Add MathLingua README
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README.md
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# MathLingua — Adaptive Bilingual Math Tutoring System
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An adaptive tutoring system for Spanish-speaking students (grades 6–8) transitioning to English-medium mathematics education. Uses progressive bilingual scaffolding and a hybrid adaptive algorithm to personalize difficulty.
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## 📄 Documents
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| File | Description |
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|---|---|
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| [**technical_specification.md**](technical_specification.md) | Full paper-ready technical specification (~60KB, 1200+ lines) |
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| [**system_architecture.md**](system_architecture.md) | Detailed system architecture with component diagrams, data flows, API contracts |
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## 🏗️ Key Components
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### Four-Level Scaffolding
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- **L1**: Simplified English (shorter sentences, simpler vocabulary)
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- **L2**: Bilingual keywords inline (English with Spanish annotations)
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- **L3**: Full Spanish translation
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- **L4**: Step-by-step solution reveal
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### Hybrid Adaptive Algorithm
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- **Elo Rating**: Overall student ability tracking with hint-weighted outcomes (1.0/0.75/0.50/0.25/0.0)
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- **Bayesian Knowledge Tracing (BKT)**: Per-topic mastery estimation with slip adjustment for scaffold usage
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- **Thompson Sampling**: ZPD-constrained question selection with exploration/exploitation balance
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### Engineered Features
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- **Language Dependency Score (LDS)**: Quantifies reliance on linguistic scaffolding (0 = English-independent, 1 = Spanish-dependent)
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- **Math Confidence Score (MCS)**: Quantifies mathematical ability independent of language (0 = struggling, 1 = confident)
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### Technology Stack
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- Frontend: Next.js 14+ / TypeScript / Tailwind CSS
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- Backend: Firebase (Auth, Firestore, Cloud Functions)
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- LLM V1: Google Gemini 2.0 Flash
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- SLM V2: Qwen2.5-3B-Instruct (QLoRA fine-tuned)
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- Adaptive Engine: Client-side TypeScript (zero-latency decisions)
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## 📊 Difficulty Taxonomy
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15 sub-levels across 3 tiers, ordered by **linguistic complexity** (not mathematical difficulty):
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- **Level 1 (Easy)**: 1.1–1.5, FK grade 1.0–6.0
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- **Level 2 (Medium)**: 2.1–2.5, FK grade 5.5–10.0
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- **Level 3 (Hard)**: 3.1–3.5, FK grade 9.5–14.0
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Validated with monotonically increasing Flesch-Kincaid readability scores across all 15 levels.
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## 📝 License
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This project documentation is provided for educational and research purposes.
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