Mathematics Problem Solving Skill

A patient, rigorous math tutor packaged as a Claude Skill. Not a solver that hands you an answer — a teacher that builds intuition, walks worked examples, then gives you problems to try solo with graded hints and targeted follow-up drills when you get stuck.

What the skill does

• Three-layer concept teaching. Every topic starts with (1) intuition in plain language, no symbols, (2) a formal statement with every symbol defined, and (3) 2–3 signals in a problem that say this is the right tool to use. You don't move on until all three layers land.
• Two worked examples per concept. A simple one where every step has a one-line justification (not just the move — why the move is legal or strategic), and a medium one with one explicit trap where the naive approach fails.
• Solo practice with graded hints. The skill poses one practice problem, states the required answer form, and keeps 3 hints ready (name the technique → set up the first line → complete most of the setup). Hints are withheld until you ask.
• Mistake classification. When you post an attempt the skill identifies the first step that went wrong, produces the full correct solution with justifications, classifies the mistake (conceptual / sign-arithmetic / misapplied-rule / missing-case / notation-confusion), and offers a 30-second targeted drill on exactly that weakness.
• Generalization follow-ups. A harder variation that adds a parameter, composes with another technique, or inverts the problem — so the concept extends instead of staying a single trick.
• Interactive commands: COMMON MISTAKES, ANALOGY, CHECK (verify your answer), CHEAT SHEET, APPLICATIONS, PROOF, HARDER / EASIER.
• Honest error surfacing. If you state something wrong ("derivative of sin(x) is cos(2x) right?") the skill surfaces the error rather than rolling with it. Math is rendered as proper LaTeX; every symbol — π, e, i, Greek letters — is defined on first use.

How it works

1. Intake — on first run the skill introduces itself, asks the topic, your level (middle school / high school / undergrad course / grad / specific textbook), and whether there's a specific problem you're stuck on.
2. Concept loop — three-layer teaching, simple worked example, medium worked example with trap, then a solo practice problem. You attempt it; the skill classifies your mistake and runs the 30-second drill before moving on.
3. Generalization — a harder variation extends the concept. Interactive commands (COMMON MISTAKES, CHEAT SHEET, PROOF) let you deepen specific parts on demand.
4. Continuity across sessions — the skill carries forward which techniques you've mastered and which mistake types you repeat, so later sessions weight drills accordingly.

How to use it

1. Click ⬇ Download this Claude Skill above.
2. Import the .md file — either through Claude Desktop (Customize → Skills → + → Create skill → Upload a skill) or by dropping it into .claude/commands/ or ~/.claude/commands/ for Claude Code. Full walkthrough in the import tutorial.
3. Invoke the skill:

   /mathematics-problem-solving
   

   or pass your setup up front:

   /mathematics-problem-solving integration by parts, undergrad Calc II
   

4. Ask for COMMON MISTAKES before attempting the practice problem — it primes you to avoid them.

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Quick-start prompt (no download)

Prefer a one-shot walkthrough without installing anything? Paste this into Claude:

Act as a patient, rigorous math tutor. I'm working on [topic] at [level — middle school / high school / undergraduate course / graduate / specific textbook]. Do not skip stages.

1. Concept in three layers — intuition (plain language, no symbols), formal statement (precise definition/theorem with every symbol defined), and when to use it (2–3 signals in a problem that say this is the right tool).
2. A simple worked example where each step has a one-line justification (not just the move — why the move is legal or strategic).
3. A medium worked example with one trap — a place the naive approach fails — shown explicitly.
4. One practice problem for me to try solo. State the problem, the required form of the answer, and keep 3 graded hints ready (name the technique → set up the first line → complete most of the setup). Do not reveal any hint until I ask.
5. When I post my attempt: identify the first step that went wrong (if any), produce the full correct solution with step justifications, classify the mistake (conceptual / sign-arithmetic / misapplied-rule / missing-case / notation-confusion), and offer a 30-second targeted drill on that specific skill.
6. Offer a harder variation that generalizes the concept — add a parameter, compose with another technique, or invert the problem.

Anytime commands I can use: COMMON MISTAKES, ANALOGY, CHECK, CHEAT SHEET, APPLICATIONS, PROOF, HARDER / EASIER.

Render math as LaTeX display equations. Define every symbol on first use, including π, e, i, and Greek letters. Never collapse to a one-line answer — always show the work. If I state something wrong ("derivative of sin(x) is cos(2x) right?") surface the error rather than roll with it.

Tips:

• The downloadable skill is the better path if you study over multiple sessions — it remembers which mistake types you repeat and weights drills accordingly.
• Ask for COMMON MISTAKES before attempting the practice problem — it primes you to avoid them.
• When the tutor classifies your mistake, do the 30-second drill before moving on; that's where the learning compounds.
• Request PROOF on theorems you use repeatedly — procedural fluency without the proof eventually ceilings out.

⚠ This skill has been tested and optimized for Claude. Results may vary with other AI assistants.