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数学家维奥拉说:“反例可以检验你是否已经正确而深入地了解了数学的真谛,还可以锻炼你的智力,并将你的判断和推理严格的约束在一种秩序之中。”笔者将结合自己的教学实践和体会,谈谈数学反例在提高初中学生数学能力中的作用。一、数学反例可以加强学生对数学概念的理解数学课程学习过程中,对于一些不易理解和掌握的概念,学生常常容易混淆或忽略它们的某些本质属性,尽管教师反复强调,学生还是容易出错。如果教师在讲解过程中适当举出一些反例,通过反例来加强学生对这一知识点的
Mathematician Viola said: “The counter-example can test whether you have correctly and deeply understood the essence of mathematics, exercise your intelligence, and strictly restrict your judgment and reasoning to one order. ”The author will combine his own teaching practice and experience, talk about mathematical counter-examples in improving junior high school students mathematical ability. First, the mathematical counter-examples can enhance students’ understanding of mathematical concepts In the process of learning mathematics, students may easily confuse or ignore some of their essential attributes for concepts that are not easily understood and mastered. Students are still prone to make mistakes, though repeatedly emphasized by teachers. If the teacher in the process of explaining properly cited some counter-examples, through counterexamples to strengthen students on this point of knowledge