Strategies, difficulties, and written communication in solving a mathematical problem

Abstract

In an age where we live surrounded by technology, it is increasingly important to develop capabilities that differentiate us from "machines". The habit of solving problems can help us develop some of them, including the ability to solve problems, and stimulate critical thinking. It is, therefore, important to propose tasks of a diverse nature in the classroom, and to invest more in mathematical problem-solving by students. For students to solve those problems, it is essential that they know different strategies to use and it is necessary that the teacher can identify the difficulties experienced by students in solving mathematical problems, so the teacher can help students overcome them. This article aims to identify the strategies students use to solve a problem, acknowledge the difficulties students experience, and characterize students' written communication in their answers. To achieve these objectives, the answers to a mathematical problem which was solved by students of three 12th grade classes were collected and analyzed. In the resolutions analyzed, the strategy students used the most was the construction of schemes/figures. Regarding the difficulties, they were felt more at the level of information selection, as the students tended to add data that were neither in the statement nor could be deduced from it. Finally, when communicating their answers in writing, over half of the students did it with a high level of clarity, and the most frequently used type of justification was the exclusive use of schemes. In addition, the type of representation most used by the students was iconic representation.