# MathLingua — Adaptive Bilingual Math Tutoring System

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.

## 📄 Documents

| File | Description |
|---|---|
| [**technical_specification.md**](technical_specification.md) | Full paper-ready technical specification (~60KB, 1200+ lines) |
| [**system_architecture.md**](system_architecture.md) | Detailed system architecture with component diagrams, data flows, API contracts |

## 🏗️ Key Components

### Four-Level Scaffolding
- **L1**: Simplified English (shorter sentences, simpler vocabulary)
- **L2**: Bilingual keywords inline (English with Spanish annotations)
- **L3**: Full Spanish translation
- **L4**: Step-by-step solution reveal

### Hybrid Adaptive Algorithm
- **Elo Rating**: Overall student ability tracking with hint-weighted outcomes (1.0/0.75/0.50/0.25/0.0)
- **Bayesian Knowledge Tracing (BKT)**: Per-topic mastery estimation with slip adjustment for scaffold usage
- **Thompson Sampling**: ZPD-constrained question selection with exploration/exploitation balance

### Engineered Features
- **Language Dependency Score (LDS)**: Quantifies reliance on linguistic scaffolding (0 = English-independent, 1 = Spanish-dependent)
- **Math Confidence Score (MCS)**: Quantifies mathematical ability independent of language (0 = struggling, 1 = confident)

### Technology Stack
- Frontend: Next.js 14+ / TypeScript / Tailwind CSS
- Backend: Firebase (Auth, Firestore, Cloud Functions)
- LLM V1: Google Gemini 2.0 Flash
- SLM V2: Qwen2.5-3B-Instruct (QLoRA fine-tuned)
- Adaptive Engine: Client-side TypeScript (zero-latency decisions)

## 📊 Difficulty Taxonomy

15 sub-levels across 3 tiers, ordered by **linguistic complexity** (not mathematical difficulty):
- **Level 1 (Easy)**: 1.1–1.5, FK grade 1.0–6.0
- **Level 2 (Medium)**: 2.1–2.5, FK grade 5.5–10.0
- **Level 3 (Hard)**: 3.1–3.5, FK grade 9.5–14.0

Validated with monotonically increasing Flesch-Kincaid readability scores across all 15 levels.

## 📝 License

This project documentation is provided for educational and research purposes.