# Construction and Practice of English Writing Model Based on Random Matrix

Authors: Fengping Chen; Xuan Guo
Journal: Mathematical Problems in Engineering
 (2022)

---

## Abstract

Writing is an indispensable part of English comprehensive ability. It can test learners’ ability in viewpoint content, text organization, language use, and so on. In view of the many problems existing in the English writing of contemporary primary and middle school students, high school students and even college students, this paper proposes an English writing model based on random matrix. This method collects the necessary English vocabulary information through the English word database and combines the M-P law and the density spectrum value of the hybrid matrix to accurately locate students’ writing needs, clarify their writing needs, identify, and construct dynamic English compositions. The random matrix is used to judge and test the English level threshold of different students, so as to get the abnormal use of words when students write. By comparing the predicted data of students’ abnormal vocabulary with the accurate vocabulary data, different students’ writing ability is judged, and corresponding suggestions are given, and qualified writing formats are provided. The experimental results show that the English writing model based on random matrix has strong learning ability and judgment, and can better achieve one-to-one targeted teaching.


---

## Body

## 1. Introduction

With the development of society and the continuous progress of mankind, the future talent training is facing new requirements and challenges. The concept of core competence reflects the consensus of future talent training [1, 2]. The current educational goal is neither to train individuals’ ability to take examinations, nor to train subject knowledge and skills. Instead, it is to train people with humanistic spirit and scientific spirit, who learn to develop an independent and healthy life and innovative awareness of social participation [3–5].The purpose of cultivating individual core literacy is to lay a foundation for the development of individual life and the cultivation of various talents required by the society. Under this demand, the formal promulgation of the English curriculum standards for senior high schools (2017 version) [6] marks the official opening of the senior high school English curriculum reform, and also stipulates the objectives and trends of a new round of curriculum reform [7–10]. The requirements of the new curriculum standards for senior high school English writing have shifted from “comprehensive language application ability” to the core quality of the English subject, paying more attention to the nature of the subject, which puts forward higher requirements for senior high school English writing teaching [11]. The content objectives of the new curriculum standards are more specific and clear, including the requirements of genre, language and discourse, skills, and emotion, which points out the accurate direction for the reform of English Writing Teaching in senior high school. However, through the investigation of the current situation of English Writing Teaching in senior high school, it is not difficult to find that the writing level of senior high school students is generally stagnant and needs to be improved [12–14]. The main reason for the above problems is that most teachers adopt the result teaching method in writing and teaching, and the teaching mode still stays in the traditional “proposition writing correcting commenting.” In addition, writing teaching in senior high school has not been paid enough attention. The classroom is dominated by teachers and ignores the subject of writing, that is, the subject status of students, which directly affects students’ writing level and ability and seriously restricts the development of students’ Comprehensive English ability [15, 16].At present, the learning objectives of College Students’ English writing are not clear, the content of the article is empty, the organization is not clear, the logic is lacking, the topic is not clear, and the language is confused [17–19]. Few students can properly and reasonably apply the knowledge learned in college to their writing. At the same time, the students seem to turn a deaf ear to the teacher’s hard-working comments on the composition, only pay attention to the score, and never consider how to modify the article to improve their writing level. Therefore, it is necessary to change the teaching of College English writing. There are three main reasons: first, writing can promote college students’ English learning. Swain put forward the comprehensible output hypothesis, which said that in second language acquisition, writing can improve the accuracy and fluency of learners’ language output. Second, English writing is very useful for English learning, thinking, discovering, and communicating. English writing can help students objectively express their thoughts and put forward relevant views and opinions. Third, English writing ability plays an important role in the future development of college students. A good level of English writing will not only help them develop academically in the future but also improve their ability to participate in international exchanges.Many scholars and teachers believe that the current English Writing Teaching in China is still a teacher-centered teaching model [20–22]. The teacher is only the imparter of knowledge. The classroom teaching mainly teaches students writing skills, that is, reciting the relevant sentence structure, and the students just accept it passively. The classroom teaching of writing is carried out under the single teaching mode of teachers’ explanation, students’ practice and teachers’ correction of students’ errors. The main problems of this writing teaching method are as follows: first, the current college English teaching is generally a large class teaching, in which a teacher is responsible for the whole English teaching task, and there is no special writing course. Therefore, the time for teachers to guide and practice students’ writing is very limited. Sometimes it is only the teacher who arranges the composition topic, and the students write it to the teacher after class. After the teacher corrects it, make comprehensive comments on the overall level of the whole class. Students seldom have the opportunity to discuss their compositions with teachers [23, 24]. Second, at present, English Teaching in many universities is still dominated by CET-4 and CET-6. Although writing is a very important part due to the lack of sufficient attention to writing teaching in daily teaching, it is often only a few weeks before the exam to strengthen training, requiring students to be familiar with hot topics and English compositions of corresponding writing modes, analyze the model essay, or ask students to recite relevant topic sentences and keywords. Writing teaching has become a rigid imitation process. Writing training is only a kind of mechanical training, without a clear ideological theme. Third, the author found that many students’ compositions are written at one time, with empty content, loose structure and lack of organization. Many students’ English compositions use the theme sentences and structures of the model essays, which lack the logical and formal coherence that a text should have. Many students’ writing also shows that they are poor in vocabulary, seldom use new vocabulary and phrases learned in college, and have more mistakes in grammar, word selection, phrase collocation, and so on. Moreover, few students will seriously think about the composition comments written by the teacher. They just regard the teacher’s correction as a form. Therefore, the same problems and mistakes will occur repeatedly, and it is difficult to improve the writing level in the writing practice.However, writing is also an indispensable part of English comprehensive ability. It can test learners’ ability in viewpoint content, text organization, language use, and so on. In writing teaching, feedback refers to “the input from readers to the author, whose function is to provide the author with the information to modify the composition” [25]. The effect of writing feedback will directly affect the improvement of students’ writing level and can also reflect the teaching effect of teachers’ writing [26, 27]. However, in the current college English teaching, on the one hand, the large class capacity and heavy teaching tasks make most college English teachers have no energy to timely and carefully correct each student’s composition [28–30]; On the other hand, because of the lack of teachers’ supervision and timely feedback, some students’ writing enthusiasm is not high, and they do not pay much attention to writing. Many factors make the improvement of learners’ writing level ineffective. At the same time, it is easy for students to lose interest in writing and even produce disgust [31]. Therefore, in this context, this study attempts to construct a random matrix-based English writing model based on random matrix theory, in order to solve students’ writing problems.


