History of mathematics in teaching: Students’ solutions to Fibonacci’s problem “A lion, a leopard and a bear”

Abstract

This paper presents an initial exploratory analysis of the use of historical problems in mathematics education. The problems posed by Fibonacci over 800 years ago, besides offering a glimpse into the past, allow students to connect mathematics to real life and arrive at solutions different from those proposed by Fibonacci, thus enriching the learning experience. Fibonacci’s problem “Of a lion, a leopard, and a bear” was given to 113 students in a Mexican high school for solution. The task was structured so that students would follow the four steps proposed by Pólya (1989) for solving a mathematical problem. This paper presents the results of a qualitative analysis of the students’ performance in planning their solutions. Ten students found the Fibonacci’s solution. Sixteen students, using different modelling, got different solutions that might be considered correct. These students’ responses reveal not only their knowledge of mathematics and its procedures but also their understanding of the limitations of school mathematics problems when applied to real-world situations.