# Research

Our research program is about developing theories of human learning and applying them in educational situations. We focus on formally specified models of knowledge acquisition, which capture the dynamics of human learning. Using these models, we apply microeconomic principles to determine the optimal sequence, schedule, duration and organization of practice conditions so that they can be built into educational software. This research integrates the fields of cognitive psychology, educational psychology, human computer interaction, cognitive neuroscience, microeconomics, and statistics.

From my early work, I came to believe that science was failing to provide a formal understanding of human learning that was suitable for integration into educational applications. For example, despite reviewing mathematical models of memory dating back over 60 years, I could identify no existing examples of software that used a detailed memory model to optimize simple flashcard type practice. It seemed clear to me that a mathematical model of the main learning effects (e.g. recency, frequency, spacing and testing effects) could be used to compute the economically optimal schedule of practice.

My dissertation developed this idea by producing a learning efficiency equation that allows the estimation of the long-term learning gain per unit of practice time, the learning rate, which can be computed using the history of prior practice for an item. By comparing the learning rates for a collection of items in a set, I was able to determine when each item would be optimal to practice given a future test. The first three experiments in my dissertation developed these ideas and refined the model of learning effects that I was optimizing. The final experiment, using Japanese to English vocabulary items, compared a naïve schedule control condition, a control condition based on Richard Atkinson's work and an experimental condition, which scheduled according to the optimal learning rate. In this final study of my dissertation (published in Journal of Experimental Psychology: Applied), I was able to show that participants in the experimental condition were about 1 effect size more accurate and rapid in recalling the translations of Japanese words. This is the first example I am aware of that uses a fine-grained model of memory to make economic scheduling decisions.

My most recent work, since 2014, has been using the MoFaCTS (see link on the right) system to investigate optimal learning when the content invovles connected propositions organized in some type of mental model such that there are important dependencies among the information in the domain. This follow several years of work with mathematical models of transfer and practice ordering effects in learning. Understanding how to apply my optimization algorithms in the case of complex connected semantic content is now the main goal of the Optimal Learning Lab, with the realization that this understanding of complex knowledge learning must depend upon an understanding of multiple basic memory factors, such as recency, frequency, spacing and amount of practice.

## MoFaCTS

The latest system we have developed for general memory experiments and student practice using the optimal learning methods.