## 2. Basic Theory and Importance of English Writing

### 2.1. Constructivist Learning Theory

Constructivism was first put forward by the Swiss psychologist Piaget in the 1960s. George et al. (2001) made a systematic study of constructivist theory and summarized that constructivist learning design includes six basic elements [32], such as “creating situations, asking questions, building bridges, organizing cooperation, displaying results and reflection process.”Constructivist learning theory holds that learning is not a task at a certain stage, still less a static concept, but a dynamic and long-term development process. Its theoretical core is a multifaceted system of “situation,” “cooperation,” “communication,” and “meaning construction,” that is, learning is the construction of knowledge between learners through team cooperation and meaning communication in specific tasks and situations. Writing itself is a process of meaning construction. The online automatic evaluation system of correction network makes it possible for students to modify their compositions many times. In the situation created by teachers and students, students “construct meaning” through cooperation and communication with teachers or peers.


### 2.2. Process Writing Theory

Process writing theory is a second language writing theory introduced into China at the end of the twentieth century. This theory focuses on students’ writing process rather than just the final result. It emphasizes that learners are at the center of the whole writing process. Writing is a complex, cyclic, and creative process. Writers go through a cycle of writing outlines, brainstorming, independent writing, mutual inspection, and joint revision. This theory points out the direction for writing teaching: on the one hand, teachers should encourage students to explore and discover themselves and revise the text repeatedly in the process of writing. On the other hand, students should pay attention to various forms of feedback, such as peer feedback and teacher feedback, and revise their compositions repeatedly.


### 2.3. Writing Self-Efficacy

“Sense of self-efficacy” refers to “people’s confidence or belief in their ability to achieve behavioral goals in specific fields.” Writing is a cognitive and emotional activity. Writing self-efficacy refers to “the writer’s confidence in his ability to complete a specific writing task.” A large number of studies have found that self-efficacy is a significant indicator to predict writing performance. Self-efficacy can often affect writing performance by changing learners’ writing motivation and self-concept. The sense of self-efficacy in writing mainly comes from the feedback on writing tasks. However, the feedback in traditional writing teaching, whether peer feedback or teacher feedback, will be subject to certain space-time constraints. The feedback participated in by the automatic composition evaluation system breaks through the space–time constraints and can achieve timely feedback.


### 2.4. The Importance of English Writing

The cultivation of writing ability plays an important role in the process of high school English learning. English writing ability plays a key role in the cultivation of the basic skills of “listening, speaking, reading, and writing.” Many scholars believe that English writing is one of the five basic skills of “listening, speaking, reading, reading, and writing” in English learning. It is an important expression of students’ expression ability and also an important expression of students’ comprehensive language output ability [7, 21]. However, compared with the learning contents of “listening,” “speaking,” and “reading” in English teaching, English writing training puts forward higher requirements for students’ comprehensive ability, and is also one of the important methods to quickly cultivate students’ English language sense. It not only requires students to master a large number of English vocabulary but also requires students to have certain basic knowledge of grammar and certain discourse ability.English writing ability is the standard to measure senior high school students’ comprehensive language use ability. The English curriculum standard for ordinary senior high schools puts forward specific requirements for senior high school students’ English language skills: students need professional and comprehensive language training to develop language skills and lay a foundation for communication in a real language environment. English writing ability is an expression ability in language skills and an important part of language use ability [9]. At present, in the college entrance examination, the proportion of English writing scores has also increased, with more emphasis on students’ comprehensive language ability. Thus, writing teaching plays an important role in English teaching.


