The traditional ‘teacher-student’ point-to-point classroom teaching mode has been the standard mode of instruction in most of the colleges and universities. Despite the incorporation of some multimedia teaching methods in classrooms, this one mode of teaching has gradually failed to keep up with the development trend of college classroom teaching reforms [1]. In tandem with the accelerating development and deepening of education informatisation, information technology promotes the continuous improvement and innovation of educational teaching methods [2]. Online education is a newly developed form of education found in the context of education informatisation that is highly favoured by its advantages of flexibility and not being bound by time or space; especially, in the context of the new coronary pneumonia epidemic, online education has become an indispensable way of teaching in higher education worldwide [3]. For example, the emergence of massive open online courses (MOOCs) to flipped classrooms to small private online courses (SPOCs) has ushered in a new way for the reform of classroom teaching in colleges and universities. A number of online courses have been developed in response to the exploration and practice of MOOCs, and some experience has been accumulated while many branches have been developed to integrate fully online MOOC courses with face-to-face courses [4]. MOOC is a massive open online course, and SPOC is a small private online course. The ‘small’ and ‘private’ terms of SPOC are relative to MOOC [5]. The scale of SPOC's teaching objects ranges from dozens to hundreds of people, and the teaching objects are for learners who meet certain conditions, especially for college students. SPOC is the development and supplement of MOOC. It can be simply understood that SPOC is equal to MOOC plus classroom [6]. Compared with MOOC, SPOC has a good binding force on students’ learning behaviour, supervises the whole process of learning, improves the completion rate of students and promotes students’ effective learning [7]. By improving the MOOC model, it can better address the current needs of classroom learning and teaching and has become the mainstream teaching method of major institutions for higher education [8]. Therefore, it is vital to analyse the factors influencing the teaching effectiveness of SPOC and then develop strategies for improving the teaching effectiveness of online courses to promote the development of online education.
Despite the fact that online education has the advantage of being flexible and having weakly restricted teaching space and is widely used in higher education, the phenomenon still persists that students ‘can’t learn,’ ‘don’t understand’ and ‘can’t pass the test’. During the teaching SPOC, the effectiveness of the courses is limited to some degree by the teaching methods, classroom environment and other factors. Additionally, with the reform of higher education teaching methods in the last few years, more and more institutions of higher education are giving more and more attention to the transformation of the teaching mode, as well as the learning mode, where students gradually shift from passive to active learning [9]. For this reason, when analysing the influence of SPOC, it is still important to consider other student dimensions, such as students’ ability to pre-study before class, their ability to summarise after class and their ability to actively engage in problem-solving issues. Accordingly, this paper systematically compares the factors limiting the effectiveness of SPOC teaching from the perspectives of the students’ learning ability, the classroom atmosphere and teachers’ teaching design. It then clarifies the propagation paths and strengths of the influencing factors and then proposes targeted strategies to ensure the effectiveness of SPOC education in higher education.
M. Scriven, in 1967, distinguished between ‘summative evaluation’ and ‘formative evaluation’ for the first time in his book ‘The Methodology of Evaluation’. The concept of summative and formative evaluation was first introduced in. The educator B. S. Bloom introduced this assessment into the field of teaching and learning. He divided it into diagnostic, formative and summative evaluation, which Bloom saw as an integral part of teaching and learning [10]. Based upon their extensive research on teaching practice, Black and William found that objective and comprehensive classroom formative evaluation can significantly improve students’ academic performance in the short term. This is especially true for students who are otherwise underachieving [11]. Scholars have largely focussed on the application of big data technology in the field of educational assessment in terms of evaluating online teaching effectiveness. For example, Mou [12] constructed a personalised learning evaluation model based on electronic schoolbags. Based on big data analytics, Zhen-Chao et al. [13] developed a digital learning developmental evaluation system. The traditional flipped classroom teaching model was refined by Xiao et al. [14] into 10 sessions, and ‘learning assessment’ was used throughout the entire process. Concerning teaching models, Tan and Gu [15] examined the composition of learning effectiveness assessment indices for the hybrid model of open education. According to Bai [16], ‘formative assessment refers to the evaluation of students’ learning progress and refers to the evaluation of teaching and learning in the teaching process’. Formative assessment focuses on the improvement of the learning process, emphasises the timely feedback of assessment information and aims to improve students’ learning effectiveness and teachers’ teaching through regular assessment. As a result of their research, Luo and Hu [17] concluded that combining formative and summative assessment and moderately increasing the importance of formative assessment in the assessment system helps learners to pay attention to their own interests, emotions and skills when learning English.
