# An Intelligent Grey Correlation Model for Online English Teaching Quality Analysis

Authors: Xin Wei
Journal: Mobile Information Systems
 (2022)

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## Abstract

In order to improve the effect of English teaching, we study the evaluation of English teaching effect based on the grey relational model. Comparing the influencing factors of the primary index and the secondary index, the judgment matrix is constructed, the matrix weight is calculated, and the consistency is tested; after the consistency test results are determined, the variable weight comprehensive evaluation method is used to adjust the weight value of each evaluation index, and the total score is calculated by obtaining the scores of each index at the same time, so as to evaluate the teaching effect. The experimental results show that the relevance of the grey correlation method to English teaching quality is greater than 0.90, the teaching quality is good, the selection of evaluation indicators and the test-retest reliability of evaluation results are greater than 0.700, and the evaluation results are effective.


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## Body

## 1. Introduction

Students psychologically think that English is a foreign language and are unwilling to learn it, and subconsciously, there is resistance to it. What teachers need to do is to help students overcome the psychological barriers, build up a scientific English learning system, and promote English teaching and learning.The English course helps universities expand students’ knowledge, improve students’ quality education, and cultivate comprehensive composite talents useful to society [1]. The construction of a reasonable and effective evaluation system of English teaching effect is the target of key research at present [2]. In the existing studies, the data are analyzed by questionnaires, index systems are constructed, and these index systems are evaluated using the quantitative analysis methods to set a standard for evaluating teachers’ teaching effectiveness, which is of great practical significance [3, 4]. Some studies have shown that the effectiveness of teaching English is improved by improving the overall cognitive ability of learners. In that study, it is argued that if some students with poor English foundation focus on understanding the meaning and semantics of English words and ignore the learning of professional knowledge, this situation leads to poor teaching effect, and if we want to improve the teaching effect, we should start from improving students’ learning ability [5, 6], but this method emphasizes too much on the subjectivity of students’ learning and ignores the dominance of teachers.The main purpose of the current in-depth promotion of English teaching reform is improving the teaching efficiency and lecture quality of the English classroom [7, 8]. In terms of traditional English teaching, the traditional teaching methods of junior high school English teaching seem to be relatively backward under the current teaching needs, which has caused certain inhibitions to the improvement of teaching efficiency and quality of lessons [9, 10]. In this situation, the questions of “how to make students adapt to the new teaching materials,” “how to effectively realize the reform of teaching,” and “how to build a scientific English teaching system” have all become the issues of “how to make students adapt to the new teaching materials.” In order to do so, we need to establish a unique and scientific teaching system in relation to the actual teaching situation and teaching environment [11, 12].There are so many methods of teaching quality evaluation, such as qualitative evaluation methods, quantitative evaluation methods, and evaluation methods that integrate quantitative and qualitative [13, 14]. Each of these evaluation methods has its own unique evaluation advantages and scope of use, but in the detailed application process, a reasonable evaluation method needs to be chosen according to the assessment objectives and the real needs of the assessment [15, 16]. The grey correlation analysis method belongs to the evaluation method that blends qualitative and quantitative aspects and takes the grey system with incomplete and clear information as the target of research. The method is less complex in structure and less arithmetic, does not have strict constraints on the number of evaluation samples, and has better applicability [17–20].To improve the English teaching effectiveness, we study the evaluation of English teaching effectiveness based on the grey correlation model. We compare the factors of primary and secondary indicators, use them as the basis to construct a judgment matrix, calculate the matrix weights, and implement a consistency test; after determining the results of the consistency test, we adjust the weight values of the evaluation indicators using the variable weight comprehensive assessment; the overall score is calculated by obtaining the scores of each index at the same time, and the teaching effect is evaluated by the score. Based on the evaluation results, teachers can improve their teaching contents and methods, enhance their teaching level, and solve the problem of poor teaching effectiveness.