## 2.1. Constructivist Learning Theory

Constructivism was first put forward by the Swiss psychologist Piaget in the 1960s. George et al. (2001) made a systematic study of constructivist theory and summarized that constructivist learning design includes six basic elements [32], such as “creating situations, asking questions, building bridges, organizing cooperation, displaying results and reflection process.”Constructivist learning theory holds that learning is not a task at a certain stage, still less a static concept, but a dynamic and long-term development process. Its theoretical core is a multifaceted system of “situation,” “cooperation,” “communication,” and “meaning construction,” that is, learning is the construction of knowledge between learners through team cooperation and meaning communication in specific tasks and situations. Writing itself is a process of meaning construction. The online automatic evaluation system of correction network makes it possible for students to modify their compositions many times. In the situation created by teachers and students, students “construct meaning” through cooperation and communication with teachers or peers.


## 2.2. Process Writing Theory

Process writing theory is a second language writing theory introduced into China at the end of the twentieth century. This theory focuses on students’ writing process rather than just the final result. It emphasizes that learners are at the center of the whole writing process. Writing is a complex, cyclic, and creative process. Writers go through a cycle of writing outlines, brainstorming, independent writing, mutual inspection, and joint revision. This theory points out the direction for writing teaching: on the one hand, teachers should encourage students to explore and discover themselves and revise the text repeatedly in the process of writing. On the other hand, students should pay attention to various forms of feedback, such as peer feedback and teacher feedback, and revise their compositions repeatedly.


## 2.3. Writing Self-Efficacy

“Sense of self-efficacy” refers to “people’s confidence or belief in their ability to achieve behavioral goals in specific fields.” Writing is a cognitive and emotional activity. Writing self-efficacy refers to “the writer’s confidence in his ability to complete a specific writing task.” A large number of studies have found that self-efficacy is a significant indicator to predict writing performance. Self-efficacy can often affect writing performance by changing learners’ writing motivation and self-concept. The sense of self-efficacy in writing mainly comes from the feedback on writing tasks. However, the feedback in traditional writing teaching, whether peer feedback or teacher feedback, will be subject to certain space-time constraints. The feedback participated in by the automatic composition evaluation system breaks through the space–time constraints and can achieve timely feedback.


## 2.4. The Importance of English Writing

The cultivation of writing ability plays an important role in the process of high school English learning. English writing ability plays a key role in the cultivation of the basic skills of “listening, speaking, reading, and writing.” Many scholars believe that English writing is one of the five basic skills of “listening, speaking, reading, reading, and writing” in English learning. It is an important expression of students’ expression ability and also an important expression of students’ comprehensive language output ability [7, 21]. However, compared with the learning contents of “listening,” “speaking,” and “reading” in English teaching, English writing training puts forward higher requirements for students’ comprehensive ability, and is also one of the important methods to quickly cultivate students’ English language sense. It not only requires students to master a large number of English vocabulary but also requires students to have certain basic knowledge of grammar and certain discourse ability.English writing ability is the standard to measure senior high school students’ comprehensive language use ability. The English curriculum standard for ordinary senior high schools puts forward specific requirements for senior high school students’ English language skills: students need professional and comprehensive language training to develop language skills and lay a foundation for communication in a real language environment. English writing ability is an expression ability in language skills and an important part of language use ability [9]. At present, in the college entrance examination, the proportion of English writing scores has also increased, with more emphasis on students’ comprehensive language ability. Thus, writing teaching plays an important role in English teaching.


