Beyond Reach

Exploring Distances with Mathematical Modeling

Abstract

This workshop aims to elaborate and solve problems involving the calculation of inaccessible distances, having as measurement verification tools the theodolite, the measuring tape, and the trigonometric boards, that is, a manipulable material that provides the values of the sine, cosine, and tangent of the angle. The proposal is based on Mathematical Modeling understood as a learning environment in which students are encouraged to investigate real-world problems through Mathematics (Barbosa, 2001, 2009). The participants will be invited to form groups and define the inaccessible distances they wish to estimate (problem formulation). Then, they will collect the necessary data for the modeling of the problem, and finally, the resolution of the problem. From the sharing of strategies by the groups, the instructors will conduct the systematization of the concepts (in this case, the trigonometric ratios). The discussion will not end with the solution but will move toward a critical analysis of the created models, their limitations, and the validity of the results.