离散数学教学中Chain-of-Thought可验证推理能力的现状与改革方向

Current State and Reform Directions of Chain-of-Thought Verifiable Reasoning Ability in Discrete Mathematics Teaching

摘要: 随着DeepSeek、GPT等具备Chain-of-Thought (CoT)推理能力的生成式AI的普及，离散数学课程教学面临一个前所未有的教学挑战：学生应对课程作业能够轻易获取AI生成的“分步推理”的答案，但其独立判断这些推理是否正确的核心能力是否得到培养，已成为亟待关注的教学问题。本研究以2026春季学期29名离散数学学生为调查对象，通过问卷调查分析方法，系统考察了学生在AI辅助学习中的使用情况、推理能力自评及对CoT可验证推理的认知状况。研究发现：(1) 96.6%的学生在离散数学课程学习过程中使用过AI工具辅助学习，其中79.3%达到经常或偶尔使用频率，AI已深度嵌入学生的学习过程；(2) 学生在“发现证明漏洞”和“理解分步构造”两个维度自评较高(M = 4.00、4.07)，但在“判断AI生成证明是否正确”(M = 3.76)和“识别AI回答中的错误”(M = 3.86)两个维度的自评显著偏低；(3) 高频使用AI的学生在所有推理能力维度上的自评均高于低频使用者，尤其在“独立完成证明能力”上的差值达0.45，但学生对AI输出的批判性判断能力并未随使用频率增加而同步提升。基于调查结果与认知负荷理论、元认知理论的分析框架，本文提出离散数学教学亟需从“答案导向”转向“CoT可验证推理导向”，并构建“独立构造CoT推理链、AI辅助验证、人机协同修正、批判性判断”的四阶段教学框架，以重建学生在AI时代的数学推理主体性，为离散数学课程应对AI时代的教学挑战提供方向性参考。

Abstract: With the widespread adoption of generative AI models such as DeepSeek and GPT that possess Chain-of-Thought (CoT) reasoning capabilities, discrete mathematics teaching now faces an unprecedented challenge: while students can easily obtain AI-generated “step-by-step reasoning” answers for course assignments, whether their core ability to independently judge the correctness of such reasoning is being cultivated has become a pressing instructional concern. This paper investigates 29 discrete mathematics students from the 2026 spring semester as survey subjects. Through questionnaire-based analysis, it systematically examines students’ usage patterns of AI-assisted learning, self-evaluated reasoning abilities, and awareness of CoT verifiable reasoning. The findings reveal that: (1) 96.6% of students have used AI tools to assist their learning in discrete mathematics, with 79.3% using them frequently or occasionally. Thus, AI has become deeply embedded in students’ learning processes; (2) students rated themselves relatively high in “identifying proof gaps” (M = 4.00) and “understanding step-by-step construction” (M = 4.07), but rated themselves significantly lower in “judging whether AI-generated proofs are correct” (M = 3.76) and “identifying errors in AI responses” (M = 3.86); (3) high-frequency AI users scored higher on self-evaluations across all reasoning dimensions compared to low-frequency users, with a notable difference of 0.45 on “independent proof construction ability,” yet students’ critical judgment of AI-generated output did not improve correspondingly with increased usage frequency. Drawing on the analytical frameworks of Cognitive Load Theory and Metacognitive Theory, this paper argues that discrete mathematics education urgently needs to shift from an “answer-oriented” approach to a “CoT verifiable reasoning-oriented” paradigm. To reestablish students’ mathematical reasoning agency in the AI era, it proposes a four-stage instructional framework, i.e. independently constructing CoT reasoning chains, AI-assisted verification, human-AI collaborative revision, and critical judgment, thereby providing directional guidance for discrete mathematics courses to address pedagogical challenges in an AI-driven academic environment.