Using a Crossing Method as an Alternative Approach for Teaching, Learning, and Solving Quadratic Equations

This paper introduces the crossing method as an alternative approach for teaching and solving quadratic equations, particularly in secondary schools. Based on this research, the traditional methods used by in-service mathematics teachers—factorization, the general formula (quadratic formula), the graphical method, and completing the square—all yield the same solutions despite differing in approach. However, the crossing method is not documented in existing literature nor commonly used in teaching, even though it produces the same ac-curate results as the traditional methods. By presenting this new approach and comparing its outcomes with those of the four common methods, this paper makes a significant contribution to the field of mathematics education. The implications of the crossing method in teaching and learning quadratic equations are substantial, as it may enhance conceptual understanding by providing an intuitive way for students to grasp quadratic equations, especially through visualization. Since the crossing method involves comparing intersections, it might also increase student engagement through an interactive learning process. Additionally, mathematics teachers and educators can incorporate this method as an alternative pedagogical tool to cater to different learning styles. This research suggests that the crossing method could be a valuable complement to existing methods, potentially making quadratic equations more accessible to students. By demonstrating that it yields correct and consistent solutions, this study establishes the method as a viable alternative in mathematics instruction.