In English education and teaching in colleges and universities, cross-cultural education can enable students to better understand the differences between Chinese and American cultures, such as the differences in social customs, values and morality between Chinese and American cultures [1]. Only by guiding students to correctly understand the cultural differences between China and the United States through cross-cultural education and teaching can students better master the essence of English culture [2]. In the primary stage of English learning, teachers generally pay more attention to the learning of English language knowledge due to various pressures of entering a higher school, thus ignoring culture teaching, which is lack of comprehensive English learning.

A previous study [3] states that colleges and students should not only use normal class time to study but also make full use of external leisure time to study hard and constantly accumulate and master Chinese culture, so as to make better use of and spread Chinese culture. Another study [4] believes that understanding and adjusting the differences between Chinese and Western cultures in teaching is one of the effective means of teaching quality. This article expounds the differences between China and the West, analyses its reasons, introduces the differences between Chinese and Western education and teaching modes and puts forward some suggestions to eliminate the differences between China and the West. One other study [5] from the perspective of micro-class, combined with modern teaching methods, created a diversified classroom teaching model suitable for business education and carried out educational reform. It is helpful to broaden students’ vision and expand and optimise the allocation of school resources. An upgraded classroom model can also better promote students’ enthusiastic participation, cultivate students’ learning enthusiasm and provide a high-quality platform for cultivating all-round talents suitable for market demand and professional skills. A previous study [6] takes the educational concept of the new curriculum as the basic guiding concept, fully invests in the process of educational practice, constantly develops and innovates, explores educational methods more suitable for the characteristics of modern society, further improves the effect of classroom teaching and realises the efficient education of high school teaching. Yet another study [7] integrates multimodal teaching strategies to diversify listening teaching modes in colleges and universities, which is helpful to cultivate students’ subjective initiative and multimodal cognitive ability. This article expounds the connotation of the multimodal theory, analyses the current situation of college listening teaching mode under the multimodal environment and puts forward the way of reform. A previous study [8] analyses the problems existing in the current high-school English teaching and puts forward a feasible teaching reform scheme under the background of big data, so that the English writing ability can be realised under the background of real modernisation.

College English teaching is in the deep water of information reform, and the teaching reform strategy has become the focus of research. This article proposes a study on the reform of college English education inspired by the cultural differences between China and the United States. First, we aim to understand the cultural differences between China and the United States and analyse the background and current situation of college English information teaching, aiming at the existing problems; establish a matrix factor model to obtain the characteristic values of cultural differences; predict the efficiency of the development trend of college English education reform according to the VaR identification model; strive to give full play to the role of information-based teaching ideas and means and improve the quality of English teaching in higher vocational colleges.

Campus culture is not only reflected in the core competitiveness, levels and characteristics of students but also in the campus after the social economy has developed to a certain level [9]. With the continuous development of today's society, the exchanges between China and the United States are increasing, and the cultural exchanges and collisions are constantly formed. The campus cultures of China and the West gradually show their fascinating charm and very strong vitality in the exchanges and collisions [10]. However, there are some cultural differences between the two sides. This article makes an in-depth discussion on the differences between Chinese and American campus culture, investigates the reasons and analyses their advantages on this basis, so as to promote the development direction of China's education in the future.

Let students understand the living habits and customs of American society and the law of language action, which will help students better master the key points of knowledge in English learning [11]. First, in terms of privacy, Chinese people do not shy away from personal conditions such as age and work, while Americans believe that such inquiries involve personal privacy. Second, Americans are rigorous. Chinese people are often used to forgiving each other's small mistakes and giving each other a chance. Chinese people do not like to look directly into each other's eyes in daily communication, thinking it will be very uncomfortable, while Americans think it is one of the ways of equal communication [12]. In China, the folk custom of hospitality has been almost well known all over the world. Once the Chinese are the host, they are bound to entertain the guests warmly and say some polite words. Compared with Americans, they are more straightforward and would not be too polite to each other. Therefore, in the cross-cultural English education and teaching between China and the United States in colleges and universities, we need to help students understand the connotation knowledge and differences of Chinese and American cultural backgrounds, and understand the obstacles caused by Chinese and American cultural differences in students’ learning, so that students can better understand the connotation of English teaching culture [13].

