Fibonacci's motion problem "Two travellers": The solutions given by junior high-school students who were trained for Mathematical Olympiad
María Araceli, Juárez Ramírez, Lidia Aurora, Lidia Aurora Hernández Rebollar, Josip Sliško · 2014
Numerical problems are today an important part of physics textbooks. One of the most popular motion problems is related to the situations in which two motions are combined. Although numerical problems appeared in physics textbooks in the middle of XIX century, a particular problem situation (combination of a motion at a constant speed and a motion at a constant acceleration) was present in mathematics textbooks since the beginning of the XIII. In the design of the research instrument we used the problem formulation proposed by Fibonacci in 1203 (the problem of two travellers). In this article we report performances of junior high-school students who participated in the training program for Mathematical Olympiad at the Facultad de Ciencias Fisico Matematicas of the Benemerita Universidad Autonoma de Puebla (Puebla, Mexico). This initial qualitative study presents the results of the analysis of strategies students used in solving the problem of two travellers. Beside various acceptable solutions (some conceptually clearer than the solution given by Fibonacci!), we analyzed also the errors made by students in order to know how they understood the problem and how planned to solve it.