## 2. Evaluation Method of Public English Teaching Quality

### 2.1. Evaluation Index Selection Method Based on Optimal Data Clustering Criteria

The standard value interval for setting the clustering categories of public English teaching quality evaluation indexes isf, which needs to be at the best value according to the optimal clustering requirements. f is usually set by experts so that the attributes of the clustering results can be maximized. The attributes of evaluation indicators are set as X, the clustering categories of quality evaluation indicators are set as c, the value of each attribute among college public English teaching quality evaluation indicators is set as xn, and the clustering deviation δ2X among each evaluation indicator is as follows:(1)δ2X=1n∑k=1nxn−x¯2,where x¯ is the mean value of the set of evaluation indicator attributes x, i.e., x¯x¯=1/n∑k=1nxk.This value is larger when the value difference between evaluation index attributes inX is larger, and vice versa means that the value approximation between evaluation index attributes in X is higher, and n is the number of indicators.The errorδ2Xi,Xi¯ of the evaluation index clustering result i is(2)δ2Xi,Xi¯=1n∑k=1nxn−Xi¯2.The mean ofc clustering errors is(3)δ2Xi,Xi¯=1/c∑i=1nδ2Xi,Xi¯ξ2X,where Xi¯,δ2Xi,Xi¯ are c clustering mean, clustering close water mean, δ2Xi,Xi¯ a smaller value represents c evaluation index spacing is small; evaluation index interval becomes larger, the value becomes larger, and this value can describe the clustering effect of clustering evaluation index.The mean value of distance betweenf clusters DX,R is(4)DX,R=12c∑i=1c∑j=1cri−rj,where the centers of clusters i,j are set in order to ri,rj.The clustering needs to take into account the interclass closeness and interclass distribution status. Setting the weights toα,β, the evaluation index for obtaining the optimal clustering is(5)SX,R=δ2X,X¯β/α+αDX,R,where δ2X,X¯ describes the high level of clustering closeness; α/DX,R describes the correlation between the state of the cluster distribution and the geometric orientation of the cluster centers, which is used to balance the interference of the 2 evaluation metrics on the clustering criterion [21–24].


### 2.2. Public English Teaching Quality Evaluation Index System

Figure1 shows how to construct the public English teaching quality evaluation index system in colleges and universities. In this paper, cross validation (method in Section 2.1) and secondary indicators are used to verify the performance of this scheme, which is evaluated by several key factors. With the development of Internet and video communication technology, online education is in full swing, and the data generated by online education platform are increasing day by day The research and application of big data in the field of online education is very important for the efficiency of online education. Firstly, it defines the basic concept, classification, and characteristics of big data on the online education platform. Secondly, it introduces the relevant technologies such as education data mining, learning analysis, and knowledge Atlas. Then, it builds a big data model for the online education field. Finally, it focuses on describing the functions of big data according to the classification of service objects and outlines the basic outline of big data application on the future online education platform. It will play a guiding role in the research and development of big data in the field of online education.Figure 1
Flowchart of evaluation index system construction.Figure 2
Evaluation index system of teaching quality.The process is as follows:(1)
Setting multiple primary evaluation indicators with multiple secondary indicators.(2)
Implementing evaluation of key levels of indicators using the Telfer method, removing nonkey indicators according to key levels and retaining indicators with higher key levels.(3)
Construct an evaluation index system for the quality of public English teaching. The results of constructing the system are shown in Figure2.


