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在数学发展史上,反例和证明同等重要.在教学中,恰当地引入精炼、典型、具有针对性的反例,可以帮助学生理解数学概念,突破教学重难点,提升数学思维,掌握和巩固课堂知识.和正例相反,反例是指出某命题不成立的例子,引导学生去构造、辨析反例,可以帮助学生及时巩固、消化和吸收数学知识,加深对知识的正确理解,避免在解题过程中因为对数学概念掌握得不全面、不深入而出现的这样或那样的错误,建立灵活的数学
In the history of mathematics, counterexamples and proofs are equally important.In the teaching, proper introduction of refined, typical and targeted counterexamples can help students to understand mathematics concepts, break through teaching difficulties and difficulties, improve mathematical thinking, master and consolidate classroom knowledge. Contrary to the positive example, the counter-example refers to the example that a certain proposition is not established to guide the students to construct and discriminate counter-examples, which can help students to consolidate, digest and absorb mathematical knowledge in time and deepen their understanding of knowledge in a timely manner. One or more of these mistakes, incomplete or in-depth, and flexible mathematics