The Construction and Application of Rural Teachers’ Educational Research Literacy Indicator System in the Context of Deep Learning

Principal component analysis utilizes the idea of dimensionality reduction, the analysis process is to transform multiple variables into a smaller number of composite variables (principal components), the transformed principal components are not related to each other, are the form of linear combinations of the original variables, so that a large amount of information can be demonstrated through the form of linear combinations, and this information will not be repeated between the variables used to describe the object of the study assumed that there are Z₁, Z₂, ⋯, Z_p A total of P variables, Z=(Z1,Z2,⋯,Zp)t$$Z = {\left( {{Z_1},{Z_2}, \cdots ,{Z_p}} \right)^t}$$ is a P dimensional random variable, Z is made up of hypothesized P variables. Z random vector is assumed, Σ is a covariance matrix of Z and μ is the mean of Z [25]. A linear combination of the original variables is considered and the random vector Z is treated as a linear variation: (1){ F1=μ11Z1+μ12Z2+…+μ1pZp F2=μ21Z1+μ22Z2+…+μ2pZp ⋯⋯ Fn=μml1Z1+μm2Z2+…+μnpZp$$\left\{ {\begin{array}{*{20}{c}} {{F_1} = {\mu_{11}}{Z_1} + {\mu_{12}}{Z_2} + \ldots + {\mu_{1p}}{Z_p}} \\ {{F_2} = {\mu_{21}}{Z_1} + {\mu_{22}}{Z_2} + \ldots + {\mu_{2p}}{Z_p}} \\ { \cdots \cdots } \\ {{F_n} = {\mu_{ml1}}{Z_1} + {\mu_{m2}}{Z_2} + \ldots + {\mu_{np}}{Z_p}} \end{array}} \right.$$

Linear combination F1,F2,⋯,Fm(m≤p)$${F_1},{F_2}, \cdots ,{F_m}\left( {m \leq p} \right)$$ is uncorrelated with the principal component, and the largest variance in linear combination Z₁, Z₂, ⋯, Z_p is F₁, in linear combinations uncorrelated with F₁, F₂ is the largest variance,..., and in linear combinations unrelated to F_lF₂, ⋯, F_m; F_m is the largest variance.

In the use of principal component analysis, the analysis process generally has the following six steps: 1)

Pre-processing of the original variable data for normalization, in the process of statistical analysis, because the original data itself in the nature of certain differences will affect the statistical analysis, the purpose of pre-processing is to eliminate the impact; standardization of the original variable data, after processing the original variable data in the number of levels and the differences in the quantitative outline of the data will be eliminated, and then get the analytical convenience of the Standardized matrix.

And then the selection of principal components, to follow the principle that in the eigenvalue is greater than 1 on the basis of its cumulative contribution rate to reach 80%, the eigenvalue λ₁, λ₂, ⋯, λ_n in the corresponding 1,2,⋯,m(m≤p)$$1,2, \cdots ,m\left( {m \leq p} \right)$$, the number of the final selection of the principal components is m (m is an integer). 4)

The scores of the principal components are calculated, and the initial factor loading matrix is constructed to interpret the principal components. The correlation coefficient Rij=(Fi,Zj)$${R_{ij}} = \left( {{F_i},{Z_j}} \right)$$ between the principal component F_i and the original index Z_j is the factor loading, which can be used to better explain the economic significance of the principal components, indicating the degree of correlation between each variable and the principal component. Assuming that U_ij is the eigenvector corresponding to each eigenvalue, there are: (3)Uij=Rij/λi$${U_{ij}} = {{{R_{ij}}} \bigg/ {\sqrt {{\lambda_i}} }}$$