From the above analysis, it is evident that the current scope of research on learning assessment methods is relatively extensive. Scholars have proposed learning behaviour analysis and prediction models based on big data, but they have not assessed the learning effects of the blended teaching model, particularly the SPOC model, and empirical research on learning assessment methods for online and offline blended teaching models is still insufficient. Xiao et al. [14], for instance, proposed a multifaceted evaluation system that combined pre-class and in-class assessments, but further application and evaluation are required for the flipped classroom teaching effect. Tan and Gu [15] proposed the effect assessment index of the blended teaching model but only validated this set of effect assessment index through a questionnaire survey.
The objective of this paper is to reconstruct a more ideal learning effectiveness evaluation model for evaluating students’ learning abilities and application skills through the evaluation of three exogenous latent variables using structural equation modelling: the teacher's teaching method, students’ learning ability and the classroom environment.
Before constructing the SPOC evaluation model, a study of the SPOC teaching mode has been conducted using the course ‘Aviation Broadcasting’ from the Zhengzhou Institute of Aviation Industry Management in China as an example. The nature, teaching format, teaching objectives and methodologies, as well as the teaching process of SPOC, were examined, as well as factors affecting the evaluation of SPOC with full-time undergraduate university students in the classes of 2019, 2020 and 2021. ‘Aviation Broadcasting’ is a course oriented to cultivate students’ comprehensive ability of aviation service and management. Through the study of this course, students can adapt to the context and control the scene according to the cabin environment, maintain cabin safety and improve cabin service quality. As a result of sorting out the factors affecting course evaluation from the available data, three dimensions affecting SPOC evaluation, namely, student learning ability
Fig. 1
Conceptual model of factors influencing the teaching effectiveness of SPOC courses. SPOC, small private online courses

The following hypothesis is also proposed.
H1: Student learning ability has a positive effect on the teaching effectiveness of SPOCs.
H2: Teacher instructional design has a positive effect on the teaching effectiveness of SPOCs.
H3: Classroom learning atmosphere has a positive effect on the teaching effectiveness of SPOCs.
H4: Students’ learning ability has a positive effect on teachers’ instructional design.
H5: Classroom learning atmosphere has a positive effect on students’ learning ability.
H6: Teachers’ instructional design has a positive impact on classroom learning climate.
A SEM may replace regression analysis, analysis of variance, correspondence analysis, factor analysis and cluster analysis to clarify the roles of individual indicators on the total and their interactions with one another [18]. In structural equation modelling, variables that cannot be measured directly and accurately are called latent variables and are measured indirectly through external indicators [19]. Using the research in the education sector and the operability and orientation of evaluation indicators, this study selects 19 observed variables to form a model and forms an index system of SPOC course teaching effectiveness influences, as shown in Table 1.
Indicators of observed variables influencing the teaching effectiveness of SPOCs
Student learning ability | Pre-learning abilities before class | Before the start of the course, students prepare course-related materials | [14] |
After-class summary review | Students summarise their takeaways from the course and discuss them at the end of the lesson | [16, 19] | |
Find resource capacity | Using multiple media, students locate resources related to the course | [20, 21] | |
Active thinking ability | Students can find out what they do not understand when faced with known information | [23, 24] | |
Problem solving ability | Students use effective information to solve various problems encountered in learning | [18] | |
Extended extension capability | Students’ extension of known information based on existing course content | [24, 25] | |
Teamwork ability | Students can express their own views clearly, listen to those of others, distil effective information and form an overall impression in a group setting | [21, 22] | |
Teacher instructional design | Classroom planning and organisation | Faculty members plan and organise course material | [23] |
Course schedule | Teacher's schedule of class time for the course's teaching schedule | [26] | |
Teaching style | Ways and means for teachers to teach | [21, 26] | |
Teaching method | Teaching methods of faculty lectures | [24, 25] | |
Teaching style | Performance style of faculty teaching | [12, 15] | |
Assignment volume and assignment design | Assignment volume and difficulty designed by the teacher in a reasonable manner | [11] | |
Achievement rating | Criteria for evaluating students’ performance that are reasonable and fair | [19, 25] | |
Classroom learning atmosphere | Teacher-student interaction | Interaction between teachers and students in regard to frequency, manner, method and effectiveness | [26] |
Classroom communication | Communication between students and teachers in online and offline classes | [22, 26] | |
Task undertaking | Actively participate in group activities and take initiative to complete assigned tasks | [22, 25] | |
SPOC teaching effect | Course satisfaction level | The overall satisfaction of students with the SPOC course, including overall satisfaction, gaps with expectations, and gaps with ideal | [13] |
Evaluation of the completion of the course learning objectives | To determine whether students have completed the learning objectives set for the course and whether they have acquired the appropriate knowledge and skills | [24] |
SPOC, small private online courses.
