The Shaping Problem-Solvers: The Role of Diverse Methods in Advancing Mathematical Confidence

Formación de Solucionadores de Problemas: El Rol de los Métodos Diversificados en el Desarrollo de la Confianza Matemática

Abstract

This article investigates how exposure to diverse methods for solving quadratic equations influences the development of mathematical confidence and problem-solving skills among undergraduate students in community college algebra courses. Recognizing that students often enter with varying levels of prior knowledge and limited experience in flexible problem-solving, the instructional model introduced multiple strategies, including Grouping, Completing the Square, Trial and Error, the Quadratic Formula, and Slide-Divide-Bottoms-Up. Student perceptions, preferences, and self-reported confidence were collected through surveys and analyzed to assess both procedural proficiency and conceptual understanding. Findings reveal that engaging with multiple solution methods enhances students’ confidence, encourages strategic thinking, and promotes adaptability in selecting appropriate approaches for different problem types. The results also demonstrate that students develop greater mathematical maturity, characterized by reflective reasoning, method comparison, and persistence in problem-solving. These insights suggest that integrating diverse methods into algebra instruction fosters a mindset of flexible and independent problem-solving, providing a pathway for students to approach complex mathematical challenges with confidence and resilience.