First of all, Chinese and American civilisations have endowed human beings with different cultures in different regional environments. When praised by others, Chinese people prefer to answer in a modest way, while Americans will accept and thank them directly. It can be seen that the Chinese believe that modesty and prudence are important, while the Americans believe that their expression is true and respectful, resulting in differences in values on the same issue [14]. Second, in English teaching, teachers’ praise to students often makes students feel shy, and then teachers will say some words of encouragement and warning, while American students will accept it calmly and show sincere confidence.

Collectivism is widely respected in China, while Americans advocate individualism and sense of independence and put personal interests first, which is completely opposite to the concept of Chinese collectivism, which is to worry about the world first and enjoy the world later [15]. Chinese people always believe that many people have great power, but Americans advocate personal supremacy [16]. In the face of these problems caused by the differences in morality and values, college students will eventually be hindered by obstacles in English cross-cultural learning. If they cannot treat the differences equally and objectively, they will eventually be unable to acquire the essence of English culture under the background of the obstacles of cultural differences between China and the United States.

At present, college education still adopts the traditional way of education and does not pay attention to the grammar, key points of knowledge, English words and technical application of basic knowledge and relative English. Higher education has carried out many reforms and innovations, but it has not changed the shortcomings of higher education from the source. Some students continue to study after entering the era from kindergartens to primary and secondary schools, middle schools, ordinary high schools and colleges and spend a lot of time learning and training, but in the final application, the result is not ideal [17]. In public places and workplaces, learning cannot be integrated with daily life.

In today's globalisation, the use of English has become very common. The utilisation rate of various countries is also very large, so the education work of colleges and universities should make rapid progress and cultivate professional talents [18]. The connection between ordinary high-school education and social development can be smoother in the future application. In classroom teaching, we should cultivate professional talents in an all-round way and cultivate students’ quality. The systematisation of higher education is the final goal of colleges and universities and the overall goal of continuous pursuit of perfection.

Set up _{t}_{t}_{1} × _{2} dimension matrix [19], and the formula is as follows:
_{t}_{1} = _{2} = _{t}_{t}_{1} × _{2} (_{1},_{2} ≪ _{1} a pre-dimensional load matrix, _{2} a post-dimensional load matrix and _{t}_{1} = _{t}_{t}C^{′} + _{t}_{t}_{t}

Keep the row and column load matrix unchanged, and the factor matrix after dimension reduction _{t}_{F} is the _{1}_{2} × _{1}_{2} dimensional coefficient matrix and _{V} is the representative
_{t}_{V}. The number of parameters to be estimated is [^{2}. However, in the matrix-valued factor model, the high-dimensional covariance matrix to be estimated can be described by the low-dimensional factor matrix, and _{F}. The total number of matrix parameters to be estimated is Φ_{F}. Therefore, the matrix-valued coefficient model can effectively reduce the matrix dimension and greatly reduce the number of prediction parameters [24].

Lack of interest is one of the main reasons why students’ English performance is not ideal. In order to enable students to learn English well, students should first have a strong interest in this kind of English [25]. In the teaching strategy, we should implement the teaching concept of ‘teachers leading students’ and adopt a variety of practice strategies to stimulate students’ interest in learning [26]. Teachers should give flexible guidance, choose the best teaching methods, encourage students to actively participate in the classroom and improve the teaching effect.

Using the construction method of the realised covariance matrix [27], for the reform of college English education, it is assumed that the number of courses in the whole day is

The reform of college English education mainly includes three aspects: subject information, curriculum learning management and educational information. The subject information is mainly composed of student information, curriculum information and teacher information [29]. Curriculum learning management is mainly composed of students’ classroom expression, students’ homework expression and students’ expression. Teaching information is mainly composed of teachers’ experience information, teachers’ observation information and teachers’ intuition information. The guiding method of education mode is shown in Figure 1.

The cultivation of English intercultural communicative competence should be emphasised in teachers’ teaching process. Therefore, a high level of cross-cultural English and correct values are necessary for every teacher [30]. On this basis, teachers should constantly strengthen their knowledge of anthropology and geography. It can make teachers more quickly and effectively understand the process of the formation and development of Chinese and American culture and the differences between Chinese and American cultures and expand teachers’ cross-cultural vision [31]. Second, teachers should strengthen the cultivation and establishment of cultural awareness, improve their mastery of professional skills and constantly strengthen and learn cross-cultural education and psychology.

