Advances in International Applied Mathematics

The auxiliary element strategy is a common and practical problem-solving approach in high school mathematics. It helps students build intermediate bridges during problem-solving, gradually transforms complex problems into clear and solvable steps, and reduces cognitive load. However, many students do not fully understand this strategy and lack the awareness to use it actively. Using college entrance examination mathematics problems as examples, this paper focuses on three common types of problems: functions, geometry, and sequences. It selects representative problems for analysis to guide students in gradually forming a way of thinking that involves constructing auxiliary elements during actual problem-solving. This enhances their ability to grasp problem structures and improves the overall coherence of their solutions.

Auxiliary element strategy; Senior high school mathematics; Problem-solving