解题过程的思维活动往往是复杂，而教学过程中教师对学生思维能力的培养更
是复杂。本研究旨在探讨以波利亚解题理论为指导，以提升学生数学学科核心素养为
目标的教学案例设计。研究分析了波利亚解题理论在数学学科核心素养培养中的作
用，结合具体案例将其运用到教学实践中。创新地将波利亚解题理论与数学学科核心
素养相结合，设计了实施性较强的教学案例，旨在为教师提供借鉴与参考。
波利亚解题理论在数学竞赛等题目较难场景下使用较多，而在中学数学的课堂
中使用率并不高。将波利亚解题理论引入中学课堂可以在数学学科核心素养培养中
具有重要作用，但目前相关研究较为匮乏。本研究通过文献研究和教学案例设计，深
入探讨了波利亚解题理论与数学学科核心素养之间的关系，并且以三种不等式作为
具体教学案例，提出了一系列优化策略，旨在帮助教师更好地引导学生培养数学学科
核心素养。
通过以基本不等式、柯西不等式以及伯努利不等式为例的教学案例的设计与实
践，研究验证了波利亚解题理论优化策略的有效性。结果表明，将波利亚解题理论运
用于教学实践中，有助于提升学生解题能力和数学学科核心素养。这对于教师的教学
思维优化和学生的综合素养提升具有重要意义，也为数学教育的发展提供了新的理
论支撑和实践路径。

The thought process involved in problem-solving is often intricate, and the cultivation
of students' thinking abilities by teachers during the teaching process is even more complex.
This study aims to explore the design of teaching cases guided by Polya's problem-solving
theory with the goal of enhancing students' core mathematical literacy. The research
analyzes the role of Polya's problem-solving theory in the cultivation of core mathematical
literacy and applies it to teaching practice through specific cases. Innovatively combining
Polya's problem-solving theory with core mathematical literacy, this study designs teaching
cases with strong implementability, aiming to provide guidance and reference for teachers.
Polya's problem-solving theory is frequently utilized in challenging scenarios such as
mathematics competitions, but its usage in secondary school mathematics classrooms is not
very common. Introducing Polya's problem-solving theory into secondary school
classrooms can play an important role in the cultivation of core mathematical literacy, yet
there is currently a lack of related research. Through literature review and the design of
teaching cases, this study delves into the relationship between Polya's problem-solving
theory and core mathematical literacy. Using three types of inequalities as specific teaching
cases, a series of optimization strategies are proposed to assist teachers in better guiding
students to cultivate core mathematical literacy.
Through the design and implementation of teaching cases using examples such as basic
inequalities and Cauchy inequalities and Bernoulli inequality, the study validates the
effectiveness of Polya's teaching theory optimization strategies. The results indicate that
applying Polya's problem-solving theory in teaching practice helps improve students'
problem-solving abilities and core mathematical literacy. This is significant for optimizing
teachers' teaching strategies and enhancing students' comprehensive literacy, providing new
theoretical support and practical pathways for the development of mathematics education.