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在人教A版教材必修2-2的第二章“推理与证明”中,先学习合情推理(归纳与类比)、演绎推理与直接证明、间接证明,最后学习数学归纳法.这样的安排合乎逻辑顺序,因为数学归纳法既有归纳(但不同于一般的归纳)又有证明(用有限来证明无限),具有内容的抽象性与逻辑严密性.因此,相应的教学设计主要关注两点,一是化抽象为形象的情境设计,二是将严密性逐步分解的过程设计.而相关评价也立足于两点,首先是否抓住概念的本质,其次是否关注学生的理解.前者基于知识与能力(理解)的立意,后者基于以生为本的立意.
In the second chapter of the teaching of A textbook compulsory 2-2, “Reasoning and Proof”, the first to learn reasoning reasoning (induction and analogy), deductive reasoning and direct proof, indirect proof, the last to learn mathematical induction. Because the mathematical induction is both inductive (but different from the general inductive) and proved (with finite to prove the infinite), with the content of the abstract and logical rigor.Therefore, the corresponding instructional design is mainly concerned Two points, one is the abstract design of the context for the image, the other is the gradual decomposition of the tightness of the process design.And the relevant evaluation is also based on two points, first of all whether to seize the essence of the concept, and secondly whether the students concerned about the understanding of the former based on Knowledge and ability (understanding) of the conception, the latter is based on the concept of health-based.