基础数学与统计课程对本科生创新创业实践能力的影响与群体分异研究——基于上海立信会计金融学院的实证分析

A Study on the Impact of Basic Mathematics and Statistics Courses on Undergraduates’ Innovation and Entrepreneurship Practical Competence and Group Differentiation —An Empirical Analysis Based on Shanghai Lixin University of Accounting and Finance

摘要: 为支撑应用型高校创新创业人才培养，亟需实证检验基础数学与统计课程对本科生创新创业实践能力的实际作用。本研究基于上海立信会计金融学院188名本科生的课程成绩与科创数据，结合斯皮尔曼相关分析与层次聚类，系统考察《数学分析》(理论型)与《数理统计》(工具型)的影响差异及群体分异。结果表明：1) 基础课程整体与双创能力显著正相关(r = 0.65~0.69, p < 0.001)，但《数学分析》的预测力(r = 0.665)远高于《数理统计》(r = 0.369)，凸显抽象思维训练的核心价值；2) 过程性投入度(基于学习时长、作业独立完成度、课堂互动质量等多维指标构建的复合变量)与双创能力显著负相关(r = −0.586)，揭示真实学业能力比表层学习行为更关键；3) 学生可划分为“双优型”(29.3%)、“主流型”(35.1%)与“挑战型”(35.6%)三类，能力转化效率存在结构性差异。研究基于认知迁移理论与布鲁姆教育目标分类学，深入阐释了理论课程深层认知加工相较于工具课程程序性知识的高阶迁移优势。研究建议通过分层教学、课程内容优化与能力导向评价，实现创新人才精准培养。

Abstract: To support the cultivation of innovative and entrepreneurial talents in application-oriented universities, it is urgent to empirically examine the actual impact of fundamental mathematics and statistics courses on undergraduates’ innovation and entrepreneurship practice ability. Based on course grades and innovation data of 188 undergraduates from Shanghai Lixin University of Accounting and Finance, this study systematically investigates the differential effects and group differentiation of Mathematical Analysis (theory-oriented) and Mathematical Statistics (tool-oriented) using Spearman correlation analysis and hierarchical clustering. The results indicate that: 1) Overall, fundamental courses are significantly positively correlated with innovation and entrepreneurship ability (r = 0.65~0.69, p < 0.001), but the predictive power of Mathematical Analysis (r = 0.665) is significantly higher than that of Mathematical Statistics (r = 0.369), highlighting the core value of abstract thinking training; 2) Process engagement (a composite variable constructed based on multi-dimensional indicators including study duration, homework independence, and classroom interaction quality) is significantly negatively correlated with innovation and entrepreneurship ability (r = −0.586), revealing that authentic academic ability is more critical than surface learning behaviors; 3) Students can be classified into three types: “Dual-Excellent” (29.3%), “Mainstream” (35.1%), and “Challenge” (35.6%), with structural differences in ability transformation efficiency. Based on the Transfer of Learning theory and Bloom’s Taxonomy of Educational Objectives, this study deeply explains the higher-order transfer advantages of deep cognitive processing in theoretical courses compared to procedural knowledge in tool courses. The study recommends achieving precise cultivation of innovative talents through stratified teaching, curriculum content optimization, and ability-oriented evaluation.