Empirical Examination of a Learning Hierarchy Using an Item Response Theory Model

In this paper, the use of several measurement models for the analysis of data arising from learning hierarchies is discussed, and the results of an empirical investigation of the application of an Item Response Theory (IRT) model to a learning hierarchy in subtraction are examined. The analysis confronts the test developer’s original intentions with empirical data through the use of the IRT model, and three ways that the model can be useful in explicating the patterns of empirical results from a learning hierarchy are described.