In classroom teaching, teachers should actively guide students’ learning, stimulate students’ diversified appreciation ability, establish correct values for them, make them face the differences and obstacles between Chinese and Western English cultures and help students form an objective and fair cultural awareness system [32]. Teachers should combine language and culture closely with English teaching, guide students to experience the differences between Chinese and Western cultures and ensure the realisation of the purpose of cross-cultural communication.

As one of the subjects of teaching, teachers should constantly enrich their English language knowledge, teaching theory and thought; timely grasp the development trend of educational theory of the times; choose reasonable teaching methods [33]; learn from the successful teaching experience in history, actively adapt to the corresponding teaching reform work; push through the old and adopt a people-oriented way to find teaching methods suitable for students to learn English cross-cultural knowledge, so as to improve the teaching effect.

In teaching, teachers should correctly treat the cultural differences between China and the United States and guide students to analyse them from an objective and fair perspective [34]. First, colleges and universities should increase the investment in hardware facilities and build a good multimedia equipment environment. In classroom teaching, teachers can use the Internet to ‘learn and check’, use the Internet to search the relevant teaching cultural background in a short time, give students a comprehensive explanation, construct a sound Chinese and American cultural database and update it in time and provide the latest journals, magazines and documents, enabling students to learn the most cutting-edge knowledge of American culture [35]. Second, the teaching curriculum should be rich and diversified. Rich and diverse English courses can make students feel the culture of different levels and backgrounds, and the range of culture students will receive will be broader. Teachers should encourage students to develop the concepts of equality and language equality. In the research, teachers should overcome prejudice and eliminate the restrictions starting from their own values [36]. In education, teachers should provide students with more opportunities for learning strategies and training strategies.

In the development of college English education and teaching, we should pay attention to the infiltration of cross-cultural education, and it is very important to show it in the cultural connotation [37]. Teachers should actively adopt new teaching methods; infiltrate cross-cultural education into the teaching of reading, grammar and oral English; and establish new English learning ideas for students by expanding the scope of English learning. At the same time, teachers can transform the existing teaching mode, make students play a role in English cross-culture and stimulate students’ interest in English learning. In the setting of English teaching content, we need to get rid of the influence of stereotyped thinking. We should introduce the rich content of cross-cultural awareness and look at the problem from a global perspective. The world is an organic whole. American English culture is only a part of it. Teachers should help and guide students to understand the formation of English culture in various countries and the West, establish an open learning attitude for them and encourage students to take English as a tool to understand the world, so as to establish a standard and correct English cross-cultural learning attitude for students.

In view of the problems in the process of college English teaching, how to find and eliminate the possible adverse effects as soon as possible is the focus of this article. Using the powerful data analysis and processing ability of discriminant model, we can provide scientific means and basis for the prediction of actual teaching effect.

Set up _{1} and _{2} all _{t}_{m}_{m}_{m}_{m}_{m}_{m}_{1} and _{2} are frontal space. _{1}), _{2}), _{1} and _{2} column space, and the formula is as follows:
_{t,j}, _{j}, _{j}_{m,j}, _{m, j} separately as _{t}_{m}_{t}_{m}_{0}, defined as:
_{1} is a linear combination of the whole column. Therefore, _{1}) is estimated according to the eigenvector of the observed value of rotating _{1}) is as follows:
_{1} eigenvectors corresponding to the maximum eigenvalues
_{t}

According to _{1}, the determination method recorded

The vectorisation operation of

In the research process, a total of 26 items were prepared by the questionnaire survey, including three fields: structured data of research subject information, semi-structured data of research process learning management and unstructured data of educational information research [39]. A questionnaire survey was conducted on 400 students in a university in a city. Through the questionnaire survey, the current situation, achievements and existing problems of students’ learning process were objectively reflected. According to the model designed in this study, suggestions on the mode of higher education were put forward.

