1. MATHEMATICS K-12 PRESENTATION MARCH 2008

2. RATIONALE OF KEY LEARNING AREAS IN SCHOOL CURRICULUM MATHEMATICS One of eight Key Learning Areas in K6-12 Curriculum An integral part of daily life Understanding other key learning areas in the whole school curriculum Effective and systematic communication tool Logical problem solving process 2 11390691 Peta Evans

3. SYLLABUS STRUCTURE & INCLUSIONS SYLLABUSES Mathematics K-6 Syllabus Mathematics Years 7-10 Syllabus Mathematics 2/3 Unit Years 11-12 Syllabus Mathematics 4 Unit Years 11-12 Syllabus Mathematics Years 11-12 General Syllabus Mathematics Years 11-12 Life Skills Syllabus 3 11390691 Peta Evans

4. STRUCTURES OF K-6, YEARS 7-10 AND YEARS 11-12 SYLLABUS Rationale Aim Objectives Outcomes and Contents Assessment and Reporting 4 11390691 Peta Evans

5. OVERVIEW OF SUBJECTS & COURSES FOR MATHEMATICS K-12 COURSES Early Stage 1: Mathematics Stage 1: Mathematics Stage 2: Mathematics Stage 3: mathematics Stage 4: Mathematics Stage 5.1: Mathematics Stage 5.2: Mathematics Stage 5.3: Mathematics Stage 6: Mathematics Life skills Stage 6: Mathematics General Stage 6 Preliminary & HSC Stage 6: Mathematics Preliminary & HSC Stage 6: Mathematics Extension 1 Preliminary & HSC Stage 6: Mathematics Extension 2 HSC 5 11390691 Peta Evans

6. PATHWAY FROM K-12 Mathematics Stage 5.2 Mathematics Years 11-12 Mathematics Years 7-10 Mathematics K-6 Mathematics Early Stage 1 to Stage 3 Mathematics Stage 4 Mathematics Stage 5.1 Mathematics Stage 5.3 Mathematics Life Skills Stage 6 Mathematics Life Skills Stage 6 General Mathematics Stage 6 Mathematics Stage 6 Mathematics Extension 1 Stage 6 Mathematics Extension 2 Mathematics Stage 5.2 LEGEND Other available Pathway Usual Pathway Figure 1: Pathways for K-6, Years 7-10 and Years 11-12 Mathematics (BOS, 2003). 6 11390691 Peta Evans

7. SUBJECTS K-10  Number  Pattern and Algebra  Data  Measurement  Space and Geometry Years 11-12 Table 1: Summary of Stage 6 subjects (BOS, 2000, 2007d, 1997a, 1997b). 7 11390691 Peta Evans Mathematics Life Skills General Mathematics Mathematics/ Mathematics Extension 1 Mathematics Extension 2 6 Modules5 units18 Topics8 Topics

8. OVERVIEW OF STRANDS IN STAGE 5 PATHWAY FOR STAGE 5 Stage 5.1- Designed to meet the needs of students who achieved stage 4 during Year 9 or 10. Stage 5.2- This stage builds on and includes stage 5.1 content. This was designed for students who have achieved stage 4 by the end of Year 8 or early in Year 9. Stage 5.3- Includes the content of both 5.1 and 5.2 and is designed for students who achieved Stage 4 outcomes before Year 8. 8 11390691 Peta Evans

9. STRANDS & CONTENT FOR STAGE 5 S TRAND STAGE WORKING MATHEMATICALL Y NUMBER PATTERN & ALGEBRA DATAMEASUREMENT SPACE & GEOMETRY STAGE 5.1 This contain interrelated processes for all stages Questioning Applying strategies Communicating Reasoning Reflecting  Rational Number  Consumer Arithmetic  Probability  Algebraic Techniques  Coordinate Geometry  Data Representation analysis  Perimeter and Area  Trigonometry STAGE 5.2  Rational Number  Consumer Arithmetic  Algebraic Technique  Coordinate Geometry  Graph of Physical Phenomena  Data Analysis and Evaluation  As stage 5.1  Surface Area and Volume  Properties of Geometrical Figures STAGE 5.3  Real Number  Probability  All of stage 5.2  Curve Sketching  Polynomials  Functions  Logarithms  As Stage 5.2  Surface Area and Volume  Trigonometry  Deductive Geometry  Circle Geometry Table 2: Syllabus content for Stage 5 9 11390691 Peta Evans

10. OVERVIEW OF STAGE 6 SYLLABUS STAGE 6 MATHEMATICS SYLLABUS Non- Calculus based Mathematics Syllabus  Mathematics Life Skills Course Syllabus  General Mathematics Stage 6 Syllabus Calculus based Mathematics Syllabus  Mathematics 2/3 Unit Years 11-12 Syllabus  Mathematics 4 Unit Year 12 Syllabus 10 11390691 Peta Evans

