| # 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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| | [**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 | |
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| ## 🏗️ Key Components |
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| ### 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 |
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| ### 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 |
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| ### 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) |
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| ### 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) |
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| ## 📊 Difficulty Taxonomy |
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| 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 |
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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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