# Notes to the Introduction to the Mathematics General Syllabus

These notes should be read in conjunction with the PowerPoint presentation titled Introduction to the Mathematics General Syllabus.

**SLIDE 1**

## Purpose of the presentation

This presentation has been developed for the use of mathematics faculties and teachers in schools, and by other interested stakeholders, in relation to the introduction of the new Mathematics General Stage 6 Syllabus (2012).

The courses within the new syllabus are for initial implementation as follows:

- the Preliminary Mathematics General (Board Developed) course in Year 11 2013
***** - the HSC Mathematics General 2 (Board Developed) course in Year 12 2014 (ie from Term 4 2013)
- the HSC Mathematics General 1 (Content Endorsed) course in Year 12 2014 (ie from Term 4 2013).

***** Please note:

- Students studying the current General Mathematics Stage 6 Syllabus (1999) in ‘compressed’ form (ie Preliminary and HSC courses in the same year) in 2013 will study the General Mathematics (1999) Preliminary course (and HSC course).
- School Developed Board Endorsed Courses, which have been in place in many schools up to and including 2012 under the common Board-specified title ‘Mathematics Applied’, cannot be studied in Year 11 in, or beyond, 2013.
- Schools that have Board of Studies approval to teach a Mathematics Applied course in 2013 may do so in Year 12 (only).

**SLIDE 3**

## Background

The Preliminary Mathematics General, HSC Mathematics General 2 and HSC Mathematics General 1 courses were originally developed in 2007 and 2008 as part of the review and redevelopment of NSW Stage 6 mathematics courses.

The new suite of courses was endorsed by the Board of Studies in 2009, but was not approved by the Minister for implementation at that time.

From 2009 to 2012, schools could apply to use the outcomes and content of the Preliminary Mathematics General and HSC Mathematics General 1 courses (or another course developed directly by the school) as a School Developed Board Endorsed Course (SDBEC) under the common Board-specified title ‘Mathematics Applied’.

During this period, the Australian Government increased the school leaving age to 17 years and the number of schools offering a Mathematics Applied course increased significantly.

In response, the Board of Studies agreed to release the *Mathematics General Stage 6 Syllabus* (2012) to replace the existing *General Mathematics Stage 6 Syllabus* (1999) and the various Mathematics Applied courses being offered in schools.

The final Mathematics General syllabus represents and includes, with a small number of minor updates, the Preliminary Mathematics General, Mathematics General 2 and Mathematics General 1 courses developed in 2007 and 2008.

**SLIDE 4**

## Courses within the syllabus

The new Mathematics General syllabus is available in the ‘HSC Syllabuses’ section of the Board of Studies website and incorporates the Preliminary Mathematics General (Board Developed) course, the HSC Mathematics General 2 (Board Developed) course and the HSC Mathematics General 1 (Content Endorsed) course.

HSC Board Developed Courses (BDCs) are examined at the HSC, while HSC Content Endorsed Courses (CECs) are not examined at the HSC.

The Preliminary Mathematics General course allows students to access either the HSC Mathematics General 2 course or the HSC Mathematics General 1 course in their HSC year.

The Preliminary Mathematics General/HSC Mathematics General 2 pathway replaces the General Mathematics (1999) course from Year 11 2013 and Year 12 2014. (The initial HSC examination for Mathematics General 2 will be conducted in 2014.)

The HSC Mathematics General 1 course is an additional course in the suite of Stage 6 HSC Mathematics courses. It has been designed to better meet the needs of students who wish to study mathematics in Stage 6 but whose purposes are not accommodated through the study of the HSC Mathematics General 2 course (see the first Broad Direction in Broad Directions for the revision and development of Stage 6 Mathematics).

As with other Content Endorsed Courses, the HSC Mathematics General 1 course will be subject to internal assessment only, and not formal examination at the HSC.

**SLIDE 5**

## Nature of the courses

The Preliminary Mathematics General course, the HSC Mathematics General 2 course and the HSC Mathematics General 1 course are highly contextualised and are designed to promote the development of knowledge, skills and understanding in areas of mathematics that have direct application to the broad range of human activity.

Effective participation in a changing society is enhanced by the development of mathematical competence in contextualised problem-solving. Experience in such problem-solving is gained by students gathering, analysing and interpreting mathematical information, and applying mathematics to model situations.

The opportunities for creative thinking, communication and contextualised problem-solving within the courses, through the use of a range of techniques and tools, assist students in finding solutions for the broad range of problems encountered in life beyond secondary schooling.

The purpose of the courses is to provide an appropriate mathematical background for students who wish to enter a range of post-school pathways that require the use of a variety of mathematical and statistical techniques.

As well as introducing some new mathematical content, the Focus Studies within the courses give students the opportunity to apply, and develop further, the knowledge, skills and understanding initially developed in the five Strands: Financial Mathematics, Data and Statistics, Measurement, Probability, and Algebra and Modelling.