An expression for each principal component F_i score can then be obtained: (4){ F1=U11Z1+U12Z2+…+U1pZp F2=U21Z1+U22Z2+…+U2pZp ⋯⋯⋯⋯ Fm=Um1Z1+Um2Z2+…+UmpZp(i=1,2,…,m;j=1,2,…,p)$$\left\{ {\begin{array}{*{20}{l}} {{F_1} = {U_{11}}{Z_1} + {U_{12}}{Z_2} + \ldots + {U_{1p}}{Z_p}} \\ {{F_2} = {U_{21}}{Z_1} + {U_{22}}{Z_2} + \ldots + {U_{2p}}{Z_p}} \\ { \cdots \cdots \cdots \cdots } \\ {{F_m} = {U_{m1}}{Z_1} + {U_{m2}}{Z_2} + \ldots + {U_{mp}}{Z_p}} \end{array}\left( {i = 1,2, \ldots ,m;j = 1,2, \ldots ,p} \right)} \right.$$

5)

ZScore_n is the teacher composite score function, which is applied to calculate the composite value of educational research literacy of rural teachers and the resulting results are ranked in descending order. The principal components composite model was calculated by taking the proportion of the eigenvalues of each principal component in the sum of the eigenvalues of the extracted principal components that each principal component occupies in it as weights. The resulting model is shown below: (5)ZScoren=M1F1+M2F2+⋯+MiFi$$ZScor{e_n} = {M_1}{F_1} + {M_2}{F_2} + \cdots + {M_i}{F_i}$$

(i = 1, 2, ⋯, m; n is the number of samples, M; the principal component F; the proportion of the corresponding eigenvalues to the sum of the total eigenvalues of the principal components).

1)

Convergent processing of raw data

The normalization process is carried out in accordance with the following formula: (6)Yj′=1/|Yi−Yi|(i=1,2,…,m)$${Y'_j} = {1 \bigg/ {\left| {{Y_i} - {Y_i}} \right|}}\left( {i = 1,2, \ldots ,m} \right)$$

Where, Yj′$${Y'_j}$$ is the data after the normalization process, Y_i is the original formula indicator data, and Yi¯$$\overline {{Y_i}}$$ is the Y_i average value. 2)

The standardization of the original data

The index value selected in this paper is not comparable because the unit and size of each value are relatively large when the relevant data are selected, so it is difficult to compare, and the original data that are difficult to compare are standardized to achieve the elimination of the differences between different variables caused by the difference in the scale. (7)Zi=(Yi′−Y¯i)/σYi$${Z_i} = \left( {Y_i^\prime - {{\bar Y}_i}} \right)/{\sigma _{{Y_i}}}$$ (8)Yi′¯=EYi′=∑j=1nYij′/n$$\overline {{Y_i}^\prime } = E{Y_i}^\prime = \sum\limits_{j = 1}^n {{{{{Y_{ij}^\prime}}} \bigg/ n}}$$ (9)σYi=DYi′=∑j=1n(Yij′−Yi′¯)2/(n−1)(i=1,2,…,mj=1,2,…,m)$${\sigma_{{Y_i}}} = \sqrt {D{Y_i}^\prime } = {{\sum\limits_{j = 1}^n {{{\left( {{Y_{ij}}^\prime - \overline {{Y_i}^\prime } } \right)}^2}} } \bigg/ {\left( {n - 1} \right)}}\left( {i = 1,2, \ldots ,mj = 1,2, \ldots ,m} \right)$$

In the above equation, Z₁ indicates that the data have been standardized, Y¯1$${\bar Y_1}$$ and σYi$${\sigma_{{Y_i}}}$$ are the mean and variance of Yi′$${{Y_i}^\prime}$$, respectively. In this paper, the data processing, the use of SPSS software to automatically standardize the data, according to the relevant theoretical knowledge of statistics can be known, the data after the standardized treatment to comply with the form of standard normal distribution, the data after the standardized treatment of the later statistics and analysis of the work has a great help.

Artificial neural networks are, after all, a mathematical model of information processing that applies a structure similar to the synaptic connections of the brain, a neural network or neural-like network consisting of a large number of artificial neurons interconnected in a similar way to natural nerve cells. A neural network is an arithmetic model consisting of a large number of nodes (or neurons) and their interconnections, which emphasizes synergy between a large number of neurons and problem solving through learning. Each node represents a specific output function called the excitation function. The weights are the weighted values of the connection signals between two nodes, which is equivalent to the memory of an artificial neural network. The different values of weights and excitation functions determine the different outputs of the network.

