• Communications of Mathematical Education
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• v.26 no.1
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• pp.51-69
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• 2012

The cognition of an intrinsic attribute play an important role in the process of theoretical generalization. It is the aim of this paper to study how the theoretical generalization is made. First of all, we suggest the What-if-only-strategy(WIOS) which is the strategy helping the cognition of an intrinsic attribute. And we propose the process of the theoretical generalization that go on the cognitive stage, WIOS stage, conjecture stage, justification stage and insight into an intrinsic attribute in order. We propose the process of generalization adding the concrete process cognizing an intrinsic attribute to the existing process of generalization. And we applied the proposed process of generalization to two mathematical theorem which is being managed in middle school. We got a conclusion that the what-if-only strategy is an useful method of generalization for the proposition. We hope that the what-if-only strategy is helpful for both teaching and learning the mathematical generalization.