As described in Table 1, the observed variables are the measurement errors or residuals, which are represented by the residual term
Fig. 2
SEM of factors influencing the teaching effectiveness of SPOCs. SEM, structural equation model; SPOC, small private online courses

Fig. 3
SPOC course

This study refers to the teaching questionnaire of the relevant SPOC and develops a questionnaire in conjunction with the relevant situation of the course ‘Aviation Broadcasting’ at the Zhengzhou Institute of Aviation Industry Management, China, and distributes it via an online survey during the course cycle. In the first part of the questionnaire, the students are asked basic information, such as their age, gender and grade level; the second part is the main part of the questionnaire, and it covers three aspects, including students’ learning ability, teachers’ teaching designs and the classroom learning environment. The questions in the questionnaire were based on a 10-point Likert scale [20] where 1 represents ‘very low’ or ‘very poor’ and 10 represents ‘very high’ or ‘very good’ and students were asked to respond according to their thoughts. Students of the class of 2018, 103 students of the class of 2019, and 107 students of the class of 2020 at the Zhengzhou Institute of Aviation Industry Management in China were surveyed. A total of 358 questionnaires were distributed, 302 valid questionnaires were returned and the effective return rate was 84.4%.
Generally, data reliability is defined as the degree of consistency or stability of the measurement results, and a high degree of reliability indicates greater confidence in the measured results. SPSS 17.0 software was used to analyse the model data for internal consistency reliability and to proofread the abnormal data. The reliability of internal consistency is usually determined by the Cronbach's
Results of analysis of latent variable reliability
Student learning ability | 7 | 0.874 |
Faculty instructional design | 7 | 0.947 |
Classroom learning atmosphere | 3 | 0.875 |
Teaching effectiveness of SPOCs | 2 | 0.931 |
SPOC, small private online courses.
In Table 2, it can be seen that the
To ensure the validity of the questionnaire, the validity of this study was analysed using an exploratory factor analysis to assess the validity within and among factors. The KMO and Bartlett tests were conducted on the question items to examine the suitability of the study sample for factor analysis. The results are shown in Table 3.
KMO test and Bartlett's sphericity test
0.858 | ||
---|---|---|
Bartlett's sphericity test | Approximate cardinality | 1337.334 |
Degree of freedom | 69 | |
Significance | 0 |
The Kaiser KMO measures are as follows: ≥ 0.9 means very suitable, 0.8 means suitable, 0.7 means average, 0.6 means not very suitable and ≤ 0.5 means extremely unsuitable. The KMO value approaches 1 when the sum of squared simple correlation coefficients among all variables is greater than the sum of squared partial correlation coefficients. The closer the KMO value is to 1, the stronger the correlation between variables and the more suitable the original variables are for factor analysis. According to Table 3, the KMO value of this study is 0.858, the Bartlett's sphericity test value approximates the chi-square 1337.333, the degree of freedom is 69 and the
Model test analysis was performed using AMOS, and the study used the cardinality ratio of freedom (
Model fit test of factors influencing the teaching effectiveness of SPOCs
Standard value | <3 | <0.9 | <0.9 | <0.9 | <0.9 | <0.05 | <0.9 |
Actual value | 1.098 | 0.939 | 0.92 | 0.993 | 0.993 | 0.019 | 0.991 |
Fitting results | Support | Support | Support | Support | Support | Support | Support |
AGFI, adjusted goodness-of-fit index; CFI, comparative fit index; GFI, goodness-of-fit index; RMSEA, root mean square error of approximation; SPOCs, small private online courses
The cardinality ratio of freedom value of 1.098 is less than the standard value of 3, and the model fit is excellent; meanwhile, the RMSEA value 0.019 is <0.05, and the GFI, NFI, RFI, IFI and TLI values are all >0.9, indicating that the model is well constructed and the results are reliable.
