如何量化一场考试？——基于复杂网络的物理考试证据
How to quantify an examination? Evidence from physics examinations via complex networks
AI总结：
本文提出基于复杂网络构建考试知识点网络（KPN）的量化方法，通过分析2006-2020年35份高考物理试卷，揭示其无标度、同配性及社区结构，并利用拓扑量提出难度评估指标Fd，为考试分析与教学改进提供新途径。
摘要：
鉴于考试在持续改进方面尚未开发的潜力，对考试的量化研究可以指导大幅提升学习效率和评估效果，从而极大地帮助学习者和教育者。然而，目前普遍缺乏用于研究考试的量化方法。为弥补这一空白，我们通过复杂网络提出了一种新度量，即：通过将知识点（概念、定律等）表示为节点，并在这些知识点出现在同一道题目中时添加连边，来构建考试的知识点网络（KPN）。随后，KPN的拓扑量，如度、中心性和社区，可用于系统地探索考试的结构属性和演变。在本工作中，以2006年至2020年间全国高考（NCEE）中的35份物理试卷作为证据进行了研究。我们发现所构建的KPN在大多数情况下是无标度网络，表现出强同配性和小世界效应。KPN内的社区结构明显，关键节点主要与力学和电磁学相关。不同的题型与特定的知识点相关联，导致KPN在结构上出现显著差异。此外，不同年份考试之间KPN拓扑的变化可能为高考改革提供见解。基于平均度、网络密度、平均聚类系数和网络传递性等拓扑量，我们提出了Fd来评估考试难度。上述所有结果表明，我们的方法能够全面量化知识结构和考试特征。这些网络可能为教育者阐明全面的考试知识图谱，并指导教学改进。
英文摘要：
Given the untapped potential for continuous improvement of examinations, quantitative investigations of examinations could guide efforts to considerably improve learning efficiency and evaluation and thus greatly help both learners and educators. However, there is a general lack of quantitative methods for investigating examinations. To address this gap, we propose a new metric via complex networks; i.e., the knowledge point network (KPN) of an examination is constructed by representing the knowledge points (concepts, laws, etc.) as nodes and adding links when these points appear in the same question. Then, the topological quantities of KPNs, such as degree, centrality, and community, can be employed to systematically explore the structural properties and evolution of examinations. In this work, 35 physics examinations from the NCEE examination spanning from 2006 to 2020 were investigated as an evidence. We found that the constructed KPNs are scale-free networks that show strong assortativity and small-world effects in most cases. The communities within the KPNs are obvious, and the key nodes are mainly related to mechanics and electromagnetism. Different question types are related to specific knowledge points, leading to noticeable structural variations in KPNs. Moreover, changes in the KPN topology between examinations administered in different years may offer insights guiding college entrance examination reforms. Based on topological quantities such as the average degree, network density, average clustering coefficient, and network transitivity, the Fd is proposed to evaluate examination difficulty. All the above results show that our approach can comprehensively quantify the knowledge structures and examination characteristics. These networks may elucidate comprehensive examination knowledge graphs for educators and guide improvements in teaching.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
