从分化到收敛：财经院校本科生数学学业适应的演化路径与分层支持体系构建

From Differentiation to Convergence: Evolutionary Trajectories of Mathematical Academic Adaptation and the Construction of a Stratified Support System for Undergraduates in Universities of Finance and Economics

摘要: 从高中到大学的数学学业适应是影响财经类人才培养质量的关键环节。本研究针对该阶段普遍存在的知识衔接不畅与学生群体分化问题，以上海立信会计金融学院2021级本科生的多源学业数据为基础，采用描述性统计、相关性分析、凝聚层次聚类等多元方法，系统考察学生数学学业适应的群体特征、影响因素与类型模式。研究发现：1) 学生的数学学业适应呈现“初期分化–中期调整–后期收敛”的动态轨迹，大学数学教学体系对成绩分布具有显著的“校准效应”；2) 高中数学基础对大学学业表现的预测力有限(不同专业类型分类下相关系数普遍在0.05~0.1左右，生源地分类下相关系数普遍在0.1~0.4之间)，其作用强度受到专业属性与生源地背景的显著调节；3) 大学数学课程体系的内部衔接性(微积分(一)与(二)相关系数集中在0.3~0.6)，远强于高中与大学之间的知识延续性；4) 聚类分析识别出三类典型适应群体：优势稳定型(63.9%)、主流适应型(22.2%)与适应挑战型(13.9%)，其在专业与生源地分布上存在系统性差异，且访谈发现学习习惯、心理韧性与教学适配感是驱动分数演变的深层行为机制。基于上述结论，文章从教学改革视角提出系统建议：构建覆盖“诊断–分层–支持”的精准教学干预体系；强化以思维转型为导向的高中–大学课程衔接；推进融合专业场景的数学课程内容重构；建立注重过程的发展性评价与支持生态。本研究为财经类院校实施以学生为中心、以证据为基础的数学教学改革提供了实证依据与行动框架。

Abstract: The transition from high school to university in mathematical academic adaptation represents a critical juncture affecting the quality of talent cultivation in finance and economics. Focusing on the prevalent issues of poor knowledge articulation and student group differentiation, this study utilizes multi-source academic data from 2021 undergraduates at Shanghai Lixin University of Accounting and Finance as a basis, employing descriptive statistics, correlation analysis, and agglomerative hierarchical clustering to systematically investigate the group characteristics, influencing factors, and typological patterns of student adaptation. The research findings indicate: 1) students’ mathematical academic adaptation follows a dynamic trajectory of “initial differentiation, mid-term adjustment, and late-stage convergence”, wherein the university mathematics teaching system exerts a significant “calibration effect” on grade distribution; 2) the predictive power of the high school mathematical foundation on university performance is limited—with correlation coefficients generally falling between 0.05 and 0.1 across different major types and between 0.1 and 0.4 across different student source regions—and its influence is significantly moderated by professional attributes and regional educational backgrounds; 3) the internal continuity of the university mathematics curriculum system, where correlation coefficients between Calculus I and II are concentrated between 0.3 and 0.6, proves substantially stronger than the knowledge continuity between high school and university; 4) cluster analysis identified three typical adaptation groups: “Stable Advantage” (63.9%), “Mainstream Adaptation” (22.2%), and “Adaptation Challenge” (13.9%), which exhibit systematic differences in major and regional distribution; qualitative interviews further revealed that learning habits, psychological resilience, and subjective perception of teaching compatibility serve as the underlying behavioral mechanisms driving score evolution. Based on these conclusions, this paper proposes systemic suggestions for pedagogical reform: constructing a precision teaching intervention system covering “diagnosis-stratification-support”; strengthening high school-to-university curriculum transition oriented toward “thinking transformation”; advancing the reconstruction of mathematics course content integrated with professional scenarios; and establishing a process-oriented developmental evaluation and support ecology. This study provides empirical evidence and an action framework for student-centered and evidence-based mathematics teaching reform in universities of finance and economics.