Research on the construction and reform path of online and offline mixed English teaching model in the internet era

3.1 Student CD based on time-sensitive deterministic input, noise, and gate (TDING) model

To reform the OOM ET model, it is first necessary to construct an accurate algorithm model to conduct CD for students, understand their mastery of knowledge points (KP), and make personalized resource recommendations. The most widely used cognitive diagnostic model in research is the latent classification model [19,20]. However, the hidden impact factors in the potential classification model are not overall. Hence, this study is based on relevant psychological diagnostic techniques, combined with students’ previous KP, and based on potential classification models, presented a TDING model. Figure 1 indicates the algorithm of the TDING model.

Figure 1

TDING model algorithm flowchart.

The TDING model assumes that the target student is u i , and filters redundant data with smaller relationships in view of the basic information of student u i for getting the initial student set US = { u 1 , u 2 , u 3 , … , u m } , test question (TQ) set TS = { t 1 , t 2 , t 3 , … , t n } , and KP set KS = { k 1 , k 2 , k 3 , … , k l } . After that, the students related data in the system is used to construct a related matrix and record it as R m × n , as shown in formula (1).

The KP inspection matrix is constructed by using the KP data labeled by some discipline experts from universities and colleges. The matrix is marked as Q n × l , and the matrix Q is shown in formula (2).

Then, each student u i could get a KP mastery vector (MV), α l → = { α i 1 , α i 2 , α i 3 , … α i l } is set, where α i j = 1 indicates that student u i has KP k j , and α i j = 0 showcases that student does not have KP k j . The TDING model ultimately is for obtaining the student KP mastery matrix A = { α 1 → , α 2 → , α 3 → , … , α m → } , and the initial response situation of the students is defined as shown in formula (3).

where ξ i j = 1 illustrates that student u i has mastered well all the KP examined by TQ t j , whereas ξ i j = 0 indicates that the student u i did not master all the KP examined by TQ t j . In the learning process, students may make certain mistakes and guesses when answering questions. Therefore, the definition of error rate (ER) and guess rate (GR) is shown in formula (4).

where p denotes the probability, s is the ER, and g is the GR. Combining the related formula and matrix, the positive response rate p ( r i j = 1 ∣ α i ) is calculated using the formula shown in formula (5).

The personalized information of students will affect the positive response rate. Combining formula (5) for obtaining the final positive response rate of students is shown in formula (6).

where λ and α serve as constant parameters, parameter β serves as the case of students answering questions t j in history, and parameter T is a time parameter. The TDING model in this study considers that students have a forgetting effect on questions answered in history, and the times they answer questions have a consolidation memory effect. At the same time, both of these effects belong to a function of time. Therefore, the study brings a factor for enhancing the model. If the student answers correctly, the value is 1, otherwise, the value is 0, indicating the times the student answers the TQ. By maximizing the edge likelihood in the formula, obtain the maximum likelihood estimator (MLE) of the gain/loss ER s j ¯ and the MLE of the GR g j ¯ , and ultimately obtain the student’s KP MV estimator α i ¯ . Due to the existence of multiple hidden variables in the TDING model that cannot be directly observed, it is essential to address the parameter estimation for incomplete data. The TDING model is a conditional distribution α i ¯ of response data given a student’s KP MV r i j . Here it is assumed that the student’s response to each question is independent given the attribute vector, so the conditional distribution of r i → is shown in formula (7).

where L is a likelihood function, and the conditional probability distribution of the score matrix R for m students U can be obtained as shown in formula (8).

where A is the KP mastery matrix. To calculate the estimators of guess factors and error factors, the total likelihood function of the response data is given as shown in formula (9).

The MLE of ER and GR obtained by combining the maximum expectation algorithm is shown in formula (10).

where I j k ( 0 ) represents the expected number of students who fully master all the KP examined in the first TQ, and is the expected number of students in the k KP mastery mode. R j k ( 0 ) represents the expected number of students who correctly answer the j TQ in I j k ( 0 ) . The meanings of I j k ( 1 ) and R j k ( 1 ) are similar to those of R j k ( 0 ) and I j k ( 0 ) , except that I j k ( 1 ) and R j k ( 1 ) are the values obtained when the students master all the KP tested in the first TQ. Therefore, the values of I j k ( 0 ) , R j k ( 0 ) , I j k ( 1 ) , and R j k ( 1 ) can be calculated from the estimates, and new estimates of ER s j and GR g j can be obtained. The calculation is repeated until each component converges. The MLE of the loss ER and the MLE of the GR are found. Finally, the formula is combined with the maximum posterior probability algorithm to obtain the student’s KP MV estimator, followed by obtaining the student’s KP mastery matrix A . This process leads to the completion of the diagnosis of the student’s cognitive ability level.

