Mathematics education in Australia


Mathematics education in Australia

Mathematics education in Australia varies considerably between various states due to the different education systems in place in each state.

Contents

New South Wales

Higher School Certificate

The Higher School Certificate (HSC) in NSW contains a number of mathematics courses catering for a range of abilities. There are four courses offered by the Board of Studies for HSC Study:

  • General Mathematics (2 unit): A basic mathematics course containing precalculus concepts, the course is heavily based on practical mathematics used in everyday life.[1]
  • Mathematics (2 unit): An advanced level course based on Calculus also with detailed study in trigonometry, curve sketching and other complex algebraic disciplines such as locus. It is the highest level non-extension mathematics course.[2]
  • Mathematics Extension 1 (1 unit): A more advanced course building on concepts in calculus, trigonometry, polynomials and basic combinatorics. Mathematics must also be studied in conjunction with this course.[2]
  • Mathematics Extension 2 (1 unit): A highly advanced mathematics course containing an introduction to Complex Numbers, Advanced Calculus & Curve Sketching, advanced Polynomials, Mechanics, Conics and Harder Mathematics Extension 1 topics. Mathematics (2 unit) and Mathematics Extension 1 must also be studied in conjunction with this course, however students are not directly assessed on Mathematics (2 unit) material.[3]

Victoria

Victorian Certificate of Education

The Victorian Certificate of Education (VCE) mathematics subjects are designed to cater for the varying abilities and aptitudes of Victorian students. There are four courses offered for VCE study:[4]

  • Further Mathematics (4 Units): Further Mathematics is considered to be the least demanding of the four maths subjects. It deals with topics including matrices, trigonometry, straight line geometry, business-related mathematics and other precalculus concepts.
  • Mathematical Methods (4 Units): Mathematical Methods is the most common non-compulsory prerequisite for tertiary study in Victoria. Methods deals with concepts including differential calculus, integral calculus, circular functions, probability and the behaviour of functions with a single real variable.
  • Mathematical Methods (CAS) (4 Units): The Mathematical Methods (CAS) course closely resembles the Mathematical Methods course. However, in contrast to Methods, Methods (CAS) incorporates the use of computer algebra system technology (CAS) throughout the course.
  • Specialist Mathematics (2 Units): Specialist Mathematics is considered the most advanced high school mathematics subject in Victoria. The Year 11 subjects General Mathematics and Mathematical Methods (Units 1 & 2) are both prerequisites for the study of Specialist Mathematics. The subject covers concepts including conic sections, complex numbers, differential equations, kinematics, vector calculus and mechanics. The idea behind Specialist Mathematics is to integrate already learnt concepts of calculus into other fields of mathematics, thus giving Specialist Mathematics a far more practical orientation than standard mathematical subjects.

Queensland

In Queensland, the senior (years 11 and 12) curriculum is divided into three parts: Maths A, Maths B, and Maths C.

Mathematics A

Maths A is the easiest of all three, but it is still OP eligible. Maths A is designed to help students to develop an appreciation of the value of Mathematics to humanity. Students learn how mathematical concepts may be applied to a variety of life situations including business and recreational activities. The skills encountered are relevant to a vast array of careers (trade, technical, business etc). Assessments in the subject include both formative and summative written tests, assignments and practical work. It is assessed in the categories: Knowledge & Procedures (KAPS); Modelling to Problem Solving (MAPS); Communication & Justification (CAJ). Although Maths A is not a pre-requisite subject, but it is sufficient for entrance to many tertiary courses.[5]

The course is divided into four (4) semesters (1 semester = 2 terms). The skills learned in each semester are as follows:

Semester 1 (Year 11/Form 5):

  • Data Analysis
  • Managing Money
  • Applied Geometry
  • Linking 2 and 3 Dimensions

Semester 2 (Year 11/Form 5):

  • Land Measurement
  • Applied Geometry
  • Statistics
  • Managing Money

Semester 3 (Year 12/Form 6):

  • Managing Money
  • Land Measurement
  • Data Analysis
  • Operations Research

Semester 4 (Year 12/Form 6):

  • Statistics
  • Land Measurement
  • Navigation
  • and an elective topic on Data

Mathematics B

Maths B is the second hardest of the three. Maths B (in some schools) can be studied at the same time with either Maths A or Maths C, but not both. Maths B gives students an understanding of the methods and principles of mathematics and the ability to apply them in everyday situations and in purely mathematical contexts; the capacity to model actual situations and deduce properties from the model; an interest and ability in framing and testing mathematical hypotheses; the ability to express and communicate any results obtained; some knowledge of the history of mathematics; encouragement to think independently and creatively. Assessments are similar as those of Maths A, which includes both formative (Semester 1) and summative (Semesters 2,3 and 4) written tests, assignments and post-assignment tests. It is also assessed in the three categories Knowledge & Procedures (KAP); Modelling & Problem Solving (MAP); Communication & Justification (CAJ). Maths B is a pre-requisite for any tertiary course which deals with or uses math and/or science.[6]

