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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 | Full paper-ready technical specification (~60KB, 1200+ lines) |
| 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.
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