基于APOS理论的“函数奇偶性”概念建构教学设计

APOS Theory-Based Instructional Design for Conceptual Construction of “Parity of Functions”

摘要: 函数的性质是高中数学的核心内容，教学中普遍存在学生机械记忆符号结论、难以把握本质特征的“形式化困境”，制约了数学核心素养的落实。APOS理论为概念建构教学提供了系统的认知框架。本研究以“函数奇偶性”为例，构建基于APOS四阶段的教学方案(活动阶段创设情境→过程阶段抽象定义→对象阶段辨析本质→图式阶段整合应用)。通过单组前后测(高一年级，n = 42)，聚焦“定义域对称”关键前提的考察：后测中85.7%的学生能正确辨析该前提(较前测54.8%显著提升)，验证了教学设计有效破解了“形式化困境”，为函数性质的概念教学提供可操作范式。

Abstract: The properties of functions represent a core content in high school mathematics, yet students often face a “formalized dilemma” characterized by rote memorization of symbolic conclusions without grasping essential characteristics, which hinders the cultivation of mathematical core competencies. APOS theory provides a systematic cognitive framework for concept-building instruction. This study takes “function parity” as a case to develop a four-stage APOS-based instructional design (activity stage: situational context creation → process stage: definition abstraction → object stage: essence analysis → schema stage: integration and application). A single-group pretest-posttest design (Grade 11, n = 42) focused on assessing the critical prerequisite of “domain symmetry”. Results showed that 85.7% of students correctly identified this prerequisite in the posttest (a significant improvement from 54.8% in the pretest), validating the effectiveness of the instructional design in resolving the “formalized dilemma”. This study offers an operational paradigm for conceptual teaching in function properties, bridging the gap between procedural knowledge and deep understanding.