically address slope as a fundamental concept, emphasising its connection to the concept of function.

Teaching mathematics: A brightly wrapped but empty gift box

Abstract: In a research study conducted with first year prospective primary school teachers, beliefs about and attitudes towards mathematics were investigated. It was found that prospective teachers generally perceived good mathematics teaching to include the provision of enjoyable experiences. However, most of the student teachers did not perceive enjoyment as having an intellectual component. Further, they often expressed the belief that being knowledgeable about mathematics was a disadvantage for a primary school teacher. It was as if student teachers see mathematics teaching as brightly coloured wrapping around an empty box. Implications of these findings for mathematics teaching and teacher education are discussed.

Classroom Reform Five Years Down the Track: The Experiences of Two Teachers

Abstract: This case study research investigated changing teacher roles associated with two teachers’ use of innovative mathematics materials at Grade Six level, in a setting which contained all the ideal ingredients for professional growth. Participant observation and interviews with the teachers over a seven-month period early in the use of the innovative materials and for a brief time five years later provided a picture of changing teacher roles, but also a sense of issues that had emerged. or persisted in the longer term. The greatest changes in these teachers’ roles (in the short and long term) related to increasing comfort with posing non-routine problems to students and allowing them to struggle together, and the provision of structured opportunities for student reflection upon activities and learning. However, little change was evident over the five year period in the teachers’ use of assessment practices or in their articulation of the “big ideas” of mathematics in the middle school years.

Applying constructivist theory to practice in a technology-based learning environment

Abstract: This paper describes a research study where constructivism was used as the rationale for the design, implementation and evaluation of four technology-based investigations for Year 12 Applicable Mathematics students. Analysis is given of the successes and difficulties encountered by students and teachers of four classes, including my own, in which the investigations were implemented. The results showed that, for learning activities involving school assessment, many students chose not to work collaboratively — a strategy suggested by social constructivism. The extent to which this may have been detrimental to their learning is discussed. The study illustrates how engaging in research can be a means for teachers to understand theory. In particular, the paper describes the meaning made of constructivism through this example of teaching practice and research activity.

Teachers' Strategies for Implementation of De-streaming in Secondary Mathematics Classes.

Abstract: Moves toward the adoption of a middle school philosophy and to outcomes-focused education, both of which are apparent in Australia, are likely to be accompanied by a move away from streaming or tracking students into ability groups. It is claimed that successful teaching of students in unstreamed classes requires an enriched program that caters for the needs of the wide range of students, new approaches to instruction, and the adoption of a variety of assessment strategies. This study reports on the strategies adopted by a group of teachers in Ontario, Canada, as they implemented de-streaming with Grade 9 classes. Teachers were found to be making special provision for both low- and high-achieving students and employing a wide range of techniques for assessing student progress. However, they did not embrace cooperative learning techniques as one of their teaching strategies, nor was problem solving found to be a prominent feature of their lessons.

Dollars and sense: A case of distributed cognition in a problem-solving session

Abstract: Social discourse among students has come to be seen as a vital aspect of knowledge production in mathematics classes. Discourse among small groups of students is often viewed as a way for individuals to validate ideas or as a way by which more capable students guide knowledge production in heterogeneous groups of students. This report provides an example of a problem-solving session which goes beyond peer tutoring or cooperative breaking up of problems to focus on knowledge construction of a truly collaborative nature. This serves as a demonstration that groups can function productively even when there is not a more capable member of the group and provides a pragmatic example for classroom teachers to consider as they strive to establish productive group work in their classrooms.

The lives and contributions of women mathematicians and educators

Abstract: Concentrating on twentieth century women in mathematics is a particular strength of this biographical dictionary which adds substantially to what is known about women's contributions to mathematics. There are entries for 59 women, the vast majority of whom are still alive and working. Most are mathematicians in the traditional sense. The editors have also chosen to include several key researchers in the field of gender and mathematics education. The stories of six well-known female mathematicians who lived and worked in ancient times (e.g., Hypatia of Alexandria), the eighteenth century (e.g., Sophie Germain), and the nineteenth century (e.g., Ada Lovelace), have also been included in the collection. I would have preferred not to have seen these entries. For me, they detracted from the emphasis on the contributions of women of this century. The editors could have divided the book into two sections. This would have highlighted the following point made in the introduction:

Introductory algebra: Four approaches or one?

Abstract: This edited volume is a worthy attempt to draw together recent debate and research regarding the traditionally difficult problem of presenting algebra to those not enculturated into the world of algebraic process and thought. The early "errors" orientation of research into children's ability to work in an algebraic mode, undertaken by writers such as Kiichemann (1981) and Booth (1984), seemed to indicate that the focus on decontextualised operations led to many misconceptions and an unwillingness or inability to transfer the skills to problem­ solving situations. Since then many attempts have been made to identify alternative approaches to algebraic instruction with the aim of widening the availability of algebraic skills in the community. This book is an attempt to synthesise the progress thus far. Those readers who have followed the work of the Algebra special interest group at the international conferences of the International Group for the Psychology of Mathematics Education (PME) in the 1990s would be familiar with most of the writers and the nature of the debate, if not with some of