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探索性问题是近年数学教学和高考研究的热门课题.其形式有三:(1)给出条件或结论中的一方探索另一方;(2)变更条件或结论中的一方之后,探索另一方的变化;(3)探索问题的存在性,其特点在于“未定”和“变通”.学生们对其解法感到很棘手,本文以实例谈谈如何运用辩证思想寻求解题途径.一、肯定与否定对于结论不确定的存在性问题,在作出“肯定”或“否定”的假设之后,推演的结果或是对肯定之肯定,或是对肯定之否定,或是对否定之肯定,或是对否定之否定.肯定与否定之间相互对立和相互贯通的辩证关系,既为解决探索性问题奠定理论基础,又为解题时的变
Exploratory issues are hot topics in mathematics teaching and college entrance examination research in recent years. There are three forms: (1) give one of the conditions or conclusions to explore the other; (2) change one of the conditions or conclusions, and then explore the changes of the other party. (3) Exploring the existence of the problem, which is characterized by “undetermined” and “flexible.” Students find it difficult to solve the problem. This article uses an example to talk about how to use dialectical thinking to find solutions to problems. First, affirmation and negation The conclusion of the existence of uncertainty, after making “positive” or “negative” assumptions, the result of the deduction is either affirmation of affirmation, or affirmative negation, affirmation of negation, or negation The negation. The dialectical relationship between affirmation and negation that are mutually antagonistic and interpenetrating, not only lays the theoretical foundation for solving exploratory problems, but also changes for solving problems.