# A Study on the Application of Random Matrix Theory in the Construction of the Evaluation System of Public English Flipped Classroom Teaching in Higher Education Institutions

Authors: Xuemei Sun; Xun Lin
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

With the development of science and technology, the advent of the knowledge era, the Internet era, the WeChat era, and the mobile era as well as the development of multimedia have brought about great changes in the dissemination, communication, construction, and sharing of knowledge. This series of changes has led to unprecedented changes in teaching philosophy, teaching mode, teaching objectives, teaching design, teaching methods, and teaching approaches in higher vocational education. With the deepening of the new round of curriculum reform, flipped classroom teaching has been generally accepted and widely used. Therefore, it is essential to evaluate flipped classroom teaching. Based on the introduction of the random matrix theory, this paper attempts to establish a complete and scientific evaluation index system in conjunction with the flipped public English classroom in higher education institutions, so as to provide students and teachers with a reliable means of evaluation and thus promote the practical application of English teaching in higher education.


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## Body

## 1. Introduction

In October 2015, the Ministry of Education released the Ten-Year Development Plan for Education Informatization (2011–2020). In July 2015, the Ministry of Education's opinions on deepening the Teaching Reform of Vocational Education and Comprehensively Improving the Quality of Talent Cultivation vigorously promoted the application of information technology to facilitate the teaching reform of higher vocational education and comprehensively improve the talent cultivation of higher vocational institutions quality and to vigorously promote educational philosophy [1], teaching purposes, teaching forms, teaching methods, teachers’ roles, and assessment in the information technology era [2]. In October 2015, the Ministry of Education released the Action Plan for the Innovative Development of Higher Vocational Education (2015–2018), which promotes the reform of curriculum system and teaching methods. Therefore, the use of flipped classroom in the teaching of public English in higher vocational institutions is to meet the current trend and tendency of education information reform.The introduction and implementation of the flipped classroom has changed the traditional teaching methods of “class teaching” and “duck-filling,” providing new ideas for the reform of English courses in higher education in the information age. The combination of advanced information technology and specific teaching activities has greatly made up for the shortcomings of the current English courses in vocational colleges; the emphasis on students’ subjectivity has stimulated their learning efficiency and effectiveness to the greatest extent possible, enabling students’ subjectivity and initiative to be fully developed [3] and has injected new vitality into the implementation of educational information technology reform in the teaching of higher vocational courses in China’s education sector.With the advancement of the new curriculum reform, the issue of integration of information technology and curriculum has received increasing attention from educators. At the time of the new curriculum reform, the Ministry of Education emphasised the need to vigorously promote information technology to integrate it effectively with professional courses and to gradually adapt to the needs of the times, integrate various teaching resources, make full use of information technology, and create various educational environments and learning tools for teachers and students’ learning [4]. This shows the importance of information technology in the new round of curriculum reform. How to use computer technology effectively is the development trend of education in today’s world and worldwide.


## 2. Introduction to the Relevant Theory

### 2.1. Components of Random Matrix Theory

To understand a random matrix, it is first necessary to understand it. Probability theory, mathematical statistics, stochastic processes, and matrix theory are the theoretical foundations of random matrices. A random matrix is a matrix of arbitrary variables in which the number of columns and rows of the matrix is close to infinity, called a large dimensional random matrix [5].The existing classical limit theories all assume that the dimensionality of the data is fixed, but due to their own limitations, traditional limit theory can no longer be applied to large dimensional data. As we said before, the most common method of dealing with dimensionality reduction is to lose it in the initial data. As a result, in the 1930s, random matrices were proposed by Wishart et al. Later, some laws were slowly discovered, such as Wigner’s discovery in the 1950s and others.Depending on the dimensionality of the data, random matrix theory can be divided into asymptotic random matrix theory (infinite dimension) and nonasymptotic matrix (finite dimension). Based on this, this paper proposes a new method to extend the infinite-dimensional random matrix theory to reality [6], where the dimensionality of the matrix is no longer limited to infinite dimensions, thus bringing the random matrix theory closer to reality.Figure1 shows a system consisting of the random matrix principle. In it, the asymptotic theory focuses on the convergence of the spectral distribution function of an arbitrary matrix on an infinite-dimensional space. Since, in reality, the dimensionality of matrices is not infinite, such large-scale samples are separated from real life. Nonasymptotic theory, in contrast to asymptotic theory, focuses on the convergence exhibited by its spectral distribution function in a finite dimensional space. In comparison with asymptotic theory, it is closer to reality.Figure 1
Composition of random matrix theory.


### 2.2. Teaching Public English in Higher Education

The term “higher vocational” is an abbreviation for higher vocational and technical education. The second is the scope of vocational and technical education. The purpose of cultivating higher vocational and technical talents is to cultivate highly skilled and comprehensive higher vocational and application-oriented talents who can adapt to the first line of production, construction, management, and service [7–9].Public English is the basic course for higher vocational and technical talents and is an important course offered by higher vocational colleges. By comparing the basic English course in general vocational schools and the university English course, the connotation and characteristics of the public English course are discussed. From the perspective of professional English, the English courses in vocational colleges require students’ language knowledge and application ability to be higher than the basic English in secondary vocational schools; although the teaching requirements of higher vocational public English are not high, compared to general university English teaching, it focuses more on professional skills as the orientation and on the relevance, practicality, and foundation of English teaching.From this, we can see that the teaching principle of public English in higher education is “practical and appropriate,” focusing on the students’ ability to use the language and their subjectivity. In addition, the poor basic knowledge of English in higher education institutions, the poor application of English and the needs of vocational English teaching make it necessary to emphasise not only basic knowledge and language skills but also the characteristics of vocational education [10].


