mathematical-problem-solving
Polya's four-phase method applied to mathematical problems, extended with Schoenfeld's control/monitoring layer. Covers understand, devise plan, carry out, look back. Includes heuristics specific to math (specialize, generalize, vary the problem, introduce auxiliary elements) and the metacognitive discipline that separates routine computation from genuine problem solving.
npx skills add majiayu000/claude-skill-registry --skill mathematical-problem-solving --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Mathematical Problem Solving Mathematics is the original proving ground for problem-solving theory. Polya's *How to Solve It* introduced the four phases (understand, plan, execute, review) that every subsequent framework builds on. Schoenfeld showed that phases alone are insufficient: without active monitoring ("control"), novices spend 20 minutes on a dead end without noticing. This skill combines the two: Polya's phases as the scaffold, Schoenfeld's control as the supervisor. **Agent affinity:** polya-ps (overall framing), schoenfeld (control and monitoring), simon (search structure) **Concept IDs:** prob-problem-representation, prob-goal-decomposition, prob-pattern-recognition, prob-simplification, prob-systematic-listing ## The Four Phases at a Glance | Phase | Polya question | Schoenfeld control check | |---|---|---| | 1. Understand | What is the unknown? What is given? What is the condition? | Do I actually understand this, or am I about to solve the wrong problem? | | 2. Plan | Do I know a related problem? Can I solve part of it? | Is this plan likely to work, and how much budget do I give it? | | 3. Execute | Can I check each step? | Is this step still making progress, or
- The Four Phases at a Glance
- Phase 1 — Understand the Problem
- Phase 2 — Devise a Plan
- Phase 3 — Carry Out the Plan
- Phase 4 — Look Back
- Schoenfeld's Control Layer
- Worked Example — A Geometry Problem
- When Mathematical Problem Solving Fails
- Cross-References
What does the mathematical-problem-solving skill do?
Polya's four-phase method applied to mathematical problems, extended with Schoenfeld's control/monitoring layer. Covers understand, devise plan, carry out, look back. Includes heuristics specific to math (specialize, generalize, vary the problem, introduce auxiliary elements) and the metacognitive discipline that separates routine computation from genuine problem solving.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill mathematical-problem-solving --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.