A neuron is a nonlinear information processing element with multiple inputs and single outputs, which can be abstracted as a simple mathematical model based on its properties and functions [26].

Its input-output relationship can be described as: (10){ Xj=∑i=1WijXi−θj yj=f(Xj)$$\left\{ {\begin{array}{*{20}{l}} {{X_j} = \sum\limits_{i = 1} {{W_{ij}}} {X_i} - \theta j} \\ {{y_j} = f\left( {{X_j}} \right)} \end{array}} \right.$$

Xi(i=1,2,⋯,n)$${X_i}\left( {i = 1,2, \cdots ,n} \right)$$ is the input signal to the neuron; each input to the neuron has a weighting coefficient Wij(i=1,2,⋯,n)$${W_{ij}}\left( {i = 1,2, \cdots ,n} \right)$$ called the weight value, which represents the connection weights from neuron i to neuron j. Its positive and negative values simulate synaptic excitation and inhibition in biological neurons, and its magnitude represents the different connection strengths of the synapses; and y_j is the output of the jth neuron; f(⋅)$$f\left( \cdot \right)$$ is the excitation function, which determines in which way the j neuron outputs when co-stimulation by the input neuron Xi(i=1,2,⋯,n)$${X_i}\left( {i = 1,2, \cdots ,n} \right)$$ reaches a threshold value; θj denotes the threshold value of the neuron.

The basic principle of the BP network model to process information is: input signal I_i in the input layer, through the intermediate nodes (hidden layer points) act on the output node, after a nonlinear transformation, to produce the output signal O_k, the network training samples include the input vector I and the output expected value T, there is a deviation between the network output value O_k and the expected value T, through the adjustment of the linkage weight w_ji between the input node and the hidden layer node and the linkage weight w_jk between the hidden layer node and the output node and the threshold value, so that the error decreases along the gradient direction. and the linkage weight 8 between the output node and the output node as well as the threshold value, so that the error decreases along the gradient direction, and after repeated learning and training, the network parameters (weights and thresholds) corresponding to the minimum error are determined, and then the training is terminated. The trained neural network can be input to similar samples, train and learn on its own and output information that minimizes the error after nonlinear transformation.

The adjustment formula for the weights thresholds is: (11)wkj(t+1)=Δwkj+wkj(t)=−α∂Ewkj+wkj(t)=αδkHj+wkj(t)$${w_{kj}}(t + 1) = \Delta {w_{kj}} + {w_{kj}}(t) = - \alpha \frac{{\partial E}}{{{w_{kj}}}} + {w_{kj}}(t) = \alpha {\delta_k}{H_j} + {w_{kj}}(t)$$ (12)wji(t+1)=Δwji+wji(t)=−α∂Ewji+wji(t)=ασjIi+wji(t)$${w_{ji}}(t + 1) = \Delta {w_{ji}} + {w_{ji}}(t) = - \alpha \frac{{\partial E}}{{{w_{ji}}}} + {w_{ji}}(t) = \alpha {\sigma_j}{I_i} + {w_{ji}}(t)$$ (13)θk(t+1)=Δθk+θk(t)=−β∂Eθk+θk(t)=βδk+θk(t)$${\theta_k}(t + 1) = \Delta {\theta_k} + {\theta_k}(t) = - \beta \frac{{\partial E}}{{{\theta_k}}} + {\theta_k}(t) = \beta {\delta_k} + {\theta_k}(t)$$ (14)θj(t+1)=Δθj+θj(t)=−β∂Eθj+θj(t)=βδj+θj(t)$${\theta_j}(t + 1) = \Delta {\theta_j} + {\theta_j}(t) = - \beta \frac{{\partial E}}{{{\theta_j}}} + {\theta_j}(t) = \beta {\delta_j} + {\theta_j}(t)$$

