Common Circular Demonstration Problems, Value Review and Enlightenment in High School Mathematics Learning

逻辑推理是六大核心素养之一，数学证明过程中所涉及的循环论证与学生的逻辑推理等核心素养有着很强的相关性。在实际教学中，循环论证并不少见。研究结合人教版普通教科书2019版(以下简称人教版)及各类练习题，按照知识点归纳高中数学学习中常见的循环论证问题，分为函数单调性、勾股定理、三角函数和立体几何四部分，为教材改革和教师教学提供新的方向。Logical reasoning is one of the six core literacy, and the circular argument involved in the mathematical proof process has a strong correlation with the core literacy of students’ logical reasoning. In actual teaching, circular argumentation is not uncommon. The research combines the 2019 edition of the ordinary textbook of the People’s Education Edition (hereinafter referred to as the People’s Education Edition) and various exercises to summarise the common circular argumentation problems in high school mathematics learning according to the knowledge points, which are divided into four parts: function monotony, Pythagorean theorem, trigonometric function and three-dimensional geometry, providing a new direction for textbook reform and teacher teaching.