MATHEMATICS K-12 PRESENTATIONMARCH 2008

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

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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

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STRUCTURES OF K-6, YEARS 7-10 AND

YEARS 11-12 SYLLABUS

RationaleAim ObjectivesOutcomes and ContentsAssessment and Reporting

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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

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PATHWAY FROM K-12

Mathematics Stage 5.2

Mathematics Years 11-12Mathematics Years 11-12Mathematics Years 7-10Mathematics Years 7-10Mathematics K-6Mathematics K-6

Mathematics Early Stage 1 to

Stage 3

MathematicsStage 4

Mathematics Stage 5.1

Mathematics Stage 5.3

Mathematics Life Skills

Stage 6Mathematics

Life Skills

Stage 6General Mathematics

Stage 6Mathematics

Stage 6 Mathematics Extension 1

Stage 6Mathematics Extension 2

MathematicsStage 5.2

LEGEND

Other available Pathway Usual Pathway

Figure 1: Pathways for K-6, Years 7-10 and Years 11-12 Mathematics (BOS, 2003).

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SUBJECTSK-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) .

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MathematicsLife Skills

General Mathematics

Mathematics/ Mathematics Extension 1

Mathematics Extension 2

6 Modules 5 units 18 Topics 8 Topics

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.

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STRANDS & CONTENT FOR STAGE 5STRAND

STAGE

WORKING

MATHEMATICALLY

NUMBER PATTERN &

ALGEBRA

DATA MEASUREMENT 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 59

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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

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STAGE 6 SYLLABUS CONTENTS

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MathematicsLife Skills

General MathematicsStage 6

2/3 Unit Mathematics

4 Unit Mathematics

Program of HSC studyGuideline for SchoolsContinuum for Stage 6 Life Skills StudentsAimObjectivesCourse structureObjectives and OutcomesKey CompetenciesModulesPost –school OpportunitiesAssessment and ReportingGlossary

Program of HSC studyGuideline for SchoolsContinuum for Stage 6 Life Skills StudentsAimObjectivesCourse structureObjectives and OutcomesPreliminary Course ContentHSC Course ContentCourse RequirementsPost –school opportunitiesAssessment and Reporting

Course descriptionIntroductionPart A- Statement of Syllabus Topics Part B: Additional Information on Syllabus Content

Mathematics K-12 Statement of PrinciplesThe Mathematics 4 Unit SyllabusGraphsComplex NumberConicsIntegrationVolumesMechanicsPolynomialsHarder 3 Unit Topics

Table 3: Summary of Stage 6 Syllabus contents (BOS, 1997a, 1997b, 2000, 2003, 2007d)

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

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PROPOSED NEW STAGE 6 COURSES

O

CURRENT COURSES

* Preliminary Mathematics General* HSC Mathematics General

Figure 2: Non calculus based courses proposal

1. Non Calculus based courses

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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.

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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 COURSETable 4: Course of study for Stage 6 Mathematics (BOS, 2007b, pp. 14-15).

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PROPOSED NEW STAGE 6 SYLLABUS CONTENTS

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Current 2/3 unit Mathematics Syllabus Contents

Current 4 Unit Mathematics Syllabus Contents

Proposed new Syllabus Contents for Stage 6 Mathematics

Course descriptionIntroductionPart A- Statement of Syllabus Topics Part B: Additional Information on Syllabus Content

Mathematics K-12 Statement of PrinciplesThe Mathematics 4 Unit SyllabusTopic 1: GraphsTopic 2: Complex NumberTopic 3: ConicsTopic 4: IntegrationTopic 5: VolumesTopic 6: MechanicsTopic 7: PolynomialsTopic 8: Harder 3 Unit Topics

RationalAimObjectivesContent organisationOutcomesContent Use of technologyAssessment & HSC ExaminationGlossarySupport MaterialsAppendix

Table 5: Comparison between current and proposed Syllabus Contents (BOS, 1997a, 1997b, 2007b)

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 MathematicsData analysis MeasurementProbabilityAlgebra and modelling

Basic arithmetic and algebraPlane geometryProbabilityReal function of a real variable and their geometrical representationTrigonometry ratios- review and some preliminary resultsLinear functions and linesSeries applicationsThe tangent to a curve and the derivative of a functionThe quadratic polynomial and the parabolaGeometrical applications of differentiationIntegrationLogarithmic and exponential functionsThe trigonometry functionsApplications of calculus to the physical worldInverse functions and the inverse trigonometric functionsPolynomialsBinomial theoremPermutations, combinations and further probability

GraphsComplex NumberConicsIntegrationVolumesMechanicsPolynomialsHarder 3 Unit Topics

Areas of studyFinancial MathematicsData analysis MeasurementProbabilityAlgebra and modelling

Focus studiesMathematics & communicationMathematics & drivingMathematics & designMathematics & household financeMathematics & health & leisure industriesMathematics& Natural Resource Management

Counting TechniquesProbabilityReal functions & their graphsTrigonometryDifferential calculusData analysisSequence & seriesIntegral calculusLogarithmic & exponential functionsMathematic modelling

Circle geometryFurther algebraTransformation of graphsOther inequalitiesPolynomialsElementary difference equations and the discrete logistic growth modelMathematic inductionThe binomial theorem, binomial identities and binomial probability distributionFurther trigonometryMethods of integrationInverse functionsFurther application of calculus involving mathematical modelling

Further inequalitiesComplex numbers and polynomials over complex fieldGraphsIntegration techniquesVolumesFirst and second order ordinary differential equations and modelling

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Table 6: Comparison of current Mathematics courses Vs proposed new Mathematics courses

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.

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BOARD OF STUDY REQUIREMENTS

BOS Requirements

K-6 Must meet minimum requirement of K-6 Syllabus

School Certificate Must 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

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Table 7: Summary of Board of Studies requirements adapted from (BOS, 2003a)

INTERNAL ASSESSMENT

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Assessment Components Knowledge , Understanding and Skills

Application Mark

weighting

General Mathematics 40 60 100

Mathematics 80 20 100

Mathematics Extension 1 35(70*) 15(30*) 50(100*)

Mathematics Extension 2 60 40 100

MathematicsLife 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.

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.

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