## 3. Basic Theory of Random Matrix

In order to distinguish the noise part from the nonnoise part of the matrix, we divide it into two parts. One part is the “noise” that conforms to the random matrix property, and the other part is the “information” that deviates from the prediction. Prediction is based on theoretical value‚ and we can determine the theoretical maximum and minimum values. According to this range, we can distinguish “information” from “noise.” Its main idea is to remove the eigenvalues corresponding to noise while preserving the eigenvalues corresponding to real information as much as possible. Because the eigenvalues corresponding to noise do not contain real information, they are basically meaningless.The basic method of RMT filtering the correlation matrix is to replace the “noise” eigenvalue of the correlation matrix with zero, while keeping the trace of the replaced matrix equal to that of the original matrix. The “noise” eigenvalue here refers to the part less than or equal to the maximum theoretical eigenvalue of the corresponding random matrix. The maximum eigenvalue of a random matrix is usually estimated by the theoretical value in the limit case. In addition, the maximum eigenvalue can also be calculated directly from the results of Monte Carlo simulation. For example, when the number of assets is relatively small. In this paper, the maximum eigenvalue predicted by RMT theory is also used.This method proposed by Plerou (1999) considers anN×N matrix M, Λ is the diagonal matrix composed of its eigenvalues, and E is the corresponding eigenvector matrix. Define as follows:(1)Λnoisy=λ∈Λ:λ≤λmax,Λnoisy represents the characteristic value of noise and λmax represents the maximum value of RMT theory. The filtered characteristic values are defined as follows:(2)Λfiltered=Λnew∪Λ−Λnoisy,where Λnew=λi:λi=0.That is, replace the characteristic value within the theoretical value range with zero. The filtered characteristic values are formed by this method‚ then the original eigenvector matrix is used to construct the filtered correlation coefficient matrix. Namely(3)Mfiltered=EDfilteredE−1,where Dfiltered is a diagonal matrix with Λfiltered as diagonal elements. To ensure that the trace of the matrix does not change before and after filtering, the diagonal elements of the filtered matrix are all set to 1.The random matrix theory takes the matrix as the unit, which can process independent identically distributed (IID) data [33] and has more advantages in detecting and locating the use of abnormal words. The random matrix theory only requires that the dimension of the data matrix tends to infinity and does not require the distribution and characteristics of the source data. However, more accurate results can be observed in the matrix with a dimension of tens to hundreds, which are the premise for the random matrix theory to be applied to practical engineering [33]. Ring law is one of the characteristics of limit spectrum analysis of random matrix theory. Its advantage is that it can accurately describe the limit spectrum distribution of random matrix, and the calculation results are more visual and convenient for quantitative analysis [32–36]. On this basis, we further study linear eigenvalue statistics (LES) of random matrices, and mean spectral radius (MSR) is a specific object constructed by LES.Suppose a non-Hermitian random matrixX^=x^i,jM×N, when the matrix scale is expanded to nearly infinite, the empirical spectrum distribution of the eigenvalues of Z˜ almost certainly satisfies the single ring theorem, and the probability density function is(4)fYλ=2πcLλ2/L−1,1−cL/2≤λ≤1,0,Other,where L is the number of random matrices; c is the determinant ratio; λi is the eigenvalue of the random matrix.Mean spectral radius (MSR) is used as the test function of linear eigenvalue statistic (LES), including(5)rMSR=1N∑i=1NλiY,where rMSR is the average spectral radius; N is the number of eigenvalues.The two theories are as follows:


### 3.1. Single Ring Theorem

For any matrixX^=x^i,jM×N with expectation of μx^i and variance of σx^i, the non-Hermitian matrix X˜=x˜i,jM×N can be obtained by the following formula:(6)x˜i,j=x^i,j−μx^iσx˜iσx^i+μx˜i.Each element inX˜ is an independent identically distributed Gaussian random variable, and the matrix expects μx˜i and the variance is σx˜i. The singular value equivalent matrix Xu can be obtained by the following transformation:(7)Xu=UX˜X˜H.In equation (7), U is a Haar matrix, and the superscript H represents a conjugate transpose, that is, XuHXu=X˜X˜H. For L such non-Hermitian matrices X˜ii=1,2,…,L, after the above transformation, each can obtain the corresponding singular value equivalent matrix Xu,ii=1,2,…,L. The product matrix Y˜ of singular value equivalent matrix is(8)Y˜=∏i=1LXu,i.In this paper,L is taken as 1, and the standard matrix Y is obtained according to the following formula: (9)yi=y˜iMσy˜ii=1,2,…,M.yi is each element of matrix Y. When the row column ratio c = M/N is constant and M, N approaches infinity, the empirical spectral distribution of Y eigenvalue λi converges to the given limit, and its probability density function is (10)fYλ=2πcLλ2/L−1,1−cL/2≤λ≤1,0,Other,where c∈0,1 is a constant. The single ring theorem shows that each element of a standard non-Hermitian matrix Y is an independent identically distributed Gaussian random variable, and the eigenvalues in the complex plane are roughly distributed in a ring with outer diameter r1=1 and inner diameter r2=1−cL/2.


### 3.2. Linear Eigenvalue Statistics

LES can reflect the distribution of eigenvalues of random matrix. The average spectral radiusrMSR is a common form of LES, which is defined as the average of the distribution radii of all eigenvalues of the matrix on the complex plane:(11)rMSR=1N∑i=1NλiY,λiY is the distribution radius of all eigenvalues of matrix Y on the complex plane. A single eigenvalue cannot reflect the statistical characteristics of matrix elements. LES describes the trace of random matrix and can reflect the statistical characteristics of matrix. Therefore, the average spectral radius can be used as a criterion.


## 3.1. Single Ring Theorem

For any matrixX^=x^i,jM×N with expectation of μx^i and variance of σx^i, the non-Hermitian matrix X˜=x˜i,jM×N can be obtained by the following formula:(6)x˜i,j=x^i,j−μx^iσx˜iσx^i+μx˜i.Each element inX˜ is an independent identically distributed Gaussian random variable, and the matrix expects μx˜i and the variance is σx˜i. The singular value equivalent matrix Xu can be obtained by the following transformation:(7)Xu=UX˜X˜H.In equation (7), U is a Haar matrix, and the superscript H represents a conjugate transpose, that is, XuHXu=X˜X˜H. For L such non-Hermitian matrices X˜ii=1,2,…,L, after the above transformation, each can obtain the corresponding singular value equivalent matrix Xu,ii=1,2,…,L. The product matrix Y˜ of singular value equivalent matrix is(8)Y˜=∏i=1LXu,i.In this paper,L is taken as 1, and the standard matrix Y is obtained according to the following formula: (9)yi=y˜iMσy˜ii=1,2,…,M.yi is each element of matrix Y. When the row column ratio c = M/N is constant and M, N approaches infinity, the empirical spectral distribution of Y eigenvalue λi converges to the given limit, and its probability density function is (10)fYλ=2πcLλ2/L−1,1−cL/2≤λ≤1,0,Other,where c∈0,1 is a constant. The single ring theorem shows that each element of a standard non-Hermitian matrix Y is an independent identically distributed Gaussian random variable, and the eigenvalues in the complex plane are roughly distributed in a ring with outer diameter r1=1 and inner diameter r2=1−cL/2.