11. STAGE 6 SYLLABUS CONTENTS 11 11390691 Peta Evans Mathematics Life Skills General Mathematics Stage 6 2/3 Unit Mathematics 4 Unit Mathematics  Program of HSC study  Guideline for Schools  Continuum for Stage 6 Life Skills Students  Aim  Objectives  Course structure  Objectives and Outcomes  Key Competencies  Modules  Post –school Opportunities  Assessment and Reporting  Glossary  Program of HSC study  Guideline for Schools  Continuum for Stage 6 Life Skills Students  Aim  Objectives  Course structure  Objectives and Outcomes  Preliminary Course Content  HSC Course Content  Course Requirements  Post –school opportunities  Assessment and Reporting  Course description  Introduction  Part A- Statement of Syllabus Topics  Part B: Additional Information on Syllabus Content  Mathematics K-12 Statement of Principles  The Mathematics 4 Unit Syllabus  Graphs  Complex Number  Conics  Integration  Volumes  Mechanics  Polynomials  Harder 3 Unit Topics Table 3: Summary of Stage 6 Syllabus contents (BOS, 1997a, 1997b, 2000, 2003, 2007d)

12. OVERVIEW OF PROPOSED CHANGES TO STAGE 6 CURRICULUM STAGE 6 SYLLABUS REVIEW PROCESS In 1998- BOS agreed to review 2/3/4 Unit Mathematics courses December 2004- BOS endorsed the plan for review of the Mathematics Syllabuses March 2006- Review process started 2007/2008- Consultation and write up process 2010- Implementation of Year 11 new mathematics syllabus 2011- Implementation of Year 12 new mathematics syllabus 12 11390691 Peta Evans

13. PROPOSED NEW STAGE 6 COURSES O CURRENT COURSES * Preliminary Mathematics General * HSC Mathematics General PROPOSED NEW COURSES * Preliminary Mathematics General * Mathematics General 1-HSC * Mathematics General 2 -HSC Figure 2: Non calculus based courses proposal 1. Non Calculus based courses 13 11390691 Peta Evans

14. PROPOSED NEW STAGE 6 COURSES 2. Calculus Based Courses CURRENT COURSES * Preliminary Mathematics * HSC Mathematics *Preliminary Mathematics Extension 1 * HSC Mathematics Extension 1 * HSC Mathematics Extension 2 PROPOSED NEW COURSES * Preliminary Mathematics Advanced * HSC Mathematics Advanced * Preliminary Mathematics Extension * Mathematics Extension 1 * Mathematics Extension 2 Figure 3: Calculus based courses proposed changes. 14 11390691 Peta Evans

15. PROPOSED COURSE OF STUDY FOR STAGE 6 MATHEMATICS COURSE MATHEMATICS GENERAL 1 MATHEMATICS GENERAL 2 MATHEMATICS ADVANCED MATHEMATICS EXTENSION 1 MATHEMATICS EXTENSION 2 PRELIMINARY MATHEMATICS GENERAL COURSE HSC MATHEMATICS GENERAL 1 COURSE HSC MATHEMATICS GENERAL 2 COURSE PRELIMINARY MATHEMATICS ADVANCED COURSE HSC MATHEMATICS ADVANCED COURSE PRELIMINARY MATHEMATICS EXTENSION COURSE HSC MATHEMATICS EXTENSION 1 COURSE HSC MATHEMATICS EXTENSION 2 COURSE Table 4: Course of study for Stage 6 Mathematics (BOS, 2007b, pp. 14-15). 15 11390691 Peta Evans

16. PROPOSED NEW STAGE 6 SYLLABUS CONTENTS 16 11390691 Peta Evans Current 2/3 unit Mathematics Syllabus Contents Current 4 Unit Mathematics Syllabus Contents Proposed new Syllabus Contents for Stage 6 Mathematics  Course description  Introduction  Part A- Statement of Syllabus Topics  Part B: Additional Information on Syllabus Content  Mathematics K-12 Statement of Principles  The Mathematics 4 Unit Syllabus  Topic 1: Graphs  Topic 2: Complex Number  Topic 3: Conics  Topic 4: Integration  Topic 5: Volumes  Topic 6: Mechanics  Topic 7: Polynomials  Topic 8: Harder 3 Unit Topics  Rational  Aim  Objectives  Content organisation  Outcomes  Content  Use of technology  Assessment & HSC Examination  Glossary  Support Materials  Appendix Table 5: Comparison between current and proposed Syllabus Contents (BOS, 1997a, 1997b, 2007b)

