/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.

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 runnable code (depending on type). Coding solutions must actually run; if Bash + R/Stata are available, execute the snippet and paste real output.
2. A "why this matters" explainer — 1-2 sentences linking the answer to the broader concept (the imported pattern's signature: every problem ships with a short rationale, not just a number).

Phase 3: Write student set + solution key

Emit two files (paths configurable; default under the working directory):

• exercises/<topic-slug>_problems.md — the student set: sections, problems, any data, NO answers.
• exercises/<topic-slug>_solutions.md — the solution key: each problem restated, its worked solution, and its explainer.

The split is load-bearing: never leak a solution into the student file. With --no-solutions, write only the student set and stop.

Output / Report format

Student set:

markdown
# Problem Set: [Topic]  (Difficulty: core)

## Section 1 — Analytical
**1.** [Motivation sentence.] [Prompt.]

## Section 2 — Empirical
**2.** Using `data/<file>` (vars: ...), [estimate + interpret prompt].

## Section 3 — Coding (R)
**3.** [Implement-X prompt.]

Solution key mirrors the numbering, adding ### Solution and > Why this matters: blocks per problem. Close your chat reply with a one-line manifest: files written, problem count by type, and whether code solutions were executed or only drafted.

Exit behavior

• Print the two output paths (absolute), the per-type counts, and the seed if a dataset was simulated.
• If a coding solution could not be executed (no R/Stata, or it errored), flag it as DRAFTED — NOT RUN rather than implying it was verified.
• If any empirical problem references variables not present in the supplied dataset, stop and surface the mismatch instead of inventing columns.

Flags

• --difficulty — intro | core | advanced (default core); calibrates step depth as in Phase 1.
• --count — total number of problems (default 6); split across types per the Pre-Flight counts.
• --types — comma-separated subset of analytical,empirical,coding (default all three).
• --dataset — path to a real dataset for empirical problems; omit to simulate one with a seeded DGP.
• --no-solutions — write only the student set; skip the solution key (Phase 2/3 key file).

Cross-references

• .claude/skills/create-lecture/SKILL.md — build the lecture these exercises practice; shares notation-reuse + motivation-first conventions.
• .claude/skills/data-analysis/SKILL.md — for empirical problems whose reference solution needs a full R estimation pipeline.
• .claude/skills/simulation-study/SKILL.md — when a problem demonstrates an estimator's finite-sample behavior; reuse its seeded-DGP discipline.
• .claude/skills/lit-review/SKILL.md — source advanced problems from current papers on the topic.
• .claude/skills/interview-me/SKILL.md — turn a fuzzy "I want a set on…" into concrete learning objectives first.
• templates/skill-template.md — house style for authoring/extending this skill.

What this skill does NOT do

• Does not grade student submissions or auto-check answers against a key.
• Does not run a timed exam or enforce assessment policy (point weights, rubrics, proctoring).
• Does not invent data — empirical problems use a supplied dataset or an explicitly seeded simulation, never fabricated numbers.
• Does not leak solutions into the student file, and does not deploy/publish anything (no /deploy).
• Does not auto-invoke other skills — it references siblings; it does not call them.