Reflections: August 1999

Contents of Volume 24, No. 3

Editorial 

Point of view 

• The proposed new non-calculus HSC course, Anne Hastings
• 2 Unit HSC exam papers 'Are they too difficult for too many 2 Unit students'?, Keith Hartmann 2 

Reflections on higher school certificate examinations 

• Learning from their mistakes, HSC 1998, Robert Yen 3Learning from their mistakes, HSC 1998, Robert Yen 3
• Taking chances on the 1998 HSC gambling question for MIS, or, why gambling is bad, Robert Yen 9Taking chances on the 1998 HSC gambling question for MIS, or, why gambling is bad, Robert Yen 9

Reflections on teaching senior mathematics 

• An overview of the 2 Unit course, Bill Pender 10An overview of the 2 Unit course, Bill Pender 10
• Sketching curves without using calculus, John Komaromi 22Sketching curves without using calculus, John Komaromi 22
• A 4 Unit mathematics problem, Tom Beeh 27A 4 Unit mathematics problem, Tom Beeh 27

Reflections on Technology 

• Modelling with the Geometer's Sketchpad, Barry McCrae 28Modelling with the Geometer's Sketchpad, Barry McCrae 28
• Calculus meets technology, Anthony Harradine 31Calculus meets technology, Anthony Harradine 31

Reflections on senior assessment 

• Anticipating the impact of ready access to computer algebra systems on teaching and assessment, David Leigh-Lancaster and Max Stephens 36Anticipating the impact of ready access to computer algebra systems on teaching and assessment, David Leigh-Lancaster and Max Stephens 36
• Challenges for teachers in assessment for senior secondary mathematics in Queensland, Ian Cronk 39Challenges for teachers in assessment for senior secondary mathematics in Queensland, Ian Cronk 39

• Playing with the harmonic series, Gerry Foley 43Playing with the harmonic series, Gerry Foley 43

The maths exchange 

In this issue, the first Point of View is a letter written by Anne Hastings to the Minister of Education, John Aquilina regarding the impending implementation of the single non-calculus course for the HSC. This letter is reproduced here as it represents the feelings of many MANSW members and describes a large number of teachers' concerns regarding this proposed new course. By publication date, a firm decision will have been made about the course(s) that will be available for the bottom fifty per cent of the mathematics candidature. The Editorial Committee would value your views on the final course structure as well as teaching and programming ideas to assist teachers in its implementation. The second Point of View, submitted by Keith Hartmann, describes concerns about the level of difficulty of the current 2 Unit course. 
The papers in this issue of Reflections focus on teaching senior secondary students and include comments about students' responses to last year's HSC papers, recommendations for teaching senior students, ideas for the use of technology, and issues about senior assessment. Yen has written the latest version of "learning from their mistakes" based on the HSC Examiners' Report from 1998. In addition he has collated some of the rather amusing (or worrying!) student responses to the Mathematics in Society Chance and Gambling question from last year. Pender provides a detailed and informative overview of the current 2 Unit Course, showing the interconnectedness of many of the ideas. Komaromi describes many examples of curve sketching without calculus and Beeh presents a favourite 4 Unit problem. 
Several papers focus on the use of technology and implications for future assessment practices. McCrae presents examples of modelling using the Geometer's Sketchpad, while Harradine describes student activities using the graphic calculator for introducing calculus. Harradine's paper formed the basis of a workshop at the 1998 MANSW Conference. Leigh-Lancaster and Stephens discuss the potential impact on teaching and assessment of regular student access to computer algebra systems. Finally, Cronk describes the impact on teachers of school-based assessment practices in Queensland. 
The papers by McCrae, Cronk, and Leigh-Lancaster and Stephens were originally published in the Proceedings of the Seventeenth Biennial Conference of the Australian Association of Mathematics Teachers held in Adelaide in January, 1999 and are reprinted here with permission. The full reference for the proceedings is: 
Baldwin, K. & Roberts, J. (1999). Mathematics: The Next Millennium. AAMT, Adelaide. The proceedings are now available on CD-ROM from the AAMT office and can be ordered by contacting staff on (08) 8363 0288 (phone), (08)Ý8362 9288 (fax), aamtinc@nexus.edu.au (email), or by visiting the web site on www.aamt.edu.au. 
AAMT conferences provide excellent opportunities to share teaching ideas and to discuss issues affecting mathematics teachers from all states of Australia. The next conference, Mathematics: Shaping Australia, will be held in Canberra on 15?19 January, 2001 and will be hosted by the Canberra Mathematical Association in collaboration with the Riverina Mathematics Association. 
The final paper in this issue, by Foley, examines harmonic series and may provide extra stimulus for talented senior students. 
The Maths Exchange provides more photocopiable worksheets for your students. Please consider contributing to this section by sending in your favourite worksheet to Robert Yen at Hurlstone Agricultural College, Roy Watts Road, Glenfield, 2167. 
The collage on the cover of this issue combines photographs of senior students from several schools in the southern Sydney area. Please send in photographs of your class(es) so that your students can enjoy seeing themselves on future covers.