Developing an Empirically-Based Applied Algebra Tutor

Abstract

To design computer tutorials that effectively teach conceptual skills, we need accurate cognitive models of both students and their learning processes. This article describes a tutorial designed to teach students how to generate algebraic equations for story problems. The starting point was earlier research that suggested that what differentiates good applied math students from weaker students is a general ability to map across representational systems (algebraic, graphical, natural language, and imagistic). The tutor was set up to teach students this skill and feedback to students' equations was geared to representational errors. The adequacy of this conceptualization was tested by collecting data in the form of automatically generated transcript files of all students and computer responses. The tutorial has undergone four cycles of development, test, and revision, that have led to an enrichment and diversification of the working models of both students and tutoring techniques.