Abstract: Learning analytics system (LAS) has the potential to pull together diverse resources and services to leverage the best practices for education. As the central component of this system, current LAS engines have been limited in function and vaguely defined as well as poor scalability and extensibility to other
contexts and institutions. This paper first proposed engine ontology, role, source, time and control, to describe and distinct four engine functions: Prediction, Reflection, Recommendation, and Adaptation, in order to establish a common language and practice for LA engines, and in turn improve interoperability between different LA applications. Based on those ontological engines, this study further designed a mechanism of LAS engines and applied mathematical
modeling to explain its decomposition and recombination techniques. This LAS engines is expected to power an open and integrated LAS that is capable of scaling up and extensible to any context.

Key words: learning analytics, learning analytics system, learning analytics system engines, mathematical modeling