Collaborative research: Fostering conceptual understanding and skill with an intelligent tutoring system for equation solving

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This Education and Human Resources Core Research project addresses a persistent challenge in designing effective mathematics instruction: how to foster deep learning of concepts and skills, with strong connections among them. This challenge arises especially in middle school and high school algebra; far too often, students in algebra courses come away with only a moderate level of skill at procedures (e.g., equation solving) with almost no conceptual understanding of why these procedures work. This lack of deep understanding is unfortunate, because algebra is an important stepping stone to advanced mathematics as well as to future educational and employment opportunities. Thus, there is a great need for algebra instruction that helps students acquire well-integrated knowledge of key concepts and problem-solving procedures. This project tackles this issue using, as a platform, a software-based intelligent tutoring system that will extend an existing tutoring system for algebra. The new, enhanced tutoring system will support both practice in solving equations and new conceptually-oriented algebra activities. It will provide detailed and targeted guidance that adapts to individual students' errors, strategies, and developing algebra knowledge. Lab-based and classroom studies will investigate three key questions: (1) What mix of conceptual and procedural activities best helps students acquire deep skill and conceptual knowledge of algebra? (2) How frequently should students shift back and forth between the two types of activities? (3) How effective is the new tutoring system compared to commonly-used software, namely, Khan Academy, or a standard intelligent tutoring system that provides procedural practice only? The project will lead to new knowledge about how to create effective instruction for middle school and high school algebra, together with new intelligent tutoring software that embodies this knowledge.Based on past research, it is commonly accepted that in many domains, gains in conceptual knowledge can lead to gains in procedural knowledge, and vice versa. Further, there is some evidence that instruction that shifts back and forth between conceptually-oriented activities and procedurally-oriented activities is especially effective. However, it is not yet known what sorts of activities best support the development of conceptual knowledge, or how they should be integrated with activities that target learning of procedures so that students might make connections between the two. To address these issues, the project will extend existing tutoring system for equation solving (called Lynnette) with conceptual activities, based on past research that suggests that worked examples, self-explanation, visual representations (namely, bar diagrams), and activation of prior knowledge can be effective for promoting gains in conceptual knowledge. In doing so, this will leverage an established technical infrastructure for intelligent tutoring systems research and development, called CTAT/Tutorshop. The project will conduct two lab studies and two classroom studies to investigate what mix of conceptually-oriented activities is the most effective complement to the system's current set of procedurally-oriented activities, how frequently students should shift back and forth between procedurally- and conceptually-oriented activities, and how effective the resulting tutoring system is, compared to two control conditions in which students work with commonly used types of software for algebra learning (Khan Academy and Lynnette). The project will generate new knowledge about how to design effective instruction that helps students acquire well-integrated conceptual and procedural knowledge that is effective in real educational settings. This knowledge could lead to better, more conceptually-oriented instruction in algebra, and it has the potential to improve instruction in other STEM learning environments. The project will also create a new intelligent tutoring system for algebra that is much more effective than current systems. The system will be made available to teachers and schools free of charge.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.