Implement Real-Time Student Performance Analytics Database

Design a scalable MongoDB schema for tracking granular student performance metrics across multiple learning platforms. Create a normalized data model that can handle complex nested data from LMS systems like Canvas, Moodle, and custom platforms. Develop an aggregation pipeline that can generate real-time performance dashboards, including time-series analysis of learning progress, skill acquisition rates, and predictive learning trajectory calculations. Implement efficient indexing strategies to ensure sub-100ms query responses for dashboards serving 10,000+ concurrent educational institutions.