Advances in International Applied Mathematics

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.

Functions and equations; Thinking set; Variable transformation