问题导向的初中数学境脉式教学案例设计——以《一次函数的应用》为例

Problem-Oriented Case Design for Contextual Junior High School Mathematics Teaching—Taking “Applications of Linear Functions” as an Example

摘要: 为解决传统初中数学教学中知识灌输化、学生应用能力弱等问题，本研究聚焦问题导向与境脉式教学的深度融合，以提升学生数学核心素养为目标，开展教学实施案例设计研究。提出真实性、问题链建构、境脉连续性的案例设计原则与对应教学流程，结合“阶梯电价计费决策”的真实复杂情境，融入学生数据收集环节，构建“数据–模型–决策”的完整探究链。依托认知负荷理论与脚手架策略，细化各教学环节的教师微观干预策略，深描学生常见错误概念与针对性引导话术，形成可操作性强的教学案例。问题导向的境脉式教学可有效促进初中数学教学质量提升，为初中数学同类知识点的情境化教学设计提供实践参考，最后指出研究在案例普适性与实证数据支撑上的不足及未来改进方向。

Abstract: To address issues such as knowledge-centered instruction and weak application skills in traditional junior high mathematics education, this study focuses on the deep integration of problem-based and context-based teaching approaches. Aiming to enhance students’ core mathematical literacy, it conducts case-based instructional design research. It proposes case design principles—authenticity, problem chain construction, and contextual continuity—along with corresponding teaching processes. Using the complex real-world scenario of “tiered electricity pricing decision-making”, it incorporates student data collection to build a complete inquiry chain: “data - model - decision”. Drawing on cognitive load theory and scaffolding strategies, the study refines micro-intervention tactics for teachers at each instructional stage. It provides detailed descriptions of common student misconceptions and targeted guiding prompts, resulting in highly actionable teaching cases. Problem-oriented contextual teaching effectively enhances the quality of junior high mathematics instruction, offering practical guidance for designing contextualized teaching for similar mathematical concepts. Finally, the study acknowledges limitations in the universality of the case and empirical data support, while outlining future improvement directions.