新课标背景下高中生数学抽象素养培养的策略研究——以“函数”为例

Research on the Cultivation Strategies of Senior High School Students’ Mathematical Abstract Literacy under the Background of the New Curriculum Standard—Taking “Function” as an Example

摘要: 《普通高中数学课程标准》将数学抽象列为六大核心素养之首，函数是培养该素养的关键载体。针对当前高中函数教学存在的情境浅层化、概念教学机械化、评价功利化等问题，本文界定数学抽象素养内涵，构建情境直观–符号形式–结构系统三级递进水平体系，提出情境具象化、概念生成化、多元表征转化、问题结构化、评价过程化五大培养策略，并以《函数的概念》为例开展教学设计。实践表明，该策略体系可有效促进学生抽象思维进阶，为新课标下高中数学核心素养落地提供理论参考与实践范式。

Abstract: “The General High School Mathematics Curriculum Standard” lists mathematical abstraction as the first of the six core competencies, and function is a key carrier for developing this competency. In response to the problems existing in current senior high school function teaching, such as superficial situation creation, mechanical concept teaching, and utilitarian evaluation, this paper defines the connotation of mathematical abstraction literacy, constructs a three-level progressive system of situational intuition—symbolic formalism—structural system, and puts forward five cultivation strategies: concretization of situations, generation of concepts, transformation of multiple representations, structuring of problems, and proceduralization of evaluation. Meanwhile, a teaching design is carried out with The Concept of Function as an example. Practice shows that this strategy system can effectively promote the advancement of students’ abstract thinking, and provide a theoretical reference and practical paradigm for the implementation of senior high school mathematics core competencies under the new curriculum standard.