A Case Study of R&E Instruction for Middle School Students: Focusing on the Search for Winning Solutions of NIM Games and the Development of Modified NIM Games

Abstract

This is a case study of R&E instruction for middle school students in Science Gifted Education Center who explored the winning solution of the NIM game, a type of two-person finite turn-based fixed complete information game, and modified the game. It is not difficult for middle school students to understand the solution of the NIM game and solve the problem while obtaining the logical sum expressed in binary. However, unlike the enrichment course, R&E education for gifted students explores new mathematical properties beyond the given problem-solving method, and experiences the rediscovery of principles, reinvention of forms, and re-creation of games through various transformations (making, development). We should be able to guide them through these methods. As a result of re-creation mathematics through recreational activities, students created a modified NIM game that extended it in addition to several known modified NIM games. The results of this study can be used for the development of modified NIM games and will be helpful for teaching R&E in the secondary school course.