Learning by teaching with constructive tutee inquiry for robust learning in algebra

Algebra is a gateway for broad STEM pathways. Yet, many students fail to achieve proficiency in algebra, which is arguably a primary cause of inability to pursue advanced STEM disciplines and further hesitancy in taking STEM pathways. This project aims to advance the knowledge in how students learn robust knowledge in algebra. It will allow students to not only derive answers for stereotypical problems but also draw analytical reasoning for unseen problems. The investigators hypothesize that one of the challenges in learning algebra is due to the complication of the web of algebraic knowledge students need to learn. It is argued that the web of knowledge involves conceptual and procedural knowledge and their relations, which the investigators call the connected knowledge. The investigators propose to develop a transformative technology in the form of teachable agent to amplify the effect of learning by teaching. The smart teachable agent asks students questions to justify their reasoning while solving equations. When a student’s response needs to be elaborated, the smart teachable agent further provides a follow up question to solicit a response that reflects a connection between procedural operations and conceptual justifications. The smart teachable agent may ask follow-up questions two to three times. The proposed question-based dialogue between the student (a tutee) and the smart teachable agent (a tutor) is called a constructive tutee inquiry.To implement the constructive tutee inquiry, the investigators will develop an innovative application of large language models (LLM) where multiple LLM invocations will be combined, including one for generating an ideal response to the agent’s question and another one for generating a follow up question based on the gap between the student’s response and the ideal response. The proposed dialogue system will be embedded into an existing online learning environment where students learn to solve linear equations by teaching a teachable agent. As a learning science contribution, the investigators will study a theory of how students learn connected knowledge and how acquisition of connected knowledge facilitate robust learning in algebra. Classroom evaluation studies using the existing systems with the proposed constructive tutee inquiry will be conducted with middle school students in their algebra classrooms. This project is funded by the Research on Innovative Technologies for Enhanced Learning (RITEL) program that supports early-stage exploratory research in emerging technologies for teaching and learning.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.