where H_j is the output of the hidden layer node, I_i is the input signal from the input node i, w_kj(t) and w_kj(t + 1) are the connection weights between the hidden layer node j and the output layer node k during the two training periods before and after, w_ji(t) and w_ji(t + 1) are the connection weights between the input node i and the hidden layer node j during the two training periods before and after, θ_k and θ_j are the thresholds at the output node k and the hidden layer node j, respectively; α and β are the learning parameters, which are generally taken as 0.1~0.9; δ_k and σ_j are the error signals of output layer node k and hidden layer node j, respectively, which are computed as Eqs: (15)δk=−αE∂Ik=(Tk−Ok)Ok(1−Ok)$${\delta_k} = - \frac{{\alpha E}}{{\partial {I_k}}} = \left( {{T_k} - {O_k}} \right){O_k}\left( {1 - {O_k}} \right)$$ (16)σj=−αE∂Ij=∑δkwkjHj(1−Hj)$${\sigma_j} = - \frac{{\alpha E}}{{\partial {I_j}}} = \sum {{\delta_k}} {w_{kj}}{H_j}\left( {1 - {H_j}} \right)$$

T_k is the target output value of the sample at the output node k; O_k and H_j are the actual output values of the sample at the output node k and the hidden layer node j of the network, respectively, where the hidden layer output is computed as: (17)Hj=f[∑i=1mwjiIi+θj]$${H_j} = f\left[ {\sum\limits_{i = 1}^m {{w_{ji}}} {I_i} + {\theta_j}} \right]$$

M is the number of input nodes and f is the type S activation function: (18)f(x)=11+e−x$$f(x) = \frac{1}{{1 + {e^{ - x}}}}$$

The output layer outputs are summed using linear weighting: (19)Ok=∑j=1swkjHj+θk$${O_k} = \sum\limits_{j = 1}^s {{w_{kj}}} {H_j} + {\theta_k}$$

Since the desired output T and the actual output O do not coincide, an error arises, which is usually expressed in terms of variance, calculated as: (20)E=12∑t=1q(Tt−Ot)2$$E = \frac{1}{2}\sum\limits_{t = 1}^q {{{\left( {{T_t} - {O_t}} \right)}^2}}$$

The initial weights and thresholds of the BP neural network are randomly assigned, and the determination of the final weights relies heavily on the selection of the initial weights, but the BP neural network is slow to converge, is very easy to fall into the local extreme point, and is extremely sensitive to the network’s initial weights, its own learning rate, and momentum and other parameters, which need to be constantly trained in order to be gradually fixed, and over-training leads to the phenomenon of overfitting, thus affect the generalization ability of the network.

PSO, as a population theory optimization tool, combines PSO with BP neural network and uses PSO algorithm to optimize the weights and thresholds of the neural network, which can improve the performance of the BP neural network. PSO algorithm guides the optimization search through the group intelligence generated by the cooperation and competition among the particles in the population. The optimized algorithm has fast convergence speed, high robustness, strong global search ability, and the search efficiency is improved.

The process of using PSO algorithm to adjust the weights of BP neural network is: first of all, the PSO algorithm is used to replace the gradient descent method in the BP neural network to repeatedly optimize the combination of weights and parameters of the BP neural network model, until the fitness of the solution is no longer reduced, based on this, then use the BP neural network to further accurately optimize the parameters of the network obtained above until the search for the optimal parameters of the network, which can be obtained. The precise optimal parameter combination.

The PSO-BP model is a three-layer structure, which is the input layer, the hidden layer and the output layer. The number of neurons in the output layer is set to 1. In this paper, according to the empirical formula, it is concluded that the number of nodes in the hidden layer can be initially determined as 5-13 layers, and then the number of neurons in the hidden layer is finally determined according to the method of trial and error [27].

The specific design steps to realize the combination of particle swarm and BP neural network are as follows: 1)

Determine the number of population particles

Based on the research experience of experts and scholars, when using particle swarm optimization algorithm to solve general function optimization problems, the number of particles is generally taken as 10, so the number of particles in the PSO-BP neural network model in this paper is 10.

