1. The what, when, how, and why of the secondary school mathematics curriculum
Merrilyn Goos

2. Here’s the plan … What mathematics gets taught in Queensland schools?
When are the main topics introduced and how much time is allocated to them?
Who makes the big curriculum decisions (about what gets taught to whom and why)?
How has the school mathematics curriculum changed over time and what might happen next?

3. Years 1-10 Mathematics Content: Number (numeration, operations)
Algebra (patterns, functions, equations)
Measurement (length, mass, area, volume)
Space (shape, location and direction)
Chance and Data
Processes (Working Mathematically):
Representation
Estimation
Problem solving
Applications
Reasoning
Justification
Communication
Reflection

4. Minimum time allocations for Years 1-10 Mathematics
Years 1-3: 200 hours/year (5 hours/week)
Years 4-7: 160 hours/year (4 hours/week)
Years 8-10: 80 hours/year (2 hours/week)
In practice, more time is allocated, especially in Years 8-10 (about 3 hours/week).

5. Years 11 and 12 Mathematics
Three subjects: Mathematics A (financial mathematics, applied geometry, statistics & probability + electives) Mathematics B (algebra, functions, calculus, statistics; no electives) Mathematics C (group theory, complex numbers, matrices, vectors, advanced calculus, structures & patterns + options)
General objectives (and assessment criteria):
Knowledge and procedures
Modelling and problem solving
Communication and justification
Minimum time allocation:
110 hours/year
In practice, timetabled for 3.5 hours/week.

6. Choosing senior mathematics subjects
Mathematics A: precursor to training in technical trades, administrative and managerial employment, some tertiary studies with moderate mathematical demand.
Mathematics B: precursor to tertiary studies with high mathematical demand (science, medicine, engineering, info tech, mathematics, finance, business, economics).
Mathematics C: recommended companion subject to Mathematics B; provides additional preparation for tertiary studies with high mathematical demand.

7. A day in the life … Families of functions Trig functions
Exponential & log functions
9-10 pm
Optimisation
Intro to integration
Applied statistical analysis
11pm – 12 am
Rates of change
Derivatives of trig, exponential, log fns
10-11 pm
Yr 1
Yr 3
Yr 5
Yr 7
Yr 9
Yr 10
Yr 11
Yr 12
Rational numbers
Index notation
Variables
Manipulation of algebraic expressions
Solution & graphing of linear equations
Similarity
Simple deductive geometry
5-7 pm
Solution of quadratic and simultaneous equations
7-9 pm
Place value to 100s
Represent simple fractions
5-7 am
Simple equivalent fractions
Decimal fractions to hundredths
Symmetry
Transformations
9-11 am
Integers
Addition of fractions with same denominator
Conversion between fractions, decimals, %
Order of operations
Tables of values
Congruence
1-3 pm

8. Notional time allocations for topics in Mathematics B (over 2 years)
Introduction to functions
35 hrs
Rates of change
Periodic functions & applications
30 hrs
Exponential and logarithmic functions & applications
Introduction to integration
25 hrs
Applied statistical analysis
Optimisation
TOTAL
215 hrs
Equivalent to 28 minutes
in a “day in the life” of a mathematics student, some time after 11pm!

9. Who makes curriculum decisions?
Potential stakeholders:
Ministers for Education
Officers of state education departments, Catholic Education, independent schools
State curriculum and assessment authorities
Teachers and teacher unions
Teacher professional associations
Principals
Parent organisations
Students
Employers and business organisations
University academics
Textbook writers and publishers
Media
Educational consultants and lobby groups
Curriculum
Mathematics
Society
Learner
Sources of influence on curriculum content

10. How does mathematics syllabus development work in Queensland?
Queensland Studies Authority is responsible for developing, revising, maintaining syllabuses via subject based Syllabus Advisory Committees (SACs).
SAC membership includes teachers (all levels of schooling, all sectors), university education academics; representatives of teacher unions, professional associations, parent organisations, business organisations. Each SAC is supported by a subject based professional officer of the QSA.
Senior syllabus revisions occur on a 7 year cycle. Consultation takes place with teachers (state wide survey), university academics (subject specialists), business organisations leading to preparation of a design brief for syllabus revision. SAC sub-committees made up of experienced teachers are established to undertake the revision, with support from QSA officers and oversight from the SAC.
The revised syllabus must be approved by the QSA Curriculum Committee.
Major syllabus revisions have a trial/pilot stage and state wide professional development, provided by the QSA, before full implementation.

11. How have school mathematics curricula changed over time?
1800
Influence of English curriculum models and newly established universities (Sydney, Melbourne). Curriculum was narrowly focused in preparing students for university entrance examinations.
1900
1960
“New Maths” – Cold War influence – emphasis on abstraction and mathematical structures.
1970
1980
Social and economic changes led to new emphasis on problem solving and real life applications.
1990
First attempt at a national curriculum – 8 Key Learning Areas and outcomes focus.
2000
2010
Second attempt at a national curriculum – making explicit what teachers must teach, what students should learn, and to what standard.

12. What will the national mathematics curriculum look like?
Three content strands:
Number and algebra
Measurement and geometry
Statistics and probability
Four proficiency strands:
Understanding (conceptual)
Fluency (procedural)
Problem solving (strategic competence)
Reasoning (adaptive)

13. Proposed national curriculum structure
All students to experience the full mathematics curriculum to the end of Year 9, with mathematics remaining compulsory in Year 10.
Differentiation of subjects in Years 11 and 12 (schools must preserve for all students the possibility of studying mathematics in Year 11).
Probably three levels of mathematics in Years 11 and 12: “elementary” (cf Maths A), “intermediate” (cf Maths B), “advanced” (cf Maths C).

14. Challenges for the national mathematics curriculum
Engage more students, especially in the middle years, and increase the proportion of students taking advanced subjects in the senior secondary years.
Cater for the great spread of achievement amongst students, but …
Impose no barriers to progression in mathematics before the senior secondary years.
Identify and emphasise the “big ideas” or core topics in mathematics (thin out the crowded curriculum).

15. Your questions?