Erroneous and Non-rational Solutions in Absolute Value Problems

This paper presents a methodological approach where students are provided with erroneous or non-rational solutions to problems to enhance their learning process. Specifically, the study focuses on equations and inequalities with absolute value. The proposed incorrect or non-rational solutions to equations and inequalities involving absolute value help students to identify mistakes, analyze them, and correct their misconceptions, thereby facilitating deeper understanding of the material. After presenting each erroneous solution, an analysis and explanation follow, guiding students toward the correct and rational solution. This study demonstrates the significant advantages of using erroneous solutions to engage students in deeper reflection, foster self-correction, and develop a critical attitude towards problem-solving in mathematics education.