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在数学的发展史中 ,反例和证明占有同等重要的地位 .一个正确的数学命题需要严密的证明 ,谬误则靠反例即可否定 .因此 ,在中学数学的教学中 ,反例也有着极为重要的意义 ,它在发现和认识数学真理 ,强化数学基础知识的理解和掌握 ,培养学生思维能力和创造能力 ,以及提高学生解题
In the history of mathematics, counterexamples and proofs occupies an equally important position. A correct mathematical proposition requires rigorous proof, and falsehood can be negated by counterexamples. Therefore, in the teaching of middle school mathematics, counterexamples also have extremely important significance. It discovers and recognizes the truth of mathematics, strengthens the understanding and mastery of basic knowledge of mathematics, develops students’ thinking ability and creative ability, and improves students’ problem solving.