The course is divided into four (4) semesters. The skills learned each semester are as follows:

Semester 1 (Year 11/Form 5):

  • Functions (Linear, Quadratic, Absolute Value)
  • Periodic Functions (Trigonometry, Sin/Cosine Functions)
  • Applied Statistics (Mean, Median, Mode, Lie Factor)
  • Applied Statistics 2 (Linear/Quadratic Regression, Residual Plots)

Semester 2 (Year 11/Form 5):

  • Exploring Data / Statistics
  • Indices and Logarithms/ Exponential Functions


Semester 3 (Year 12/Form 6):

  • Exponential and Log Functions
  • Optimization Using Derivatives
  • Integration
  • Integral Calculus

Semester 4 (Year 12/Form 6):

  • Applied Statistical Analysis
  • Integration
  • Differential Calculus 2
  • Optimisation (Other Methods)

Mathematics C

Maths C is considered to be the hardest of the three maths and must be studied in conjunction with Maths B. Maths C gives the students an understanding of the methods and principals of mathematics and the ability to apply them in everyday situations and in purely mathematical contexts; the capacity to model actual situations and deduce properties from the model; an interest and ability in framing and testing mathematical hypotheses; the ability to express and communicate any results obtained; some knowledge of the history of mathematics; encouragement to think independently and creatively. Assessments are in the same as the other two courses, formative and summative written tests, assignments and practical work. The student is assessed in the areas of Knowledge & Procedures (KAPS); Modelling to Problem Solving (MAPS); Communication & Justification (CAJ). Maths C can be a pre-requisite to tertiary courses with a heavy maths/science basis. Some skills learned in Maths C would be found in business and economics degrees.[7]

The course is divided into four (4) semesters. The areas learned are in the following:

Semester 1 (Year 11/Form 5):

  • Real and Complex Numbers
  • Matrices
  • Vectors
  • Groups
  • Structures & Patterns

Semester 2 (Year 11/Form 5):

  • Applications of Matrices
  • Vectors
  • Real and Complex Numbers
  • Dynamics
  • Structures and Patterns

Semester 3 (Year 12/Form 6):

  • Structures and Patterns
  • Real and Complex Numbers
  • Matrices
  • Periodic Functions
  • Calculus
  • Option I & II

Semester 4 (Year 12/Form 6):

  • Vectors
  • Calculus
  • Dynamics
  • Vectors
  • Option I & II

Western Australia

Year 11 & 12 mathematics in Western Australian began a change in 2009 now complete in 2010. The new "courses of study" are: Maths 1A/1B Maths 1C/1D Maths 2A/2B Maths 2C/2D Maths (MAT) 3A/3B Maths (MAT) 3C/3D Maths (MAS) 3A/3B Maths (MAS) 3C/3D

MAS is Maths Specialist formerly Geometry & Trigonometry, while MAT is formerly Calculus.

Syllabus is available from the Western Australian Curriculum Council website.

South Australia

In South Australia the mathematics courses are split into three levels:

  • Mathematical Applications[8]
  • Mathematical Methods[9]
  • Mathematical Studies[10]
  • Specialist Mathematics - more advanced topics that complement and are taken concurrently with Mathematical Studies.[11]

References

  1. ^ http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths_general_syl.pdf (PDF), General Mathematics syllabus.
  2. ^ a b http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths23u_syl.pdf (PDF), Mathematics 2/3 Unit syllabus.
  3. ^ http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths4u_syl.pdf (PDF), Mathematics 4 Unit syllabus.
  4. ^ http://vcaa.vic.edu.au/vce/studies/mathematics/mathsstd.pdf (PDF), VCE Mathematics Study Design Units 1-4: 2006-2009.
  5. ^ http://www.qsa.qld.edu.au/yrs11_12/subjects/maths_a/syllabus.pdf (PDF), Mathematics A syllabus.
  6. ^ http://www.qsa.qld.edu.au/yrs11_12/subjects/maths_b/syllabus.pdf (PDF), Mathematics B syllabus.
  7. ^ http://www.qsa.qld.edu.au/yrs11_12/subjects/maths_c/syllabus.pdf (PDF), Mathematics C syllabus.
  8. ^ http://www.ssabsa.sa.edu.au/docs/cs-2007/2mme-cs-2007.pdf (PDF), Mathematical Applications syllabus.
  9. ^ http://www.ssabsa.sa.edu.au/docs/cs-2007/2mme-cs-2007.pdf (PDF), Mathematical Methods syllabus.
  10. ^ http://www.ssabsa.sa.edu.au/docs/cs-2007/2msu-cs-2007.pdf (PDF), Mathematical Studies syllabus.
  11. ^ http://www.ssabsa.sa.edu.au/docs/cs-2007/2msl-cs-2007.pdf (PDF), Specialist Mathematics syllabus.

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