### 2.3. Comprehensive Evaluation Method

(1)
If there arem factors of public English teaching quality evaluation indexes and n evaluation subjects, the original data matrix can be obtained in(6)X=x11x12…x1mx21x22…x2m⋮⋮…⋮xn1xn2…xnm.Let there be households of evaluation levels in the evaluation criteria, then the evaluation set isL=L1,L2,…,LP.Implement the homogenization operation of the original judgment matrix to obtain the mean value ofn evaluation targets for m indicator factors, set to 11, and set this mean value to the reference sequence.Implement quantification for each evaluation level in the evaluation setL, and extract the judgment matrix of m indicators corresponding to the quantified values, and the matrix is(7)L=l11l12…l1ml21l22…l2m⋮⋮…⋮lp1lp2…lpm.Set this judgment matrixL as a comparison matrix.(2)
Calculate the correlation coefficient and correlation degree between the corresponding elements of the comparison matrix and the reference matrix.The reference sequencexoj and the comparison sequence xij are normalized to the matrix by the dimensionless operation, and the elemental algorithm is(8)xij′=xojxij.In equations (9) and (10), it operates the correlation coefficient and correlation degree:(9)ξij=miniminjx0j′−xij′+ρjmaximaxjx0j′−xij′x0j′−xij′+ρjmaximaxjx0j′−xij′.(10)γi=1m∑i=1mξij,wherex0j′−xij′,miniminjx0j′−xij′ is the corresponding absolute difference of the i-th kind of the j-th index, the minimum value of the absolute difference of the two levels, maximaxjx0j′−xij′,ρj is the maximum value of the absolute difference of the two levels with the judgment coefficient, respectively.(3)
If a certain comparison series and the reference series are very close, then the correlation value of the two is larger, indicating that each index factor to be evaluated is very close to this comparison series [25–27].


## 2.1. Evaluation Index Selection Method Based on Optimal Data Clustering Criteria

The standard value interval for setting the clustering categories of public English teaching quality evaluation indexes isf, which needs to be at the best value according to the optimal clustering requirements. f is usually set by experts so that the attributes of the clustering results can be maximized. The attributes of evaluation indicators are set as X, the clustering categories of quality evaluation indicators are set as c, the value of each attribute among college public English teaching quality evaluation indicators is set as xn, and the clustering deviation δ2X among each evaluation indicator is as follows:(1)δ2X=1n∑k=1nxn−x¯2,where x¯ is the mean value of the set of evaluation indicator attributes x, i.e., x¯x¯=1/n∑k=1nxk.This value is larger when the value difference between evaluation index attributes inX is larger, and vice versa means that the value approximation between evaluation index attributes in X is higher, and n is the number of indicators.The errorδ2Xi,Xi¯ of the evaluation index clustering result i is(2)δ2Xi,Xi¯=1n∑k=1nxn−Xi¯2.The mean ofc clustering errors is(3)δ2Xi,Xi¯=1/c∑i=1nδ2Xi,Xi¯ξ2X,where Xi¯,δ2Xi,Xi¯ are c clustering mean, clustering close water mean, δ2Xi,Xi¯ a smaller value represents c evaluation index spacing is small; evaluation index interval becomes larger, the value becomes larger, and this value can describe the clustering effect of clustering evaluation index.The mean value of distance betweenf clusters DX,R is(4)DX,R=12c∑i=1c∑j=1cri−rj,where the centers of clusters i,j are set in order to ri,rj.The clustering needs to take into account the interclass closeness and interclass distribution status. Setting the weights toα,β, the evaluation index for obtaining the optimal clustering is(5)SX,R=δ2X,X¯β/α+αDX,R,where δ2X,X¯ describes the high level of clustering closeness; α/DX,R describes the correlation between the state of the cluster distribution and the geometric orientation of the cluster centers, which is used to balance the interference of the 2 evaluation metrics on the clustering criterion [21–24].


## 2.2. Public English Teaching Quality Evaluation Index System

Figure1 shows how to construct the public English teaching quality evaluation index system in colleges and universities. In this paper, cross validation (method in Section 2.1) and secondary indicators are used to verify the performance of this scheme, which is evaluated by several key factors. With the development of Internet and video communication technology, online education is in full swing, and the data generated by online education platform are increasing day by day The research and application of big data in the field of online education is very important for the efficiency of online education. Firstly, it defines the basic concept, classification, and characteristics of big data on the online education platform. Secondly, it introduces the relevant technologies such as education data mining, learning analysis, and knowledge Atlas. Then, it builds a big data model for the online education field. Finally, it focuses on describing the functions of big data according to the classification of service objects and outlines the basic outline of big data application on the future online education platform. It will play a guiding role in the research and development of big data in the field of online education.Figure 1
Flowchart of evaluation index system construction.Figure 2
Evaluation index system of teaching quality.The process is as follows:(1)
Setting multiple primary evaluation indicators with multiple secondary indicators.(2)
Implementing evaluation of key levels of indicators using the Telfer method, removing nonkey indicators according to key levels and retaining indicators with higher key levels.(3)
Construct an evaluation index system for the quality of public English teaching. The results of constructing the system are shown in Figure2.


