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, a foundational algebraic skill serving as a gateway to college-level STEM coursework and frequently identified as a conceptual hurdle for students transitioning from arithmetic to algebraic thinking. Using a mixed-methods pre–post quasi-experimental design, 39 undergraduate students enrolled in developmental mathematics participated in a CDMS-based intervention focusing on multiple solution methods for factoring trinomials. The research investigated performance changes across trinomial types, method usage patterns, and student experiences. Results revealed large effect sizes significantly exceeding typical educational interventions, with substantial improvements across all trinomial types. Method diversity increased from two to four approaches, with students shifting from single-method dependency to flexible use of multiple strategies, particularly visual methods like Box and Tic-Tac-Toe methods. Qualitative findings indicated increased student confidence and strategic thinking, with nearly half expressing appreciation for multiple solution methods. The intervention was consistently effective across different algebraic structures and complexity levels. These findings provide the first empirical evidence for implementing CDMS in developmental mathematics at the college level, demonstrating that multiple solution methods can produce meaningful learning gains among undergraduate students who traditionally struggle with algebraic concepts.