# Mathematics Stage 6 Review and Development Project

## Report on *Syllabus
Review* Phase
(March-December 2006)

A plan for the review and development of NSW Stage 6 Mathematics
courses was endorsed by the Board of Studies in December 2004. The
implementation of the plan in 2006, with the commencement of the *Mathematics Stage 6 Review and Development Project*, recognised the importance of teachers having
appropriate time to focus on the implementation of the new *Mathematics Years
7-10 Syllabus*, and the value of obtaining
further feedback on the implementation during 2005.

The first phase of
the project, *Syllabus Review*, commenced in March
2006, in accordance with the following timeline: *Syllabus Review* March-December 2006, *Writing Brief Development* January-July 2007, *Syllabus Development* August 2007-November 2008.

The
main purpose in undertaking the *Syllabus Review *phase
was to review the existing Mathematics course provision and to establish Broad
Directions for revision and development. The Board received reports on the
progress of the *Syllabus Review* phase at its June 2006, August
2006, September 2006 and October 2006 meetings.

A range of strategies was used to gather data in the *Syllabus
Review* phase. Two significant initial
strategies were the call for oral submissions and written submissions from key
organisations and individuals. These submissions provided an early opportunity
for the Board to gauge perspectives on the current Stage 6 Mathematics
curriculum, as well as what may be required in any revision of the syllabuses.

The oral submissions were heard by a panel which included the President of the Board of Studies and the Chair of the Mathematics Stage 6 Board Curriculum Committee. Presenters could choose to address specific and/or general issues in Stage 6 Mathematics.

The organisations and individuals invited to present a written submission to the review were advised that, while the content of written submissions should relate to the current situation in Mathematics and/or any preferred direction to be taken in NSW, respondents could choose to focus on particular aspects of Mathematics, the syllabuses, or general issues.

The written submissions were read and analysed by Board of Studies curriculum officers, as well as representatives of the Stage 6 Mathematics Board Curriculum Committee in order to obtain independent validation of the key themes/issues identified.

A number of common views were expressed through the oral and written submissions. It was felt that there should be a suitable Board-developed Mathematics course for every student, with consideration being given to an additional non-calculus-based course below the level of difficulty of the current General Mathematics course. Presenters and respondents were also of the view that the structure of the current Mathematics, Mathematics Extension 1 and Mathematics Extension 2 courses, and the calculus basis of these courses, should be retained. It was felt that measures should be taken to consolidate and extend the Mathematics ('2 Unit')-only candidature, and to ensure appropriate balance in the level of difficulty of Preliminary and HSC courses.

Some presenters and respondents expressed their support for the addition of one or more courses of study or topics in statistics. There was general support for the use of technology in teaching and learning; however, there were two distinct points of view expressed in relation to the use of technology in the HSC examinations for the calculus-based courses.

A further important data-gathering strategy was a survey of NSW schools offering Board-developed Mathematics courses in Years 11 and 12. The survey was conducted in the period August-September 2006, following the identification of a sample of 100 schools.

The set of schools from which the sample was drawn was defined as all NSW schools with HSC candidates for each of the General Mathematics, Mathematics and Mathematics Extension 1 courses in 2006.

The sample was stratified according to schooling sector and location. Schools were divided into three sectors (Government, Catholic Systemic, Independent) and four location categories (Coastal Country, Eastern Sydney, Inland Country, Western Sydney). In this way, a total of twelve school categories was specified.

Schools were selected randomly within the twelve categories, with the number of schools selected in each category determined by the proportion of students studying the Mathematics courses specified above at schools in that particular category.

The selected sample also included a diversity of other school features, including school type (eg comprehensive, selective, specialist), gender (boys, girls, co-educational), socioeconomic status, significant enrolment of Aboriginal students, and significant enrolment of students of non-English-speaking background.

There were 74 responses received from 66 schools. As for the written submissions, the survey responses were read and analysed by Board of Studies curriculum officers and representatives of the Stage 6 Mathematics Board Curriculum Committee.

The key themes/issues identified in the oral and written submissions were also identified in the survey responses. In addition, a range of survey responses expressed the need for syllabus support documents incorporating programming approaches, teaching ideas, resources, and assessment strategies. There was also a general view that there should not be any increase in the amount of content contained in the various courses, and that there should be a review of the approach currently taken to the naming of the Mathematics ('2 Unit') course.

