The primary objective of this project is to develop new methods for optimizing an automated pedagogical agent to improve its teaching efficiency through customization to individual students based on information about their responses to individual problems, student individual differences such as level of cognitive development, spatial ability, memory retrieval speed, long-term retention, effectiveness of alternative teaching strategies (such as visual vs. computational solution strategies), and degree of engagement with the tutor. An emphasis will be placed on using machine learning and computational optimization methods to automate the process of developing efficient Intelligent Tutoring Systems (ITS) for new subject domains. The approach is threefold. First, a methodology based on hierarchical graphical models and machine learning will be developed and evaluated for automating the creation of student models with rich representations of student state based on data collected from populations of students over multiple tutoring episodes. Second, methods will be developed and evaluated for deriving pedagogical decision strategies that are effective and efficient not just over the short-term (from one math problem to the next one), but over the long-term where retention over a period of at least one month is the objective. Third, a systematic study will be conducted of the role that known and powerful latent and instructional variables can have on performance through their inclusion in student models. Research in cognitive and educational psychology clearly shows the critical role that latent variables such as short-term memory and engagement play in learning, and that instructional variables such as over-learning and review, and massed and distributed practice have on the rate at which material is learned. The investigators jointly have strengths in the areas of intelligent tutoring, machine learning and optimization, and cognitive, mathematical and educational psychology, strengths that are needed in order to make the synergistic advances that are being proposed. Our preliminary simulations and classroom experiments suggest that we can significantly reduce the time it takes students to learn new material based on improved pedagogical decisions. For intellectual merit, he proposed research should advance fundamental knowledge of the learning and teaching of basic mathematics and more advanced algebra and geometry. It should add to the set of growing statistical and computational techniques that are available to estimate the complex hidden hierarchical structures that govern human behavior. The research should also significantly broaden the capabilities of machine learning systems by addressing learning scenarios that are grounded on the real and challenging problem of mathematics education than the abstract scenarios typically studied at present. For broader impact, this foundational educational research will lead to the broadening of participation of underrepresented groups, especially women, in a variety of science, technology, engineering and mathematics (STEM) disciplines. It will advance discovery and understanding of learning and engagement as predictors of individual differences in learning and will result in intelligent tutors that are more sensitive to individual differences. It will unveil the extent to which students of different genders and cognitive abilities learn more efficiently with different forms of teaching. This research will benefit society as machine learning methods, which provide a core technology for building complex systems, will be applicable to a variety of teaching systems.