17. PROPOSED NEW STAGE 6 MATHEMATICS SUBJECTS General Mathematics Mathematics/ Mathematics Extension 1 Mathematics Extension 2 General Mathematics 1 &2 Advanced Mathematics Mathematics Extension 1 Mathematics Extension 2  Financial Mathematics  Data analysis  Measurement  Probability  Algebra and modelling  Basic arithmetic and algebra  Plane geometry  Probability  Real function of a real variable and their geometrical representation  Trigonometry ratios- review and some preliminary results  Linear functions and lines  Series applications  The tangent to a curve and the derivative of a function  The quadratic polynomial and the parabola  Geometrical applications of differentiation  Integration  Logarithmic and exponential functions  The trigonometry functions  Applications of calculus to the physical world  Inverse functions and the inverse trigonometric functions  Polynomials  Binomial theorem  Permutations, combinations and further probability  Graphs  Complex Number  Conics  Integration  Volumes  Mechanics  Polynomials  Harder 3 Unit Topics Areas of study  Financial Mathematics  Data analysis  Measurement  Probability  Algebra and modelling Focus studies  Mathematics & communication  Mathematics & driving  Mathematics & design  Mathematics & household finance  Mathematics & health & leisure industries  Mathematics& Natural Resource Management  Counting Techniques  Probability  Real functions & their graphs  Trigonometry  Differential calculus  Data analysis  Sequence & series  Integral calculus  Logarithmic & exponential functions  Mathematic modelling  Circle geometry  Further algebra  Transformation of graphs  Other inequalities  Polynomials  Elementary difference equations and the discrete logistic growth model  Mathematic induction  The binomial theorem, binomial identities and binomial probability distribution  Further trigonometry  Methods of integration  Inverse functions  Further application of calculus involving mathematical modelling  Further inequalities  Complex numbers and polynomials over complex field  Graphs  Integration techniques  Volumes  First and second order ordinary differential equations and modelling 17 11390691 Peta Evans Table 6: Comparison of current Mathematics courses Vs proposed new Mathematics courses

18. BOARD OF STUDY REQUIREMENTS Education Act 1990 The Education Act 1990 established the minimum curriculum requirements for students attending New South Wales schools and it has authorised the Board of Studies to establish guidelines for the course of study and minimum requirements for the award of School Certificate and Higher School Certificate. 18 11390691 Peta Evans

19. BOARD OF STUDY REQUIREMENTS BOS Requirements K-6Must meet minimum requirement of K-6 Syllabus School CertificateMust meet minimum requirement of Years 7-10 Mathematics Syllabus Indicative hours Monitoring and Reporting student Achievement Credential for achievement in School Certificate Higher School Certificate Must meet minimum requirement of Years 11-12 Mathematics Syllabus Assessment 19 11390691 Peta Evans Table 7: Summary of Board of Studies requirements adapted from (BOS, 2003a)

20. INTERNAL ASSESSMENT 20 11390691 Peta Evans Assessment ComponentsKnowledge, Understanding and Skills Application Mark General Mathematics4060100 Mathematics8020100 Mathematics Extension 135(70*)15(30*)50(100*) Mathematics Extension 26040100 Mathematics Life Skills Report of student’s achievements will be in a Profile Report based on the profile of students achievement of the outcomes for each module in the syllabus. Table 8: Summary of Assessment Components for Stage 6 Mathematics. Note: * indicating Mathematics Extension 1 assessment marks for those students who study Mathematics Extension 2.

21. REFERENCES New South Wales Board Of Studies.(n.d.). Assessment and curriculum information for Mathematics. Retrieved 1 March 2008, from http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths_assess_curr_info.pdf. New South Wales Board Of Studies. (1997a). Mathematics 2/3 Unit Years 11-12 Syllabus. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (1997b). Mathematics 4 Unit Year 12 Syllabus. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (2000). General Mathematics Stage 6 Syllabus. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (2002). Mathematics K-6 Syllabus. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (2003a). K-10 Curriculum framework. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (2003b). Mathematics Years 7-10 Syllabus. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (2007a). Mathematics Stage 6 Consultation Report. Sydney. New South Wales Board of Studies. NSW Board Of Studies. (2007b). Mathematics Stage 6 Writing Brief Courses Mathematics Advanced, mathematics Extension 1, mathematics Extension 2. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (2007c). Mathematics Stage 6 Writing brief Courses Mathematics General 1,Mathematics General 2. Sydney: New South Wales Board of Studies. New South Wales Board Of Studies. (2007d). Stage 6 Mathematics Life Skills Course Syllabus. Sydney: New South Wales Board of Studies. Nicholas, Z. (2007). EMM441 Curriculum Method 1: Mathematics Subject Outline. Bathurst: Charles Sturt University. NSW, Department of Education and Training. (2007). Curriculum Support. Retrieved February 28 2008, from http://www.curriculumsupport.education.nsw.gov.au/secondary/index.htm. New South Wales Parliamentary Councel’s Office. (2007e). Education Act 1990. Sydney. New South Wales Parliamentary Councel’s Office. 21 11390691 Peta Evans