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Research Article
Construction and Practice of English Writing Model Based on
Random Matrix
Fengping Chen and Xuan Guo
Foreign Language Department, Ganzhou Teachers College, Ganzhou, Jiangxi 341000, China
Correspondence should be addressed to Fengping Chen; cfp0413@sina.com
Received 15 July 2022; Revised 12 August 2022; Accepted 23 August 2022; Published 16 September 2022
Academic Editor: Ning Cao
Copyright ©2022 Fengping Chen and Xuan Guo. is is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Writing is an indispensable part of English comprehensive ability. It can test learners’ ability in viewpoint content, text or-
ganization, 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. is 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. e 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. e 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.
1. Introduction
With the development of society and the continuous
progress of mankind, the future talent training is facing new
requirements and challenges. e concept of core compe-
tence reflects the consensus of future talent training [1, 2].
e 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 partic-
ipation [3–5].
e 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]. e
requirements of the new curriculum standards for senior
high school English writing have shifted from “compre-
hensive 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]. e 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]. e 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
Hindawi
Mathematical Problems in Engineering
Volume 2022, Article ID 4502806, 9 pages
https://doi.org/10.1155/2022/4502806
commenting.” In addition, writing teaching in senior high
school has not been paid enough attention. e 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. erefore, it is necessary to
change the teaching of College English writing. ere are
three main reasons: first, writing can promote college stu-
dents’ English learning. Swain put forward the compre-
hensible 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 objec-
tively express their thoughts and put forward relevant views
and opinions. ird, English writing ability plays an im-
portant 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]. e teacher is only the imparter of
knowledge. e classroom teaching mainly teaches students
writing skills, that is, reciting the relevant sentence structure,
and the students just accept it passively. e classroom
teaching of writing is carried out under the single teaching
mode of teachers’ explanation, students’ practice and
teachers’ correction of students’ errors. e 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.
erefore, the time for teachers to guide and practice stu-
dents’ writing is very limited. Sometimes it is only the
teacher who arranges the composition topic, and the stu-
dents 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 oppor-
tunity 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. ird, 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 sen-
tences 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. ey just regard the teacher’s correction as a form.
erefore, the same problems and mistakes will occur re-
peatedly, 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 view-
point 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]. e 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]. erefore, 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 eory. 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. e online automatic evaluation
2Mathematical Problems in Engineering
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 eory. Process writing theory is a
second language writing theory introduced into China at the
end of the twentieth century. is theory focuses on stu-
dents’ 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. is theory points out the direction for
writing teaching: on the one hand, teachers should en-
courage 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 perfor-
mance. Self-efficacy can often affect writing performance by
changing learners’ writing motivation and self-concept. e
sense of self-efficacy in writing mainly comes from the
feedback on writing tasks. However, the feedback in tra-
ditional writing teaching, whether peer feedback or teacher
feedback, will be subject to certain space-time constraints.
e feedback participated in by the automatic composition
evaluation system breaks through the space–time con-
straints and can achieve timely feedback.
2.4. e Importance of English Writing. e 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’ compre-
hensive 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 re-
quires students to master a large number of English vo-
cabulary 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.
e 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 de-
velop language skills and lay a foundation for communi-
cation 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. us, 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 “infor-
mation” from “noise.” Its main idea is to remove the ei-
genvalues 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.
e 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. e “noise” eigenvalue
here refers to the part less than or equal to the maximum
theoretical eigenvalue of the corresponding random matrix.
e maximum eigenvalue of a random matrix is usually
estimated by the theoretical value in the limit case. In ad-
dition, the maximum eigenvalue can also be calculated di-
rectly 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.
is method proposed by Plerou (1999) considers an
N×Nmatrix M,Λis the diagonal matrix composed of its
eigenvalues, and Eis the corresponding eigenvector matrix.
