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不论在数学发展史上,还是在数学教学上,反例都有着很重要的地位。建构主义认为,学生的错误不能单纯依靠正面的示范和反复的练习得以纠正,举反例的教学方式常常能使学生兴趣盎然,直观、简洁的反例更使人拍案叫绝。数学家盖尔鲍母也曾指出:一个数学问题用一个反例予以解决给人的刺激犹如一场好戏。若能适当的运用反例,对于学生牢固掌握数学知识,发展思维能力颇有好处。下面谈谈在小学数学课堂教学中怎样运用反例。
Both in the history of mathematics development and mathematics teaching, counter-examples all play an important role. Constructivism holds that mistakes made by students can not be corrected simply by positive demonstrations and repeated exercises. Contrasting teaching methods often make students interested, intuitive and concise counterexpanding. The mathematician Geir Bowman also pointed out: A mathematical problem to solve with a counter-example to stimulate people is like a good show. If the appropriate use of counterexamples, for students to grasp the mathematical knowledge, the development of thinking is quite good. Here to talk about how to use counterexample in primary school mathematics classroom teaching.