Discrepancy of Creative Reasoning and Imitative Reasoning

NCTM of America recognized reasoning and proof as fundamental aspects. So Mathematical education focus on thinking types. The paper discussed the two distinctive reasoning way: creative reasoning and imitative reasoning. Defining two reasoning types and relationship among them, the paper penetrated into arguing the factors and structure of mathematical reasoning sequence which included six tasks, analysis, exploration, planning, implementation, verification. in relation to which the paper addressed the discrimination between creative reasoning and imitative reasoning. On the basis of the empirical research, the suggestion were pointed out by relation to discrepancy between two reasoning types.