Abstracts of Research Papers:

Research Papers

The Victorian Curriculum and Assessment Authority Mathematical Methods computer algebra pilot study and examinations
David Leigh-Lancaster¹, Pam Norton² and Michael Evans³, ¹Victorian Curriculum and Assessment Authority Manager Mathematics, ²Monash University, Victoria, ³Scotch College, Melbourne, Australia
leigh-lancaster.david.d@edumail.vic.gov.au, p.norton@sci.monash.edu.au michael.evans@scotch.vic.edu.au

Computer algebra systems (CAS) have now become much more readily accessible for use in secondary school mathematics on both hand-held and computer platforms. While the initial focus of work with CAS from the early 1980’s has generally been with respect to pedagogical and curriculum issues, as familiarity with CAS in senior secondary mathematics contexts has evolved around the world, systems and organisations have responded in various ways to the increasing availability of CAS and its impact on assessment, in particular end of secondary schooling formal examinations. This paper discusses key design and development aspects of the first examinations for the Victorian Curriculum and Assessment Authority (VCAA) Mathematical Methods (CAS) pilot study in 2002, provides some preliminary analysis and commentary with respect to student performance on these examinations, and discusses related issues for systems with respect to implementation of a CAS active subject of this kind.

Computer Algebra Systems and Mathematics Examinations: a comparative study
Roger Brown
Swinburne University of Technology

There is a move towards the adoption of Computer Algebra Systems (CAS) assumed examinations within examination systems. This paper will consider two such systems, the Danish Ministry of Education (DME) and the Australian Victorian Curriculum and Assessment Authority (VCAA) and will be guided by two questions:

The paper will use a framework developed by the author to investigate the role that the CAS plays within the CAS assumed examinations, some comparison will be made with identical non-CAS graphics calculator assumed examinations. The results reveal surprisingly little difference in the types of questions used; however, the CAS greatly enhances the range of solution strategies available to students.

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Communication Of Mathematical Thinking In Examinations: Features Of CAS And Non-CAS Student Written Records For A Common Year 12 Examination Question
Lynda Ball
Department of Science and Mathematics Education, University of Melbourne, Melbourne, Victoria, Australia.
lball@unimelb.edu.au

This paper is concerned with features of student written records when students are communicating mathematical thinking in examinations. Included is a comparison of written records of solutions for a common examination question for students who had access to a CAS and those who had a graphics calculator only. In this initial study it was found that CAS students tended to give shorter written solutions than non-CAS students and that there was a move towards use of a mixture of mathematical notation and words in documenting how problems were solved.

Using Assessment Principles to Evaluate CAS-Permitted Examinations
Peter Flynn
Department of Science and Mathematics Education, The University of Melbourne, VICTORIA, 3010, AUSTRALIA
p.flynn@pgrad.unimelb.edu.au

In 2002, two mathematics examinations governed by policy approving student use of different CAS calculators were conducted in Victoria, Australia for high-stakes assessment of student mathematical knowledge. This paper outlines the development and use of a set of Examination Assessment Principles (Mathematics, Learning and Equity) used to evaluate these pilot CAS-permitted examinations. It is reported that the features of CAS exerted a significant effect on examination question design. Preliminary analysis suggests users of no one brand of CAS seemed significantly advantaged, although brand differences affected student success rates on some examination questions. Inequities between different CAS were offset largely by making a wide variety of solution methods available. Future work on examination assessment must focus on widening the bandwidth of mathematical knowledge assessed and improving the testing of symbolic reasoning.

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