3.2 Recommendation of TR based on the CUMF model

The research combines intelligent algorithms to personalized recommend ETR for students based on the student CD, improving teaching effectiveness, and promoting the reform of OOM ET models. The study combines a Convolutional Neural Network (CNN) with a cognitive diagnostic model built based on TDING to propose a TR recommendation method in view of the Convolutional Unified Probability Matrix Factorization (CUMF) model. Based on multi-layer deep neural networks, CNN has introduced a more effective feature learning component, making it more capable of feature learning. Specifically, it has introduced local displacement-connected convolutional layers and pooling layers before the original fully connected layer [21,22]. The overall hierarchical structure of CNN is shown in Figure 2.

Figure 2

Overall hierarchical structure of CNNs.

The main function of CNN is to reveal the potential features of ETR, obtain implicit feature vectors (IFV) for English tests, and construct implicit feature matrix (IFM) representations of tests with CNN weight parameters for training in JPM DM. The CUMF model combined with the convolutional network is shown in Figure 3.

Figure 3

CNN-CUMF model diagram.

CUMF combines factors such as students’ past answers, knowledge levels, mastery of English test sites, and forgetting effects. Meanwhile, it uses CNN to mine ETR, and through non-linear transformation by CNN, it is incorporated into a JPM DM for forecasting student performance. Finally, combined with the related matrix obtained from the TDING model, personalized ETR is recommended to improve students’ learning efficiency and ultimately improve teaching effectiveness. The CUMF recommendation algorithm is shown in Figure 4.

Figure 4

CUMF recommendation algorithm framework.

The CUMF recommendation algorithm framework first filters out exam information based on English students’ response records and then divides the related information into English word sets through word segmentation. Then, the word is transformed into a word vector (WV) through word embedding technology, and the English WV is used as the input of the CNN. Certain transformations related layers obtain the implicit matrix (IM) of the test with CNN and use the IM of the test as the IM parameter in the JPM DM. Last, through the KP mastery matrix from the TDING model, the test KP correlation matrix from specialists, and the test score matrix (TSM) based on the student exam situation, a random gradient descent algorithm is used to obtain each matrix, and these implicit feature matrices are used to obtain the TSM. The implicit matrices’ dot product operation is used to predict students’ performance in testing ETR. Finally, based on students’ cognitive abilities, whether to recommend video TR is chosen. This study combines CNN with a JPM DM, and presents a DM for convolutional joint probability matrices, as shown in Figure 5.

Figure 5

Convolutional JPM DM.

The prior probabilities of initializing implicit feature matrices U and K follow a Gaussian distribution (GD) with a mean value of 0 and a variance of σ 2 , and the weight probability distribution of convolutional network neurons is shown in formula (11).

where G is a prior probability, U and K are IFM, and W serves as the weight of the convolutional neural network. The probability distribution of the IFV D j from the CNN and the IFM D for Test j is shown in formula (12).

where T j is the WV of the TQ generated by word embedding technology, and ε j is the Gaussian noise. The implicit vector (IV) U i of student i and the IV D j of the TQ j illustrate that the scoring probability r i j of student i on the TQ is respectively distributed and independent of a GD with a mean value of h and a variance of σ A 2 . The related mathematical expression is shown in formula (13).

where I i j R serves as an indicator function (IF). If student i has done KP j , then I i j R = 1 . Or else, I i j R = 0 and h ( x ) are sigmoid functions, that is, the value of U i T Cnn ( W , T j ) is mapped to the range of (0, 1). Similarly, the IFV U i of student i and the IFV K j of KP j , showcase that the grasping α i j of KP j by student i satisfies a GD with an average value of h ( U i T K j ) and a variance of σ A 2 . The related expression for a conditional probability distribution is shown in formula (14).

where I i j A serves as an IF. If student i grasped KP j , then I i j A = 1 , if not, then I i j A = 0 . Similarly, the IFV v of TQ i and the IFV K j of KP j indicate that the association between TQ i and KP j meets a GD with a mean value of h ( Cnn ( W , T j ) T K j ) and a variance of σ Q 2 . The related distribution is shown in formula (15).

