Analyzing and Generating Mathematical Models: An Algebra II Cognitive Tutor Design Study

This paper reports a formative analysis of a Math Modeling Tool in the Algebra II Cognitive Tutor. This tutor is designed to support algebraic reasoning about real world problems. This study focuses on reasoning about situations that can be modeled with general linear form expressions (c = ax + by). Formative evaluations of an early general linear form lesson showed that it helped students comprehend the underlying problem situations, but was less successful in helping students construct symbolic models of the situations. These evaluations guided design of a new tool to scaffold students’ understanding of the componential structure of these symbolic models and the mapping of model components to the problem situation. An empirical evaluation shows that the new tool successfully helps students understand the structure of these mathematical models and learn to construct them.