Siri Xu

Thesis Advisor: Dr. Dagan Karp (Harvey Mudd College - Department of Mathematics)

Second Reader: Prof. Robin Wilson (Loyola Marymount University - Department of Mathematics, Statistics, and Data Science)

Contact: sirxu@g.hmc.edu

Abstract Description of project here

This project investigates four primary cognitive and affective barriers students face in mathematical problem-solving: initiation paralysis, naive empiricism, computational derailment, and imposter syndrome. Drawing on metacognitive scaffolding and the commognitive framework, the research examines the gap between passive mathematical knowledge and active executive control. By equipping educators and peer tutors with actionable pedagogical interventions, such as fostering self-regulatory dialogue and guiding the transition from empirical exploration to structural proof, this work seeks to humanize mathematics instruction. Ultimately, the project provides a framework to empower students, cultivating mathematical agency, rigorous reasoning, and a resilient academic identity.