Collaborative Research: Cognitively Optimized Mathematics through Peer Analogous Reflective Exchanges

Many elementary students struggle to monitor their thinking, evaluate their progress, and adjust their strategies while solving mathematics problems. As a result of these struggles, they may get frustrated and fail to advance to higher-level problem-solving. These self-regulated learning skills are critical for success in mathematics, as well as Science, Technology, Engineering, and Mathematics (STEM) disciplines. These learning skills help students plan, reflect on, and learn from mistakes. Digital learning technologies have the potential to support these skills, but most existing systems rely on complex expert-designed models that can be difficult to develop and scale. This project will investigate a new approach to using teachable agents (computer-based learning partners) that facilitate students in explaining their ideas, evaluating worked examples, and guiding during problem solving. By helping students reflect on their own thinking and compare it to the approaches of others, the project seeks to improve students’ understanding of fractions, strengthen their self-regulated learning skills, and advance the design of educational technologies that support learning across STEM fields. The project will directly engage elementary students and teachers in the design process and will produce freely available educational tools and research findings for schools and researchers. This project will develop and study a data-driven teachable agent embedded within Dream2B, an existing game-based learning environment focused on fraction concepts in grades 3–6. The research will investigate how students’ self-regulated learning processes become evident and evolve during gameplay, how peer-analogous worked examples support students’ reflection on mathematical problem solving, and whether combining self-explanation, peer evaluation, and teaching interactions improves learning outcomes. The project will employ an iterative co-design process with teachers and students, incorporating learning analytics, gameplay trace data, focus group interviews, think-aloud protocols, and classroom implementation studies. Technically, the project will develop a conversational teachable agent that uses student-generated data, interaction networks, and privacy-preserving language models rather than traditional expert-built domain models. The agent will support students through a continuum of interactions that includes independent problem solving, evaluation of worked examples, and explanation-based instruction. Research outcomes will contribute new knowledge about self-regulated learning in mathematics, the design of teachable agents, and the use of scalable educational artificial intelligence systems that leverage authentic student thinking to support learning. This project is supported by NSF's Research on Innovative Technologies for Enhanced Learning (RITEL) program. The RITEL program supports early-stage research in emerging technologies such as AI, robotics and immersive or augmenting technologies for teaching and learning that respond to pressing needs in real-world educational environments. 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.