## 2.3. Comprehensive Evaluation Method

(1)
If there arem factors of public English teaching quality evaluation indexes and n evaluation subjects, the original data matrix can be obtained in(6)X=x11x12…x1mx21x22…x2m⋮⋮…⋮xn1xn2…xnm.Let there be households of evaluation levels in the evaluation criteria, then the evaluation set isL=L1,L2,…,LP.Implement the homogenization operation of the original judgment matrix to obtain the mean value ofn evaluation targets for m indicator factors, set to 11, and set this mean value to the reference sequence.Implement quantification for each evaluation level in the evaluation setL, and extract the judgment matrix of m indicators corresponding to the quantified values, and the matrix is(7)L=l11l12…l1ml21l22…l2m⋮⋮…⋮lp1lp2…lpm.Set this judgment matrixL as a comparison matrix.(2)
Calculate the correlation coefficient and correlation degree between the corresponding elements of the comparison matrix and the reference matrix.The reference sequencexoj and the comparison sequence xij are normalized to the matrix by the dimensionless operation, and the elemental algorithm is(8)xij′=xojxij.In equations (9) and (10), it operates the correlation coefficient and correlation degree:(9)ξij=miniminjx0j′−xij′+ρjmaximaxjx0j′−xij′x0j′−xij′+ρjmaximaxjx0j′−xij′.(10)γi=1m∑i=1mξij,wherex0j′−xij′,miniminjx0j′−xij′ is the corresponding absolute difference of the i-th kind of the j-th index, the minimum value of the absolute difference of the two levels, maximaxjx0j′−xij′,ρj is the maximum value of the absolute difference of the two levels with the judgment coefficient, respectively.(3)
If a certain comparison series and the reference series are very close, then the correlation value of the two is larger, indicating that each index factor to be evaluated is very close to this comparison series [25–27].


## 3. Experimental Results and Analysis

Taking three teachers A, B, and C as examples, the method of this paper was used, and the evaluation index system established by the method of this paper is shown in Figure2. The details of the judgment matrix of the first-level are shown in Figure 3.Figure 3
Details of the judgment matrix of the first-level evaluation indexes.Because of the differences in the scale, order of magnitude, and performance mode of each evaluation index in the teaching quality evaluation index system, direct comparison could not be achieved, so the experiment implemented normalization with the secondary indexes shown in Figure2.In Figure4, the maximum correlation is 0.95, 0.89, 0.69, 0.59, and the maximum correlation is 0.95. The maximum correlation is very good, so the result of the teaching quality is very good; the correlation of teacher B’s teaching quality is 0.98, 0.88, 0.65, 0.45, and the maximum correlation is 0.98. The maximum correlation is 0.98, and the maximum correlation is very good; therefore, the teacher's teaching quality evaluation result is very good; the maximum correlation of teacher C’s teaching quality is 0.99, and the teacher’s teaching quality evaluation result is also very good. Thus, it can be seen that the evaluation results of public English teaching quality in all three universities are very good.Figure 4
Correlation of teaching quality among 3 teachers.Retest reliability also belongs to retest reliability, which is a common reliability evaluation method. It can describe the stability and consistency of evaluation results across time and can be interpreted as follows: using the same evaluation method, implementing multiple evaluations of the same evaluation target, computing the correlation level of multiple evaluation results, and the correlation level. If the correlation level is significant, it means the evaluation results are consistent and stable, and the evaluation results are valid. The retest reliability is calculated by(11)s=∑FG·∑F∑G/M∑F2·∑F2/M∑G2·∑G2/M.Among them,F and G denote the evaluation results of the quality of public English teaching with different evaluation times, and M is the number of evaluation times of the quality of public English teaching.To test the reasonableness of the primary and secondary indicators selected by the method of this paper in evaluating the quality of public English teaching, the stability and consistency of the evaluation content of the evaluation indicators of public English teaching quality in colleges and universities across time are analyzed with the retest reliability as the test index.From the results, the primary and secondary indicators are reasonably selected in evaluating the teaching quality of the three college public English teachers, and the retest reliability of the evaluation indicators of college public English teaching quality is greater than 0.700 across time, and the stability and consistency of the evaluation contents meet the application requirements.The retest reliability of the teaching quality evaluation results of the three college public English teachers is shown in Figure5.Figure 5
Retest reliability of the evaluation results of public English teaching quality in colleges and universities.From Figure5, we can see that the retest reliability of the evaluation results of this method is as high as 0.757 after evaluating the teaching quality of three public English teachers in colleges and universities. The large reliability coefficient indicates that this method has significant stability and consistency across time and the evaluation results are valid.


