Math Teaching Problem Set

Contract

• Input: topic(s), audience level, problem count.
• Output: LaTeX problem set + rubric + variants.
• Side effects: none.
• Dependencies: none.
• Stop condition: artifacts saved; variants distinct.
• Risk: low.
• Boundary: produces teaching artifacts; no live grading.

Math Teaching — Problem Sets and Exams

Design a problem set or exam that tests the right concepts at the right difficulty, with grading rules and exam-ready variants.

When to use

• A course needs a problem set, midterm, or final.
• An instructor wants multiple variants for exam integrity.
• A grader needs a rubric with partial credit.

Process

1. Define the scope

• Course level — undergrad / graduate / competition.
• Topics — explicit list of concepts to test.
• Time — exam length; per-problem estimate.
• Allowed aids — open-book, calculator, none.

Completion criterion: scope explicit.

2. Build difficulty progression

Order problems so each builds on the prior:

• Tier 1 — recall: definitions, standard computations.
• Tier 2 — apply: use a known method in a new setting.
• Tier 3 — analyse: choose a method, justify.
• Tier 4 — synthesise / prove: construct a new argument or counterexample.

Each problem tags its tier.

Completion criterion: tiers labelled; progression tested.

3. Generate variants

For each problem, generate N variants (default 4) by:

• Permuting numerical parameters within the same difficulty.
• Swapping roles (e.g. domain/codomain swap).
• Re-arranging order without changing difficulty.

Variants must be provably distinct (different numerical answer or different proof).

Completion criterion: N variants exist; distinctness argued.

4. Rubric

For each problem, write a rubric:

• Total points.
• Per-step credit — which sub-step earns how much.
• Common mistakes — and their deductions.
• Proofs vs computation — partial credit for partial proofs.

Completion criterion: rubric saved with concrete point allocations.

5. Accessibility and layout

• Use LaTeX with semantic commands (\theorem, \lemma).
• Add alt text for figures (TikZ).
• Avoid colour-only signalling.
• Provide a print-friendly PDF and a screen-reader-friendly version.

Completion criterion: accessibility checklist completed.

Notes

• Pair with math-paper-collaboration for sharing and versioning.
• Use Overleaf for collaborative editing; tag each term's set.