### 2.3. Flipped Classroom

The flipped classroom is an innovative teaching method known as “reversing the classroom” or “reversing the classroom,” which is FCM; that is, the teacher redesigns and adjusts inside and outside the classroom, giving the initiative of learning to the students; the teacher integrates the lecture content, the key points of the course, the new The teacher integrates the lecture content, course focus, and new knowledge, produces a course video, and uploads it to the Internet [11] so that students can consult the relevant teaching materials after class, or watch the course video and plan the learning content independently and complete personalised learning so as to absorb and internalise the new knowledge; in teaching, the teacher does not need to spend too much time in class to teach the knowledge but has to achieve the understanding of the new knowledge through interactive discussion and communication so as to achieve the internalisation of knowledge. The teacher does not need to spend too much time teaching in the classroom but rather to internalise the new knowledge through interactive discussion and communication. The flipped classroom is about changing both the teaching methods and the educational objectives and about changing the concept of education.Flipped classroom has two meanings. First, flipped classrooms turn the traditional inside and outside of the classroom “upside down.” Traditional learning takes place in the classroom, and flipped classroom teaching allows students to complete their learning before class, transforming the absorption of knowledge within the classroom into an understanding of knowledge [12]; second, flipped teaching reverses the roles of teachers and students. In the classroom, students are free to plan their learning time, content, pace, and learning style, thus gaining the right to learn on their own, rather than passively. The teacher plays a guiding role in the whole process, meeting the needs of the students, individualising their learning and acting as a direct implementer of behaviour. This is the major difference between “flipped” and “traditional” teaching.


## 2.1. Components of Random Matrix Theory

To understand a random matrix, it is first necessary to understand it. Probability theory, mathematical statistics, stochastic processes, and matrix theory are the theoretical foundations of random matrices. A random matrix is a matrix of arbitrary variables in which the number of columns and rows of the matrix is close to infinity, called a large dimensional random matrix [5].The existing classical limit theories all assume that the dimensionality of the data is fixed, but due to their own limitations, traditional limit theory can no longer be applied to large dimensional data. As we said before, the most common method of dealing with dimensionality reduction is to lose it in the initial data. As a result, in the 1930s, random matrices were proposed by Wishart et al. Later, some laws were slowly discovered, such as Wigner’s discovery in the 1950s and others.Depending on the dimensionality of the data, random matrix theory can be divided into asymptotic random matrix theory (infinite dimension) and nonasymptotic matrix (finite dimension). Based on this, this paper proposes a new method to extend the infinite-dimensional random matrix theory to reality [6], where the dimensionality of the matrix is no longer limited to infinite dimensions, thus bringing the random matrix theory closer to reality.Figure1 shows a system consisting of the random matrix principle. In it, the asymptotic theory focuses on the convergence of the spectral distribution function of an arbitrary matrix on an infinite-dimensional space. Since, in reality, the dimensionality of matrices is not infinite, such large-scale samples are separated from real life. Nonasymptotic theory, in contrast to asymptotic theory, focuses on the convergence exhibited by its spectral distribution function in a finite dimensional space. In comparison with asymptotic theory, it is closer to reality.Figure 1
Composition of random matrix theory.


## 2.2. Teaching Public English in Higher Education

The term “higher vocational” is an abbreviation for higher vocational and technical education. The second is the scope of vocational and technical education. The purpose of cultivating higher vocational and technical talents is to cultivate highly skilled and comprehensive higher vocational and application-oriented talents who can adapt to the first line of production, construction, management, and service [7–9].Public English is the basic course for higher vocational and technical talents and is an important course offered by higher vocational colleges. By comparing the basic English course in general vocational schools and the university English course, the connotation and characteristics of the public English course are discussed. From the perspective of professional English, the English courses in vocational colleges require students’ language knowledge and application ability to be higher than the basic English in secondary vocational schools; although the teaching requirements of higher vocational public English are not high, compared to general university English teaching, it focuses more on professional skills as the orientation and on the relevance, practicality, and foundation of English teaching.From this, we can see that the teaching principle of public English in higher education is “practical and appropriate,” focusing on the students’ ability to use the language and their subjectivity. In addition, the poor basic knowledge of English in higher education institutions, the poor application of English and the needs of vocational English teaching make it necessary to emphasise not only basic knowledge and language skills but also the characteristics of vocational education [10].


## 2.3. Flipped Classroom

The flipped classroom is an innovative teaching method known as “reversing the classroom” or “reversing the classroom,” which is FCM; that is, the teacher redesigns and adjusts inside and outside the classroom, giving the initiative of learning to the students; the teacher integrates the lecture content, the key points of the course, the new The teacher integrates the lecture content, course focus, and new knowledge, produces a course video, and uploads it to the Internet [11] so that students can consult the relevant teaching materials after class, or watch the course video and plan the learning content independently and complete personalised learning so as to absorb and internalise the new knowledge; in teaching, the teacher does not need to spend too much time in class to teach the knowledge but has to achieve the understanding of the new knowledge through interactive discussion and communication so as to achieve the internalisation of knowledge. The teacher does not need to spend too much time teaching in the classroom but rather to internalise the new knowledge through interactive discussion and communication. The flipped classroom is about changing both the teaching methods and the educational objectives and about changing the concept of education.Flipped classroom has two meanings. First, flipped classrooms turn the traditional inside and outside of the classroom “upside down.” Traditional learning takes place in the classroom, and flipped classroom teaching allows students to complete their learning before class, transforming the absorption of knowledge within the classroom into an understanding of knowledge [12]; second, flipped teaching reverses the roles of teachers and students. In the classroom, students are free to plan their learning time, content, pace, and learning style, thus gaining the right to learn on their own, rather than passively. The teacher plays a guiding role in the whole process, meeting the needs of the students, individualising their learning and acting as a direct implementer of behaviour. This is the major difference between “flipped” and “traditional” teaching.