## 3.2. Linear Eigenvalue Statistics

LES can reflect the distribution of eigenvalues of random matrix. The average spectral radiusrMSR is a common form of LES, which is defined as the average of the distribution radii of all eigenvalues of the matrix on the complex plane:(11)rMSR=1N∑i=1NλiY,λiY is the distribution radius of all eigenvalues of matrix Y on the complex plane. A single eigenvalue cannot reflect the statistical characteristics of matrix elements. LES describes the trace of random matrix and can reflect the statistical characteristics of matrix. Therefore, the average spectral radius can be used as a criterion.


## 4. Construction of English Writing Model Based on Random Matrix

Before constructing the English writing model, according to Markowitz’s hypothesis, we should first know the basic information of English writing, that is, the great types of compositions that may appear in the process of English writing. Taking the postgraduate entrance examination compositions of college students as an example, the English compositions in recent years are divided into the following types, including ((1) letter of apology, (2) letter, (3) letter of recommendation, (4) application, (5) letter of resignation, (6) proposal, (7) letter of appeal, (8) letter of thanks, (9) letter of invitation, (10) letter of inquiry).After mastering the basic information of the English writing for the postgraduate entrance examination, we can standardize the English writing model according to the basic information and requirements of the English writing for the postgraduate entrance examination, and carry out constraint training with the real questions and related technologies in previous years. At the same time, we can calculate the best choice according to the semantic data shown by the arrangement and reorganization of English words. Finally, the model can be used to train the composition needs of the required writing, and the random error of the training can be calculated in the training process. Specifically, first, divide the data records of the training template paper into two equal length records to calculate the correlation matrix; second, filter the correlation matrix according to the method introduced in Section1 of this study; third, construct the investment portfolio using the prefiltering and postfiltering matrices, respectively, and find the optimal investment portfolio and the effective frontier. The flow chart of English writing mode based on random matrix theory is shown in Figure 1.Figure 1
Flow chart of English writing model based on random matrix theory.


## 5. Analysis of Writing Examples

### 5.1. Analysis Object

Before the experiment, we first read a large number of literature and bound the rules of the experiment according to the existing literature. Through the investigation, we found that the main responsibility of the experiment is to select the experimental objects, and the selected objects must include the following points: first, the experimental objects must meet the requirements of the experiment, that is, they are interested in participating in the postgraduate entrance examination and are preparing for the postgraduate entrance examination throughout the whole process. Second, the subjects of the experiment must be the same, and they all contain English 2 or English 1. This paper takes the students of English 2 as the subjects of the experiment. Third, the experimental subjects must include the whole population, that is, the birth conditions and family conditions of the students must be diversified. In this experiment, a total of 10 non-English majors from different universities in 2020 were selected to participate in the experiment. They are not business administration students with good English level, nor are they relatively poor students who have not reviewed the subject. These students are majoring in various majors of the university (including five different majors of civil engineering of engineering, information engineering of computer science, and history of humanities). They can represent the general learning level of students in 2020. The subjects come from different places in China and have different family backgrounds, so their learning motivation, learning habits, and personality are completely different, and their thinking methods and views on problems are also different. During the whole process of the experiment, no one avoided the problem or withdrew from the experiment for any reason.


### 5.2. Experiment Time

This experiment is from March 2019 to December 2020, for a review cycle of postgraduate entrance examination. The subjects reviewed English every week at the same time and according to their work and rest habits. During this period, there was no interference from any external environmental factors. They were preparing for the second English review of the postgraduate entrance examination.In this nearly one year, the early stage mainly focused on learning or self-help review. The experimental administrator did not participate in the time arrangement of the experimental testers, but only supervised the progress of the experimental subjects. In the later stage, before and after all the students who participated in the experiment completed the review, that is, one week before the postgraduate entrance examination and one week after the postgraduate entrance examination, two tests and three composition writing exercises were conducted, with an average of once a week. In order to make it easier for students to choose topics, the two times are to cooperate with college English intensive reading textbooks. On the one hand, writing exercises are to cooperate with textbooks to discuss topics related to topics, on the other hand, they are to choose topics close to students’ real life and can express real ideas. Students can also draw up their own questions according to the relevant contents. The two writing styles are expository and narrative. Students form study groups in a voluntary manner and can discuss at any time. At the beginning, in the middle and after the writing of each composition, students should have at least one discussion with group members, and can discuss with teachers by e-mail at any time. After writing, the groups will correct each other and write down their own revision opinions. Different from the previous CET-4 and CET-6 writing exercises, such writing exercises have no requirements on the number of words and time, mainly to encourage students to fully express their ideas. The last composition is a project-centered exploratory expository text, which is designed to train students to think and explore from multiple perspectives and experience the openness, practicality, and inquiry of learning activities.


