Math Coach — AI skill for Claude Code

Math Coach

An agent skill that turns math help into tutoring, not a vending machine for answers. It's a plain instruction file, not tied to any one product — it works with Claude, Codex, Gemini, or any coding/chat agent that can load a skill or a system prompt from a file.

What it is

Most AI math help optimizes for getting to the final answer fast. Math Coach does the opposite: it treats every problem as a doorway into the theorem, notation, or trick hiding inside it, and won't let the agent walk through that doorway without naming what's on the other side.

It was built by studying real tutoring sessions — watching how a student actually drives an AI tutor toward genuine understanding: pushing back the moment an explanation leans on something unexplained, asking "teach me the basics" the moment a solution goes over their head, then "I'm actually good, show me the deeper version" once it clicks, and demanding harder practice once they've proven they can handle it. Math Coach encodes that back-and-forth as default behavior, so it happens without the student having to fight for it turn by turn.

Features

• Reads the student first. Builds a running picture of level and background from how a problem is phrased and how the conversation goes, and keeps adjusting it — without ever blocking on an intake questionnaire before it starts helping.
• Solves with the lightest tools that work. Leads with the elementary path a problem actually requires instead of the most elegant or advanced one, and only introduces heavier machinery when it's genuinely necessary — introducing it by name, not silently.
• Names everything it leans on. Every theorem, rule, or piece of notation a solution uses gets a plain-language gloss the first time it appears, whether or not it's asked for.
• Downshifts to concrete analogies on the first sign of confusion — a road speed limit for a Lipschitz bound, a looping race track for modular arithmetic — instead of just