where I i j Q serves as an IF. If TQ i examines KP j , then I i j Q = 1 , or else I i j Q = 0 . Combining the above prior probability distribution formula, a posterior probability distribution of the matrix can be obtained, and then the implicit characteristic matrix (ICM) for students, the ICM for TQ, and the ICM for KP can be obtained to further obtain the variance parameter φ A = σ R 2 σ A 2 of the correlation matrix for students’ mastery of KP and the variance parameter φ Q = σ R 2 σ Q 2 of the correlation matrix for KP annotated by experts. Then, by multiplying the IFM of the student and the IFM of the TQ, the student’s score is inferred. Finally, based on this score and students’ grasping of KP, personalized TR can be recommended for students.

4.1 Analysis of students’ cognitive diagnostic efficiency

To ensure the effectiveness of OOM ET models and verify the TDING model’s effectiveness proposed in the study in students’ CD, a comparative experiment was conducted between TDING and classical CD methods. Since the test results of different hardware devices may have large differences, the study was conducted in the same experimental environment, which is shown in Table 1.

The study utilized the publicly available dataset English Language Learner Corpus (ELLC). This dataset is provided by the International Agency for the Teaching of English as a Foreign Language and contains learning data from English learners from different countries and at different stages of learning. The ELLC dataset contains the learning data of more than 10,000 students at different levels of proficiency, ranging from basic to advanced. The data are not only rich in content but also highly diverse and representative because learners come from different countries and cultural backgrounds. The comparative objects include Item Response Theory and Deterministic Inputs, Noise, and Gate (DINA) models. During the experiment, 10, 30, 50, and 70% of the datasets were chosen as test datasets, and commonly utilized evaluation criteria in the industry, namely, Pattern Match Rate (PMR) and Root Mean Square Error (RMSE) indicators, were utilized to detect the modeling effects. PMR is a measure of the predictive accuracy of a model. It evaluates the performance of a model by comparing the similarity between the output patterns predicted by the model and the actual observed data patterns. The higher the PMR value, the better the predictive ability of the model. In cognitive diagnostic models, PMR can effectively reflect the accuracy of the model’s judgment of the learner’s ability level and knowledge mastery and is a key indicator for assessing the effectiveness of the model in actual teaching applications. RMSE is a measure of prediction error. It calculates the square root of the average of the squared values of the differences between the predicted and actual values. The lower the RMSE, the higher the predictive accuracy of the model. The RMSE can visualize the differences between the model predictions and the actual data, which helps to evaluate the accuracy and reliability of the model in detail. The experimental results of different cognitive diagnostic model values under the proportions of each test dataset are shown in Figure 6.

Figure 6

Experimental results of cognitive diagnostic model values. (a) PMR values for each model. (b) RMSE values for each model.

In Figure 6, when modeling students for CD, the PMR value of the TDING model as a whole has increased by 4.664% compared to the other two classical modeling methods, while the RMSE value has decreased by 1.412% compared to the other two modeling methods. The above results indicated that the TDING method significantly enhanced the CD and the diagnostic modeling. To further verify the reliability of the cognitive diagnostic model for students in OOM ET, the study used the Receiver Operation Characteristic Curve (ROC) for estimating the function of the cognitive diagnostic model, as shown in Figure 7.

Figure 7

Performance evaluation of cognitive diagnostic models by ROC. (a) ROC curves of course selection probabilities. (b) ROC curves of different algorithms.

The ROC curve is a graphical presentation of the performance of a classification model, which evaluates the model’s classification ability by comparing the True Positive Rate and the False Positive Rate. In the field of CD, the ROC curve helps to determine the efficacy of the model in distinguishing between different cognitive states (e.g., mastery vs non-mastery), and is an important tool for evaluating the diagnostic accuracy of the model. Figure 7 showcases that compared to the feature selection method of genetic algorithm combined with a light gradient boosting machine, the TDING model has the highest authenticity and can more realistically reflect the actual process of students’ answering questions, thereby improving the accuracy of the cognitive diagnostic model.

4.2 Quality analysis of ETR

To verify the reliability of OOM ET models, the study used multiple public datasets for testing the research recommendation algorithm. Table 2 showcases each dataset.

