This project will continue the development of a new theory of learning in which the progress of students learning over time is modeled probabilistically as a Markov stochastic process. This theory is designed to provide responses to key questions about learning processes such as : What is the distribution of the knowledge states at the beginning of a particular grade in school, such as grade 4? What are the most frequently traveled learning paths? What are the easiest items for a student to learn given a particular knowledge state? How long does it take, on the average, for a student with a particular learning rate to go from one knowledge state to another? Do the students in school district A tend to follow different paths from those in school district B? This theory is a potentially powerful tool for the precise monitoring of students' learning. However, crucial work remains to be done for this theory to be easily applied by practitioners. So far it has been applied only to the special case of a single test given at a particular time. The cases of two or more tests (on the same sample of students) raise a number of technical issues (some of which are related to parameter estimations) which will be addressed in the research. The PI will also conduct an application of the theory.
