A Study of Goal Motivation Strategies Based on Dynamic Planning Methods to Enhance the Effectiveness of Public English Teaching in Universities

Learner learning data generated in online education is usually viewed as a specified sequence of learning, with the answering situation denoted by x_t, where x_t is described as a binary x_t = {e_t, a_t}, e_t denotes the question answered at the moment of t, and a_t denotes the corresponding answering result. In general, a_t takes the binary value 0 or l, indicating whether the question was answered correctly or not.

The knowledge tracking problem is to track and analyze the entire learning process by modeling the learning sequence {x1,x2,x3,⋯,xt}$$\left\{ {{x_1},{x_2},{x_3}, \cdots ,{x_t}} \right\}$$ in chronological order and predicting the performance of the answer at the next moment x_t+1. Define K as the set of knowledge points, E as the set of exercises, and k_t ⊆ K denotes the set of knowledge points involved in the exercises e_t. Matrix M^K(d_k × |K|) represents the embedded representation of all |K| knowledge points, and each d_k column vector represents the embedded representation of one of the knowledge points. Matrix Miv(dv×|K|)$$M_i^v({d_v} \times |K|)$$ represents the embedding matrix of the student’s knowledge point mastery at the end of the t moment of learning, while matrix MiFV(dv×|K|)$$M_i^{FV}({d_v} \times |K|)$$ represents the embedding matrix of the student’s knowledge point mastery before the start of the t moment of learning. Matrix MiFV$$M_i^{FV}$$ is obtained from matrix Mi−1v$$M_{i-1}^{v}$$ by forgetting process. Definition level_t is the student’s knowledge mastery at the end of the tth moment of learning, which is represented by a number between (0, 1), where 0 means no mastery at all and 1 means full mastery.

The knowledge tracking model in this paper, whose whole knowledge tracking process not only focuses on the answering situation under the time series, but also combines factors such as the difficulty of exercises, answering intervals, and answering cycles. The model mainly consists of five modules: weight calculation, forgetting processing, learning simulation, result prediction and knowledge level output, and uses LSTM network for modeling, which finally leads to a more accurate prediction result [29].

The role of weight calculation is to compute the weights associated with the exercise questions and the corresponding knowledge points. The inputs to the module are the student’s current exercise topic e_t and the set of knowledge points covered by the topic k_t. e_t is then multiplied with the embedding matrix A(d_k × |E|) to obtain a d_k-dimensional exercise embedding vector v_t. The knowledge point embedding vector matrix is N_t, where each d_k-dimensional vector represents a knowledge point embedding vector. The inner product of the exercise embedding vector v_t and the covering knowledge point embedding vector N_i(i) is computed first, and then the inner product is computed by the Softmax function to obtain the associated weight vector w_t of the exercises and knowledge points, i.e.: 1wt(i)=Softmax(vtTNt(i))$${w_t}(i) = {\text{Softmax}}(v_t^T{N_t}(i))$$

The act of forgetting occurs immediately after the act of learning, and the rate of forgetting slows down gradually. The theory of the forgetting curve shows that students’ forgetting of knowledge is mainly influenced by two aspects: the number of repetitions of learning and the time interval between two learning sessions. In the process of knowledge tracking, there is not only the learning process, but also the forgetting process. The present study proposes four factors for forgetting behavior: the time interval between repetition of the same knowledge point (RK), the time interval from the last learning (RL), the number of repetitions of the same knowledge point (KT), and the degree of mastery of the knowledge point (KM).

Since the forgetting behavior is carried out with respect to the students’ knowledge mastery, the matrix of the students’ forgetting factors regarding each knowledge point is obtained first. First, RK, RL and KT are combined to obtain C_t(i) = [RK(i), RL(i), KT(i)], which represents the first three factors affecting the forgetting process of students on knowledge point i, and then the vector C_i(i) of each knowledge point is combined to obtain the matrix . The student’s mastery matrix of the knowledge point is denoted by Mi−1v$$M_{i-1}^{v}$$, which is the fourth factor of forgetting, KM. C_t is combined with KM to obtain the matrix Ft=[Mi−1V,Ci]$$F_t=[M_{i-1}^{V},C_i]$$, which represents the four factors affecting the forgetting.

To perform the forgetting process, the knowledge mastery state matrix of the previous moment is erased, and then the knowledge mastery matrix is updated. The main structure of the forgetting module is shown in Figure 1.

Figure 1.