### 5.3. Experimental Process

The following is the process of writing twice (taking narrative writing as an example):(1)
First of all, in the first writing class, students will be introduced to the arrangement and requirements of writing this semester, and the necessity of cooperation and composition evaluation methods will be told to students so that students can have a basic understanding of the whole arrangement. Students form a group of four.(2)
Introduce the basic elements of the narrative to the students and the aspects that should be paid attention to in the writing of the narrative. Choose a life-oriented topic to lead the students to dictate the composition so that the students can observe the teacher’s thinking process and have a preliminary understanding of the writing of the narrative. Then, the teacher lists several questions according to the content of the text and the students’ life. The questions try to be close to the students’ life and create a real situation. Students can also draw up their own topics. There is no time and word number requirements. Students are encouraged to write as much as possible to express their true feelings.(3)
Emphasize the discussion among the group members before, during, and after writing, and tell the students how to correct their peer compositions and write comments.(4)
When students write the first draft, they can discuss the content and theme with teachers and peers.(5)
After the first draft is completed, the team members review each other, write comments according to the “composition Checklist,” and then exchange views with each other without making changes.(6)
Students revise according to their peers’ opinions, complete the second draft, and submit it to the teacher for review.(7)
Students review peer comments on students, then review the second draft and write comments. It is best to discuss with students, explain their views, and put forward suggestions for revision.(8)
Students write the third draft, and their peers review it again. If there are no major problems, they will give it to the teacher for review; If the problem still exists, modify it again.(9)
The random matrix-based English writing model constructed in this paper is used to review and modify the writing of different students, give written feedback accordingly, and give feedback to students for modification.(10)
The teacher revised and reviewed the English compositions of the 10 students under the three conditions of machine review, student review, and original documents, and gave the evaluation scores accordingly. Summarize the teacher’s evaluation scores and analyze the results


### 5.4. Evaluation of Experimental Results

The English writing scores of each student before and after the test are shown in Table1 The English writing scores after mutual revision and review by students are shown in Tables 2 and 3 and shows the English writing scores after the modified writing mode based on random matrix constructed in this paper.Table 1
Students’ original English writing scores twice (full score is 100 points).
Student numberFirst writing scoreSecond writing score188.076.0286.082.0372.089.0491.086.0568.086.0684.083.0775.064.0884.095.0984.076.01090.077.0Table 2
Students’ two revised writing scores (full score of 100 points).
Student numberFirst writing scoreSecond writing score186.074.0288.086.0380.088487.081.0574.075.0680.074.0775.071.0878.092.0987.086.01093.082.0Table 3
Two revised writing scores using this method (full score of 100 points).
Student numberFirst writing scoreSecond writing score192.090.0289.094.0384.096.0492.086.0586.082.0685.086.0789.079.0888.092.0984.087.01088.091.0Carry out data statistical analysis on Table1, and the data statistical chart is shown in Figure 2. It can be seen from Table 1 that the scores of 10 students who participated in the experiment in the two times of writing, that is, the statistical law in Figure 2, show that these students show irregular characteristics in the scores of these two times of writing papers, which shows the referential value of the experiment and also confirms the effectiveness of the scores of this random test.Figure 2
Statistical chart of original score data.It can be seen from Figure3 and Table 2 that the performance rules of different students’ writing are also inconsistent after students’ mutual correction. Some students’ writing ability has been improved after students’ criticism and correction, with a maximum increase of 10 points, but the overall score has only increased by 0.3 points, and the scores of a large number of students have decreased, with a maximum decrease of 9 points. Therefore, the courseware, Students’ mutual review is of little help to the improvement of students’ writing ability, and even has side effects. The reason is that, on the one hand, some students’ writing ability is not high, on the other hand, students’ thinking and cognition of writing are not enough, which easily leads to the above problems.Figure 3
Students’ two writing scores after mutual revision.It can be seen from Figure4 and Table 3 that the students’ English composition scores after the modification of the English writing mode based on random matrix proposed in this paper have significantly improved. The average scores of the two scores have increased by 5.1 points and 6.3 points, respectively, with a maximum increase of 15 points and a minimum decrease of only 3 points. It can be seen from the data that all the reduced scores are due to the fact that the original scores of these students are more than 90 points. The English writing model based on the random matrix theory constructed in this paper has good application ability and is of great help to the improvement of students’ English writing ability.Figure 4
Two revised writing scores using this method.


