从“解题”到“讲理”：数学本科毕业论文写作的思维转型与教学路径探索

From “Problem Solving” to “Reasoning”: Exploring the Cognitive Shift and Pedagogical Strategies in Undergraduate Mathematics Theses Writing

摘要: 数学本科毕业论文是培养学生科研素养的关键环节。然而，当前数学教学主要侧重于“解题”训练，导致学生在“解题”与“讲理”思维之间存在断层，表现为论证逻辑薄弱和学术表达不规范等问题。文章界定了解题思维与讲理思维的核心内涵，明确了二者在目标、方法及表达维度上的转型要求。基于课程改革理论与认知学徒制的支持，提出了“三阶四维”教学路径。该路径通过重构课程体系(增设学术写作专项课程、融合数学建模课程)、强化实践环节(学年论文、建模竞赛、科研课题参与)以及实施多元评价，系统培养学生的学术规范、逻辑论证能力和创新思维，从而提升论文的学术质量与科研创新能力。

Abstract: The undergraduate thesis in mathematics is a critical component for cultivating students’ research literacy. However, current mathematics education predominantly focuses on problem-solving training, resulting in a cognitive gap between “problem-solving” and “reasoning” thinking modes. This gap manifests in weak argumentative logic and non-standard academic expression among students. This paper defines the core connotations of problem-solving and reasoning thinking, clarifying the transformational requirements across objectives, methodologies, and expressive dimensions. Supported by curriculum reform theories and the cognitive apprenticeship model, a “Three-Stage Four-Dimension” instructional approach is proposed. This approach systematically fosters students’ academic norms, logical reasoning skills, and innovative thinking by restructuring the curriculum (introducing specialized academic writing courses and integrating mathematical modeling courses), strengthening practical components (annual theses, modeling competitions, participation in research projects), and implementing diversified assessments, thereby enhancing the academic quality of theses and students’ research innovation capabilities.