In recent years, the advantage of cheap labour in China has gradually disappeared, and the economic development mode relying on resource consumption and low labour cost is facing numerous challenges. According to the law of economic market development, education progress is the most effective way to promote economic development, and it is also the only way to improve production efficiency [1, 2]. Only by playing the role of education, can we turn the progress of education into the driving force of development, thus playing an effective role in promoting development in the socialist market economy with Chinese characteristics. Among them, the implementation of ideological and political education (IPE) is often ignored; as the main battlefield of production, operation and management, higher vocational colleges have a far-reaching impact on the promotion of industrial upgrading and economic transformation . As China’s economic development has entered the stage from high-speed growth to high-quality development, higher requirements are needed for applied talents; therefore, it is an important move to train technical talents with high moral and technical skills through ideological and political teaching, so as to enhance the driving force of China’s economic development [4, 5].
Nowadays, in higher education system, the homogenisation of education is more serious, which directly leads to the difficulty in meeting the needs of social talents for the output of university education, thus making the development of regional economy lag behind . In addition, in the Western region, the level of ideological and political identity among college students in minority areas is low, which has seriously restricted the regional talent training and economic development [7, 8]. In the future, IPE will be conducive to promote economic growth and become a vital force to improve social production.
In order to develop higher education, we must rely on continuous investment in education funds. Only sustained and numerous investment can support the material demand and strategic change of IPE, which is related to the future development of the whole country, so it must be the focus of financial security [9, 10]. Therefore, it is of great significance to advance the level of regional IPE and stimulate the development of regional economy.
Under the background of multiculturalism, the innovation of IPE in colleges and universities has adhered to the basic principles of flat development and diversified practice, which fully absorbed advanced educational ideas in multi-cultural, so as to enhance the advancement and foresight of IPE and ensure that the IPE work in colleges can play a positive role in education and guidance, which should be carried out with high efficiency. Through the summary and analysis, IPE in colleges in China has the characteristics of a development stage, as shown in Figure 1.
As can be seen from Figure 1, at present, the popularisation of IPE in colleges has gradually increased. Under the current economic background, by combining with the national development strategy and based on the needs of economic development, an in-depth study of economic thought in the new era has been constantly integrated into the IPE and its internal management, decision-making mechanism, and teaching form and so has undergone multiple changes.
Improvement of the education level is closely related to the development of economy . As shown in Figure 2, there are many different funding channels for higher education in China, including special expenditure of the state finance, donations from social organisations and organisations, funds from many private schools, business income and other sources.
In addition, there are also some sources of income, which are from the investment of schools, and the funds paid by the units subordinate to the schools. To sum up, we can divide the five funds mentioned in Figure 2 into two types according to whether they are allocated by the government finance: financial education funds and non-financial education funds. As the total amount of education funds is concerned, due to the higher degree of attention and the better and better level of economic development, the funds invested in higher education are constantly increasing .
The development of IPE can provide numerous high-level talents for the society and improve intellectual support for social development. Therefore, the long-term and sustained development of higher education is the top priority of future work, which needs continuous investment to ensure the advance of higher education, thereby providing human capital for the society. The internal relationship between IPE investment and economic growth is shown in Figure 3.
In the incremental investment analysis method, education investment can be regarded as human capital, which can promote economic growth. In the calculation of specific contribution rate (CR), economic growth should be regarded as the output rate and education investment as the capital item [13,14]. The analysis process of this method firstly finds out the growth surplus according to the production function, uses the counterfactual measurement method to obtain the increment of education investment, finally calculates the contribution of education to the growth of national income through the rate of return on education investment. Many scholars regard capital as the only factor to promote economic development and apply it to the construction of production function, but they could not obtain the obvious relationship between IPE and economic growth. Therefore, this study adopts the improved fuzzy clustering algorithm to establish the calculation model of the CR of China’s IPE.
Cluster analysis is an important data analysis method used to gather a certain class of the same things together to study and then analyse their overall characteristics and differences [15,16]. Fuzzy clustering analysis introduces fuzzy functions into clustering analysis, and through the similarity between data samples, the data sets are divided into several common data sets, and the membership degree of data samples to each class is given. The calculation principle is as follows:
Assume data set
Fuzzy clustering of sample data sets is to divide the set
At present, the existing fuzzy clustering algorithms are improved on the basis of existing clustering algorithms, such as fuzzy C-means clustering algorithm and fuzzy spectrum clustering algorithm, but these algorithms have the following shortcomings:
The number of clusters must be given, which reduces the credibility of the classification results. The classification algorithm has high requirements on the objective function; is sensitive to the selection of initial value, which is easy to fall into local optimum; and is difficult to achieve the global optimum.
The number of clusters must be given, which reduces the credibility of the classification results.
The classification algorithm has high requirements on the objective function; is sensitive to the selection of initial value, which is easy to fall into local optimum; and is difficult to achieve the global optimum.
Therefore, in this study, the gravity search method is used to optimise fuzzy clustering, and the genetic algorithm is used to determine the classification data sets in the eastern, western and central regions of China. The calculation principle of the gravity search method is as follows:
Central force optimisation is an evolutionary algorithm based on Newton’s law of universal gravitation. The core formula of the algorithm is as follows:
The introduction of the criterion can better determine the optimal classification number The calculation of tightness is too arbitrary. The distance between the sample data and its class centre is taken as the measure of compactness. In extreme cases, when the number of categories approaches the number of sample data, the distance between the sample data and its class centre decreases monotonously and tends to zero, thus making compactness lose its due utility. The topological structure of the sample data set is not considered. When two classes have overlapping data or no overlapping data, their class spacing may be equal, and the existing separation formula is indistinguishable.
The calculation of tightness is too arbitrary. The distance between the sample data and its class centre is taken as the measure of compactness. In extreme cases, when the number of categories approaches the number of sample data, the distance between the sample data and its class centre decreases monotonously and tends to zero, thus making compactness lose its due utility.
The topological structure of the sample data set is not considered. When two classes have overlapping data or no overlapping data, their class spacing may be equal, and the existing separation formula is indistinguishable.
Therefore, in this study, the classification number is adaptively determined by using the genetic algorithm, and the criterion function is optimised by using the gravity search method. The specific steps of the algorithm are shown in Figure 4.
Step 1. Initialise
Step 2. Convert
Step 3. Randomly generate a population
Step 4. Calculate the membership degree of each individual according to formula (1) such that
Step 5. If
Step 6. Take the reciprocal of formula (1) as a fitness function and select individuals to enter the next-generation population, according to the principle of greed;
Step 7. Update the individual velocity and acceleration vector according to formula (5);
Step 8. Calculate the fitness function
Step 9. Seek optimal solution of max
From the perspective of algorithm design, giving the upper and lower bounds of classification numbers is helpful to improve the efficiency of the algorithm. Obviously, the lower bound of the classification number is 1. Considering that China is divided into seven parts, geographically, it is appropriate to define the upper bound of the classification number as 7. Numerical experiments are completed based on the aforementioned example information by utilising the proposed algorithm, and the boundaries of the algorithm are set as follows : the value range of
According to the China Statistical Yearbook (2014–2020 edition), the annual GDP, fixed asset investment, household consumption level, and employment population data of each province are obtained, and the algorithm mentioned before is used for regional classification. The results are shown in Table 1.
Classification results of provinces.
|A||Sichuan, Zhejiang, Shandong, Guangdong|
|B||Shaanxi, Xinjiang, Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Guangxi, Yunnan, Henan Hunan, Hebei|
|C||Tibet, Gansu, Qinghai, Ningxia, Guizhou|
As can be seen from Table 1, Tibet, Gansu, Qinghai, Ningxia and Guizhou are located in the border areas, with weak industrial foundation, low population base, large proportion of agricultural population, relatively backward level of higher education and IPE, which belong to the least-developed areas in China, and their overall economic level is relatively backward, which requires special attention.
Similarly, the CR of the labour input, material capital input and human capital input in the
Similarly, the CR of material capital investment in each region is given as follows:
The CR of labour capital investment in each region is as follows:
The calculation of the CR of IPE progress is represented as
The calculation process of the CR of IPE is shown in Figure 5.
Data acquisition: According to the production factors in the calculation model, data are collected, and sample data of each production factor and the sample data classified according to the level of educational progress are obtained. Elastic coefficient estimation: The elastic coefficient of material capital investment in different regions is estimated by using the regression method, where Calculate the progress rate of IPE. Firstly, the annual average growth rates of output, material capital, labour force and human capital of various regions are calculated according to formulas (11) – (14); Then, according to the Solow value equation in the combination model, the progress rate of IPE in each region
Data acquisition: According to the production factors in the calculation model, data are collected, and sample data of each production factor and the sample data classified according to the level of educational progress are obtained.
