Mathematics education in Australia

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

Contents

[edit] New South Wales

[edit] 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 units): A basic mathematics course containing precalculus concepts, the course is heavily based on practical mathematics used in everyday life.[1]
  • Mathematics (2 units): 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 (3 units): A more advanced course building on concepts in calculus, trigonometry and basic combinatorics. Mathematics must also be studied in conjunction with this course.[2]
  • Mathematics Extension 2 (4 units): A highly advanced mathematics course containing an introduction to Complex Numbers, Advanced Calculus & Curve Sketching, Polynomials, Mechanics, Conics (Conics will be removed in 2009 and harder differentiation will replace it) and Harder Mathematics Extension 1 topics. Mathematics Extension 1 must also be studied in conjunction with this course and Mathematics (2units) is assumed knowledge when studying the course.[3]

[edit] Victoria

[edit] 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 (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.

[edit] Queensland

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

[edit] 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 stuations 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

[edit] 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 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 texting 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 (KPS); Modelling to Problem Solving (MPS); Communication & Justification (CJ). 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):

  • Functions (Inverse Functions)
  • Indices and Logarithms/ Exponential Functions
  • Polynomials
  • Rates of Change
  • Differential Calculus

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)

[edit] 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 and 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 hypothese; 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

[edit] Western Australia

Year 12 mathematical subjects in Western Australia include:[8]

  • Applicable mathematics: This course is a branch of T.E.E. math. The one year syllabus is broken down into a number of sections ranging from bivariate data to probability.
  • Calculus
  • Discrete Mathematics
  • Modelling with Mathematics

[edit] South Australia

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

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

[edit] 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.curriculum.wa.edu.au/pages/syllabus_manuals/volumes/IV_maths/maths.htm, Mathematics syllabus information.
  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.