An Analysis of Students' Problem-Solving Barriers in Derivative Tangent-Line Problems and Teaching Optimization Strategies

Ding Jiayi, Chen Zhaoying

University of Jinan

Abstract：

Derivative tangent-line problems are the opening topic when students first learn derivatives and have long been a hot spot in the Gaokao. Focusing on two basic problem types—”the tangent at a point” and “the tangent through a point”—this paper sorts out three types of barriers: psychological and cognitive barriers, computational barriers, and barriers in mathematical thinking. In light of the competency requirements of the new Gaokao, it analyzes students’ problem-solving barriers and, based on teaching practice, proposes teaching optimization strategies.

Key Words：

senior high school mathematics; derivative tangent lines; problem-solving barriers; teaching strategies