Weighting the Problem-Solving Task in a SAC
A school's Specialist Mathematics team is designing a single School-Assessed Coursework task for Unit 3, Outcome 1 (mathematical methods and reasoning). The task is worth 40 marks and is scored against three performance descriptors: 'Methods and reasoning' (weighted 40%), 'Modelling and problem-solving' (weighted 30%), and 'Communication and clarity' (weighted 30%). A draft marking scheme awards marks as follows: 28 marks for correct final answers, 6 marks for correct method shown, 4 marks for notation and setting out. The panel also notes that the total coursework contribution to the Unit 3 study score is 17 per cent, and that the task must be completed under supervised conditions in one continuous period. One teacher argues the draft is fine because 'most marks are for maths'. The panel chair is uneasy.
1. Using the descriptor weightings, evaluate whether the draft marking scheme is defensible. Show the reasoning with numbers.
Read the worked answer
Convert the draft to percentage shares of the 40 marks:
- Final answers: 28/40 = 70%
- Method shown: 6/40 = 15%
- Notation and setting out: 4/40 = 10%
Compare with the intended descriptor weightings:
- Methods and reasoning: 40% intended vs roughly 15% (method) + part of answers
- Modelling and problem-solving: 30% intended vs 0% explicitly
- Communication: 30% intended vs 10%
The draft is heavily skewed to answer-getting (70%) and gives no explicit credit to modelling or problem-solving. A student who sets up a correct model but slips on arithmetic would be penalised disproportionately, while a student who guesses or reproduces a memorised procedure gains most marks. The scheme is therefore not defensible: it does not operationalise the published descriptors. A revision should allocate marks roughly in the ratio 16:12:12 across methods/reasoning, modelling/problem-solving and communication, with mark descriptors written for each band so that partial credit reflects the quality of reasoning, not just the final value.
2. The task is completed in one continuous supervised period. A student asks mid-task whether they may use a CAS calculator to solve a differential equation numerically. What should the supervising teacher do, and how does this connect to the 'modelling and problem-solving' descriptor?
Read the worked answer
The teacher must follow the school's documented task instructions, not improvise. If the task specification permits CAS, the answer is yes; if it does not, the teacher must decline and record the request. Improvising mid-task would compromise comparability across students and undermine the validity of the assessment.
The deeper issue is alignment. If the descriptor awards 30% for modelling and problem-solving, the task should be designed so that numerical solution by CAS is either explicitly permitted (and then the modelling marks reward sensible choice of technique, interpretation and validation) or explicitly excluded (and then the modelling marks reward analytical setup). Either way, the instruction sheet must state the technology rule before the task begins. The teacher's response is therefore a procedural one: apply the pre-stated rule and note the incident for the panel, which should review whether the technology rule matches the descriptor intent.
3. A colleague proposes moving this task to an unsupervised take-home format to allow more time for modelling. Give two reasons why this conflicts with the assessment requirements and one way to preserve modelling depth within supervision.
Read the worked answer
Two conflicts:
- Authentication. School-assessed coursework contributing to the study score must be completed under conditions that allow the teacher to authenticate each student's work. A take-home task cannot reliably establish authorship, so the result is not defensible for a scored contribution.
- Comparability and equity. Take-home conditions vary (time, help, resources), so scores are not comparable across students or against the descriptor bands. This undermines the validity of the 17 per cent contribution.
A way to preserve modelling depth: design a shorter supervised task with a rich, unfamiliar context and staged prompts - for example, a scaffolded modelling question where students must choose assumptions, set up a relation, interpret a parameter, and critique the model's limitations. Depth comes from the quality of the modelling decisions, not from elapsed time. The teacher can also provide a pre-released context brief (no solutions) so that reading time is not consumed during the supervised period.