Sigma
Run a Bloom-style 1-on-1 mastery tutor in your agent terminal when you need to deeply learn a new stack, domain, or concept before you build or ship.
Overview
Sigma is a journey-wide agent skill that runs Bloom-style 1-on-1 mastery tutoring with Socratic questioning—usable whenever a solo builder needs verified understanding of a topic before committing to build or ship decisi
Install
npx skills add https://github.com/sanyuan0704/sanyuan-skills --skill sigmaWhat is this skill?
- Socratic questioning that guides discovery instead of dumping final answers
- Mastery gate: advance only after roughly 80% understanding on a calibrated rubric
- Misconception tracking with counter-examples and resolution follow-up
- Spaced repetition inspired by SM-2 when you resume sessions
- Interleaved review mixing prior mastered concepts to reduce forgetting
- ~80% rubric mastery threshold before advancing to the next concept
- Bloom 2-Sigma framing: about 2 standard deviations above conventional classroom performance under mastery tutoring
- SM-2 inspired spaced repetition scheduling on session resume
Adoption & trust: 2.1k installs on skills.sh; 3.6k GitHub stars; 3/3 security scanners passed (skills.sh audits).
What problem does it solve?
You are tackling an unfamiliar topic but one-shot explanations and skimming docs do not confirm what you actually understand or which misconceptions will break your implementation later.
Who is it for?
Solo builders learning a new language, framework, or product domain who want interactive tutoring with an explicit ~80% mastery bar before they implement.
Skip if: Quick syntax lookups, copy-paste snippets, or situations where you already have an approved spec and only need execution—not a multi-session learning ritual.
When should I use this skill?
You want to deeply learn or relearn a topic with one-on-one tutoring, misconception repair, and mastery gating—not a single-shot answer—before or during product work.
What do I get? / Deliverables
You work through a mastery-gated tutoring loop with tracked misconceptions, spaced and interleaved review, and visual study artifacts until rubric scoring shows you are ready to apply the material in real work.
- Session progress and mastery state tracked across resumes
- HTML learning dashboards and Excalidraw-style concept maps
- Generated visual explanations tied to the active lesson
Recommended Skills
Journey fit
Useful at every journey phase - explore requirements and options before committing to a direction.
Where it fits
Master how vector databases differ before you pick an embedding stack for a side project.
Tutor through pricing and packaging concepts until you can defend a minimal viable offer without hand-wavy assumptions.
Interleaved Socratic drills on auth flows and session edge cases while you implement your first production login.
Resume spaced review after an outage to close gaps in how retries and idempotency actually behaved in your code.
Build durable mental models for SEO entities you will write about so content matches how search systems classify topics.
How it compares
Use instead of passive docs or unstructured chat explanations when you need mastery-checked tutoring, not a single summarized answer.
Common Questions / FAQ
Who is sigma for?
Sigma is for solo and indie builders using Claude Code, Cursor, Codex, Windsurf, or similar agents who want a structured personal tutor for any technical or conceptual topic, not a static course dump.
When should I use sigma?
Use it during Idea research when exploring a new stack, in Validate when you must understand scope tradeoffs before prototyping, during Build when onboarding to unfamiliar APIs, and in Operate when post-incident learning needs misconception repair and spaced review.
Is sigma safe to install?
Treat it like any third-party agent skill: review the Security Audits panel on this Prism page and your agent’s permissions before enabling filesystem or network-backed visual generation in your environment.
SKILL.md
READMESKILL.md - Sigma
# Sigma Personalized 1-on-1 AI tutor agent skill. Based on Bloom's 2-Sigma mastery learning — the finding that students tutored one-on-one with mastery methods perform **2 standard deviations** above conventional classroom students. Sigma guides you through any topic with Socratic questioning, adaptive pacing, and rich visual output (HTML dashboards, Excalidraw concept maps, generated images). Compatible with any AI agent terminal: **Claude Code** / **Cursor** / **Trae** / **CodeX** / **Windsurf** and more. <p align="center"> <img src="https://img.shields.io/badge/Agent_Skill-Tutor-blue" alt="Agent Skill" /> <img src="https://img.shields.io/badge/Method-Bloom's_2--Sigma-green" alt="Bloom's 2-Sigma" /> <img src="https://img.shields.io/badge/License-MIT-yellow" alt="MIT License" /> </p> ## Installation ```bash npx skills add sanyuan0704/sanyuan-skills --path skills/sigma ``` ## Features - **Socratic Questioning** — Never gives answers directly; guides you to discover them yourself - **Mastery Learning** — Advances to the next concept only when you demonstrate ≥80% understanding via calibrated rubric scoring - **Misconception Tracking** — Identifies wrong mental models behind incorrect answers, designs counter-examples to dismantle them, tracks resolution - **Spaced Repetition** — SM-2 inspired review scheduling on resume; mastered concepts are re-tested at increasing intervals to fight the forgetting curve - **Interleaving** — Mixes questions about previously mastered concepts into the current learning flow, improving long-term retention by ~43% - **Practice Phase** — Requires learners to DO something (write code, design, explain) before a concept is marked mastered — understanding ≠ ability - **Self-Assessment Calibration** — Detects fluency illusion by comparing learner's self-assessment with rubric scores - **Adaptive Pacing** — Speeds up when you're flying, slows down when you're struggling - **Visual Roadmap** — Live HTML dashboard tracking your progress through every concept - **Concept Maps** — Excalidraw diagrams showing relationships between topics - **Cross-Topic Learner Profile** — Remembers your learning style, misconception patterns, and strengths across different topics - **Session Persistence** — Save and resume learning sessions anytime - **Multilingual** — Follows your language automatically; technical terms stay in English with translation ## Usage After installation, invoke with: ```bash /sigma Python decorators /sigma 量子力学 --level beginner /sigma React hooks --level intermediate --lang zh /sigma linear algebra --resume # Resume previous session ``` ### Arguments | Argument | Description | |----------|-------------| | `<topic>` | Subject to learn (required, or prompted) | | `--level <level>` | Starting level: `beginner`, `intermediate`, `advanced` (default: diagnose) | | `--lang <code>` | Language override (default: follow user's input language) | | `--resume` | Resume previous session from `sigma/{topic-slug}/` | | `--visual` | Force rich visual output every round | ## How It Works ``` Input → Parse Topic → Diagnose Level → Build Roadmap → Tutor Loop → Session End ↑ | | (mastery < 80%) | +----------------------------------+ ``` ### 1. Diagnose Sigma starts by probing your current understanding with 2-3 diagnostic questions — mixing multiple choice and open-ended — to calibrate exactly where you are. ### 2. Build Roadmap Decomposes the topic into 5-15 atomic concepts ordered by dependency, then generates a visual HTML roadmap showing your learning path. ### 3. Tutor Loop For each concept: - **Introduce** with a question, not a lecture - **Question cycle** alternating structured choices, open-ended questions, and interleaving with past concepts - **Misconception tracking** — wrong answers are diagnosed for underlying wrong mental models, counter-examples a