This article presents a mathematical modeling activity for students related to the process of memorization in which students collect their own data to drive their model development, parameterization, and validation. Engaging in the data collection gives them insight to critique and evaluate various models. This task is a low-floor high ceiling problem that offers both a relatable context and a window to quantitative approaches in cognitive science. Experimental results of students participation in this activity are discussed. This article also includes pedagogical recommendations with a focus on fostering equitable teaching practices and a detailed analysis of the situation comprised of several mathematical approaches to model the memorization process that highlight the richness of the problem. Instructors can adapt and implement this modeling exploration for use in various undergraduate courses, from introductory to advanced, depending on the emphasis of the lesson.