Analysis of a teaching experiment on fair distribution with secondary school students

Abstract

The aim of this study is twofold. The first is to investigate the ability of secondary school students to understand the different distribution schemes and thus, indirectly, to contribute to the educational discussion and approach to be used for distribution problems so as to lessen reliance on the ubiquitous cross-multiplication rule in proportional distribution. The experiment was conducted with secondary school students using a specifically devised scenario involving a distribution problem. We present an analysis of the students’ performance with respect to their concept of fair distribution in a given situation. Their ability to apply the various rules in a new situation is determined. The results provide an insight into the possibilities offered by teaching different distribution methods, especially with mathematically gifted students. The second aim is for instructors to appreciate the value of teaching other distribution methods that apply in real life in addition to a proportional distribution so that they may include in the mathematics classes some recently developed concepts from the field of cooperative game theory.

Keywords:

• bankruptcy problems
• fair distribution
• cooperative game theory
• middle school level

Acknowledgements

We appreciate the selfless help provided over the course of our research by Professors Luis Cutillas, Enrique Freaza and Francisco Aguiar, who collaborated in administering the activity to their gifted mathematics students. We also acknowledge the numerous suggestions made by Dr Josefa Hernández to improve this article. We also thank Professor Luis Balbuena for suggesting The distribution of misery as the title for the activity.

This research was conducted as part of Research Project SEJ2006-10290 (Ministry of Science and Technology, Madrid, National Program for R&D).