  In this paper we present a method of modeling and analysis that permits the
extraction and quantitative display of detailed information about the effects
of instruction on a class's knowledge. The method relies on a congitive model
that represents student thinking in terms of mental models. Students frequently
fail to recognize relevant conditions that lead to appropriate uses of their
models. As a result they can use multiple models inconsistently. Once the most
common mental models have been determined by qualitative research, they can be
mapping onto a multiple choice test. Model analysis permits the interpretation
of such a situation. We illustrate the use of our method by analyzing results
from the FCI.