## 3. Application Methodology Design

### 3.1. Overview of the Framework of the Flipped Classroom Teaching Evaluation System

While traditional classroom assessment methods are more homogeneous and based on summative assessment, the flipped classroom focuses on the assessment of the teaching and learning process [13]. The two assessment methods and objectives are very different, specifically in the following ways. First, the flipped page classroom shifts from summative to process-based assessment, emphasising the teaching process rather than outcomes, and is judged on the basis of performance on written tests, with more emphasis on students’ academic performance. The flipped classroom teaching evaluation system for public English in higher education institutions designed in this study is a teaching evaluation technique after adding the introduction of a random matrix to the flipped classroom teaching evaluation system, the framework diagram of which is shown in Figure 2.Figure 2
Framework diagram of the evaluation system.While traditional classroom assessment is relatively homogeneous and focuses on summative assessment of students, page-turner assessment focuses on the teaching and learning process. There are significant differences in the approach and purpose of these two assessments, particularly below. First, the page-turner moves away from summative assessment to process assessment, which emphasises the teaching and learning process rather than the outcomes.


### 3.2. Basic Principles of an Evaluation Indicator System

The construction of an indicator system is not an empty exercise but follows certain basic principles and laws so as to be more rational and operational.


#### 3.2.1. Reason of Completeness

Completeness means that the evaluation indicators must cover as much as possible the various behaviours of teachers and students in teaching, should be able to accurately and objectively reflect the teaching level of students and teachers, and should not omit the indicators that can reflect the teaching performance of teachers and students. Only by establishing a perfect indicator system can we better reflect the effect of education [14].


#### 3.2.2. Objectivity

Objectivity refers to the objective assessment of the specific situation of teachers and students in teaching activities. When constructing evaluation indicators, care should be taken not to mix with personal subjective factors, and the indicators chosen should be compatible with the new educational philosophy and with the “flipped classroom” teaching model.


#### 3.2.3. Operability

Operability refers to the operability of the evaluation indicator system in teaching practice, with each indicator being clear and unambiguous. At the same time, its system of indicators is simple and clear, enabling assessors to make scientific judgements about students and teachers based on the system of indicators. The assessment system is set up for the development of teaching and learning, which is the only way to benefit teachers and students. Assessment does not create an unnecessary workload for teachers but rather identifies problems early and facilitates future teaching.


#### 3.2.4. Principle of Independence

At the same level, there must be no interdependence, the indicators must be independent of each other, and there must not be any indicators that can cause a chain effect. For example, the scores of indicator one and indicator two are the same on several occasions, which indicates that they are highly correlated. The same indicator cannot be the cause and effect of other indicators, and it is important to ensure that the same indicator has relative independence [15–17]. Only in this way can we ensure that the evaluation indicators are fair and just and acceptable to every teacher and student.


### 3.3. Construction of the Traditional Flipped Classroom Teaching Evaluation System

Based on the analysis of flipped classroom teaching, the second level of teaching indicators is constructed according to the theory of flipped classroom teaching, the basic principles of flipped classroom teaching evaluation, and the construction of teaching evaluation index system, so as to build the evaluation index system of higher vocational English flipped classroom teaching.From the process of classroom teaching, the three stages are the teacher’s classroom knowledge transfer, classroom knowledge internalisation, and postclass extension. At the same time, it is divided into process evaluation and outcome evaluation according to the principle of combining procedure and outcome. In process assessment, the first assessment indicator is divided into prelesson assessment, classroom assessment, and postlesson assessment in accordance with the flow of classroom teaching. In outcome assessment, learning outcomes are used as the first indicator. Therefore, in the classroom teaching evaluation index system, the first evaluation indicators are preclass evaluation, classroom evaluation, postclass evaluation, and learning outcome evaluation [18].(1)
Establish a secondary indicator of “preclass evaluation”: The precourse education of the flipped classroom is mainly for students to watch the teaching video or other multimedia courseware produced by the teacher, while the assessment centres on the courseware is produced by the teacher and assesses students’ independent learning, and the assessment is based on the process assessment. Process assessment in the flipped classroom is not only about assessing students’ learning behaviour but also about assessing their learning outcomes. The second indicator of “preclassroom assessment” is therefore the quality of the learning materials, preclassroom behaviour, and preclassroom learning outcomes.(2)
A second level of indicators has been established for “classroom assessment”: The classroom phase is a collaborative inquiry process between teachers and students, emphasising the role of the teacher and the student as the “dominant subject,” and during this phase, the teacher’s performance and the students’ academic performance are assessed. In the classroom, students learn by working in groups, discussing problems, debating topics, asking and answering questions, presenting results, and exchanging experiences. The variety of student learning activities makes it difficult to assess specific student learning behaviours, but it is possible to assess students based on the commonalities of their various activities. Formally, students’ classroom learning consists mainly of active individual participation and collective inquiry. This paper therefore proposes to assess students’ classroom learning behaviours in terms of both active classroom participation and collaborative inquiry learning. On the other hand, the process of evaluating a page-turning classroom is not only about assessing students’ learning behaviours but also about assessing their learning outcomes. Therefore, the second indicator of “classroom assessment” can be divided into “classroom performance,” “classroom participation,” “cooperative group learning,” “effectiveness of classroom learning,” and “classroom learning effectiveness.”(3)
Establishing secondary indicators for “out-of-class assessment”: In this paper, the second indicator of “after-school assessment” combines after-school learning and learning outcomes into “after-school learning status.”(4)
Establishing a secondary indicator of “learning outcomes”: The new curriculum reform focuses on the three-dimensional objectives of knowledge and skills, processes and methods, and emotional attitudes and values [19]. The purpose of the “learning assessment” is to assess the achievement of this three-dimensional goal based on process assessment, while the “learning outcome” assessment is the assessment of knowledge and skills, emotional attitudes, and values. The second measure of “learning outcomes” is “cognitive and operational outcomes” and “emotional attitudes and values.”


