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教学实践证明:学生对只通过肯定事例的教学所获取的知识和对知识的理解是不够深刻的。为培养学生思维的深刻性,在通过肯定事例教学的基础上,可精心设计与肯定事例“貌”似而“质”别的否定事例(反例),引导学生通过认真思考识别,促使学生从正反两方面加深对所学知识的理解。识别反例加深理解概念内涵概念是思维的细胞。在概念教学中,当学生的思维循着“感知——表象——抽象”的过程,对所学概念有了初步认识的基础上,可设计适当反例,适时引导学生进行识别。例如,学生初步认识了整除的意义后,可出示如下的练习:
The teaching practice proves that students’ knowledge and understanding of knowledge obtained only through affirmative examples are not profound enough. In order to cultivate students’ deep thinking, based on the affirmation of case teaching, we can design and affirm the negative cases (counterexamples) of the appearances and appearances of the cases, and guide the students through serious thinking and recognition to prompt the students to learn from Against the two aspects, they deepened their understanding of what they had learned. Identifying counterexamples Deepening understanding of concepts The concept of connotation is the cell of thinking. In the concept teaching, when the student’s thinking follows the process of “perceiving-representation-abstract” and has a preliminary understanding of the concepts they have learned, appropriate counterexamples can be designed to guide students to identify at a proper time. For example, after a preliminary understanding of the meaning of divisibility, students can present the following exercises: