探究式教学培育高中生数学思维的案例研究——以“等比数列”为例

A Case Study on Cultivating High School Students’ Mathematical Thinking through Inquiry-Based Teaching—Focusing on “Geometric Sequence”

摘要: 在高中数学教育中，培养学生的数学思维能力是核心任务之一。探究式教学作为一种以学生为中心、强调知识建构过程的教学模式，为实现这一目标提供了有效路径。本文以人教A版高中数学“等比数列”的概念教学为例，构建了一个完整的探究式教学案例。通过分析教学背景、设定递进式教学目标，并设计了“情境导入–类比归纳–推导验证–联系拓展–应用反思”的探究式教学流程。本研究通过课堂教学实践，采用前测–后测对比、课堂观察、学生访谈等方法，系统收集量化与质性数据，实证检验探究式教学的效果。案例实践表明，探究式教学通过创设问题情境、引导学生自主探索、合作交流，能够有效激发学生的学习兴趣，加深其对数学概念本质的理解，并在此过程中显著培育其逻辑推理、数学抽象、直观想象和数学建模等关键数学思维能力。

Abstract: In high school mathematics education, cultivating students’ mathematical thinking ability is one of the core tasks. Inquiry-based teaching, as a student-centered instructional model that emphasizes the process of knowledge construction, provides an effective pathway to achieve this goal. This paper takes the conceptual teaching of “geometric sequence” from the People’s Education Press Version A high school mathematics textbook as an example, constructing a comprehensive inquiry-based teaching case. By analyzing the teaching context, setting progressive teaching objectives, and designing an inquiry-based teaching process of “situational introduction-analogical induction-derivation and verification-connection and extension-application and reflection”, this study implements the teaching plan in real classes, systematically collects and presents pretest and post-test papers, and uses content analysis and coding to demonstrate students’ progress in thinking depth and modeling ability. Classroom observation records and student interview transcripts are added to ensure conclusions are based on solid data. the case study demonstrates that inquiry-based teaching, through creating problem situations, guiding students in independent exploration, and promoting collaborative communication, can effectively stimulate students’ interest in learning, deepen their understanding of the essence of mathematical concepts, and significantly foster key mathematical thinking abilities such as logical reasoning, mathematical abstraction, intuitive imagination, and mathematical modeling in the process.