### 3.4. Random Matrix Combined with Flipped Classroom Teaching Evaluation System Construction

This paper proposes a random matrix-based method to improve the effectiveness of feedback in classroom teaching. This paper presents a GSV method based on GSV for the first time, which is applicable to the teacher to multiple students situation.The specific implementation process of the GSV algorithm is as follows:(1)
Analysing the indicators to be tested using multiple directional detection portals(2)
Expressing the full range of analysed index data in terms of a sampling matrix(3)
Solving the singularities of the sampling matrix and determining the maximum and minimum(4)
Comparing the ratio of the maximum to the minimum singularity (singularity diffusion rate) with the determination threshold(5)
Based on the size relationship from the previous step, determine the criterion and the ratio of the maximum singularity to the minimum singularity is equal to or equal to the confidence and validity of the judgement threshold


#### 3.4.1. Weighted Matrix Analysis based on the Characteristic Spectrum

On this basis, a weighting matrix based on the random matrix is proposed and its eigen spectrum analysis is carried out to find the most critical indicators from which a high judgement ratio is obtained. The most value of the eigenvalue of the weight matrix is shown in Figure3.Figure 3
The most eigenvalues of the weight matrix.From the above figure, we can very obviously understand that the difference between the maximum and minimum eigenvalues of the weight matrix of evaluation indicators is very large [20], which is due to the variability among individuals of evaluation indicators making some elements of the weight matrix particularly large, while most of the elements are 0, resulting in a more obvious effect of the matrix in certain eigenvectors, thus making the distribution of the eigenvalue maximums disparate.


## 3.1. Overview of the Framework of the Flipped Classroom Teaching Evaluation System

While traditional classroom assessment methods are more homogeneous and based on summative assessment, the flipped classroom focuses on the assessment of the teaching and learning process [13]. The two assessment methods and objectives are very different, specifically in the following ways. First, the flipped page classroom shifts from summative to process-based assessment, emphasising the teaching process rather than outcomes, and is judged on the basis of performance on written tests, with more emphasis on students’ academic performance. The flipped classroom teaching evaluation system for public English in higher education institutions designed in this study is a teaching evaluation technique after adding the introduction of a random matrix to the flipped classroom teaching evaluation system, the framework diagram of which is shown in Figure 2.Figure 2
Framework diagram of the evaluation system.While traditional classroom assessment is relatively homogeneous and focuses on summative assessment of students, page-turner assessment focuses on the teaching and learning process. There are significant differences in the approach and purpose of these two assessments, particularly below. First, the page-turner moves away from summative assessment to process assessment, which emphasises the teaching and learning process rather than the outcomes.


## 3.2. Basic Principles of an Evaluation Indicator System

The construction of an indicator system is not an empty exercise but follows certain basic principles and laws so as to be more rational and operational.


### 3.2.1. Reason of Completeness

Completeness means that the evaluation indicators must cover as much as possible the various behaviours of teachers and students in teaching, should be able to accurately and objectively reflect the teaching level of students and teachers, and should not omit the indicators that can reflect the teaching performance of teachers and students. Only by establishing a perfect indicator system can we better reflect the effect of education [14].


### 3.2.2. Objectivity

Objectivity refers to the objective assessment of the specific situation of teachers and students in teaching activities. When constructing evaluation indicators, care should be taken not to mix with personal subjective factors, and the indicators chosen should be compatible with the new educational philosophy and with the “flipped classroom” teaching model.


### 3.2.3. Operability

Operability refers to the operability of the evaluation indicator system in teaching practice, with each indicator being clear and unambiguous. At the same time, its system of indicators is simple and clear, enabling assessors to make scientific judgements about students and teachers based on the system of indicators. The assessment system is set up for the development of teaching and learning, which is the only way to benefit teachers and students. Assessment does not create an unnecessary workload for teachers but rather identifies problems early and facilitates future teaching.


### 3.2.4. Principle of Independence

At the same level, there must be no interdependence, the indicators must be independent of each other, and there must not be any indicators that can cause a chain effect. For example, the scores of indicator one and indicator two are the same on several occasions, which indicates that they are highly correlated. The same indicator cannot be the cause and effect of other indicators, and it is important to ensure that the same indicator has relative independence [15–17]. Only in this way can we ensure that the evaluation indicators are fair and just and acceptable to every teacher and student.


## 3.2.1. Reason of Completeness

Completeness means that the evaluation indicators must cover as much as possible the various behaviours of teachers and students in teaching, should be able to accurately and objectively reflect the teaching level of students and teachers, and should not omit the indicators that can reflect the teaching performance of teachers and students. Only by establishing a perfect indicator system can we better reflect the effect of education [14].


## 3.2.2. Objectivity

Objectivity refers to the objective assessment of the specific situation of teachers and students in teaching activities. When constructing evaluation indicators, care should be taken not to mix with personal subjective factors, and the indicators chosen should be compatible with the new educational philosophy and with the “flipped classroom” teaching model.


## 3.2.3. Operability

Operability refers to the operability of the evaluation indicator system in teaching practice, with each indicator being clear and unambiguous. At the same time, its system of indicators is simple and clear, enabling assessors to make scientific judgements about students and teachers based on the system of indicators. The assessment system is set up for the development of teaching and learning, which is the only way to benefit teachers and students. Assessment does not create an unnecessary workload for teachers but rather identifies problems early and facilitates future teaching.


## 3.2.4. Principle of Independence

At the same level, there must be no interdependence, the indicators must be independent of each other, and there must not be any indicators that can cause a chain effect. For example, the scores of indicator one and indicator two are the same on several occasions, which indicates that they are highly correlated. The same indicator cannot be the cause and effect of other indicators, and it is important to ensure that the same indicator has relative independence [15–17]. Only in this way can we ensure that the evaluation indicators are fair and just and acceptable to every teacher and student.


