CAS-CAT Research Project 2000-2002

Informing policy change in mathematics curriculum and assessment: The challenge of computer algebra systems

Chief Investigators
Professor Kaye Stacey (University of Melbourne)
Mr Gary Asp (University of Melbourne)
Dr Helen Chick (University of Melbourne)
Mr Barry McCrae (ACER, formerly University of Melbourne)

Partner Investigator
Mr David Leigh-Lancaster (VCAA)

Project officer
Ms Lynda Ball (University of Melbourne)

PhD student with Australian Post-graduate Award
Mr Peter Flynn (University of Melbourne)

Associate researchers
Dr Robyn Pierce (University of Ballarat)
Dr Margaret Kendal (University of Melbourne)

The research project (2000-2002)

This classroom based research project was funded through a grant from the Australian Research Council (ARC) Strategic Partnerships with Industry –Research and Training scheme (SPIRT). The project was undertaken at the University of Melbourne in conjunction with four industry partners: Texas Instruments Australia Ltd, Hewlett-Packard Australia Ltd, Shriro Australia (Casio) and the Victorian Curriculum and Assessment Authority. The research was carried out in three schools: Ballarat Grammar School, Kew High School and Our Lady of Sion College.

Aims of the project
The aims of the project were to investigate the changes to learning, teaching and assessment in senior secondary mathematics classrooms when students had access to CAS calculators for all work, including assessment. The study aimed to investigate the feasibility of offering a subject where CAS was the expected technology for students.

The new subject Mathematical Methods (CAS) was developed by the research team and others, accredited by the VCAA and accepted for university entrance from 2002.

As we worked on the project more specific research questions were investigated. These related to algebraic insight, effective use of CAS, assessment design in a CAS environment, evolution of teachers' pedagogy when CAS was available, changing nature of written records and goals for a CAS-active curriculum. Click here to access papers related to these and other research questions. Click here to access teaching resources.

The CAS pilot in Victoria 2002
In Victoria, schools provide Year 11 and 12 subjects for the Victorian Certificate of Education (VCE). Final grades for VCE subjects, which are used for various purposes including selection to university courses, are derived from tasks set at the school and external examinations. The project students studied a new subject called Mathematical Methods (CAS) which was a special adaptation of Mathematical Methods, suitable for students who have access to CAS. Both are introductory functions and calculus based courses.

During 2002, the year 12 pilot students were allowed to use CAS for all work, including their end of year external examinations. The students at each school used a different type of CAS (TI89, HP40G or Casio FX2.0). The pilot has since been extended, and the new subject will be available to all schools from 2006.

Project support for teachers and students
The research project investigated the changes to learning, teaching and assessment in senior secondary mathematics when students and teachers had access to CAS calculators for all work and assessment, including examinations. Access to CAS was important and the project teachers and students were provided with the necessary hardware for the duration of the project. An extremely important element of the implementation phase was that the teachers were provided with adequate ongoing support. This included professional development, curriculum support (exams, classroom material, worksheets etc) and individual technical support. An important message from the project teachers was that ongoing support was crucial for any future implementation of CAS. Curriculum material developed for use by project schools is freely available in resources for teachers .

The researchers worked very closely with the project schools. We carried out classroom observations, collected sample student work and questionnaire responses, conducted teacher and student interviews and had a number of meetings with teachers. Meetings focussed on approaches for teaching with CAS as well as research findings and possible implications for the classroom. Between project meetings an ongoing dialogue was maintained via email, phone calls and through classroom visits. This provided the opportunity to share ideas related to both the opportunities and challenges of implementing a CAS curriculum and also enabled response to teacher and student queries regarding technical aspects of CAS, such as syntax. In addition, the research team provided documents related to a number of issues that arose from implementation of CAS.

Impact of the research project
The research project has impacted on the Victorian mathematics curriculum and provided information regarding teaching and learning with CAS to the broader Australian and international audiences. In Victoria, Australia the new pilot VCE Mathematics subject has increasing enrolments.

Members of the project team have presented many invited keynote addresses both nationally and internationally in addition to sharing project findings at research and teacher conferences. Members of the team have also conducted numerous professional development sessions for teachers and shared project resources via this website. There has been widespread interest in the findings of the project as well as the teaching resources developed.

Acknowledgements
The project was supported by the Australian Research Council, the Victorian Curriculum and Assessment Authority, Hewlett-Packard Australia, Shriro (Casio) and Texas Instruments Australia. The research team would like to thank our industry partners and the project schools, teachers and students. We are especially grateful to the project teachers and students for welcoming us into their classrooms.

Course outline for Mathematical Methods (CAS)
The course outline for the pilot study for Mathematical Methods (CAS) can be accessed on the VCAA website at: http://www.vcaa.vic.edu.au/vce/studies/MATHS/caspilot.htm

2002 Examinations for Mathematical Methods (CAS)
The examinations for the 2002 pilot study can be accessed from the VCAA website at: http://www.vcaa.vic.edu.au/vce/Exams/EndYear.htm