Treat the unknown as the known and appreciate the charm of mathematics
把未知当已知，领略数学之魅

摘要

在解决函数和方程问题时，题设常以特定符号预设变量关系，而在惯性思维的影响下，学生常常会以固定的符号，如 ， 等为未知量或者解题时执着于结论推导，导致思路受限.本文通过典型案例分析，提出一种创新思维策略：将未知条件视为已知参与推导，或将目标结论作为已知辅助解题.该方法能有效突破思维定式，简化解题流程，并为数学思想的教学提供新视角。同时本文还对如何在教学中系统实施该策略提出可行建议，包括教师教学引导和学生反思训练与两个维度，为数学课堂注入更具启发性的思维训练方式。

Abstract

When solving problems related to functions and equations, the problem settings often presuppose variable relationships through specific symbols. However, under the influence of inertial thinking, students tend to use fixed symbols, such as x, y, etc., as unknowns or be obsessed with the derivation of conclusions during problem-solving, which limits their thinking. Through the analysis of typical cases, this paper proposes an innovative thinking strategy: treating unknown conditions as knowns to participate in the derivation, or taking the target conclusion as a known to assist in problem-solving. This method can effectively break through the thinking pattern, simplify the problem-solving process, and provide a new perspective for the teaching of mathematical thinking. At the same time, this paper also puts forward feasible suggestions on how to systematically implement this strategy in teaching, including two dimensions: students' reflective training and teachers' instructional guidance, to inject more inspiring thinking training methods into mathematics classrooms.