## 3.3. Construction of the Traditional Flipped Classroom Teaching Evaluation System

Based on the analysis of flipped classroom teaching, the second level of teaching indicators is constructed according to the theory of flipped classroom teaching, the basic principles of flipped classroom teaching evaluation, and the construction of teaching evaluation index system, so as to build the evaluation index system of higher vocational English flipped classroom teaching.From the process of classroom teaching, the three stages are the teacher’s classroom knowledge transfer, classroom knowledge internalisation, and postclass extension. At the same time, it is divided into process evaluation and outcome evaluation according to the principle of combining procedure and outcome. In process assessment, the first assessment indicator is divided into prelesson assessment, classroom assessment, and postlesson assessment in accordance with the flow of classroom teaching. In outcome assessment, learning outcomes are used as the first indicator. Therefore, in the classroom teaching evaluation index system, the first evaluation indicators are preclass evaluation, classroom evaluation, postclass evaluation, and learning outcome evaluation [18].(1)
Establish a secondary indicator of “preclass evaluation”: The precourse education of the flipped classroom is mainly for students to watch the teaching video or other multimedia courseware produced by the teacher, while the assessment centres on the courseware is produced by the teacher and assesses students’ independent learning, and the assessment is based on the process assessment. Process assessment in the flipped classroom is not only about assessing students’ learning behaviour but also about assessing their learning outcomes. The second indicator of “preclassroom assessment” is therefore the quality of the learning materials, preclassroom behaviour, and preclassroom learning outcomes.(2)
A second level of indicators has been established for “classroom assessment”: The classroom phase is a collaborative inquiry process between teachers and students, emphasising the role of the teacher and the student as the “dominant subject,” and during this phase, the teacher’s performance and the students’ academic performance are assessed. In the classroom, students learn by working in groups, discussing problems, debating topics, asking and answering questions, presenting results, and exchanging experiences. The variety of student learning activities makes it difficult to assess specific student learning behaviours, but it is possible to assess students based on the commonalities of their various activities. Formally, students’ classroom learning consists mainly of active individual participation and collective inquiry. This paper therefore proposes to assess students’ classroom learning behaviours in terms of both active classroom participation and collaborative inquiry learning. On the other hand, the process of evaluating a page-turning classroom is not only about assessing students’ learning behaviours but also about assessing their learning outcomes. Therefore, the second indicator of “classroom assessment” can be divided into “classroom performance,” “classroom participation,” “cooperative group learning,” “effectiveness of classroom learning,” and “classroom learning effectiveness.”(3)
Establishing secondary indicators for “out-of-class assessment”: In this paper, the second indicator of “after-school assessment” combines after-school learning and learning outcomes into “after-school learning status.”(4)
Establishing a secondary indicator of “learning outcomes”: The new curriculum reform focuses on the three-dimensional objectives of knowledge and skills, processes and methods, and emotional attitudes and values [19]. The purpose of the “learning assessment” is to assess the achievement of this three-dimensional goal based on process assessment, while the “learning outcome” assessment is the assessment of knowledge and skills, emotional attitudes, and values. The second measure of “learning outcomes” is “cognitive and operational outcomes” and “emotional attitudes and values.”


## 3.4. Random Matrix Combined with Flipped Classroom Teaching Evaluation System Construction

This paper proposes a random matrix-based method to improve the effectiveness of feedback in classroom teaching. This paper presents a GSV method based on GSV for the first time, which is applicable to the teacher to multiple students situation.The specific implementation process of the GSV algorithm is as follows:(1)
Analysing the indicators to be tested using multiple directional detection portals(2)
Expressing the full range of analysed index data in terms of a sampling matrix(3)
Solving the singularities of the sampling matrix and determining the maximum and minimum(4)
Comparing the ratio of the maximum to the minimum singularity (singularity diffusion rate) with the determination threshold(5)
Based on the size relationship from the previous step, determine the criterion and the ratio of the maximum singularity to the minimum singularity is equal to or equal to the confidence and validity of the judgement threshold


### 3.4.1. Weighted Matrix Analysis based on the Characteristic Spectrum

On this basis, a weighting matrix based on the random matrix is proposed and its eigen spectrum analysis is carried out to find the most critical indicators from which a high judgement ratio is obtained. The most value of the eigenvalue of the weight matrix is shown in Figure3.Figure 3
The most eigenvalues of the weight matrix.From the above figure, we can very obviously understand that the difference between the maximum and minimum eigenvalues of the weight matrix of evaluation indicators is very large [20], which is due to the variability among individuals of evaluation indicators making some elements of the weight matrix particularly large, while most of the elements are 0, resulting in a more obvious effect of the matrix in certain eigenvectors, thus making the distribution of the eigenvalue maximums disparate.


## 3.4.1. Weighted Matrix Analysis based on the Characteristic Spectrum

On this basis, a weighting matrix based on the random matrix is proposed and its eigen spectrum analysis is carried out to find the most critical indicators from which a high judgement ratio is obtained. The most value of the eigenvalue of the weight matrix is shown in Figure3.Figure 3
The most eigenvalues of the weight matrix.From the above figure, we can very obviously understand that the difference between the maximum and minimum eigenvalues of the weight matrix of evaluation indicators is very large [20], which is due to the variability among individuals of evaluation indicators making some elements of the weight matrix particularly large, while most of the elements are 0, resulting in a more obvious effect of the matrix in certain eigenvectors, thus making the distribution of the eigenvalue maximums disparate.


## 4. Application of Experimental Analysis

### 4.1. Selection of Objects

After the evaluation index system has been established, its use in practice is tested. In order to ensure the correctness of the experimental results, two classes of the basic teaching department of Chuzhou Vocational and Technical College were selected as the experimental objects in this paper, and English courses offered by different teachers were chosen.