Define as follows:
Λnoisy �λ∈ Λ:λ≤λmax
,(1)
Λnoisy represents the characteristic value of noise and λmax
represents the maximum value of RMT theory. e filtered
characteristic values are defined as follows:
Λfiltered �Λnew ∪ Λ −Λnoisy
,(2)
where Λnew �λi:λi�0
.
at is, replace the characteristic value within the the-
oretical value range with zero. e filtered characteristic
values are formed by this method‘ then the original
Mathematical Problems in Engineering 3
eigenvector matrix is used to construct the filtered corre-
lation coefficient matrix. Namely
Mfiltered �EDfilteredE−1,(3)
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.
e 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. e random matrix theory only
requires that the dimension of the data matrix tends to
infinity and does not require the distribution and charac-
teristics 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 con-
structed by LES.
Suppose a non-Hermitian random matrix
X�
xi,j
M×N, when the matrix scale is expanded to nearly
infinite, the empirical spectrum distribution of the eigen-
values of
Zalmost certainly satisfies the single ring theorem,
and the probability density function is
fY(λ) �
2
πcL |λ|(2/L−1),(1−c)L/2 ≤|λ|≤1,
0,Other,
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩(4)
where Lis the number of random matrices; cis the deter-
minant ratio; λiis the eigenvalue of the random matrix.
Mean spectral radius (MSR) is used as the test function
of linear eigenvalue statistic (LES), including
rMSR �1
N
N
i�1
λi(Y)
,(5)
where rMSR is the average spectral radius; Nis the number of
eigenvalues.
e two theories are as follows:
3.1. Single Ring eorem. For any matrix
X�
xi,j
M×Nwith
expectation of μ(
xi)and variance of σ(
xi), the non-Her-
mitian matrix
X�
xi,j
M×Ncan be obtained by the fol-
lowing formula:
xi,j �
xi,j −μ
xi
σ
xi
σ
xi
+μ
xi
.(6)
Each element in
Xis an independent identically dis-
tributed Gaussian random variable, and the matrix expects
μ(
xi)and the variance is σ(
xi). e singular value equivalent
matrix Xucan be obtained by the following transformation:
Xu�U�����
X
XH
.(7)
In equation (7), Uis a Haar matrix, and the superscript H
represents a conjugate transpose, that is, XH
uXu�
X
XH. For
Lsuch non-Hermitian matrices
Xi(i�1,2,. . . , L), after the
above transformation, each can obtain the corresponding
singular value equivalent matrix Xu,i(i�1,2,. . . , L). e
product matrix
Yof singular value equivalent matrix is
Y�
L
i�1
Xu,i.(8)
In this paper, Lis taken as 1, and the standard matrix Yis
obtained according to the following formula:
yi�
yi
��
M
√σ
yi
i�1,2,. . . , M. (9)
yiis each element of matrix Y. When the row column
ratio c�M/Nis constant and M,Napproaches infinity, the
empirical spectral distribution of Yeigenvalue λiconverges
to the given limit, and its probability density function is
fY(λ) �
2
πcL |λ|(2/L−1),(1−c)L/2 ≤|λ|≤1,
0,Other,
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩(10)
where c∈(0,1]is a constant. e single ring theorem shows
that each element of a standard non-Hermitian matrix Yis
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−c)L/2.
3.2. Linear Eigenvalue Statistics. LES can reflect the distri-
bution of eigenvalues of random matrix. e average
spectral radius rMSR is a common form of LES, which is
defined as the average of the distribution radii of all ei-
genvalues of the matrix on the complex plane:
rMSR �1
N
N
i�1
λi(Y)
,(11)
|λi(Y)| is the distribution radius of all eigenvalues of matrix
Yon the complex plane. A single eigenvalue cannot reflect
the statistical characteristics of matrix elements. LES de-
scribes the trace of random matrix and can reflect the
statistical characteristics of matrix. erefore, 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
4Mathematical Problems in Engineering
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 ar-
rangement 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 Section 1 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. e flow chart of English
writing mode based on random matrix theory is shown in
Figure 1.
