Research on the Teaching of Chapter Opening Lessons in High School Mathematics from the Perspective of Problem Posing - Taking "Lines and Circles" as an Example

Mathematical problem posing has emerged as a prominent topic in the international field of mathematics education. China attaches great importance to this, emphasizing the cultivation of students' ability to propose mathematical problems and highlighting the requirement for the structuring of mathematical content in the Mathematics Curriculum Standards for Compulsory Education (2022 version). Taking the chapter opening lesson of "Equations of Lines and Circles" in high school mathematics as an example, this paper explores the teaching design and practical paths of chapter opening lessons from the perspective of problem posing. The study constructs a four-dimensional holistic questioning scaffold of "time-space-external domain-internal domain" to guide students in understanding "why to learn" through holistic questioning; further employs the "What-If-Not" strategy to build a systematic questioning scaffold, enabling students to explore various attributes of the mathematical objects being studied and clarify "what to learn"; finally, guides students to actively propose high-order mathematical problems based on the extracted attributes, thereby realizing the transformation of teaching paradigm from passive acceptance to active inquiry.