## 4. Case Study

The students and teachers of the foreign language department of a 985 comprehensive university in the class of 2018 were taken as the subjects of the study. The department was divided into English teacher training, Japanese language, and business English majors, with a total number of 220 students, 73 males and 147 females, 141 English majors and 12 teachers in the team. The teacher has been teaching in colleges and universities for 20 years and has been awarded the title of associate professor in recent years, accumulating rich teaching experience, extensive knowledge, and having her own characteristics in teaching methods. Fifty of the 141 English majors of the class of 2018, with a 50/50 ratio of men and women, were selected to implement the evaluation of this teacher’s teaching effectiveness based on the method of this paper, which started on October 17, 2018.It can be seen that, excluding the speaking level index and the interactivity index, the teacher’s teaching effectiveness assessment is above 90, and the speaking level index and the interactivity index scores are 89 and 88, respectively.According to the results, we can see that most teachers are satisfied with the evaluation effect of this paper, and the number of teachers who are satisfied reaches 85% in the statistical results. Most teachers think that they can get feedback on teaching effect through students’ evaluation and then adjust their teaching attitude and teaching level according to this feedback, which helps the virtuous circle; some teachers respond that they are not satisfied with this evaluation method of this paper, and the statistics found that most of the teachers in this part are highly respected old professors who are not satisfied with their teaching being evaluated by students, and they gradually accept this evaluation method after coordination by the university. It can be seen that the majority of students are satisfied with the evaluation method of this paper, and the number of dissatisfied students is 0. Most students reflect that the teachers who have been evaluated by the method of this paper, after receiving the evaluation, have modified their teaching methods, improved students’ learning enthusiasm, and their learning performance has been effectively improved.Since September 2018 when teachers’ teaching was evaluated using the method of this paper, teachers made partial modifications and adjustments to their teaching methods and teaching contents based on the evaluation results, and students’ evaluation of English teaching effectiveness was organized every month from September 2018 to December 2018. Three of the English teachers were selected to implement tracking statistics.It can be seen from the results that each teacher modifies their teaching methods every month according to the feedback of the evaluation results of this paper, which makes the evaluation scores improve every month.


## 5. Conclusion

To evaluate the quality of public English teaching in colleges and universities, this paper proposes an evaluation method based on grey relational analysis. The method proposed in this paper is applied to the public English teaching quality evaluation of a university, and the evaluation results show that the results are very good. This paper only does a preliminary research on the evaluation of the effect of English teaching in colleges and universities, and further research can be carried out from the following aspects in future research:(1)
To build a more complete, operable, and comprehensive index system from multiple angles and directions, and to make a holistic and global evaluation of the evaluation content(2)
Teachers in colleges and universities do not teach English only to achieve the dissemination of educational information, but more importantly, to achieve the training of language ability and learning ability. Teachers should summarize the shortcomings of teaching according to students’ evaluation results, increase teacher-student interaction, and motivate students to learn.(3)
Teachers can combine language and physical activities to increase opportunities for language practice and practice learning content.(4)
Future research can be combined with other evaluation methods, such as fuzzy evaluation methods, to further improve the evaluation effect.



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