Forgetting module structure

The student’s forgetting factor F_i(i) for knowledge point i is converted into a forgetting vector fe_i(i) by a sigmoid function: 2fet(i)=Sigmoid(FETFt(i)+bfe)$$f{e_t}(i) = {\text{Sigmoid}}(F{E^T}{F_t}(i) + {b_{fe}})$$

The fully connected layer weight matrix FE is of the shape of (d_v + d_c) × d_v and the bias vector b_fe is d_v-dimensional.

The students’ forgetting factors F_t(i) for the knowledge points i are then converted into update vectors fu_t(i) by a Tanh function: 3fut(i)=Tanh(FUTFt(i)+bjα)$$f{u_t}(i) = \operatorname{Tanh} (F{U^T}{F_t}(i) + {b_{j\alpha }})$$

The weight matrix FU is in the shape of (d_v + d_ó) × d_τ and the bias vector b_fu is d_v-dimensional.

The student’s knowledge mastery state matrix Mi−1v$$M_{i - 1}^v$$ is then updated based on the obtained forgetting and updating vectors to obtain matrix MiFV$$M_i^{FV}$$: 4MtFV(i)=Mt−1V(i)(1−fet(i))(1+fut(i))$$M_t^{FV}(i) = M_{t - 1}^V(i)(1 - f{e_t}(i))(1 + f{u_t}(i))$$

The forgetting layer was processed to get the knowledge mastery matrix of the students before the start of this study MiFV$$M_i^{FV}$$.

The main role of the learning simulation module is to update the knowledge mastery matrix MiFV$$M_i^{FV}$$ of the student before starting this study, generate the knowledge mastery matrix MiV$$M_i^V$$ at the end of the study, and construct a model of the student’s learning behavior based on the results of the student’s answers. As an input is the result of the student’s answer at moment t, which is represented by binary group (e_t, a_t). Multiply the binary group (e_t, a_t) with the answer result embedding matrix B(d_υ × 2|E|) to obtain the d_v-dimensional answer result embedding vector r_t. Then the answer result embedding vector r, with the knowledge point weight vector related to the exercise w_i, is used as an input to update the student’s knowledge mastery state through the LSTM network to complete the modeling of the learning behavior, that is: 5MiV(i)=LSTM(ri,wi(i)MiFV(i))$$M_i^V(i) = LSTM({r_i},{w_i}(i)M_i^{FV}(i))$$

In this study, the difficulty of the exercise is represented by a Tanh function calculation, i.e.: 6dt+1=Tanh(WDTvt+1+bD)$${d_{t + 1}} = \operatorname{Tanh} (W_D^T{v_{t + 1}} + {b_D})$$

Where: W_D and b_D denote the weight vector and bias vector in the fully connected layer, respectively.

The main purpose of the result prediction module is to predict the student’s performance the next time he/she answers question e_t+1 based on his/her knowledge mastery matrix. The knowledge mastery matrix is first updated to obtain the knowledge mastery matrix Mi+1FV$$M_{i + 1}^{FV}$$ at the next start of the study, and then the probability of answering e_i+1 correctly is predicted. The weighted sum of the knowledge point related weights w_t+1 and the knowledge mastery matrix Mt+1FV$$M_{t + 1}^{FV}$$ is used to obtain the weighted mastery embedding vector m_t+1 for the knowledge points related to the exercise: 7mt+1=∑i=1Kwt+1(i)Mt+1FV(i)$${m_{t + 1}} = \sum\limits_{i = 1}^K {{w_{t + 1}}} (i)M_{t + 1}^{FV}(i)$$

Then vector m_t+1, vector v_t+1 and vector d_t+1 are combined to get the new vector [m_t+1, v_t+1, d_t+1] and it is fed into the Tanh function to get: 8ht+1=Tanh(W1T[ mt+1,vt+1,dt+1]+b1)$${h_{t + 1}} = \operatorname{Tanh} (W_1^T\left[ {\begin{array}{*{20}{c}} {{m_{t + 1}},{v_{t + 1}},{d_{t + 1}}} \end{array}} \right] + {b_1})$$

Where: W₁ and b₁ denote the weight and bias vectors in the fully connected layer, respectively.

Finally, the obtained vectors are input into the Sigmoid function to obtain the probability p_t+1 that the student will answer question e_t+1 correctly: 9pt+1=Sigmoid(W2Tht+1+b2)$${p_{t + 1}} = {\text{Sig}}\operatorname{moid} (W_2^T{h_{t + 1}} + {b_2})$$

where: W₂ and b₂ denote the weights and bias vectors in the fully connected layer, respectively.

