A Framework for Parameterized Design of Rule Systems Applied to Algebra

Creating a domain model (expert behavior) is a key component of every tutoring system. Whether the process is manual or semiautomatic, the construction of the rules of expert behavior requires substantial effort. Once finished, the domain model is treated as a fixed entity that does not change based on scope, sequence modifications, or student learning parameters. In this paper, we propose a framework for automatic learning and optimization of the domain model (expressed as condition-action rules) based on designer-provided learning criteria that include aspects of scope, progression sequence, efficiency of learned solutions, and working memory capacity. We present a proof-of-concept implementation based on program synthesis for the domain of linear algebra, and we evaluate this framework through preliminary illustrative scenarios of objective learning criteria.