Mathematics education in Australia

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.

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.

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.

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.

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:

Foundation Mathematics (2 units): Very basic, practical maths skills are taught in this strand, which is only run at a Unit 1 + 2 level.

Further Mathematics (4 Units): Further Mathematics is considered to be the second-least demanding of the four maths subjects and is the "standard" maths course taken by Victorian students. It deals with topics including basic algebra, matrices, trigonometry, straight line geometry, business-related mathematics and other concepts

Mathematical Methods (CAS) (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, incorporating the use of computer algebra system technology (CAS) throughout the course.

Specialist Mathematics (4 Units): Specialist Mathematics is considered the most advanced high school mathematics subject in Victoria. 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.

In addition to the regular mathematics courses offered in VCE, a new subject called Algorithmics (Higher Education Scored Study) began its coursework in 2015. Since it is a fully scored subject supported by members in both the University of Melbourne and Monash University, it is different from University Extension studies. Beginning with definitions of abstract data types and algorithms, this subject explores the concepts of pseudocode, sorting, common graph algorithms, recursion, algorithm design patterns, algorithm analysis and computational complexity theory.

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 covers more practical topics than Maths B and C, but it is still OP eligible. There are considerably fewer algebraic concepts in this subject, and it is suitable for students who either struggled with mathematics in Year 10, or who do not require a knowledge of abstract mathematics in the future. 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 & 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.

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 considerably more theoretical than Maths A, requiring advanced algebra skills to successfully complete. It is a common prerequisite for science and engineering courses at Queensland Universities. 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. According to the Queensland Studies Authority, in 2010, 93% of students who studied Maths B were OP eligible.

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

Limits and Differential Calculus 1

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 extends the topics taught in Maths B, and covers additional pure-maths topics (including complex numbers, matrices, vectors, further calculus and number theory). Although not necessarily more difficult, it must be studied in conjunction with Maths B. Maths C gives the 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 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 & 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.

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

Since 2010, the Year 11 and 12 mathematics courses of study were:

Mathematics 1A/1B

Mathematics 1C/1D

Mathematics 2A/2B

Mathematics 2C/2D

Mathematics 3A/3B

Mathematics 3C/3D

Specialist Mathematics 3A/3B

Specialist Mathematics 3C/3D

Mathematics courses 1A/1B and 1C/1D are non-ATAR subjects.

However, new WACE mathematics courses are to be introduced for Year 11 students in 2015 and Year 12 students in 2016 in order to align with the Australian curriculum in Western Australia.

The new WACE mathematics courses consist of four units. Each unit is studied over one semester. Therefore, Unit 1 & 2 is studied in Year 11, and Unit 3 & 4 is studied in Year 12.

The new WACE mathematics courses are:

Mathematics Preliminary General

Mathematics Foundation General

Mathematics Essential General

Mathematics Applications ATAR

Mathematics Methods ATAR

Mathematics Specialist ATAR

ATAR mathematics courses are for university-bound students, whereas general courses are for non-ATAR students.

Syllabus information is available from the School Curriculum and Standards Authority (SCSA) website.

South Australia

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

Numeracy for Work and Community Life (up to and including Stage 1)

Mathematical Pathways

Mathematical Applications

Mathematical Methods

Mathematical Studies

Specialist Mathematics - more advanced topics that complement and are taken concurrently with Mathematical Studies.