The main purpose of the Knowledge Level Output Layer is to output the student’s mastery of each knowledge point at the end of the study. This section takes as input the knowledge mastery matrix of the student at the end of the study and outputs a K-dimensional knowledge mastery level vector level_t. The mastery level of a knowledge point is represented by a number between (0, 1).

In the knowledge level output layer, only the student’s comprehensive mastery of the knowledge point is required, and here the unit vector δ_i = (0, 0, ⋯, 1, ⋯, 0) is used as the weight vector, where the value at the i-dimensional position is l.

Utilization: 10Miv(i)=δiMiv$$M_i^v(i) = {\delta_i}M_i^v$$

Extract the embedded vector of students’ mastery level of knowledge point i. Then use Eqs. (10) and xi(i)=Tanh(WiT[MiV(i),0]+bi)$${x_i}(i) = \operatorname{Tanh} (W_i^T[M_i^V(i),0] + {b_i})$$ to obtain the students’ knowledge mastery level, i.e: 11leveli(i)=Sigmoid(W2Txt(i)+b2)$$leve{l_i}(i) = Sigmoid(W_2^T{x_t}(i) + {b_2})$$

Where: W₁, b₁, W₂, b₂ Same settings as in Eq. (8) and Eq. (9). 0 vector is used to complement the vector dimension and has no practical meaning.

The general framework of the RL4ALPR model is shown in Figure 2. Assuming that the length of the learning path is N, i.e., the recommendation is divided into a total of N time step, next, the model details are explained in terms of t time steps.

Figure 2.

RL4ALPR framework

RL4ALPR is divided into the following four sub-modules: knowledge level modeling (FDKT-ED), candidate learning item screening (CN), reinforcement learning recommender (A2C), and reward computation. At each time step, FDKT-ED explores the learner’s potential knowledge level based on his/her historical interactions. CN filters a set of candidate learning items based on the learning items answered by the learner in the previous time step in a prerequisite graph, which serves as the action space for A2C. A2C provides the learner with the learning items to be answered. The reward is passed to A2C for improving the recommendation strategy.

The path generation process is modeled as a Markov decision-making process. At time step t, the state vector s_t = y_t ⊕ T composed of learner’s knowledge level y_t and learning objective T is used as the input of the policy network π(a ∣ s; θ), and the function of the policy network π(a ∣ s; θ) is to recommend a learning item k_t as an actor according to the current policy, and its output is a vector, and each dimension of the vector represents the probability that each learning item is selected, and then a learning item k_t is randomly selected in the set of candidate learning items screened out by CN according to the ε − greedy strategy. The learner’s answers to k_t generate new interaction records, and the environment generates new levels of knowledge y_t+1 and new states s_t+1 based on the learner’s interaction records. The value network v(s; w) is used as a critic for evaluating the action, i.e., the recommended learning item, with inputs as vectors s_t and outputs a scalar representing the predicted future cumulative discounted rewards, i.e., the payoffs, which are used to evaluate how good or bad the current recommended learning item k_t is and to improve the strategy π(a ∣ s; θ) for selecting the recommended learning item. The degree of change in the learner’s level of knowledge acquisition at the t time step is considered as a reward r_t for updating the parameters θ and w of the strategy network π(a ∣ s; θ), and the value network v(s; w). Each time step in the recommendation process generates a trajectory (s_t, k_t, r_t, s_t+1).

A learner’s state of mastery of a knowledge point is unobservable, but it is crucial for subsequent recommendations, because only by knowing the learner’s current state can we provide him/her with a learning program that matches his/her situation. A knowledge tracking task is defined as a task that explores a student’s state of mastery of each knowledge point based on his/her past learning activities, and can be used for knowledge level modeling and predicting the learner’s performance on the next learning item. In this paper, the deep knowledge tracking model (FDKT-ED) that incorporates the difficulty of exercises and forgetting behaviors as previously mentioned is used for knowledge level modeling.

Due to the complexity of the logical relationships between knowledge points, this paper designs a cognitive navigation algorithm based on a central node on the prerequisite graph for quickly filtering candidate nodes related to the central node. The set of learning items represented by the candidate nodes is the action space of the recommender on which the policy network in the recommender selects a learning item. The set of candidate learning items can be filtered to avoid recommending learning items that violate the logic of human cognition, and at the same time, it can reduce the search space of the policy function in the intelligent body, which serves to accelerate convergence. Given the precondition graph G, learning objective T, center node k_c, and hop count n. At each time step, the center node is the knowledge point contained in the learning item recommended to the learner at the previous time step. The time complexity of the cognitive navigation algorithm is related to the size of the precondition graph G and the number of hops n, i.e., the time complexity of the algorithm is O(|G|⋅n)$$O\left( {\left| G \right| \cdot n} \right)$$.