### 4.2. Basic Process of Validation

(1)
In order to eliminate the influence of interference, pre and post-tests were conducted in two classes. The effectiveness of the assessment system in improving the quality of teaching and learning in the classroom was tested by comparing the statistical data before and after the experiment [21].(2)
The experiment was conducted in the following manner:The two classes were divided intoA and B, with Class A as the experimental group and Class B as the reference. In the course of the experiment, the public English teacher in Class A is expected to make adjustments to teaching strategies based on the assessment system that introduces the random matrix theory, and based on the problems, it is reflected in the assessment results so as to improve students’ learning ability. The English teacher in Class B, on the other hand, assessed the teaching based on the original assessment method and made improvements to the teaching based on the assessment results so as to suppress disruptions. By comparing the before and after test results of the two classes, it is possible to test whether the assessment index system established in this study is applicable to the flipped classroom and whether it can improve the quality of teaching and learning. At the same time, based on the feedback from teachers and students on the assessment scale, the assessment scale was revised and improved, resulting in a more reasonable assessment index.


### 4.3. Analysis of Experimental Results

#### 4.3.1. Analysis of the Entrance English Scores

In this paper, the English survey was conducted on October 8, 1920, and the June 2006 National College English Application Proficiency LevelB test questions were selected as the test questions, which had high reliability and validity and were used as pretest scores for analysis and statistics. On this basis, the English scores of the experimental and control classes were statistically processed using the independent samples t-test. The comparative analysis P=0.190 > 0.05 means that there was no significant difference between the two experimental groups. The results showed that the English scores of the experimental and traditional classes were similar before the teaching experiment was conducted, and there is no significant difference as shown in Table 1.Table 1
Comparison of pretest scores.
GroupNumber of peopleMeanStandard deviationStandard error of the meanExperimental classes4277.12837.923481.09479Traditional classes4076.76258.202601.40376As shown in Table2, in the English pretest scores, sig = 0.164, which is greater than 0.05, and the variance between the two classes is homogeneous, P=0.190 > 0.05. The results indicate that, in general, the teaching quality of the control class and the experimental class is similar and comparable.Table 2
Independent samplest-test.
FSigtdfSig (bilateral)Mean differenceStandard error values95 confidence interval % of differenceLower limitUpper limitAssuming equal variances3.1700.1641.353970.1902.166581.69542−1.245325.67748Assuming unequal variances1.35093.240.2072.166581.71192−1.250435.63922


#### 4.3.2. Analysis of Post-Test Scores

The post-test scores of the traditional and experimental classes were statistically analysed using independent samplest-tests (see Tables 3 and 4). t = 3.856, two-sided test P value (Sig.) = 0.002 was less than 0.005, and the data analysis showed that there was a significant difference in English post-test scores between the experimental subjects and the traditional English group in the higher vocational English flipped classroom experimental group, which indicated the effectiveness of the teaching evaluation system for feedback in the flipped classroom after the introduction of the random matrix [22].Table 3
Comparison of post-test scores.
GroupNumber of peopleMeanStandard deviationStandard error of the meanAssuming equal variances4286.02746.103400.83655Assuming unequal variances4078.94527.852681.02876Table 4
Independent samplest-test.
FSigtdfSig (bilateral)Mean differenceStandard error values95 confidence interval % of differenceLower limitUpper limitAssuming equal variances3.1400.1643.856990.0025.378561.355242.729738.34175Assuming unequal variances3.81293.130.0025.378561.391972.708328.19574In this study, the pretest and post-test scores of the traditional and experimental classes were statistically analysed using paired samplest-tests (see Tables 5 and 6). The results of the paired design sample t-test for the pre and post-test scores in the traditional class were t = −1.564, with a two-sided test P=0.137 greater than 0.005, indicating that although there was a slight improvement in the post-test scores in the traditional class compared to the front side, there was no significant difference. In the t-test results of the paired design samples of the pretest and post-test scores of the experimental class, t = −8.692, with a two-sided test P=0.002 less than 0.005, and comparing the experimental test results shows that the post-test scores of the experimental class were significantly higher than the pretest scores, and there was a significant score difference between the pretest and post-test scores; the above experimental results show that compared with the model of teaching improvement based on the data from the feedback of the traditional course evaluation system, the model of improving teaching based on the feedback from the introduction of the random matrix in the public English course in higher education institutions can significantly improve students’ English performance, improve teaching quality, and optimise the effectiveness of classroom teaching.Table 5
Comparison of pre- and post-test results.
MeanNumber of peopleStandard deviationStandard error of the meanPair 1Lab pre-test77.1283427.923481.09479Lab post-test86.0274426.103400.83655Pair 2Traditional pre-test76.7625408.202601.40376Traditional post-test78.9452407.852681.02876Table 6
Paired samplest-test.
Component difference pairstdfSig.bilateralMeanStandard deviationStandard error of the mean95 confidence interval % of differenceLower limitUpper limitEC1–EC2−8.89914.832680.55708−7.20865−4.79045−8.692530.002CC1–CC2−2.182711.652940.37500−6.238570.49682−1.564510.137The comparison of EC1-EC2 (pre and post-test)P=0.002, which is lower than 0.05, indicates that there is a significant difference between the learning performance of the experimental class before and after the experiment; the comparison of CC1-CC2 (pre and post-test performance of the control class) P=0.137, which is higher than 0.05, which indicates that there is no significant difference between the learning and learning performance of the traditional class.Because both the experimental and traditional classes are standardised for nationalA and B levels, they will not only be monitored with cameras but also have the school’s foreign language department responsible for auditing the tests in order to ensure their fairness. The statistics of the experimental data show that the results of the experimental and traditional classes are positively correlated, with a large difference in post-test scores, and the experimental class outperformed the regular class in the post-test, showing a strong advantage. The experimental results show that the random matrix has a positive role in promoting the evaluation system of flipped classroom teaching in higher vocational English and has certain practical significance and feasibility in improving teaching quality and teaching effectiveness.


