Human learning, Pedagogical strategy, Student modeling, Transfer of learning
Efforts to improve instructional task design often make reference to the mental structures, such as “schemas” (e.g., Gick & Holyoak, 1983) or “identical elements” (Thorndike & Woodworth, 1901), that are common to both the instructional and target tasks. This component based (e.g., Singley & Anderson, 1989) approach has been employed in psychometrics (Tatsuoka, 1983), cognitive science (Koedinger & MacLaren, 2002), and most recently in educational data mining (Cen, Koedinger, & Junker, 2006). A typical assumption of these theory based models is that an itemization of “knowledge components” shared between tasks is sufficient to predict transfer between these tasks. In this paper we step back from these more cognitive theory based models of transfer and suggest a psychometric measurement model that removes most cognitive assumptions, thus allowing us to understand the data without the bias of a theory of transfer or domain knowledge. The goal of this work is to help provide a methodology that allows researchers to analyse complex data without the theoretical assumptions clearly part of other methods. Our experimentally controlled examples illustrate the non-intuitive nature of some transfer situations which motivates the necessity of the unbiased analysis that our model provides. We explain how to use this Contextual Performance Factors Analysis (CPFA) model to measure learning progress of related skills at a fine granularity. This CPFA analysis then allows us to answer questions regarding the best order of practice for related skills and the appropriate amount of repetition depending on whether students are succeeding or failing with each individual practice problem. We conclude by describing how the model allows us to test theories, in which we discuss how well two different cognitive theories agree with the qualitative results of the model.