---
name: "math-teaching-problem-set"
category: "math"
maturity: "stable"
version: "1"
description: "Design and grade math problem sets and exams — difficulty progression, rubric, anti-cheating variants, accessibility, and LaTeX layout."
license: "MIT"
capabilities: ""
outputs: ""
sideEffects: []
dependencies: []
stopCondition: "Problem-set + rubric + variants saved; difficulty progression documented."
risk: "low"
trustTier: "1"
maxIterations: "5"
promptVersion: "2.0"
artifactType: "pull-request"
modelTier: "reasoning"
evaluators: ["behavioral", "regression"]
fixturesPath: ""
diataxis: "how-to"
tags: ["math"]
compatibility: []
approvalRequired: "false"
approvalFor: []
---

## Contract

- Input: topic(s), audience level, problem count.
- Output: LaTeX problem set + rubric + variants.
- Scope: produces teaching artifacts; no live grading.
- Rule: produces teaching artifacts; no live grading.
- Rule: documented standards override defaults; explicit project rules take precedence.
- Rule: if blocked by missing context or dependencies, surface the blocker before proceeding.

## Provenance

| Question | Answer |
|---|---|
| What is the source of truth? | The user's request, originating spec/issue, and the skill's declared outputs |
| What is in scope? | Work covered by the skill's acceptance criteria and completion rules |
| What is explicitly out of scope? | Files, behaviors, and decisions outside the skill's declared boundary |
| Who or what consumes this artifact afterward? | The next skill in the workflow or the user |
| What evidence proves it is done? | Completion criteria met, artifact saved, validation passed |
| What risk remains? | Subjective judgment calls, missing context, or external dependency failures


## Artifact

Emit `MathTeachingProblemSetArtifact` as both:
- JSON: `.agents/skills/platform/artifacts/math-teaching-problem-set/{identifier}.json`
- Markdown view: same filename with `.md` extension


# 
# 
# 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.

## Completion

- the skill's completion criteria are explicitly checked
- the artifact is saved and validated
- any blockers or skipped validations are documented
- the next consumer is identified or the work is handed off
---
@include .agents/skills/platform/contract-base.xml