Multiple Solution Methods of Factoring Trinomials in Undergraduate Mathematics

This study explores the impact of the Compare and Discuss Multiple Strategies (CDMS) framework for teaching multiple solution methods for factoring trinomials. Factoring is a foundational skill that serves as a gateway to college-level STEM coursework yet remains a frequent conceptual hurdle for students transitioning to algebraic thinking. Using a mixed-methods pre-post quasi-experimental design, 39 undergraduate students in developmental mathematics participated in a CDMS-based intervention. The research investigated performance changes, method usage patterns, and student experiences. Results revealed large effect sizes that significantly exceeded typical educational interventions, with substantial improvements across all trinomial types. Method diversity increased, with students shifting from single-method dependency to the flexible use of four distinct approaches, particularly visual strategies like the Box and Tic-Tac-Toe methods. Qualitative findings indicated increased confidence and strategic thinking, with nearly half of participants explicitly valuing the exposure to multiple methods. These findings provide the first empirical evidence for implementing CDMS in college-level developmental mathematics, demonstrating that multiple solution methods can produce meaningful learning gains for students who traditionally struggle with algebraic concepts.