Where Y₁ is the number of nodes in the single implicit layer, Y₂ is the number of nodes in the output, A is the number of nodes in the input layer, according to the research design of the college students’ physical health evaluation index system, there are a total of 10 indexes, and the output is a comprehensive evaluation score, then A = 10, Y₁ = 5 − 13, and Y₂ = 1, which is to get the dimensions of the individual particles of each particle swarm of each particle is n = 61 − 157. 4)

Determine the initial position of each particle of the particle swarm

Since the dimension of each particle is 61-157, the position matrix of each particle has 61-157 elements, and according to experience, the value of each element can be between [−1.5,1.5]$$\left[ { - 1.5,1.5} \right]$$, that is, the lower limit of the position is -1.5 and the upper limit is 1.5.

Where Y_rj is the desired output in the training dataset and D_ij is the actual output of the node during training.

The PSO-BP modeling process is as follows: 1)

Establish the number of neurons in the three-layer structure of the BP neural network

In Equation (26), k is the current iteration number, and f(Pk(i))$$f\left( {P_k^{(i)}} \right)$$ is the fitness of the global optimum of the ird iteration. 8)

Determine whether to meet the conditions for iteration stopping

If the error of the algorithm reaches the preset accuracy or the maximum number of iterations, the algorithm converges, and the weights and thresholds of each dimension in the global optimal value P_g of the last iteration are the optimal solution; if the number of iterations does not reach the maximum, the algorithm returns to step (4) and continues to iterate, otherwise, the algorithm is terminated.

The flowchart of PSO-BP model is shown in Fig. 1.

Figure 1.

Flow chart of PSO-BP model

The questionnaire research was conducted by forwarding QR codes or links to rural primary and secondary school teachers on staff in a certain province to distribute questionnaires respectively, covering 14 cities. The questionnaire consists of three parts, the first part is the basic personal information of rural primary and secondary school teachers, including gender, age, teaching age, education, teaching subjects, title, the region where the school is located and the basic situation of scientific research, etc. The second part is about the basic situation of scientific research carried out by the school, including the opportunities for teachers to participate in scientific research training, and the form and frequency of scientific research activities carried out by the school. The third part consisted of a series of questions prepared in the form of a five-point Likert scale.

A total of 1850 valid questionnaires were returned. The average age of the research sample was 38.67 years old, with an average of 15.24 years of teaching experience, and the subjects taught covered fourteen subjects, including language and mathematics, currently carried out in primary and secondary schools, with the survey covering primary and secondary schools of all levels and types in villages, townships and counties.

In this study, the Cronbach’s alpha coefficient and KMO value of the data analyzed using SPSS 26.0 software were 0.962 and 0.966 respectively, indicating that the data were well suited for factor analysis, which was then standardized on the data from the observation points and then factor analysis was done. The total variance explained is shown in Table 1.

Three factors with eigenvalues greater than 1 were extracted and the cumulative contribution of the three factors reached 80.332%.

The factor loadings of the 26 original variables on the three factors were obtained after a quadratic maximum rotation. The rotated component matrix is shown in Table 2.

The results showed that Factor 1 governed 11 primitive variables such as literature review ability, Factor 2 governed 9 primitive variables such as awareness of research for teaching and learning, and Factor 3 governed 6 primitive variables such as respect for the subject of the study. Accordingly, the three factors were named, research ability factor, research awareness factor and research ethics factor.

Based on the results of the above data analysis, it was determined that the evaluation indexes of rural teachers’ scientific research literacy consisted of three dimensions and 26 indexes, and the weight assigned to each index was obtained through calculation, and the results are shown in Table 3. It can be seen that the indicator with the highest weight value is the ability to analyze information, with a weight of 0.092. This was followed by the willingness to become a research teacher with a weight of 0.052.

In the experiments, in order to reduce the influence of the initial parameters on the performance of the algorithms, the settings for the same parameters are guaranteed to be the same. Because several algorithmic models for comparison are based on BP neural network, the parameters for BP neural network are set according to the previous section.

