Optimization Problems at School: Some Examples from the 1st to the 12th Grades

Abstract

This paper presents a study involving three well-known optimization problems within the Operations Research community. These problems provide an interesting context for creating tasks for the mathematics classroom, from the 1st to the 12th grades, given the connections with real contexts that they establish. Studies, about approaches and experiences with students at the basic and high school levels, are presented and the processes standards are discussed. The three proposed problems (path optimization, packing optimization and linear programming), which can be solved at different grades, are discussed focusing on the resolution strategies and on the dynamics of the mathematics classroom, thus promoting reasoning, communication, representation, connections and problem solving processes. The results of this study show that these problems provide a rich context to involve students in their learning process and to promote mathematics discussions. They share different strategies to solve the problems, emerging and relate different representations (active, iconic and symbolic), depending on the problem and the grade. Also, they explore connections between mathematics and real life.