Planning and Developing a Program
Sequencing a course
Program planning means mapping the unit content onto a teaching calendar that respects prerequisite order. The critical dependencies are: functions and transformations → inverse functions → complex numbers; vectors in 2D → vectors in 3D → vector calculus and kinematics; differentiation → integration → differential equations. If you teach differential equations before integration techniques, students cannot solve them.
Choosing and ordering tasks
Each unit specifies School-assessed Coursework (SAC) with a set number and type of tasks. Typical task types include assignments, tests, modelling tasks, and problem-solving tasks. A sound program distributes tasks so each outcome is evidenced at least once, and weights them per the study design. Traps: overloading one outcome with multiple tasks while leaving another unassessed; scheduling a SAC immediately after teaching a topic with no revision buffer.
The modelling component
Specialist Mathematics rewards modelling tasks where students apply mathematics to a real context (projectile motion, AC circuits, population models). A good program allocates time for students to interpret results, not just compute them. Build in at least one modelling task per unit where the study design permits.
Technology and pseudocode
Programs should specify where CAS/technology is permitted and where it is not, and where pseudocode is used to describe algorithms (e.g. numerical solution of equations, Euler's method). Students must be able to read and trace pseudocode, not just run it.
Rule of thumb
Before finalising a calendar, draw a dependency graph of topics and check that no arrow points backwards. Then overlay the SAC dates and confirm each outcome is covered.
Worked example
A student plans to teach Euler's method in Week 4 and differential equations in Week 8. This is fine: Euler's method uses the derivative, and differential equations use Euler's method as a numerical tool. But teaching integration by parts after differential equations is a dependency error - reverse it.