After setting the parameters of each model, the preprocessed sample data are input into GA-BP model, SSA-BP model, PSO-BP model and BP model for training and testing respectively. First, the training samples were input into the four models for training, and after the training was completed, the testing stage was entered, and after several iterations, the results of comparing the evaluation values of the samples in the test set of each model with the real values were obtained, as shown in Fig. 4.

Figure 4.

The evaluation results of the test sample were compared with the real value

Considering the characteristics of neural network algorithms and intelligent optimization algorithms that the results of each run are different, the four algorithm models are run 30 times, and the experimental results of the performance evaluation indexes of the different models are averaged to compare the data, as shown in Table 4.

Comprehensive Figure 4 and Table 4 show that the evaluation accuracy of the PSO-BP algorithm proposed in this paper is significantly higher than the basic SSA-BP algorithm, GA-BP algorithm and traditional BP algorithm, and the value of the correlation coefficient R² is closer to 1 than that of the other three algorithms, which verifies that the model can be better applied to the problem of evaluating the scientific research literacy of rural teachers in education.

By selecting the Rastrigrin test function to set different population sizes and iteration times, the optimal population size and iteration times that enable the PSO algorithm, SSA algorithm and GA-BP algorithm to reach the optimal fitness value are finally obtained.

In order to further test the superiority of PSO-BP algorithm, the best parameters under the optimal fitness of GA-BP algorithm, SSA-BP algorithm and PSO-BP algorithm, respectively, are selected, and their algorithmic performance is analyzed through experimental comparison. Similarly, the preprocessed sample data are input into GA-BP model, SSA-BP model, PSO-BP model and BP model respectively, and after many iterations, the evaluation value of each model is obtained and compared with the real value, and the results are shown in Figure 5.

Figure 5.

Test results based on optimal population size and iteration number

The GA-BP model, SSA-BP model and PSO-BP model were set to the optimal population size and the number of iterations, respectively, and since the three algorithmic models run for too long in the case of the optimal population size and the number of iterations, the GA-BP model, the SSA-BP model and the PSO-BP model were run for 20 times, and the experimental performance evaluation indexes of each model were calculated as the The average of the result data is used to analyze and compare the performance of these models, as shown in Table 5.

As can be seen from the comparison between the evaluation values of the test set samples and the true values in Figure 5, the PSO-BP evaluation model has a better evaluation effect. Combined with Table 5, it can be seen that although the PSO-BP algorithm model is under the optimal population size and iteration number, the PSO-BP model designed in this paper is significantly higher than the SSA-BP model, the GA-BP model and the traditional BP model from the point of view of evaluation accuracy, which further proves the superiority of the PSO-BP algorithm proposed in this paper.

In order to analyze the PSO-BP model more accurately, the regression analysis and relative error of the model evaluation value and the expected output value of the sample data of the test set of the PSO-BP model are selected and analyzed, as shown in Figure 6 and Table 6, respectively. Among them, Fig. 6 (a) to (d) are the results in different sample cases, respectively.

Figure 6.

Regression analysis of model evaluation value and expected output value

From the regression analysis of the actual output value of the network and the expected output value in Fig. 6, it can be seen that the regression coefficient of the PSO-BP model is very close to 1, which indicates that the evaluation of the PSO-BP model is very good.

From the results of the relative error comparison between the model output value and the real value of the test set samples in Table 6, it can be concluded that the PSO-BP evaluation model has a small error, and the results of the grade division also match completely, which also shows that the model’s comprehensive evaluation score of the rural teachers’ education and research literacy is almost the same as that of the actual teacher’s literacy, and it has a certain degree of accuracy and feasibility, and it further proves that this model can be used in the evaluation study of the rural teachers’ education and research literacy. It further proves that this model can be used in rural teachers’ education and research literacy evaluation research.

Five rural teachers from different districts and subjects were selected and the model was applied to evaluate their educational research literacy of rural teachers. The results are shown in Table 7. The evaluation results of the five teachers outputted by the model are 52.8981, 50.2208, 72.8602, 66.2254 and 73.3937, and the evaluation grades are basically consistent with the actual situation of the teachers. It can be considered that the model in this paper has met the design expectations.