Middle School Students' Approaches to Optimization: Insights into Mathematical Modeling and Real-World Problem Solving

Abstract

This study investigates middle school students' perspectives on optimization problems in mathematics, focusing on their problem-solving processes and learning experiences. Optimization involves finding the best solution under specific constraints or maximizing/minimizing an objective function, a concept closely related to mathematical modeling. This process is designed to develop essential skills, such as logical reasoning, prediction, argumentation, and critical thinking, by framing real-world situations as mathematical challenges. Although existing research on students' problem-solving with optimization problems primarily involves high school or university students, recent studies emphasize the necessity of introducing optimization concepts earlier in education. This study administered four optimization problems to 16 middle school students to explore their experiences and opinions. Data were collected through observations, feedback forms, and individual interviews and analyzed using descriptive and content analysis methods. The findings reveal that students' limited prior exposure to optimization problems significantly contributes to their challenges. While students generally understand the optimization problems, their performance varies notably, especially in assumption-making and mathematical calculations. The study underscores the need for systematically integrating optimization problems into the middle school curriculum to enhance students' problem-solving skills and critical thinking. It suggests incorporating mathematical modeling with optimization tasks could improve students' abstraction and problem-solving abilities. Future research could investigate the effects of optimization problems on students' problem-solving skills and mathematical understanding.