The results of the hypothesis testing for the SEM are presented in Table 5, where *** indicates that
Hypothesis testing results
H1: | 0.412 | *** | Support |
H2: | 0.401 | *** | Support |
H3: | 0.173 | 0.012 | Support |
H4: | 0.355 | *** | Support |
H5: | 0.221 | 0.043 | Support |
H6: | 0.372 | 0.009 | Support |
Based on the standardised path coefficient for Hypothesis 1, which is 0.412 and
The standardised path coefficient for Hypothesis 2 was 0.401 and
According to the standard path coefficient of Hypothesis 3, which was 0.177 and
Based on the standardised path coefficient for Hypothesis 4,
Accordingly, the standardised path coefficient for Hypothesis 5 is 0.221 and
It was determined that the standardised path coefficient for Hypothesis 6 was 0.372 and
The SEM was tested and calculated using AMOS software to obtain the standardised output of the model, i.e., the observed variable path coefficients, as shown in Figure 4.
Fig. 4
SEM paths of factors influencing the teaching effectiveness of SPOCs. SEM, structural equation model; SPOCs, small private online courses

As can be seen from Figure 4, the most important influence on the teaching effect of SPOC is students’ learning ability, where the most important observed variable on students’ learning ability is students’ active thinking ability, with a path coefficient of
The most influential observed variable on teachers’ instructional design was teachers’ teaching methods with a path coefficient of
The most influential observed variable on classroom learning climate was classroom communication with a path coefficient of
In addition to
The study proposes a method for evaluating the effectiveness of SPOCs based on structural equation modelling. The paper constructs a conceptual model and an analytical framework for the factors influencing the effectiveness of SPOCs, conducts a study of learning of a select group of students in three grades of air service art and management at the Zhengzhou Institute of Aviation Industry Management, China, and analyses the measurement data of selected variables. The model was able to show the relationship between latent variables and measurement indicators, latent variables and latent variables. Based on the path coefficients, students’ learning ability, teachers’ teaching design and classroom learning environment have the most influence on the effectiveness of SPOCs. This study provides a number of insights derived from the above findings.
As opposed to the teacher's teaching design or classroom learning environment, the students’ internal motivation is more important. It is essential that students pay attention to the learning of professional courses, increase their interest in the courses and learn to think independently and build a knowledge system on their own. During cooperative tasks in the course, students should be guided by the idea of taking action and contributing to the team's success.
The teaching team actively explores flexible and effective teaching methods and integrates heuristic teaching, case studies, simulations and experiential learning. It also focuses on the interaction between teaching and learning in the classroom. By improving teaching methods, students’ interest in learning will be stimulated and their ability to innovate will be enhanced. Implement all-round guidance for students’ learning processes by categorising and organising three time dimensions: before, during and after class. In line with the teaching content, relevant learning tasks are set to clarify key points of knowledge and clarify key questions. Students complete online teaching resources, such as courseware, videos, audios and cases independently, following the prompts. Practice questions are added to the video playback to stimulate participation and enhance learning enthusiasm. The learning effects of students are evaluated through online tests after stage learning. Students provide feedback on problems they cannot solve through the learning platform, and teachers focus on key and difficult content offline based on the feedback students provide.
During the SPOPC, the advantages of online and offline integration should be fully tapped to develop multiple applications. This should take into consideration the needs of students with distinct personalities, preferences and levels of learning. Moreover, this should also combine the emphasis on cultivating theoretical research with the emphasis on cultivating time-based abilities and be involved throughout the entire course to achieve a balanced level of cultivation of comprehensive literacy and applied knowledge and abilities.
Evaluation is established as follows: develop a diversified learning evaluation system, explore a diversified assessment and evaluation model that integrates online and offline courses, integrate formative and summative evaluations, encourage independent learning, process learning and experiential learning and assess overall evaluation results of the courses based on both process and summative evaluation.
Evaluation of the course process includes online assignments from the course resource platform, classroom interaction, check-in, audio and video task points, chapter quizzes, group tasks, chapter learning times, discussion participation and scores for offline learning behaviour. By the end of the course, the summative assessment will include a theoretical knowledge question bank test and a simulated scenario-based practical training project assessment. This final assessment will test the students’ theoretical mastery and their practical application ability, measure the effectiveness of the teaching activities and comprehensively reflect the students’ learning ability and the level of the SPOC, ensuring that the learning objectives and requirements are met and the students learn what they need to know.
