Abstract
The purpose of this study is to investigate the method of exploring the winning strategy of middle school mathematic gifted students in the NIM game. we divided into one stage game for a file game, two stage game for two files game, and tree stage game for Nim game. In the first stage, it was easy to find a winning strategy through deductive reasoning. In the second stage, students approaching with deductive reasoning found a winning strategy, but students approaching only with inductive reasoning found an error in the winning strategy. In the third stage, there were students who tried to find a winning strategy with inductive reasoning, but none of them approached it with deductive reasoning. Some of the mathematically gifted students tended to trust established patterns in a limited number of cases, but they recognized the importance of justification for intuitive patterns through the experience of failure of an inferred pattern. As a result of visually presenting the binaries -box to the students, the students were able to easily find the pattern of the winning strategy and some students could reach a stage of justifying the winning strategy.
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