### 5.5. Discussion on Experimental Results

The experimental results show that, compared with the traditional writing teaching, this random matrix-based English writing teaching model can stimulate students’ interest, and the teaching effect is better.Under the guidance of random matrix theory, this writing mode is designed by referring to the concepts of process writing method, genre teaching method, and length writing method. The purpose is to make students re-recognize their learning status. They are active learning subjects, but no longer passive recipients of knowledge. Learners should be responsible for their own progress, rather than being indoctrinated and arranged by teachers. The results show that the students’ subjective initiative has been brought into play, and the effect is ideal.It stimulates students’ learning motivation and encourages students to think and deal with tasks like experts. When students actively participate in real tasks and make discoveries, it is easy to stimulate or strengthen their learning motivation and experience a kind of ownership of knowledge and tasks. With the help of this teaching model, students get enlightenment from their discussions with their peers and teachers, and feel their own progress from this interactive communication. English writing is no longer a burden, nor a person’s fantasy, but a learning process of communicating with machines by using random matrix theory to get writing feedback.


## 5.1. Analysis Object

Before the experiment, we first read a large number of literature and bound the rules of the experiment according to the existing literature. Through the investigation, we found that the main responsibility of the experiment is to select the experimental objects, and the selected objects must include the following points: first, the experimental objects must meet the requirements of the experiment, that is, they are interested in participating in the postgraduate entrance examination and are preparing for the postgraduate entrance examination throughout the whole process. Second, the subjects of the experiment must be the same, and they all contain English 2 or English 1. This paper takes the students of English 2 as the subjects of the experiment. Third, the experimental subjects must include the whole population, that is, the birth conditions and family conditions of the students must be diversified. In this experiment, a total of 10 non-English majors from different universities in 2020 were selected to participate in the experiment. They are not business administration students with good English level, nor are they relatively poor students who have not reviewed the subject. These students are majoring in various majors of the university (including five different majors of civil engineering of engineering, information engineering of computer science, and history of humanities). They can represent the general learning level of students in 2020. The subjects come from different places in China and have different family backgrounds, so their learning motivation, learning habits, and personality are completely different, and their thinking methods and views on problems are also different. During the whole process of the experiment, no one avoided the problem or withdrew from the experiment for any reason.


## 5.2. Experiment Time

This experiment is from March 2019 to December 2020, for a review cycle of postgraduate entrance examination. The subjects reviewed English every week at the same time and according to their work and rest habits. During this period, there was no interference from any external environmental factors. They were preparing for the second English review of the postgraduate entrance examination.In this nearly one year, the early stage mainly focused on learning or self-help review. The experimental administrator did not participate in the time arrangement of the experimental testers, but only supervised the progress of the experimental subjects. In the later stage, before and after all the students who participated in the experiment completed the review, that is, one week before the postgraduate entrance examination and one week after the postgraduate entrance examination, two tests and three composition writing exercises were conducted, with an average of once a week. In order to make it easier for students to choose topics, the two times are to cooperate with college English intensive reading textbooks. On the one hand, writing exercises are to cooperate with textbooks to discuss topics related to topics, on the other hand, they are to choose topics close to students’ real life and can express real ideas. Students can also draw up their own questions according to the relevant contents. The two writing styles are expository and narrative. Students form study groups in a voluntary manner and can discuss at any time. At the beginning, in the middle and after the writing of each composition, students should have at least one discussion with group members, and can discuss with teachers by e-mail at any time. After writing, the groups will correct each other and write down their own revision opinions. Different from the previous CET-4 and CET-6 writing exercises, such writing exercises have no requirements on the number of words and time, mainly to encourage students to fully express their ideas. The last composition is a project-centered exploratory expository text, which is designed to train students to think and explore from multiple perspectives and experience the openness, practicality, and inquiry of learning activities.


## 5.3. Experimental Process

The following is the process of writing twice (taking narrative writing as an example):(1)
First of all, in the first writing class, students will be introduced to the arrangement and requirements of writing this semester, and the necessity of cooperation and composition evaluation methods will be told to students so that students can have a basic understanding of the whole arrangement. Students form a group of four.(2)
Introduce the basic elements of the narrative to the students and the aspects that should be paid attention to in the writing of the narrative. Choose a life-oriented topic to lead the students to dictate the composition so that the students can observe the teacher’s thinking process and have a preliminary understanding of the writing of the narrative. Then, the teacher lists several questions according to the content of the text and the students’ life. The questions try to be close to the students’ life and create a real situation. Students can also draw up their own topics. There is no time and word number requirements. Students are encouraged to write as much as possible to express their true feelings.(3)
Emphasize the discussion among the group members before, during, and after writing, and tell the students how to correct their peer compositions and write comments.(4)
When students write the first draft, they can discuss the content and theme with teachers and peers.(5)
After the first draft is completed, the team members review each other, write comments according to the “composition Checklist,” and then exchange views with each other without making changes.(6)
Students revise according to their peers’ opinions, complete the second draft, and submit it to the teacher for review.(7)
Students review peer comments on students, then review the second draft and write comments. It is best to discuss with students, explain their views, and put forward suggestions for revision.(8)
Students write the third draft, and their peers review it again. If there are no major problems, they will give it to the teacher for review; If the problem still exists, modify it again.(9)
The random matrix-based English writing model constructed in this paper is used to review and modify the writing of different students, give written feedback accordingly, and give feedback to students for modification.(10)
The teacher revised and reviewed the English compositions of the 10 students under the three conditions of machine review, student review, and original documents, and gave the evaluation scores accordingly. Summarize the teacher’s evaluation scores and analyze the results


