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Results of a cross-sectional study of how 102 children 3 to 9 years of age play and think about Tic Tac Toe are reported. An evolution in reasoning is described by 5 general levels of play: motor and individual play, egocentric play, cooperation in beginning competition, consolidation of defensive with simple offensive strategies and coordination of advanced offensive and defensive strategies. An 8-item Guttman Scale describes nine sublevels. Kohlberg's criteria are used to assess evidence for the hierarchical sequentiality of these levels, and their transformational rather than additive character is discussed. Educational implications are suggested.
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