The role of reinforcement learning A2C algorithm [30] is to select the next moment action based on the current state, i.e., according to the learner’s current level of mastery of each knowledge point possessed by the learner, it recommends the learning items that need to be answered at the next moment, and the structure of the A2C algorithm is shown in Fig. 3.

Figure 3.

A2C structure

The reinforcement learning A2C algorithm is mainly composed of two parts, the policy network π(a ∣ s; θ) and the value network v(s; w), both of which are forward fully connected neural networks. Strategy network π(a ∣ s; θ) is an approximation to the strategy function π(a ∣ s), which controls the intelligent body to select the action a that interacts with the environment, i.e., recommending the learning item k_t, and uses the Softmax activation function to output a vector, the value of each dimension of which represents the probability that the learning item will be selected, and then randomly selects the learning item k_t according to the probability by using the ε − greedy strategy. Value network v(s : w) is an approximation to the state value function V_π(s), which serves the purpose of evaluate how good or bad the current state s is, outputting a scalar. In contrast to the action value function q(s, a; w) in actor-critic, v(s; w) it depends only on the state s and is independent of the action a and thus v(s; w) easier to train.

The A2C algorithm uses the strategy gradient algorithm with baseline to update the parameters θ of the strategy function in the actor, which can make the updated strategy have smaller variance and converge faster. The TD algorithm is used to update the parameters w of the value function in the criterion, and the parameters are usually updated using the TD algorithm with Multi-StepTDTarget because of the large amount of noise generated by the single-step update.

At each moment t during the learning path recommendation process, after observing the current state s_t, according to the policy network π(·|s_t; θ_t), the intelligent body uses a ε − greedy policy to randomly sample an action a_t, i.e. a learning item k_t, which is answered by the learner to k_t, and the environment gives a new state s_t+1 and reward r_t, to obtain a trajectory (s_t, k_t, r_t, s_t+1) at the moment of t. After that, s_t+1 will serve as an input for π(·|s_t+1; θ_t) to re-calculate a new probability of the distribution of the actions, i.e. the probability of each learning item is recommended a new probability, and then based on this probability a random sampling is done to get the learning item kt+1˜$$\widetilde {{k_{t + 1}}}$$, kt+1˜$$\widetilde {{k_{t + 1}}}$$ which does not need to be answered by the learner, and is sampled out kt+1˜$$\widetilde {{k_{t + 1}}}$$ in order to update the parameters θ and w in the strategy network and the value network.

After observing the m trajectories {(st+i,kt+i,rt+i,st+1+i)}i=0m−1$$\{ ({s_{t + i}},{k_{t + i}},{r_{t + i}},{s_{t + 1 + i}})\}_{i = 0}^{m - 1}$$ within the period from the moment t to the moment (t + m − 1), the Multi-step TD Target is calculated first, as shown in Equation (12): 12mTDTt=∑i=0m−1γi⋅rt+i+γm⋅v(st+m;w)$$mTD{T_t} = \sum\limits_{i = 0}^{m - 1} {{\gamma^i}} \cdot {r_{t + i}} + {\gamma^m} \cdot v({s_{t + m}};w)$$

where γ is the discount rate. TD Error is calculated using equation (13): 13δt=v(st;w)−mTDTt$${\delta_t} = v({s_t};w) - mTD{T_t}$$

The parameters θ of the policy network π(k_t ∣ s_t; θ_t) are updated using the policy gradient algorithm, and the derivation of the policy network π(k_t ∣ s_t; θ_t) is performed using Equation (14): 14dθ,t=∂lnπ(kt|st;θt)∂θt$${d_{\theta ,t}} = \frac{{\partial \ln \pi ({k_t}|{s_t};{\theta_t})}}{{\partial {\theta_t}}}$$

Update parameter θ using gradient ascent as shown in equation (15): 15θt+1=θt−β⋅δt⋅dθ,t$${\theta_{t + 1}} = {\theta_t} - \beta \cdot {\delta_t} \cdot {d_{\theta ,t}}$$

The parameter w of the value network v(s : w) is updated using the TD algorithm with Multi-Step TD Target, which is derived for the value network v(s_t : w), as shown in Equation (16): 16dw,t=∂v(st;w)∂wt$${d_{w,t}} = \frac{{\partial v({s_{t;w}})}}{{\partial {w_t}}}$$

