在教育教学过程中，最常见的测验方式就是试卷测评，试卷不仅涵盖了整个课程学习

中的重要知识点，也包括学生在课程中需要掌握的内容。是教师主要用来了解学生课堂

学习质量的测评工具，通过试卷测评可以针对具体知识点进行教学改进。以往教师使用

班级总分及平均分来判断学生学习情况，通过讲解易错题提高学生分数，很难去分析判

断学生对具体知识点的掌握，以及试卷考察知识点间的关联关系。而这些关联关系会在

一定程度上帮助教师更深层次了解学生学习状况，使教学更具针对性、科学性。但在教

师评测过程中，会产生大量教学数据，由于人力不足，通过教师人工批注及计算来得到

知识点间关系难度较大。教师只能凭借教学经验来主观判断试卷考察的知识点间结构。

因此，许多学者针对教学数据众多这一问题，引入了算法机制，利用机器学习来进行挖

掘，提升教学效率。在庞大的信息量中发现隐藏在数据背后，可能前人未知的，能为人

们提供潜在价值、有用的信息，这一过程称为数据挖掘。而关联规则的挖掘在数据挖掘

的应用中占有一席之地，用来发现大量数据项集之间的相关关系，为教学提供方向。目

前一些研究者已经使用众多算法来进行知识点间关联关系的研究，其中最典型的还是使

用 Apriori 算法来对知识点间关联关系进行分析。以往研究针对的更多是影响学科的影响

因素的挖掘，或者某一门具体学科，以章节作为元知识点进行挖掘，针对单一学科知识

点间的关联关系，研究存在一定的局限性。本研究在此基础上，进行不同学科间的比

较，查看基于试卷的多层级结构知识点，使用 Apriori 算法，在生成的知识点关联关系

上，会有怎样的学科差异。而在学科教学中，科学学科是我们目前学科发展中起步较

晚，但非常重要的学科。因此本研究重点针对中小学科学，发现知识点间关联能给科学

教学带来怎样的帮助和启示。

本研究通过模拟研究，基于不同的样本数、知识点属性层级结构，判断 Apriori 算法

的适用性。再进行实证研究，分别针对语文、数学、科学三门学科，分析在不同学段六

年级和九年级，试卷知识点间结构的差异，使用 Apriori 算法来得出知识点间关联规则。

针对学科间的差异，具体分析科学学科知识点间结构的分布，根据结论提出有价值的信

息，希望对科学教学的发展和教材编排起到一定的补充作用。

1研究结论主要包括：

（1）Apriori 算法能够基于认知诊断理论下建立的三种不同结构的知识点属性层级关

系的 Q 矩阵，进行知识点间关联规则的挖掘，并且有较高的准确率，与预估的情况一

致；

（2）Apriori 算法能够很好的对语文、数学、科学学科进行知识点间关联规则的分

析，使我们观察到哪些知识点会对其他知识点产生强关联关系，但是在知识点粒度划分

上可能导致知识点关联信息不够；

（3）在划分知识点粒度，并去除基础知识点后，Apriori 算法可以发现剩余知识点间

关联关系，并且能够形成可视化。直观明显地观察到学科间知识点关联的差异，且符合

之前猜想，并验证学科间差异关系。但仍旧会出现在以往教学经验中未能预想到的关联

关系，需要再进行深度的挖掘和科学的解释；

（4）关联规则又分为强有效关联和弱有效关联，我们以 lift 参数为基准，发现各个

学科的强有效关联规则，显示出较明显的学科差异，其中科学学科在不同年级的差异较

为显著；

（5）Apriori 算法的确对知识点间关联规则分析是有作用的，并且通过算法挖掘的关

联规则，可以应用到教学中，为教师教学提供一些科学的决策。

In the education teaching process, the test of the most common way is to use paper

evaluation, examination paper not only covers the whole course of knowledge, and teachers hope students need to master in the course content, is the quality of teachers is mainly used to understand students' classroom learning tool, through the teaching evaluation can target specific knowledge teaching improvement.In the past, teachers could only judge students' learning conditions by the total score and average score of the class, and improve students' scores by explaining error-prone questions. It was difficult to analyze and judge students' mastery of specific knowledge points and the correlation between knowledge points in the distribution of test papers.To some extent, these relationships can help teachers to understand students' learning conditions in a deeper level, and make teaching more targeted and scientific.However, there are

also some problems in the process of teacher evaluation, will produce a large number of teaching data, due to manpower shortage, not all of the data can be manually annotated and calculated by teachers to obtain the relationship between these knowledge points, teachers can only rely on teaching experience to roughly judge the test paper knowledge point structure.Therefore, many scholars have introduced algorithm mechanism to solve the problem of large teaching data, and used machine learning to mine and improve teaching efficiency.Through the use of technology, data mining can find hidden behind the huge amount of information, which may be unknown before, and can provide people with potentially valuable and useful information.This process is called data mining.The mining of association rules plays an important role in the application of data mining, which is used to discover the correlation between large data item sets and provide a

direction for teaching.At present, some researchers have used many algorithms to study the correlation between knowledge points, among which the most typical one is to use Apriori algorithm to analyze the correlation between knowledge points.Previous studies focused more on the mining of influencing factors affecting disciplines, or on the mining of a specific discipline by taking chapters as meta-knowledge points. However, there are certain limitations in terms of the correlation between knowledge points of a single discipline.On this basis, this study on the comparison between the different disciplines, check for multiple hierarchy knowledge based on the examination paper, using the Apriori algorithm, and in the generation of knowledge on the relationship, there will be what kind of subject, and in the discipline teaching, science is developing our current started late, but is a very important subject,Therefore, this study focuses on science in primary and secondary schools to find out what kind of help and inspiration the correlation of knowledge points can bring to science teaching.Through simulation research, this study judged the applicability of Apriori algorithm based on different sample sizes and knowledge point attribute hierarchy structure.For empirical research, three disciplines, respectively, in view of Chinese, maths, science, analysis in no students grade six and nine grade, the examination paper of the structure of the differences between knowledge, using Apriori algorithm to find association rules between knowledge points, in view of the differences between disciplines, concrete analysis between scientific discipline knowledge structure distribution, according to the conclusion put forward valuable information,It is expected to play a complementary role in the development of science teaching and the arrangement of textbooks.

The research conclusions mainly include:

(1) Apriori algorithm can mine the association rules among knowledge points based on the Q matrix of three different structures of knowledge point attribute hierarchy relationship established under the theory of cognitive diagnosis, and it has a high accuracy, which is consistent with the predicted situation;

(2) The Apriori algorithm can well analyze the association rules among knowledge points in Chinese, mathematics and science subjects, so that we can observe which knowledge points will produce strong association relations with other knowledge points. However, the granularity of knowledge points may lead to insufficient association information of knowledge points.

(3) in the division of knowledge granularity, and after removal of basic knowledge, Apriori algorithm can find the rest of the relationship between knowledge points, and the ability to form the visual, can obviously observe discipline knowledge associated with the differences between the intuitive, and consistent with the previously suspected, and verify the difference betweensubject relationship, but still will appear in the past teaching experience not envisionedrelationship,It requires further excavation and scientific interpretation;

(4) Association rules can be divided into strong effective association rules and weak

effective association rules. Taking LIFT parameter as the benchmark, we found the strongeffective association rules of each discipline, which showed significant disciplinary differences,among which science discipline showed significant differences in different grades.

(5) Apriori algorithm does play a role in the analysis of association rules among

knowledge points, and the rules mined by the algorithm can be applied to teaching to providesome scientific decisions for teachers in teaching.