The parameters under investigation adopt the Richter scale of 5 (1 = very poor, 2 = difference, 3 = normal, 4 = good, 5 = very good) [40] because the variable is level 2. Relevant research shows that the teaching mode of colleges and universities involves 27 variables, and the description of some variables is shown in Table 1. Among them, the variable allocation shows the level 5 index without ‘*’ subjective quantitative standard in the highest, maximum and best decline files.

Description of some research variables

Predict behaviour | Dependent variable | Learning behaviour | Bad = 0, good = 1 |

Subject information | Student information | Score | <5 points |

Average study time | <1 h | ||

Optimistic state | <2 articles | ||

Believability | <2 articles | ||

Course information | Degree of interest | <2 articles | |

Time investment | <3 days | ||

Acceptance | <3 days | ||

Amount of knowledge | <3 days | ||

Faculty information | Teacher rank | 5, 4, 3, 2, 1 | |

Students’ love | 5, 4, 3, 2, 1 | ||

Communicate with students | 5, 4, 3, 2, 1 | ||

Teacher status | 5, 4, 3, 2, 1 |

There are 26 difference features set in the questionnaire. According to the basic norms of row and column sampling, the number of features m selected in the difference feature column is about sqrt (m), M is the total number of features and sqrt (m) is the root mean square function. This experiment M = 5 is suitable. Figure 2 shows the test results of classifying factors and classification errors under different m values.

According to the M obtained from the aforementioned experiment, the top five variables are taken to predict the learning behaviour of high-school education model.

The analysis in Figure 2 shows that if M = 5 and the factor is 40, the effect is very good. This parameter is used in subsequent experiments; 361 valid sample data collected were tested.

In order to verify the accuracy of this prediction model, this study predicts the development trend of college English teaching reform with the methods of literature 3, literature 4 and literature 5. Two groups of validation were conducted for 361 questionnaire data, including 230 training sets and 122 test sets. The measured results are shown in Table 2.

Prediction results of the development trend of college English education reform

Paper method | 99.44 | 99.25 | 99.20 |

Literature 3 methods | 86.25 | 77.33 | 79.40 |

Literature 4 methods | 81.10 | 70.65 | 82.54 |

Literature 5 methods | 89.90 | 88.44 | 81.15 |

The results show that the accuracy of the reform method proposed in this article is as high as 99.20%. It has good adaptability, discrimination and generalisation ability for college English teaching path, which is obviously better than those of the other three methods. Then it analyses the English performance after the reform, as shown in Figure 3.

It can be seen from Figure 3 that after the reform, students’ English scores are on the rise, and the number of students whose test scores reach the pass rate is high. Therefore, the teaching model of college English reform inspired by the cultural differences between China and the United States is feasible.

From the perspective of cultural differences between China and the United States, this study focusses on the reform of college English education. Through 361 survey data, five different features can be extracted, with an accuracy of 99.20%, which verifies the feasibility and effectiveness of this scheme. In the process of English teaching in colleges and universities, we should pay attention to the strengthening of the cross-cultural education theory, actively establish correct values for students to understand the differences between Chinese and Western cultures, give full play to the important role of cross-cultural education in college English teaching and lay the foundation for building comprehensive quality English talents.

#### Prediction results of the development trend of college English education reform

Paper method | 99.44 | 99.25 | 99.20 |

Literature 3 methods | 86.25 | 77.33 | 79.40 |

Literature 4 methods | 81.10 | 70.65 | 82.54 |

Literature 5 methods | 89.90 | 88.44 | 81.15 |

#### Description of some research variables

Predict behaviour | Dependent variable | Learning behaviour | Bad = 0, good = 1 |

Subject information | Student information | Score | <5 points |

Average study time | <1 h | ||

Optimistic state | <2 articles | ||

Believability | <2 articles | ||

Course information | Degree of interest | <2 articles | |

Time investment | <3 days | ||

Acceptance | <3 days | ||

Amount of knowledge | <3 days | ||

Faculty information | Teacher rank | 5, 4, 3, 2, 1 | |

Students’ love | 5, 4, 3, 2, 1 | ||

Communicate with students | 5, 4, 3, 2, 1 | ||

Teacher status | 5, 4, 3, 2, 1 |

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Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsResearch on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network