Use Equation (17) to update parameter w: 17wt+1=wt−α⋅δt⋅dw,t$${w_{t + 1}} = {w_t} - \alpha \cdot {\delta_t} \cdot {d_{w,t}}$$

where δ_t · d_w,t is the gradient of the loss function, and the loss function is shown in Equation (18): 18Loss(w) = 1m∑i=0m−1[v(st;w)−mTDTt]2 = 1m∑i=0m−1δt2$$\begin{array}{rcl} \mathcal{L}oss(w) &=& \frac{1}{m}\sum\limits_{i = 0}^{m - 1} {{{[v({s_t};w) - mTD{T_t}]}^2}} \\ &=& \frac{1}{m}\sum\limits_{i = 0}^{m - 1} {\delta_t^2} \\ \end{array}$$

The Monte Carlo approximation calculation g(k_t; θ) is used in updating the policy network as shown in Equation (19): 19g(kt;θ) ≈ ∂lnπ(kt|st;θ)∂θ⋅[∑i=0m−1γi⋅rt+i+γm⋅v(st+m;w)−v(st;w)]−δt = ∑i=0m−1γi⋅rt+i+γm⋅v(st+m;w)−v(st;w) = mTDTt−v(st;w)$$\begin{array}{rcl} g({k_t};\theta ) &\approx &\frac{{\partial \ln \pi ({k_t}|{s_t};\theta )}}{{\partial \theta }} \cdot \left[ {\sum\limits_{i = 0}^{m - 1} {{\gamma^i}} \cdot {r_{t + i}} + {\gamma^m} \cdot v({s_{t + m}};w) - v({s_t};w)} \right] - {\delta_t} \\ &=& \sum\limits_{i = 0}^{m - 1} {{\gamma^i}} \cdot {r_{t + i}} + {\gamma^m} \cdot v({s_{t + m}};w) - v({s_t};w) \\ &=& mTD{T_t} - v({s_t};w) \\ \end{array}$$

After the execution of each action in a reinforcement learning algorithm, the environment provides an immediate reward r_t to guide the generation of the next action. For the learning path recommendation problem, when the recommended learning item is appropriate for the current learner and is beneficial to increase his/her knowledge level, the reward should encourage this behavior and vice versa should penalize this behavior. Therefore, the reward function is defined as the degree of change in the learner’s mastery level of the target knowledge point after answering the recommended learning item. At each time step in the recommendation process, the reward function is set as follows: 20rt=∑(yt+1,k−yt,k)$${r_t} = \sum {({y_{t + 1,k}} - {y_{t,k}})}$$

where k denotes the index of the knowledge point included in learning objective T, and y_t,k denotes t the learner’s mastery of the knowledge point k at the moment.

Most knowledge-tracking models indirectly measure the accuracy of knowledge state modeling through the accuracy of students’ future performance prediction on their answers. Therefore, the AUC and F1-Score of the FDKT-ED model proposed in this paper are compared with the following seven baseline models in the task of predicting students’ future performance in a public English course at a university on two online publicly available datasets, ASSIST15 and ASSISTO9: 1)

DKT: This model is a single-state knowledge tracking model which utilizes RNN to track students’ knowledge states.

The experimental results of the 8 models on the 2 datasets are shown in Table 1. From the results in Table 1, it can be seen that: 1)

Compared with the DKT model, the DKVMN model improved the AUC and F1-Score values by an average of 7.10% and 7.74% on the ASSIST15 dataset and ASSIST09 dataset, respectively. This is due to the fact that the DKT model fuses the knowledge states of all concepts in a single vector, whereas the DKVMN model is able to model finer-grained knowledge states (i.e., the knowledge states of multiple potential concepts).

Visualization of the evolution of the knowledge state was manipulated: first, a sequence of historical question-answering interactions of 2 students was selected from the ASSIST15 dataset. Subsequently, knowledge tracking was performed for each of these 2 sequences using the FDKT-ED model. Finally, the knowledge states were visualized. The visualization results of the knowledge state changes of the 2 students are shown in Figure 4, where Figures (a) and (b) represent the heatmaps of the knowledge state changes of the 1st and 2nd students, respectively. The data in the heatmap color blocks were rounded and converted to retain 2 valid decimals.

Figure 4.

