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 psychology 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 40 years, I could identify no existing examples of software that used a 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. While creating my own models, I realized that prior research in cognitive psychology almost always assumed that each practice trial had a fixed duration while my analysis was suggesting that necessary trial time was variable, mostly because the necessary time for review when recall fails is much longer than the cost of getting an item correct. Because of this realization, and the computational model I was using, I was able to provide a formal theoretical justification for why an expanding spacing of the duration between practices (i.e. where the duration between repetitions increases with each repetition) should be optimal. According to this analysis, expanding spacing is optimal because it reduces review costs dramatically. Indeed, the model behind this analysis agrees with the conventional notion that when trial durations are artificially fixed, maximal spacing does tend to be optimal, but in a flashcard procedure more similar to what people actually use, durations are not fixed.
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.
Fact and Concept Training (FaCT) System
|My work as a post-doctoral associate focused on taking the above experimental work from the laboratory into the classroom. In my case, this classroom was college Chinese, where I have been working to integrate optimally scheduled practice into the curriculum through a system I have designed called the Fact and Concept Training (FaCT) system. This application of my theory has led to a series of experiments designed to understand the best way to apply the technology in a classroom context. My most recent project is investigating how the difficulty experienced by students in learning foreign language vocabulary may influence metacognitive control. One hypothesis of this work is that difficulty causes weaker use of strategies, which in turn causes a reduction in learning.|
Bridge to Algebra Cognitive Tutor
|While the situation involved in flashcard learning is fundamental, I wanted to build on my research by examining a more complex problem in learning theory. To that end, I proposed and received a grant from the Institute of Educational Sciences (Dept of Ed) to develop add-on modules for Carnegie Learning's Bridge to Algebra Cognitive Tutor (BTACT). The research for this project has involved a careful analysis of the component skills that make up pre-algebra learning and performance. The project has so far involved data mining of past years' BTACT data (2007), and an in class experiment in which 250 students used the BTACT augmented with a component skills intervention (2008). The most recent classroom experiment involves a comparison of four different practice types (200 students). The results of these experiments have shown how difficult it is configure instruction that produces transfer of learning between perceptually dissimilar tasks that share the same essential features.|
|My work with the BTACT project and with the FaCT system has introduced me to educational research in the classroom and to its difficulties. This introduction has forced two important changes to my thinking, having to do with the interrelated issues of design and conceptual learning. The design of the software interface for the component skills intervention has proven important to consider, in part because of the difficulty we have had in producing transfer in the BTACT project. The observed lack of transfer may have been caused by the dry "vanilla" interface we used in the research, which may have led to weaker engagement and subsequently to less constructive processing. My recent literature survey of conceptual change research, however, has suggested a deeper reason. This deeper explanation supposes that the practice given to students was poorly scaffolded for conceptual learning. The practice may have been useful for learning facts, or for learning simple procedures (as evidenced by the excellent learning during the component skills intervention), but this same practice failed to allow students to develop a transferrable understanding.|
We are addressing this issue of the educational software interface in the final year of the DOED grant. In order to scientifically approach the issues of interface design, this work has begun with the creation of a theory of instructional events that is specific enough to be used to make design decisions. This theory describes events as being composed of objects, relationships, action affordances, spatial layout, temporal layout, embodiment, user efficacy, user social motivation, and user interest and places specific importance on the need to instantiate all design variables to maximize sensitivity in the detection of differences in experimental manipulations. While this new design perspective is quite general in its range of application, it has also helped to substantially organize a new IES Department of Education development proposal for submission in mid September.
The new IES proposal (with Ken Koedinger) goes a step beyond the focus on interface design issues in the last year of the BTACT grant. This new proposal, entitled Progressive Construction of General Conceptual Schemas, focuses on concept learning applied in fractions, proportions, and other pre-algebra topics. To instantiate concept learning we have developed a new procedure called the Interactive Paired Example (IPE) that involves graphic alignment of objects and relations in paired examples in different modalities (figure, picture, story, numeric problem). Following these comparative mappings, IPEs include self-explanation questions that ask the student to make inferences about the abstractions and analogical relationships mapped.