Elastic coefficient estimation: The elastic coefficient of material capital investment in different regions is estimated by using the regression method, where
Calculate the progress rate of IPE. Firstly, the annual average growth rates of output, material capital, labour force and human capital of various regions are calculated according to formulas (11) – (14); Then, according to the Solow value equation in the combination model, the progress rate of IPE in each region
It is found that education and economic development are inseparable. Therefore, education is regarded as an element of economic development . By adding the input structure in the calculation model, the model is decomposed to measure the contribution of IPE investment to economic growth. Assuming that the labour input is
Take logarithm of both sides of the aforementioned formula, Formula (16) can be obtained:
Then take the full differential of both sides with respect to time
In order to more intuitively reflect the CR of IPE to the economy, this article uses the difference quotient formula to separate the factors that affect the growth rate, and then the difference quotient is used to discretise the growth rate equation as follows:
The model of the contribution of IPE education to economic growth rate is as follows:
Under actual circumstances, it is difficult to estimate
According to the 2014–2020 edition of the China Statistical Yearbook, the annual GDP, fixed assets investment, household consumption level and employment population data of each province, as well as the statistical data of teaching efficiency and IPE quality of colleges and universities in various regions, are used the this model. The influencing factors of the CR of higher education to economic growth selected in this study are the number of students enrolled, the number of teachers and students in school, the investment scale of IPE and the number of special projects of IPE.
Although some scholars have considered the turnover rate of graduates, after analysing the system dynamics simulation model, the results show that the relative error between simulation results and actual results is only 7.33%. In addition, the data statistics of turnover rate in China are not comprehensive, so the influence of other factors such as brain turnover rate is not considered in this study.
Figure 6 reflects the CR of IPE progress in A, B and C areas, with average values of 8.46%, 5.38% and 1.99%, respectively. At present, the development of IPE in China is unbalanced among regions, with the highest level of education in class A, far exceeding that in classes B and C. Therefore, we should vigorously speed up the construction of IPE in classes B and C, implement better preferential policies and subsidy policies and guide social investment, so as to realise the common progress of higher education in all areas.
In order to more intuitively analyse the CR of IPE in different regions of China, the CR of IPE in eastern, western and central regions is compared, and the results are shown in Table 2.
Comparison of CRs of IPE in eastern, western and central regions.
|Central China||Shaanxi||4.27||Eastern China||Shanghai||8.34|
CRs, contribution rates; IPE, ideological and political education.
The level of IPE in eastern China is far higher than that in other parts of China, especially in Beijing, Shanghai and Jiangsu. At the same time, it is easy to find that these areas with a high level of higher education are also economically developed areas. Although the absolute CR of other provinces is not high, considering the economic strength of these provinces, its educational output is much higher than that of the central and western regions. In addition, the CR of the central and western regions is far lower than that of the eastern developed regions, which also shows that the CR of IPE between the two regions is greatly different due to the huge gap in economic strength.
Also, it can be seen from Table 2 that Hunan and Sichuan, as depressions of higher education, have accumulated rich educational resources, so the CR of IPE can maintain a steady and rapid growth. However, Guizhou, as a remote and poor area, has very scarce higher education resources, so the CR of IPE is very small, but it can also maintain a small growth with the economic development which also shows that it has a huge development space, as long as the investment in education is increased, the CR of education will be greatly improved.
Vigorously promoting the construction of IPE in various regions is the key to cultivating high-quality talents, which is also an important measure to strengthen the internal driving force of China’s economic development. Therefore, this article introduces the investment of IPE into the function model of social production, where fuzzy clustering is optimised by using the gravity search method, and the classified data sets of various provinces in China are determined by using the genetic algorithm. Based on the improved fuzzy clustering algorithm, the calculation model of the CR of IPE in different regions is established. The results show that at present, the development of IPE in China is unbalanced among regions, and the average CRs of IPE in A, B and C regions are 8.46%, 5.38% and 1.99%, respectively. Due to the huge gap in economic strength, the CR of the central and western regions is far lower than that of the eastern developed regions, but some of them are rich in educational resources and have great development potential, whose investment on IPE should be increased in the future.
Comparison of CRs of IPE in eastern, western and central regions.
|Central China||Shaanxi||4.27||Eastern China||Shanghai||8.34|
Classification results of provinces.
|A||Sichuan, Zhejiang, Shandong, Guangdong|
|B||Shaanxi, Xinjiang, Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Guangxi, Yunnan, Henan Hunan, Hebei|
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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 Application of improved RBF neural network algorithm in hierarchical management of enterprise 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 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Action of Aut( G) on the set of maximal subgroups of p-groups The internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research 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 sentiment analysis method based on bidirectional long short-term memory networks 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