Prospective mathematics teachers’ experiences with an alternative approach to solving quadratic equations

Source abstract

Reliance on formulas and memorization has often been reported, leading to difficulties in understanding quadratic equations. This study investigates how 22 prospective mathematics teachers perform and reflect when solving quadratic equations using an alternative approach proposed by Po-Shen Loh—an intuitive and efficient strategy. Data were collected from worksheets and semi-structured interviews with seven participants. Analysis revealed that while many did not fully grasp the conceptual foundation of the method, they could follow procedural steps to reach solutions. The method was largely understood procedurally rather than conceptually, with participants sometimes reverting to memorized strategies. Misconceptions emerged around ideas such as the arithmetic mean, particularly with negative values. This study presents an alternative solution strategy to prospective teachers and encourages reflection on its purpose and application. The findings suggest that this approach could be incorporated into high school and university level algebra curricula.