Through the Focus Studies, students develop the capacity to integrate their knowledge, skills and understanding across the Strands in contemporary contexts chosen for their ongoing relevance to the students’ everyday lives and likely vocational pathways.

**SLIDE 6**

## Pathway structure

The new *Mathematics General Stage 6 Syllabus* (2012) requires that Preliminary students undertake a common course, Preliminary Mathematics General.

The common Preliminary course means that when students are in Year 11 they are *not* locked into either ‘General 2’ or ‘General 1’, according to whether they are likely to study the HSC Mathematics General 2 course (BDC) or the HSC Mathematics General 1 course (CEC).

Schools should differentiate the teaching and learning of the content of the Preliminary Mathematics General course in order to meet appropriately the needs of their particular students.

The Preliminary Mathematics General course is a Board Developed Course and so can be used to meet the requirement that, to qualify for the award of the HSC, students must study at least six units from Preliminary Board Developed Courses.

Following satisfactory completion of the Preliminary Mathematics General course, students can study either the HSC Mathematics General 2 course or the HSC Mathematics General 1 course. It is anticipated that most students satisfactorily completing the Preliminary Mathematics General course will go on to study the HSC Mathematics General 2 course.

Schools will need to be careful in providing appropriate guidance to students who they believe are likely to study the HSC Mathematics General 1 course, as this non-examinable course cannot be used to meet the requirement of six units of HSC Board Developed Courses to qualify for the award of the HSC. Students who are likely to undertake study of the HSC Mathematics General 1 course will need to have at least six units of Preliminary Board Developed Courses from other Key Learning Areas.

**SLIDE 8**

## Which students? Which pathway?

### Preliminary Mathematics General course

The Preliminary Mathematics General course is designed on the assumption that students have studied the content and achieved the outcomes of the *Mathematics Years 7–10 Syllabus *(2002) up to, and including, the content and outcomes of Stage 5.1.

For students who intend to study the HSC Mathematics General 2 course, it is recommended that they experience at least some of the Stage 5.2 content (particularly the Patterns and Algebra topics and Trigonometry), if not all of the content.

### HSC Mathematics General 2 course

The HSC Mathematics General 2 course is designed on the assumption that students have demonstrated a high level of competence in the Preliminary Mathematics General course.

The course provides students with the opportunity to develop an understanding of and competence in further aspects of mathematics through a large variety of real-world applications for a range of concurrent HSC studies, such as in the life sciences, the humanities and business studies.

The course also provides a strong foundation for vocational pathways, in the workforce and in further training, and for university courses in the humanities, nursing and paramedical sciences.

### HSC Mathematics General 1 course

The HSC Mathematics General 1 course is designed to meet the needs of students who have demonstrated competence in the Preliminary Mathematics General course.

The course provides students with the opportunity to develop an understanding of and competence in further aspects of mathematics through a large variety of real-world applications for concurrent HSC studies, such as in vocational education and training courses, other practically oriented courses, and some humanities courses, and for vocational pathways, in the workforce and in further training.

**SLIDE 9**

## Documents

### Mathematics General syllabus

The new *Mathematics General Stage 6 Syllabus* (2012) contains the content of the:

- common Preliminary Mathematics General course in section 9
- HSC Mathematics General 2 course in section 10
- HSC Mathematics General 1 course in section 14.

Information regarding the internal assessment of the HSC Mathematics General 1 course is provided in section 15 of the syllabus. Further advice on reporting achievement in this course is to be found in support materials.

### Assessment and reporting

Assessment and Reporting in the HSC Mathematics General 2 Course contains components and weightings for internal assessment and HSC examination specifications for the HSC Mathematics General 2 course.

Suggested components and weightings for internal assessment for the Preliminary Mathematics General course are also included in this document.

**SLIDE 10**

## Strands

Within the new Mathematics General syllabus (2012), the Preliminary Mathematics General course, the HSC Mathematics General 2 course and the HSC Mathematics General 1 course are divided into the same five Strands and contain various Focus Studies. The Strands are, in general terms, the same as the Areas of Study in the General Mathematics syllabus (1999).

It is not intended that equal time be allocated to each Strand in the Preliminary Mathematics General course, the HSC Mathematics General 2 course or the HSC Mathematics General 1 course.

The approach to the coding of topics (FM1, FM2, etc) in the Mathematics General syllabus (2012) is the same as in the General Mathematics syllabus (1999). However, teachers should be aware that a particular code may not apply to the same aspects of content.

The information provided in the Mathematics General syllabus (2012) in relation to the content and to the teaching and learning of courses is similar in its level of detail and presentation to that in the General Mathematics syllabus (1999).

**SLIDE 11**

## Focus Studies

The Preliminary Mathematics General course contains two Focus Studies that have been designed for approximately one-third of the course time:

- Mathematics and Communication
- Mathematics and Driving.

The HSC Mathematics General 2 course also contains two Focus Studies that have been designed for approximately one-third of the course time:

- Mathematics and Health
- Mathematics and Resources.

