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