## 4.1. Selection of Objects

After the evaluation index system has been established, its use in practice is tested. In order to ensure the correctness of the experimental results, two classes of the basic teaching department of Chuzhou Vocational and Technical College were selected as the experimental objects in this paper, and English courses offered by different teachers were chosen.


## 4.2. Basic Process of Validation

(1)
In order to eliminate the influence of interference, pre and post-tests were conducted in two classes. The effectiveness of the assessment system in improving the quality of teaching and learning in the classroom was tested by comparing the statistical data before and after the experiment [21].(2)
The experiment was conducted in the following manner:The two classes were divided intoA and B, with Class A as the experimental group and Class B as the reference. In the course of the experiment, the public English teacher in Class A is expected to make adjustments to teaching strategies based on the assessment system that introduces the random matrix theory, and based on the problems, it is reflected in the assessment results so as to improve students’ learning ability. The English teacher in Class B, on the other hand, assessed the teaching based on the original assessment method and made improvements to the teaching based on the assessment results so as to suppress disruptions. By comparing the before and after test results of the two classes, it is possible to test whether the assessment index system established in this study is applicable to the flipped classroom and whether it can improve the quality of teaching and learning. At the same time, based on the feedback from teachers and students on the assessment scale, the assessment scale was revised and improved, resulting in a more reasonable assessment index.


## 4.3. Analysis of Experimental Results

### 4.3.1. Analysis of the Entrance English Scores

In this paper, the English survey was conducted on October 8, 1920, and the June 2006 National College English Application Proficiency LevelB test questions were selected as the test questions, which had high reliability and validity and were used as pretest scores for analysis and statistics. On this basis, the English scores of the experimental and control classes were statistically processed using the independent samples t-test. The comparative analysis P=0.190 > 0.05 means that there was no significant difference between the two experimental groups. The results showed that the English scores of the experimental and traditional classes were similar before the teaching experiment was conducted, and there is no significant difference as shown in Table 1.Table 1
Comparison of pretest scores.
GroupNumber of peopleMeanStandard deviationStandard error of the meanExperimental classes4277.12837.923481.09479Traditional classes4076.76258.202601.40376As shown in Table2, in the English pretest scores, sig = 0.164, which is greater than 0.05, and the variance between the two classes is homogeneous, P=0.190 > 0.05. The results indicate that, in general, the teaching quality of the control class and the experimental class is similar and comparable.Table 2
Independent samplest-test.
FSigtdfSig (bilateral)Mean differenceStandard error values95 confidence interval % of differenceLower limitUpper limitAssuming equal variances3.1700.1641.353970.1902.166581.69542−1.245325.67748Assuming unequal variances1.35093.240.2072.166581.71192−1.250435.63922


### 4.3.2. Analysis of Post-Test Scores

The post-test scores of the traditional and experimental classes were statistically analysed using independent samplest-tests (see Tables 3 and 4). t = 3.856, two-sided test P value (Sig.) = 0.002 was less than 0.005, and the data analysis showed that there was a significant difference in English post-test scores between the experimental subjects and the traditional English group in the higher vocational English flipped classroom experimental group, which indicated the effectiveness of the teaching evaluation system for feedback in the flipped classroom after the introduction of the random matrix [22].Table 3
Comparison of post-test scores.
GroupNumber of peopleMeanStandard deviationStandard error of the meanAssuming equal variances4286.02746.103400.83655Assuming unequal variances4078.94527.852681.02876Table 4
Independent samplest-test.
FSigtdfSig (bilateral)Mean differenceStandard error values95 confidence interval % of differenceLower limitUpper limitAssuming equal variances3.1400.1643.856990.0025.378561.355242.729738.34175Assuming unequal variances3.81293.130.0025.378561.391972.708328.19574In this study, the pretest and post-test scores of the traditional and experimental classes were statistically analysed using paired samplest-tests (see Tables 5 and 6). The results of the paired design sample t-test for the pre and post-test scores in the traditional class were t = −1.564, with a two-sided test P=0.137 greater than 0.005, indicating that although there was a slight improvement in the post-test scores in the traditional class compared to the front side, there was no significant difference. In the t-test results of the paired design samples of the pretest and post-test scores of the experimental class, t = −8.692, with a two-sided test P=0.002 less than 0.005, and comparing the experimental test results shows that the post-test scores of the experimental class were significantly higher than the pretest scores, and there was a significant score difference between the pretest and post-test scores; the above experimental results show that compared with the model of teaching improvement based on the data from the feedback of the traditional course evaluation system, the model of improving teaching based on the feedback from the introduction of the random matrix in the public English course in higher education institutions can significantly improve students’ English performance, improve teaching quality, and optimise the effectiveness of classroom teaching.Table 5
Comparison of pre- and post-test results.
MeanNumber of peopleStandard deviationStandard error of the meanPair 1Lab pre-test77.1283427.923481.09479Lab post-test86.0274426.103400.83655Pair 2Traditional pre-test76.7625408.202601.40376Traditional post-test78.9452407.852681.02876Table 6
Paired samplest-test.
Component difference pairstdfSig.bilateralMeanStandard deviationStandard error of the mean95 confidence interval % of differenceLower limitUpper limitEC1–EC2−8.89914.832680.55708−7.20865−4.79045−8.692530.002CC1–CC2−2.182711.652940.37500−6.238570.49682−1.564510.137The comparison of EC1-EC2 (pre and post-test)P=0.002, which is lower than 0.05, indicates that there is a significant difference between the learning performance of the experimental class before and after the experiment; the comparison of CC1-CC2 (pre and post-test performance of the control class) P=0.137, which is higher than 0.05, which indicates that there is no significant difference between the learning and learning performance of the traditional class.Because both the experimental and traditional classes are standardised for nationalA and B levels, they will not only be monitored with cameras but also have the school’s foreign language department responsible for auditing the tests in order to ensure their fairness. The statistics of the experimental data show that the results of the experimental and traditional classes are positively correlated, with a large difference in post-test scores, and the experimental class outperformed the regular class in the post-test, showing a strong advantage. The experimental results show that the random matrix has a positive role in promoting the evaluation system of flipped classroom teaching in higher vocational English and has certain practical significance and feasibility in improving teaching quality and teaching effectiveness.


