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生成式人工智能赋能数学概念理解的设计型研究——以定积分内容为例

Design-Based Research on Generative Artificial Intelligence Empowering Mathematical Concept Understanding — Taking Definite Integral Content as an Example

Education Study / 2026,8(3): 175-180 / 2026-03-10 66 56

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• Authors: 张宏杰¹ 蒋丹²
• Information:

  1．重庆工贸职业技术学院，重庆；
  2．鸭江中学，重庆

• Keywords:
  Generative artificial intelligence; Higher vocational mathematics; Definite integral; Conceptual understanding; Design-based research
  生成式人工智能; 高职数学; 定积分; 概念理解; 设计型研究
• Abstract: A pervasive problem in concept teaching in higher vocational mathematics is that students can “compute but not understand”. Although generative artificial intelligence (GenAI) can provide dialogic support and immediate feedback, the uncertainty of its outputs and the risk of learner dependence shift the key issue of classroom application to “how to use it in a controllable way”. Taking the learning of the definite integral concept in higher vocational mathematics as the carrier, this study adopts a design-based research method to carry out three rounds of iteration in real classrooms, and continuously refine a controllable integration scheme comprising “teacher-guided collaboration — task packages — dialogue scaffolds — classroom norms”. Guided by the logic of “interaction – mechanism – understanding”, the study constructed a minimal evidence chain centered on a conceptual understanding test and process data from classroom interactions. Operational indicators were specified for interaction quality, conceptual processing, and risk governance, and key process mechanisms were examined, including representational transformation, verification via units or counterexamples, error-source diagnosis, and metacognitive monitoring. The results indicate that, under governance mechanisms such as task constraints, verification requirements, process-evidence recording, and teacher gatekeeping, classroom discourse is more likely to shift from answer checking to explanation and verification. Representational transformation and verification behaviors occur steadily, thereby promoting the meaning construction, boundary discrimination, and transfer application of the definite integral concept, while reducing adverse outcomes such as computational errors, task noncompliance, and overreliance on GenAI. The study further summarizes the instructional design principles of generative artificial intelligence for conceptual content in higher vocational mathematics, providing an operational framework and practical reference for controllable classroom integration and governance. 高职数学概念教学中普遍存在“会算不懂”的现象。生成式人工智能虽能提供对话支持与即时反馈，但其输出不确定性与学习依赖风险，使课堂应用的关键转向“如何可控地用”。本研究以高职数学中定积分概念学习为载体，采用设计型研究方法，在真实课堂中开展三轮迭代，构建并持续优化“教师引导型协同—任务包—对话脚手架—课堂规训”的可控融合方案。研究以“互动—机制—理解”为逻辑主线，建立以概念理解测验与课堂互动过程数据为核心的最小证据链，围绕互动质量、概念加工与风险治理设置可操作指标，分析表征转换、单位或反例验证、错因定位与元认知监控等过程机制。结果表明，在任务约束、验证要求、过程证据记录与教师把关的治理机制支持下，课堂话语更易由答案核对转向解释与验证，表征转换与验证行为得以稳定发生，从而促进定积分概念的意义建构、边界辨析与迁移应用，并降低计算错误、任务不遵循与依赖等风险后果。研究进一步提炼面向高职数学概念性内容的生成式人工智能教学设计原则，为课堂可控融入与治理提供可操作框架与实践参考。
• DOI: https://doi.org/10.35534/es.0803033 (registering DOI)
• Cite: 张宏杰，蒋丹．生成式人工智能赋能数学概念理解的设计型研究——以定积分内容为例［J］．教育研讨，2026，8（3）：175-180．