During the experiment, to conclude the impact of the sparsity on different algorithms, 70, 50, 30, and 10% of all datasets were chosen as test datasets, and the remaining datasets were selected as training datasets. Moreover, this study separated TR into two resources, which are simple and complex based on a difficulty value of 0.6, and conducted a comparison of the recommended effects of various TR. The related effects (F1 value) are illustrated in Figure 8.

Figure 8

Effect of the first parameter on F1 value. (a) The effect of parameter φ _A on simple resource. (b) The effect of parameter φ _A on complex resource.

The F1 value is the reconciled average of Precision and Recall, which is a comprehensive measure of the accuracy of the model. The F1 value takes into account the precision and comprehensiveness of the model and is suitable for the case of the unbalanced dataset. In recommender systems, the F1 value can balance the precision and recall and provide a comprehensive evaluation of the model recommendation effect, especially suitable for evaluating the effectiveness of the TR recommender system. In Figure 8, when students mastered the variance parameter φ A = 0.5 of the KP correlation matrix, the F1 value reached the peak, and the recommendation effect was the best. However, when φ A > 0.5 , the F1 value gradually decreased, which meant that the recommended effect of the CUMF model gradually decreased. The variance parameters φ Q and their related impact (F1 value) are indicated in Figure 9.

Figure 9

Effect of the second parameter on F1 value.

In Figure 9, the solid line serves as the impact of parameter φ Q on the recommendation performance of complex TR models, while the dashed line serves as the impact of parameter φ Q on the recommendation performance of simple TR models. When experts labeled the variance parameter φ Q = 1 of the KP correlation matrix, the F1 value achieved a peak. When φ Q > 1 , the F1 value gradually diminished, which meant that the CUMF model’s effect started to gradually diminish. In summary, the proportion of the test dataset and the difficulty of TR did not affect the results. The F1 value of the CUMF model first grew and diminished as the variance parameters φ A and φ Q gradually increased. In the CUMF model, when the study set other parameters to 0.001, φ A to 0.5, φ Q to 1, and related dimension to 10, the recommended effect was optimal.

4.3 Effect analysis of online and offline English teaching resource recommendation

To analyze the OOM-ET model constructed through research and verify the effectiveness of English resource recommendation, this study recommended three sets of simple teaching resources (STRs) and three sets of complex teaching resources (CTRs) to students in a simulation experiment and compared the CUMF model method with other methods, including user-based CF recommendation method. Also includes considering the deterministic input noise of CD and the gate model (DINA) approach, combined with CD’s (PMF-CD) TR recommendation method, and combined with CD’s JPM (QueRec) CD recommendation method. The recommended experimental results for ETR are shown in Table 3.

Table 3 indicates that when recommending STR, the F1 value of CUMF increased by an average of 11.63% relative to the other algorithms and increased by an average of 1.977% compared to QueRec algorithm as a whole. When recommending CTR, the F1 value grew by an average of 11.54% relative to the other algorithms and increased by an average of 1.877% compared to QueRec algorithm as a whole. As the test sets continued to decrease, the training sets continued to increase, the CUMF model exceeded the four algorithms in recommendation accuracy for STR and CTR. The above data indicate that the CUMF method can significantly enhance recommendation accuracy and effectiveness. The study was conducted by comparing the response time of different algorithms to compare the computational complexity. The results are shown in Figure 10.

Figure 10

Comparison of computational complexity between different algorithms.

In Figure 10, the response time of CUMF is only longer than that of DINA, with an average single response time of 0.991 s, which is shorter than that of QueRec, PMF-CD, and User-Based CF algorithms. Considering the high accuracy brought by CUMF, the study concluded that the optimized computational complexity was acceptable. For testing the effect in the actual environment, the student data were separated into two groups, G1 and G2, G1 using the algorithm proposed in the study, and G2 using traditional algorithms. A comparative experiment was conducted on the response data through a paired sample t-test. Table 4 showcases the results.

Table 4 indicates that there is a dramatic disparity in the pre-test and post-test scores in Group G1, the experimental group, while there is no dramatic disparity in the pre-test and post-test scores in Group G2, the control group. In view of the t-test data results of G1 and G2 groups in Table 4, it showcased that the overall learning effect of G1 group students who use the TR recommended by the CUMF model-based TR recommendation algorithm elaborated by the research institute for autonomous learning is better than that of the control group, namely, G2 group students who only learn through independent search and browsing. Therefore, the effectiveness and feasibility of the proposed TR recommendation algorithm in view of the CUMF model applied in OOM English education models have been confirmed.