## 5.4. Evaluation of Experimental Results

The English writing scores of each student before and after the test are shown in Table1 The English writing scores after mutual revision and review by students are shown in Tables 2 and 3 and shows the English writing scores after the modified writing mode based on random matrix constructed in this paper.Table 1
Students’ original English writing scores twice (full score is 100 points).
Student numberFirst writing scoreSecond writing score188.076.0286.082.0372.089.0491.086.0568.086.0684.083.0775.064.0884.095.0984.076.01090.077.0Table 2
Students’ two revised writing scores (full score of 100 points).
Student numberFirst writing scoreSecond writing score186.074.0288.086.0380.088487.081.0574.075.0680.074.0775.071.0878.092.0987.086.01093.082.0Table 3
Two revised writing scores using this method (full score of 100 points).
Student numberFirst writing scoreSecond writing score192.090.0289.094.0384.096.0492.086.0586.082.0685.086.0789.079.0888.092.0984.087.01088.091.0Carry out data statistical analysis on Table1, and the data statistical chart is shown in Figure 2. It can be seen from Table 1 that the scores of 10 students who participated in the experiment in the two times of writing, that is, the statistical law in Figure 2, show that these students show irregular characteristics in the scores of these two times of writing papers, which shows the referential value of the experiment and also confirms the effectiveness of the scores of this random test.Figure 2
Statistical chart of original score data.It can be seen from Figure3 and Table 2 that the performance rules of different students’ writing are also inconsistent after students’ mutual correction. Some students’ writing ability has been improved after students’ criticism and correction, with a maximum increase of 10 points, but the overall score has only increased by 0.3 points, and the scores of a large number of students have decreased, with a maximum decrease of 9 points. Therefore, the courseware, Students’ mutual review is of little help to the improvement of students’ writing ability, and even has side effects. The reason is that, on the one hand, some students’ writing ability is not high, on the other hand, students’ thinking and cognition of writing are not enough, which easily leads to the above problems.Figure 3
Students’ two writing scores after mutual revision.It can be seen from Figure4 and Table 3 that the students’ English composition scores after the modification of the English writing mode based on random matrix proposed in this paper have significantly improved. The average scores of the two scores have increased by 5.1 points and 6.3 points, respectively, with a maximum increase of 15 points and a minimum decrease of only 3 points. It can be seen from the data that all the reduced scores are due to the fact that the original scores of these students are more than 90 points. The English writing model based on the random matrix theory constructed in this paper has good application ability and is of great help to the improvement of students’ English writing ability.Figure 4
Two revised writing scores using this method.


## 5.5. Discussion on Experimental Results

The experimental results show that, compared with the traditional writing teaching, this random matrix-based English writing teaching model can stimulate students’ interest, and the teaching effect is better.Under the guidance of random matrix theory, this writing mode is designed by referring to the concepts of process writing method, genre teaching method, and length writing method. The purpose is to make students re-recognize their learning status. They are active learning subjects, but no longer passive recipients of knowledge. Learners should be responsible for their own progress, rather than being indoctrinated and arranged by teachers. The results show that the students’ subjective initiative has been brought into play, and the effect is ideal.It stimulates students’ learning motivation and encourages students to think and deal with tasks like experts. When students actively participate in real tasks and make discoveries, it is easy to stimulate or strengthen their learning motivation and experience a kind of ownership of knowledge and tasks. With the help of this teaching model, students get enlightenment from their discussions with their peers and teachers, and feel their own progress from this interactive communication. English writing is no longer a burden, nor a person’s fantasy, but a learning process of communicating with machines by using random matrix theory to get writing feedback.


## 6. Conclusion

Through the investigation of the current situation of English Writing Teaching in senior high school, it is not difficult to find that the writing level of most senior high school students has generally stagnated, or even regressed, due to the current weak writing foundation of senior high school students, lack of interest in writing, and other objective factors. Therefore, the purpose of this study is to improve the learning and teaching model of College English writing in China by constructing an English writing model based on the random matrix theory and under the guidance of its learning environment design idea, and to carry out targeted experiments on it. By testing the second writing ability of 10 postgraduates of 2020 in different majors. Through a semester of empirical research, after two times of method guidance, all students’ composition scores have been significantly improved, and the maximum score increase has reached nearly 20 points. From this, we can find that the College English writing model based on the random matrix theory constructed in this paper can greatly improve the level of English writing, and its application research has achieved good results. It shows that it can improve some disadvantages in English writing teaching, improve students’ writing interest, to guide students’ deficiencies in the process of self-learning and promote the development of advanced cognitive skills.



---

*Source: 4502806-2022-09-16.xml*