The course is an important carrier for students’ training. In some cases, students’ attitudes and learning behaviours can objectively and truly reflect that a professional course is meeting their professional ability development needs to some extent. The college student's learning process is more independent and autonomous in comparison to that of secondary school students. In the teaching process, the teacher is the object of learning activities, while the students are the subjects of those activities.
Based upon traditional education, most students are more introverted in terms of interactive communication and they are not adept at asking questions during the learning process. There will be poor communication between students, teachers and classmates, and the effectiveness of classroom instruction will be considerably reduced. As a way to improve the learning effects of students’ courses, students should take advantage of the opportunity to communicate with others, whether through online or offline classes. Additionally, they are expected to participate in classroom discussions and research projects, create sparks of wisdom through the collision of ideas and keep a positive classroom atmosphere. By taking advantage of the opportunity to communicate with others, they will be able to break free from traditional thinking, actively participate in classroom discussions and research, create sparks of wisdom through the collision of ideas, foster an active classroom environment and cultivate a positive attitude towards learning so that they may become better learners.
Fig. 1

Fig. 2

Fig. 3

Fig. 4

Model fit test of factors influencing the teaching effectiveness of SPOCs
Standard value | <3 | <0.9 | <0.9 | <0.9 | <0.9 | <0.05 | <0.9 |
Actual value | 1.098 | 0.939 | 0.92 | 0.993 | 0.993 | 0.019 | 0.991 |
Fitting results | Support | Support | Support | Support | Support | Support | Support |
Hypothesis testing results
H1: |
0.412 | *** | Support |
H2: |
0.401 | *** | Support |
H3: |
0.173 | 0.012 | Support |
H4: |
0.355 | *** | Support |
H5: |
0.221 | 0.043 | Support |
H6: |
0.372 | 0.009 | Support |
Indicators of observed variables influencing the teaching effectiveness of SPOCs
Student learning ability |
Pre-learning abilities before class |
Before the start of the course, students prepare course-related materials | [ |
After-class summary review |
Students summarise their takeaways from the course and discuss them at the end of the lesson | [ |
|
Find resource capacity |
Using multiple media, students locate resources related to the course | [ |
|
Active thinking ability |
Students can find out what they do not understand when faced with known information | [ |
|
Problem solving ability |
Students use effective information to solve various problems encountered in learning | [ |
|
Extended extension capability |
Students’ extension of known information based on existing course content | [ |
|
Teamwork ability |
Students can express their own views clearly, listen to those of others, distil effective information and form an overall impression in a group setting | [ |
|
Teacher instructional design |
Classroom planning and organisation |
Faculty members plan and organise course material | [ |
Course schedule |
Teacher's schedule of class time for the course's teaching schedule | [ |
|
Teaching style |
Ways and means for teachers to teach | [ |
|
Teaching method |
Teaching methods of faculty lectures | [ |
|
Teaching style |
Performance style of faculty teaching | [ |
|
Assignment volume and assignment design |
Assignment volume and difficulty designed by the teacher in a reasonable manner | [ |
|
Achievement rating |
Criteria for evaluating students’ performance that are reasonable and fair | [ |
|
Classroom learning atmosphere |
Teacher-student interaction |
Interaction between teachers and students in regard to frequency, manner, method and effectiveness | [ |
Classroom communication |
Communication between students and teachers in online and offline classes | [ |
|
Task undertaking |
Actively participate in group activities and take initiative to complete assigned tasks | [ |
|
SPOC teaching effect |
Course satisfaction level |
The overall satisfaction of students with the SPOC course, including overall satisfaction, gaps with expectations, and gaps with ideal | [ |
Evaluation of the completion of the course learning objectives |
To determine whether students have completed the learning objectives set for the course and whether they have acquired the appropriate knowledge and skills | [ |
KMO test and Bartlett's sphericity test
0.858 | ||
---|---|---|
Bartlett's sphericity test | Approximate cardinality | 1337.334 |
Degree of freedom | 69 | |
Significance | 0 |
Results of analysis of latent variable reliability
Student learning ability | 7 | 0.874 |
Faculty instructional design | 7 | 0.947 |
Classroom learning atmosphere | 3 | 0.875 |
Teaching effectiveness of SPOCs | 2 | 0.931 |
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English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of 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