Reflections: May, 2000

Contents of Volume 25, No. 2

EDITORIAL

POINT OF VIEW

• Values relevant to mathematics? I'd like to see that!, Philip C Clarkson, Gail E FitzSimons, Wee Tiong Seah

REFLECTIONS ON TEACHING APPROACHES

• Seeking a rationale for particular classroom tasks and activity, Peter Sullivan
• Empirical is not mathematical!, Michael Mitchelmore

REFLECTIONS ON MATHEMATICAL CAREERS

• Mathematical jobs for the talented, James Franklin

REFLECTIONS ON FINAL HIGH SCHOOL EXAMINATIONS

• HSC mathematics examination in China - An introduction to the China National College Entrance Mathematics Examination, Cao Zhongjun

REFLECTIONS ON PROJECT MATHEMATICS

• Infinity, Sandra Ann Ritter

REFLECTIONS ON TEACHING IDEAS

• Dependent vs independent variables,Jim Stamell
• Polyhedra, James Taylor
• A simple pattern of primes, Phillip Nance
• Finding areas under curves - A recommended approach, Alby Hodge
• Problems from the past, Ed Staples

THE MATHS EXCHANGE

• Researching Pythagoras on the Internet, Laura Campisi
• Binomial squares, Sarah Hamper
• Transforming y=x cubed, Christine Wightman
• Number squares, Robert Yen

Editorial

This issue of Reflections includes a reprint of a keynote paper from the 1999 Conference of the Mathematics Education Research Group of Australasia (MERGA). These annual conferences feature presentations from researchers in the field of mathematics education and attract participants from tertiary institutions as well as teachers of secondary and primary students. In addition, the conferences provide opportunities for interesting debates that often confront the interface between theory and practice in mathematics education. Peter Sullivan's paper outlines research that examines the use of open-ended tasks in mathematics teaching and learning and provides support for the inclusion of such questions in the curriculum and in our planning of mathematics lessons. The paper is reprinted with the permission of MERGA.

A paper presented at the 1999 Conference of the Mathematical Association of Victoria has been included as a Point of View. Clarkson et al. consider the important role of values, attitudes and beliefs in mathematics teaching and learning. In particular they discuss the need for teachers to reflect on their practice in relation to the values they are promoting in their classrooms. This paper is also reprinted with permission.

Three feature papers offer different perspectives for readers. The first, written by James Franklin, outlines a selection of career paths for talented mathematics students. This paper was the basis of a presentation at MANSW's 1999 Talented Students' Day. The second paper, by Cao Zhongjun, describes some similarities and differences between the Chinese final year examinations and the NSW Higher School Certificate Mathematics Examinations. Finally, part of an entry in the 1999 Project Mathematics competition is included as the third paper, entitled 'Infinity', by Sandra Ann Ritter, a student from St Catherine's School.

Other papers in this issue offer important and useful advice to teachers. Mitchelmore describes the critical role of explanation in our teaching of mathematical ideas. He argues that explanation is important at all levels of schooling and is a necessary ingredient in developing understanding. Stamell offers suggestions about the graphing of dependent and independent variables, and Taylor provides an historical perspective about polyhedra. Hodge recommends an approach for teaching the Trapezoidal and Simpson's rules, Staples presents some problems from the past, and Nance describes a simple pattern of primes. Our popular Maths Exchange includes photocopiable masters for teacher use.

The photographs in this issue feature students from Mount St Joseph, Milperra, engaging in practical classroom tasks, as well as participating in mathematics excursions at the Royal Botanic Gardens and Australia's Wonderland.

Judy Anderson and Robert Yen