The other main data-gathering strategies used in the *Syllabus
Review *phase were a Stage 6 Mathematics
symposium and a literature and curriculum review.

The symposium was held on 19 August 2006 at the Oatley Senior High Campus of Georges River College and provided the opportunity for a broad cross-section of stakeholders, including teachers, academics, parents and students to raise and explore key issues in the review and development of Stage 6 Mathematics courses. Detailed proceedings from the symposium are available on the Board of Studies website:

Mathematics Stage 6 Symposium Proceedings (PDF, 86 pages, 2.5 MB)

A literature and curriculum review was undertaken by Dr Mary Coupland of the University of Technology, Sydney, to research, review and report on issues relevant to the teaching and learning of Stage 6 Mathematics in NSW. Dr Coupland researched relevant literature and other Australian and international Mathematics syllabuses for post-compulsory years of secondary schooling. This included an analysis of syllabuses from Australian States and Territories, the Mathematics curricula of Finland, Hong Kong, Singapore, the United Kingdom and the United States of America, and the International Baccalaureate (IB) Diploma Program. The literature and curriculum review is available in two parts:

- Part 1: A critical analysis of selected Australian and international mathematics syllabuses for the post-compulsory years of secondary schooling (PDF, 89 pages, 610 KB)
- Part 2: Literature Review and Annotated Bibliography to Inform the Stage 6 Mathematics Review (PDF, 39 pages, 475 KB)

The information obtained through the data-gathering
strategies used in the *Syllabus Review *phase
was analysed to identify issues that need to be considered in the revision and
development of Stage 6 Mathematics courses. Key findings were synthesised from
the data and a set of draft Broad Directions (listed below) for the revision
and development compiled.

### Broad Directions for the revision and development of Stage 6 Mathematics

- That the set of Stage 6 Mathematics courses include an additional offering to accommodate the purposes of students who wish to study a Board-developed Mathematics course in Stage 6 but who are currently choosing not to, as well as those whose purposes are not accommodated through the study of General Mathematics.
- That in the revision, due attention be given to clarifying the purpose of each course and identifying future learning or vocational pathways of the intended candidatures.
- That the nested structure of the current Mathematics ('2 Unit'), Mathematics Extension 1 and Mathematics Extension 2 courses, and the calculus basis of these courses, be retained.
- That any revision or development of the calculus-based courses maintain the current rigour and level of challenge of the courses.
- That the amount of content prescribed for Stage 6 Mathematics courses reflect the amount that can be taught, and learnt by the typical student, in the indicative time.
- That in reviewing the content of Stage 6 Mathematics courses, particular attention be given to the purpose of the Mathematics ('2 Unit') course for Mathematics ('2 Unit')-only students, and the appropriateness and relevance of the course content for those students.
- That the inclusion of additional study of statistics be considered, while addressing implications in relation to the extent of relevant teacher expertise, professional development, future pathways of students, school Mathematics staffing, and school timetabling.
- That the current General Mathematics course material be largely maintained within the structure of Stage 6 non-calculus-based Mathematics courses.
- That, in reviewing the content of the calculus-based courses, the appropriateness and relevance of the applications within the courses be explored, with a view to ensuring that they are contemporary and that they meet the needs of students.
- That, in the consideration of the use of technology in Stage 6 Mathematics courses, due regard must be given to the related access and equity issues.
- That the use of technology with capabilities beyond the level of scientific calculators be encouraged in the learning and teaching, and school-based assessment, of all Stage 6 Board-developed Mathematics courses.
- That the non-calculus-based Stage 6 Mathematics courses be developed with the view that technology with capabilities beyond the level of scientific calculators will need to be used for aspects of the associated HSC examinations.
- That the use of technology in HSC examinations for the calculus-based courses be further investigated and clarified in the Writing Brief phase.
- That the appropriateness of the current processes for the examination of Stage 6 Mathematics courses be reviewed, with particular emphasis on the examination of Mathematics ('2 Unit')-only candidates.
- That the syllabus documents within the Stage 6 Mathematics syllabus package incorporate applications, implications and considerations for the teaching of the syllabus content, including in relation to depth of coverage.
- That each Stage 6 Mathematics course be named so as to avoid confusion with the discipline itself.

The Board's endorsement of the Broad Directions at its
December 2006 meeting represents the conclusion of the *Syllabus Review *phase of the project. The Broad Directions will guide
the development of Writing Briefs in the period January-July 2007.