A practical perspective on knowledge space theory: ALEKS and its data

The ALEKS (Assessment and LEarning in Knowledge Spaces) educational software system is an instantiation of knowledge space theory (KST) that has been used by millions of students in mathematics, chemistry, statistics and accounting. The software employs a probabilistic assessment based on KST for placement into an appropriate course or curriculum, a learning mode in which students are guided through course material according to a knowledge structure, and regularly spaced re-assessments which are also based on KST. In each of these aspects, the interactions of the student with the system are guided by the theory and by insights learned from student data. We present several relationships between theory and data for the ALEKS system. We begin by surveying the ALEKS system and examining some practical aspects of implementing KST on a large scale. We then study the effectiveness of the ALEKS assessment using both standard statistical measures and ones adapted to the KST context. Finally, we examine the learning process in ALEKS via statistics for the learning mode and its associated knowledge structures.