scaffold-exercises

The saved excerpt is a snapshot from when this skill was listed. The external source remains the complete and most current version.

---
name: scaffold-exercises
description: Scaffold a graded problem set with sections, problems, worked solutions, and short "why this matters" explainers across analytical, empirical, and coding types. Use when user says "make a problem set on X", "scaffold exercises for this lecture", "create practice problems", "generate homework with a solution key", "build a graded assignment on topic Y". Emits a clean student set plus a separate solution key — NOT for grading submissions or auto-checking student answers.
argument-hint: "[topic] [--difficulty intro|core|advanced] [--count N] [--types analytical,empirical,coding] [--dataset path] [--no-solutions]"
allowed-tools: ["Read", "Grep", "Glob", "Write", "Bash"]
effort: medium
---

# `/scaffold-exercises` — Problem Set Scaffolder

Generate a graded problem set as two files: a clean **student set** (problems only) and a **solution key** (worked solutions + a one-line explainer per problem). Pattern imported from `mattpocock/skills`, adapted for economics teaching — the primary lens is graded coursework that mixes derivation, estimation, and code.

**Input:** `$ARGUMENTS` — a topic (e.g., "instrumental variables", "consumer theory", "quantile regression") and optional flags. See [Flags](#flags).

---

## When to use

- You have a lecture or reading and want a matching assignment with an answer key.
- You want a mix of problem types (derive, estimate, code) at a controlled difficulty, with solutions emitted **separately** so the student file stays clean.

Do **not** use this to grade submissions, auto-check answers, or build a timed exam — it scaffolds *practice/graded* material, not assessment infrastructure.

---

## Problem types

| Type | What the student does | Solution artifact |
| --- | --- | --- |
| **analytical** | Derive / prove / characterize (theory: optimization, identification, comparative statics) | Step-by-step derivation with the key lemma named |
| **empirical** | Estimate + interpret on a provided or simulated dataset | Expected estimate, sign/magnitude reasoning, common-mistake note |
| **coding** | Implement an estimator or simulation in R or Stata | Runnable reference snippet + expected output shape |

If no dataset is supplied for an empirical problem, generate a small **simulated** one with a fixed seed (YYYYMMDD) so the answer key is deterministic and reproducible.

---

## Workflow

### Phase 0: Set topic, difficulty, counts, types (Pre-Flight)

Read any source material the user points at (lecture `.tex`/`.qmd`, a paper, a dataset header) and produce a Pre-Flight Report **before** generating problems:

```markdown
## Pre-Flight Report — Problem Set

**Topic:** [topic]
**Source(s) read:** [lecture/paper/dataset — one-line takeaway each]
**Difficulty:** intro | core | advanced
**Counts by type:** analytical=N, empirical=N, coding=N  (total = `--count`)
**Dataset:** [provided path | simulated with seed YYYYMMDD | none]
**Learning objectives:** [2-4 bullets the set should exercise]
```

Resolve every flag here (interactive choices are gathered before generation, not mid-run). If the topic is too vague to write objectives, ask one clarifying question and stop. Otherwise proceed.

### Phase 1: Generate problems

For each problem, write a number, a section heading, the prompt, and any data/notation it needs. Conventions:

- **Motivation before mechanics** — one sentence on why the problem is worth solving, matching `create-lecture`'s pedagogy.
- **Notation reuse** — match symbols to the source lecture; never introduce a clashing symbol for an already-defined object.
- **Difficulty calibration** — *intro* checks one concept; *core* chains 2-3 steps; *advanced* requires a non-obvious insight or identification argument.
- **Self-contained** — each problem states its own assumptions; no "as in lecture 4" dangling references.

### Phase 2: Generate worked solutions + explainers

For every problem, write:

1. A **worked solution** — full derivation, expected estimate, or