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MATHEMATICS K-12 PRESENTATION. MARCH 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 - PowerPoint PPT Presentation
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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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