Visualization of knowledge state change of two students

From Figure 4(a), it can be seen that when a student completes the exercise about Concept C₂₄, there is a change in that student’s state of knowledge about Concept C₂₄, and a change in the state of knowledge about other knowledge concepts that have a learning-transfer relationship with Concept C₂₄, such as Concept C₅₁ and Concept C₆₄. At the same time, the student’s state of knowledge does not undergo a sudden change due to a momentary correct or incorrect answer, but is smoothly updated. For example, when a student answered four consecutive exercises about Concept C₆₃ correctly from Time Step 3 to Time Step 6, the student’s mastery of Concept C₆₃ also increased only from 0.6 to 0.8. When the student answered the exercises about Concept C₉₆ incorrectly at Time Steps 10 and 11, the student’s mastery of Concept C₉₆ changed by less than 0.1 (from 0.58524637 to 0.55741926 to 0.54124584). The change in the state of knowledge for the 2nd student was similar to the change in the state of knowledge for the 1st student.

1)

Experimental dataset

The experimental dataset used in this section is from junyiacademy.org, which consists of a knowledge graph and more than 12 million learner logs of university public English. Each record in the learner log contains information about a learner, including user ID, the name of the concept involved, session 1D, the answer to the exercise, and a timestamp. Each exercise can be mapped to a node in the knowledge graph based on the concept name. Each exercise involves only one concept. Those records with the same session ID represent that they come from the exercise data of the same learner in a learning phase.

1)

Cognitive Enhancement Evaluation Based on Environmental Modeling

According to the statistics, the median number of exercises included in a single learning stage is 25, and the length of the paths to be recommended for learning public English at university is uniformly set to 25. The average cognitive state enhancement of the paths recommended by all the models to the learners, E_p, is shown in Table 2.

As can be seen from Table 2, the proposed RL4ALPR model in this paper performs the best, with its E_p given by the environment models KSE and KEE reaching around 0.35 and 0.41, respectively. More specifically, by modeling the cognitive state, it beats CN-Random, GRU4Rec and KNN, and by filtering and recommending candidate learning items on the knowledge structure, it achieves better results than DQN, MC-10 and MC-5. By organically combining cognitive states and knowledge structures and providing immediate rewards for behavioral guidance to learners, RL4ALPR outperforms Cog. Further, it can be found that methods with knowledge structures perform better than those without in KSE, which suggests that knowledge structures have an impact on the effectiveness of recommended learning paths. It can also be found that in KEE, GRU4Rec outperforms all methods except RL4ALPR without explicit modeling of cognitive state and knowledge structure, which suggests that the simple introduction of cognitive state and knowledge structure does not necessarily guarantee an improvement in the effectiveness of recommendations. Overall, unified modeling of cognitive structures including cognitive states and knowledge structures is necessary in adaptive learning, but how to model and apply it in the recommendation process is challenging.

Figure 5.

Logical evaluation results of path learning based on expert scores

Figure 6.

Learning path length affects validation

Figure 7.

Learning path for completing_the_square_1 given by different methods

SPSS statistical software was used to study the differences in the test scores and total scores of reading, composition, and translation of students in different classes, and the descriptive statistics of students’ scores are shown in Table 3. As can be seen from Table 3, the mean score of each item in the experimental class is higher than that of the control class. The difference in the total score was the largest with 13.61 points. Reading was the next highest with a difference of 6.03 points. The smallest difference is in composition, with a difference of 1.27 points. It indicates that in this teaching experiment, the adaptive learning path planning method based on deep knowledge tracking helps students in the experimental class to improve their performance in college public English.

Independent samples t-test was utilized to study the differences in reading, writing as well as translation scores of students in different classes in the examination and the results of independent samples t-test for the scores of students in the experimental and control classes are shown in Table 4. From the results of the data in Table 4, the students in the experimental and control classes showed significant differences in their reading scores since Sig.=0.615>0.05 and therefore the variance is chi-square, while Sig.(2-tailed)=0.001<0.05. Similarly, the variance of writing and translation scores of the experimental and control classes were not homogeneous (p=0.000<0.05, p=0.001<0.05), and there was a significant difference in both writing (p=0.004<0.05) and translation scores (p=0.003<0.05). As for the total scores, the variance of the scores of the two classes was chi-square (p=0.849>0.05) and still significantly different (p=0.002<0.05). Students’ scores on ismat platform showed significant differences. And as shown in Table 3, the average scores of the experimental class in each item are higher than those of the control class, which proves that the teaching incentive strategy based on the dynamic planning method can help to improve the teaching effectiveness of university public English in this teaching experiment.