知识图谱驱动的建筑类高校高等数学教学改革探索

Knowledge Graph-Driven Teaching Reform of Advanced Mathematics in Civil Engineering and Architecture Universities

摘要: 针对高等数学知识点密集、层级递进关系复杂，而实际教学多按章节线性割裂施教的现状，本研究构建了涵盖六大章节、75个知识点的高等数学课程知识图谱，节点间以父子关系、前后置关系与关联关系三类关系连通，并据此设计了“课前自主学习–课中内化建构–课后巩固拓展”三阶段教学模式，辅以基于节点级学情数据的“定位–干预–再定位”测评方案。在北京建筑大学高等数学A (1)课程中，以109人的实验班与17位教师执教的2051人对照班开展一学期对照教学。统一期末考试显示：实验班平均分74.40分，高出对照班(63.06分) 11.34分；及格率高出约19个百分点，优秀率达到对照班的2.6倍；实验班标准差(15.20)低于对照班(21.29)，成绩分化收敛；学生问卷在知识结构呈现、概念关联理解、自主学习支持与总体学习辅助各维度的平均分均不低于4.50分。与近两千人规模的对照样本相比，以课程图谱贯穿教学全程的模式呈现出整体学业水平提升与成绩差距缩小的积极效果。

Abstract: In response to the current situation where advanced mathematics is characterized by dense knowledge points and complex hierarchical progression, yet is often taught in a linear, chapter-by-chapter and fragmented manner, this study constructed a course knowledge graph for advanced mathematics covering six chapters and 75 knowledge points, with nodes connected by three types of relationships: parent-child, prerequisite-successor, and association relationships. Based on this graph, a three-stage teaching model of “pre-class autonomous learning - in-class internalization and construction - after-class consolidation and extension” was designed, supported by a “locate-intervene-re-locate” assessment scheme driven by node-level learning analytics. A one-semester controlled teaching experiment was conducted in the course Advanced Mathematics A (1) at Beijing University of Civil Engineering and Architecture, with an experimental class of 109 students and a control group of 2051 students taught by 17 teachers. A unified final examination showed that the experimental class achieved a mean score of 74.40, which was 11.34 points higher than that of the control group (63.06); its pass rate was approximately 19 percentage points higher, its excellence rate was 2.6 times that of the control group; and its standard deviation (15.20) was lower than that of the control group (21.29), indicating a convergence in score dispersion. The mean scores of the student questionnaire were no lower than 4.50 in all dimensions, including knowledge structure presentation, understanding of conceptual connections, support for autonomous learning, and overall learning assistance. Within a control sample of nearly two thousand students, the model of integrating the course knowledge graph throughout the entire teaching process demonstrated positive effects, showing an improvement in overall academic performance and a narrowing of achievement gaps.