## 4.3.1. Analysis of the Entrance English Scores

In this paper, the English survey was conducted on October 8, 1920, and the June 2006 National College English Application Proficiency LevelB test questions were selected as the test questions, which had high reliability and validity and were used as pretest scores for analysis and statistics. On this basis, the English scores of the experimental and control classes were statistically processed using the independent samples t-test. The comparative analysis P=0.190 > 0.05 means that there was no significant difference between the two experimental groups. The results showed that the English scores of the experimental and traditional classes were similar before the teaching experiment was conducted, and there is no significant difference as shown in Table 1.Table 1
Comparison of pretest scores.
GroupNumber of peopleMeanStandard deviationStandard error of the meanExperimental classes4277.12837.923481.09479Traditional classes4076.76258.202601.40376As shown in Table2, in the English pretest scores, sig = 0.164, which is greater than 0.05, and the variance between the two classes is homogeneous, P=0.190 > 0.05. The results indicate that, in general, the teaching quality of the control class and the experimental class is similar and comparable.Table 2
Independent samplest-test.
FSigtdfSig (bilateral)Mean differenceStandard error values95 confidence interval % of differenceLower limitUpper limitAssuming equal variances3.1700.1641.353970.1902.166581.69542−1.245325.67748Assuming unequal variances1.35093.240.2072.166581.71192−1.250435.63922


## 4.3.2. Analysis of Post-Test Scores

The post-test scores of the traditional and experimental classes were statistically analysed using independent samplest-tests (see Tables 3 and 4). t = 3.856, two-sided test P value (Sig.) = 0.002 was less than 0.005, and the data analysis showed that there was a significant difference in English post-test scores between the experimental subjects and the traditional English group in the higher vocational English flipped classroom experimental group, which indicated the effectiveness of the teaching evaluation system for feedback in the flipped classroom after the introduction of the random matrix [22].Table 3
Comparison of post-test scores.
GroupNumber of peopleMeanStandard deviationStandard error of the meanAssuming equal variances4286.02746.103400.83655Assuming unequal variances4078.94527.852681.02876Table 4
Independent samplest-test.
FSigtdfSig (bilateral)Mean differenceStandard error values95 confidence interval % of differenceLower limitUpper limitAssuming equal variances3.1400.1643.856990.0025.378561.355242.729738.34175Assuming unequal variances3.81293.130.0025.378561.391972.708328.19574In this study, the pretest and post-test scores of the traditional and experimental classes were statistically analysed using paired samplest-tests (see Tables 5 and 6). The results of the paired design sample t-test for the pre and post-test scores in the traditional class were t = −1.564, with a two-sided test P=0.137 greater than 0.005, indicating that although there was a slight improvement in the post-test scores in the traditional class compared to the front side, there was no significant difference. In the t-test results of the paired design samples of the pretest and post-test scores of the experimental class, t = −8.692, with a two-sided test P=0.002 less than 0.005, and comparing the experimental test results shows that the post-test scores of the experimental class were significantly higher than the pretest scores, and there was a significant score difference between the pretest and post-test scores; the above experimental results show that compared with the model of teaching improvement based on the data from the feedback of the traditional course evaluation system, the model of improving teaching based on the feedback from the introduction of the random matrix in the public English course in higher education institutions can significantly improve students’ English performance, improve teaching quality, and optimise the effectiveness of classroom teaching.Table 5
Comparison of pre- and post-test results.
MeanNumber of peopleStandard deviationStandard error of the meanPair 1Lab pre-test77.1283427.923481.09479Lab post-test86.0274426.103400.83655Pair 2Traditional pre-test76.7625408.202601.40376Traditional post-test78.9452407.852681.02876Table 6
Paired samplest-test.
Component difference pairstdfSig.bilateralMeanStandard deviationStandard error of the mean95 confidence interval % of differenceLower limitUpper limitEC1–EC2−8.89914.832680.55708−7.20865−4.79045−8.692530.002CC1–CC2−2.182711.652940.37500−6.238570.49682−1.564510.137The comparison of EC1-EC2 (pre and post-test)P=0.002, which is lower than 0.05, indicates that there is a significant difference between the learning performance of the experimental class before and after the experiment; the comparison of CC1-CC2 (pre and post-test performance of the control class) P=0.137, which is higher than 0.05, which indicates that there is no significant difference between the learning and learning performance of the traditional class.Because both the experimental and traditional classes are standardised for nationalA and B levels, they will not only be monitored with cameras but also have the school’s foreign language department responsible for auditing the tests in order to ensure their fairness. The statistics of the experimental data show that the results of the experimental and traditional classes are positively correlated, with a large difference in post-test scores, and the experimental class outperformed the regular class in the post-test, showing a strong advantage. The experimental results show that the random matrix has a positive role in promoting the evaluation system of flipped classroom teaching in higher vocational English and has certain practical significance and feasibility in improving teaching quality and teaching effectiveness.


## 5. Conclusion

Teaching evaluation is an act of making value judgements on the teaching process and results based on the purpose of teaching so as to provide a basis for teaching decisions. Teaching assessment is a process of examining the value of teacher and student learning. Teaching assessment usually includes the assessment of teachers, students, content, methods, environment and management, but its focus is on assessing the quality of teaching and learning and the teaching process of students. This paper introduces the random matrix theory into the traditional public English flipped classroom assessment system in higher education institutions, making it more reliable and practical and laying the foundation for further improving and refining the teaching quality of vocational English flipped classroom teaching.



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*Source: 2424470-2022-09-05.xml*