The HSC Mathematics General 1 course contains four Focus Studies that have been designed for approximately two-thirds of the course time:

- Mathematics and Design
- Mathematics and Household Finance
- Mathematics and the Human Body
- Mathematics and Personal Resource Usage.

The Focus Studies are identified by unique codes, eg ‘FSCo’ for Mathematics and Communication. In the Mathematics General 1 course, these codes include ‘CEC’ for easier identification, eg ‘FSDeCEC’ represents the Mathematics and Design Focus Study within the CEC.

Each Focus Study includes up to three topics, which also have their own unique codes, eg ‘FSDr2’ represents the second topic, ‘Running costs and depreciation’, within the Mathematics and Driving Focus Study in the Preliminary Mathematics General course.

**SLIDE 12**

## Nature of the Focus Studies

The Focus Studies in the Preliminary Mathematics General course, the HSC Mathematics General 2 course and the HSC Mathematics General 1 course are mandatory and are designed so that each can be programmed over a continuous time period.

They provide students with the opportunity to apply and develop further the knowledge, skills and understanding initially developed in the Strands, while also introducing some new mathematical content. It is intended that students:

- develop, through the Focus Studies, the capacity to integrate their knowledge, skills and understanding across the Strands in contemporary contexts chosen for their ongoing relevance to the students’ everyday lives and likely vocational pathways
- are involved in identifying a broad range of up-to-date contextualised resources, many of which can be found on the internet, for use in meeting the requirements of the Focus Studies.

**SLIDE 13**

## Support materials

Support materials that are being released progressively on the Board of Studies website for the information and assistance of teachers include:

- A Guide to the New Mathematics General Stage 6 Syllabus (May 2012)
- pathway descriptions: Preliminary Mathematics General (BDC)/HSC Mathematics General 2 (BDC) Pathway; Preliminary Mathematics General (BDC)/HSC Mathematics General 1 (CEC) Pathway (May 2012)
- Assessment and Reporting in the HSC Mathematics General 2 Course (May 2012)
- Introduction to the Mathematics General Syllabus PowerPoint presentation (October 2012)
- Programming Advice (October 2012)
- support materials for the teaching of new syllabus content (December 2012)
- HSC specimen examination paper, sample marking guidelines and performance band descriptions for the HSC Mathematics General 2 course (December 2012)
- support for reporting achievement in the HSC Mathematics General 1 course (December 2012).

Note: The Department of Education and Communities, the Catholic Education Commission, other school systems, the Association of Independent Schools, and various professional associations will assist and support the ongoing implementation of the syllabus.

**SLIDE 14**

## Non-calculus-based mathematics in 2013

In 2013:

- Preliminary (ie Year 11) students will study the Preliminary Mathematics General course within the new
*Mathematics General Stage 6 Syllabus*(2012). - HSC (ie Year 12) students who have satisfactorily completed the Preliminary course of the
*General Mathematics Stage 6 Syllabus*(1999) will study the HSC course of the General Mathematics syllabus (1999), with the 2013 HSC examination based on that syllabus. - Students undertaking study in compressed form (ie Preliminary and HSC courses in the same year) in 2013 will study the Preliminary and HSC courses of the
*General Mathematics Stage 6 Syllabus*(1999), as the 2013 HSC examination will be based on that syllabus. - Students who studied the Preliminary course of a School Developed Board Endorsed Course (referred to as ‘Mathematics Applied’) in 2012 and wish to continue with mathematics will study the HSC course of their Mathematics Applied course.
- Mathematics Applied will not be available to Preliminary (ie Year 11) students in 2013. Students for whom such a course would have been considered appropriate should study the Preliminary course of the new Mathematics General syllabus (2012) in 2013, with a view to studying the HSC Mathematics General 1 course in their HSC year (2014 for most students).

**SLIDE 15**

## Non-calculus-based mathematics from 2014

From 2014:

- Preliminary (ie Year 11) students will study the Preliminary course of the new
*Mathematics General Stage 6 Syllabus*(2012). - HSC (ie Year 12) students who have satisfactorily completed the Preliminary course will study either the HSC Mathematics General 2 course (BDC) or the HSC Mathematics General 1 course (CEC) from the new Mathematics General syllabus (2012).
- Students undertaking study in compressed form (ie Preliminary and HSC courses in the same year) in 2014 will study the Preliminary Mathematics General course and one of the two HSC courses from the new Mathematics General syllabus (2012).
- Mathematics Applied (SDBEC) will no longer be available for study by either Preliminary or HSC students from 2014.

**SLIDE 16**

## Programming

Programs written for the General Mathematics course can be modified to meet the requirements of the Strands in the new Preliminary Mathematics General course, the HSC Mathematics General 2 course and the HSC Mathematics General 1 course, and many existing units of work will form the bases of effective programs. Many existing resources for the *General Mathematics Stage 6 Syllabus *(1999) will also continue to be relevant.

Each of the Focus Studies within the Mathematics General courses is designed so that it can be programmed over a continuous time period. A Focus Study can be studied at any time within a course, provided that students have studied the prerequisite Strand content.