本研贯通培养中本科生选修研究生课程的优势与实践研究——以代数学课程为例

Advantages and Practice of Undergraduates Enrolling in Graduate Courses in Integrated Undergraduate-Graduate Education—A Case Study of Algebra Courses

摘要: 本研贯通培养是新时代高校拔尖创新人才培养的重要路径之一。对于数学学科而言，本科阶段与研究生阶段之间既存在知识深度的递进，也存在思维方式、研究范式和学术共同体参与方式的转变。如何使优秀本科生在适当阶段接触研究生课程，既不造成学习负担过重，又能有效激发其学术潜能，是数学专业课程改革中亟待研究的问题。本文以代数学课程为案例，围绕本科生选修研究生课程的培养价值、实施机制、课程衔接、评价体系与支持策略展开分析。研究认为，本科生适度选修研究生层次的代数学课程，有助于促进知识结构贯通、抽象思维提升、科研素养形成和学术发展路径前移。但该模式也面临课程难度高、学分互认不充分、学生基础差异大、评价方式单一等挑战。为此，本文提出“基础诊断–桥梁课程–分层进入–过程支持–综合评价”的实施框架，并构建代数学本研课程衔接的能力发展指标体系，以期为数学学科本研贯通培养提供可操作的教学改革方案。

Abstract: Integrated undergraduate-graduate education is one of the pivotal approaches for cultivating top-notch innovative talents in universities in the new era. For the discipline of mathematics, the transition from undergraduate to graduate studies involves not only the progression of knowledge depth, but also the transformation of thinking modes, research paradigms, and patterns of engagement with academic communities. How to enable high-achieving undergraduates to access graduate-level courses at an appropriate stage, without imposing excessive academic burden while effectively unlocking their academic potential, is a pressing issue to be addressed in the curriculum reform of mathematics programs. Taking algebra courses as a case study, this paper examines the educational value, implementation mechanisms, curriculum articulation, evaluation systems, and support strategies associated with undergraduates enrolling in graduate courses. The research finds that moderate participation in graduate-level algebra courses benefits undergraduates by facilitating the integration of their knowledge structure, enhancing their abstract thinking ability, fostering their research literacy, and advancing their academic development trajectory. Nevertheless, this mode encounters multiple challenges, including high course difficulty, inadequate mutual recognition of credits, significant disparities in students’ foundational proficiency, and oversimplified evaluation methods. In response, this paper puts forward an implementation framework featuring “foundation diagnosis - bridging courses - stratified access - process support - comprehensive evaluation”, and develops a competence development indicator system for the articulation of undergraduate and graduate algebra courses. This study is expected to provide operable teaching reform solutions for the integrated undergraduate-graduate cultivation in the discipline of mathematics.