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.