“认识封闭”是数学学习与研究中的常见现象,本文拟通过教材一道错题产生原因的剖析,谈谈题目编制中的“认识封闭”现象及其矫正策略。一、问题提出1.题目呈现如图,△ABC的周长为24,面积为48,求它的内切圆的半径。与教材配套的《教师教学用书》提供的答案是:设△ABC的内切圆的半径为r,切点分别为D、E、F,连接OD、OE、OF、OA、OB、OC。由题意, “Recognition closed” is a common phenomenon in mathematics learning and research. This article intends to analyze the causes of the mis-problem of the textbook and talk about the phenomenon of “cognitive closure” in the compilation of the topic and its corrective strategies. First, the problem is raised 1. The title presents the graph, △ ABC has a circumference of 24, an area of ​​48, find the radius of its inscribed circle. The answer to the “Teacher’s Book for Teaching” provided with the teaching materials is: Set the radius of the inscribed circle of △ABC to r, the cut points to D, E, and F, respectively, and connect OD, OE, OF, OA, OB, and OC. By the question,