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 ex-
periment according to the existing literature. rough 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. is
paper takes the students of English 2 as the subjects of the
experiment. ird, the experimental subjects must include
the whole population, that is, the birth conditions and family
conditions of the students must be diversified. In this ex-
periment, a total of 10 non-English majors from different
universities in 2020 were selected to participate in the ex-
periment. ey are not business administration students
with good English level, nor are they relatively poor students
who have not reviewed the subject. ese students are
majoring in various majors of the university (including five
different majors of civil engineering of engineering, infor-
mation engineering of computer science, and history of
humanities). ey can represent the general learning level of
students in 2020. e 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. is experiment is from March 2019
to December 2020, for a review cycle of postgraduate en-
trance examination. e 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. ey 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. e experimental administrator
did not participate in the time arrangement of the experi-
mental testers, but only supervised the progress of the ex-
perimental 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
END
Result output
YES
YES
NO
No
Semantic logic
detection
Execution
window
Spectral
density
function
discrimination
Spectral
density
function
discrimination
Normal
?
Wor d s ense
detection
Lexical substitution
Calculation of equivalent
matrix in complex field
Construct random matrix
Building English word
database
Start
Figure 1: Flow chart of English writing model based on random
matrix theory.
Mathematical Problems in Engineering 5
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 co-
operate 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. e
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 require-
ments on the number of words and time, mainly to en-
courage students to fully express their ideas. e 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. e 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 coop-
eration 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 at-
tention 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. en,
the teacher lists several questions according to the
content of the text and the students’ life. e
questions try to be close to the students’ life and
create a real situation. Students can also draw up
their own topics. ere 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) e 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) e 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. e English writing
scores of each student before and after the test are shown in
Table 1 e 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.
Carry out data statistical analysis on Table 1, 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.
It can be seen from Figure 3 and Table 2 that the per-
formance rules of different students’ writing are also in-
consistent 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. erefore, the courseware,
Students’ mutual review is of little help to the improvement
of students’ writing ability, and even has side effects. e
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.
It can be seen from Figure 4 and Table 3 that the stu-
dents’ English composition scores after the modification of
the English writing mode based on random matrix proposed
in this paper have significantly improved. e average scores
of the two scores have increased by 5.1 points and 6.3 points,
6Mathematical Problems in Engineering
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. e
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.
5.5. Discussion on Experimental Results. e 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. e purpose is to make students re-rec-
ognize their learning status. ey are active learning sub-
jects, but no longer passive recipients of knowledge. Learners
should be responsible for their own progress, rather than
being indoctrinated and arranged by teachers. e results
show that the students’ subjective initiative has been brought
into play, and the effect is ideal.
It stimulates students’ learning motivation and en-
courages 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
Table 1: Students’ original English writing scores twice (full score is
100 points).
Student number First writing score Second writing score
1 88.0 76.0
2 86.0 82.0
3 72.0 89.0
4 91.0 86.0
5 68.0 86.0
6 84.0 83.0
7 75.0 64.0
8 84.0 95.0
9 84.0 76.0
10 90.0 77.0
Table 2: Students’ two revised writing scores (full score of 100
points).
Student number First writing score Second writing score
1 86.0 74.0
2 88.0 86.0
3 80.0 88
4 87.0 81.0
5 74.0 75.0
6 80.0 74.0
7 75.0 71.0
8 78.0 92.0
9 87.0 86.0
10 93.0 82.0
Table 3: Two revised writing scores using this method (full score of
100 points).
Student number First writing score Second writing score
1 92.0 90.0
2 89.0 94.0
3 84.0 96.0
4 92.0 86.0
5 86.0 82.0
6 85.0 86.0
7 89.0 79.0
8 88.0 92.0
9 84.0 87.0
10 88.0 91.0
95
90
85
80
75
70
65
60
Second writing score
Student number
65
70
75
80
85
90
95
First writing score
0
2
4
6
8
10
Original score
Figure 2: Statistical chart of original score data.
95
90
85
80
75
70
65
60
Second writing score
Student number
65
70
75
80
85
90
95
First writing score
0
2
4
6
8
10
Original score
Student revised grades
Figure 3: Students’ two writing scores after mutual revision.
Mathematical Problems in Engineering 7
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
rough 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. erefore,
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 en-
vironment design idea, and to carry out targeted experi-
ments on it. By testing the second writing ability of 10
postgraduates of 2020 in different majors. rough a se-
mester of empirical research, after two times of method
guidance, all students’ composition scores have been sig-
nificantly 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.
Data Availability
e dataset used in this paper are available from the cor-
responding author upon request.
Conflicts of Interest
e authors declared that they have no conflicts of interest
regarding this work.
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