A knowledge tracking and predicting method based on student knowledge state and learning ability

Abstract

The application discloses a kind of knowledge tracking prediction methods based on student knowledge state and learning ability, specifically include: 1) according to historical problem solving record, extract the learning ability of student on corresponding knowledge point;2) combine student ability information, encode the knowledge state of student on each time step by sequence neural network and self-attention network;3) to the question to be predicted, extract the knowledge state corresponding to the predicted question from historical time step by self-attention network;4) combine student ability and knowledge state, send it into fully connected network to predict the answering situation of student.The application proposes to integrate student learning ability into knowledge tracking model, solves the problem that existing model only feedbacks the problem solving record of student as knowledge mastery degree, and through effective mining of student's potential learning ability, the knowledge tracking prediction effect can be improved.

Description

Technical Field

[0001] This invention relates to the field of deep learning knowledge tracking technology, and in particular to a knowledge tracking and prediction method based on students' knowledge status and learning ability that integrates knowledge status and learning ability and combines sequential neural networks and self-attention technology for prediction. Background Technology

[0002] Knowledge tracking is a research direction in the field of smart education. Effectively establishing knowledge tracking models to dynamically capture students' knowledge status is a fundamental and crucial task. In traditional education, students' knowledge status is assessed through homework, exams, and potentially statistical analysis by teachers—a time-consuming and labor-intensive process. Knowledge tracking can analyze massive amounts of data, allowing for timely understanding of students' current learning progress and providing personalized guidance, such as recommending relevant exercises.

[0003] In recent years, with the vigorous promotion of the modernization of education, more and more people have begun to engage in the research of knowledge tracing. In the early days, most of the research on knowledge tracing was based on probability and logistic regression. However, with the development of artificial intelligence, many excellent deep learning models have been produced. Summary of the Invention

[0004] The purpose of this invention is to mine students' potential learning ability information based on their historical test-taking records, and to propose a knowledge tracking method that combines knowledge status and learning ability to predict students' test-taking performance. This method can significantly improve the accuracy of student test-taking prediction.

[0005] The specific technical solution for implementing this invention is as follows:

[0006] A knowledge tracking and prediction method based on students' knowledge status and learning ability mines potential student ability information and uses this information to improve the acquisition and updating of knowledge status. Finally, it combines the two information to predict students' answer performance. The method includes the following specific steps: Step 1: Calculate students' learning ability

[0007] 1.1) Given the student's problem-solving records χ={(q1,r1), (q2,r2), ...,(q T r T Encode the question and question-answer pairs, and encode the question at time step t as follows:

[0008] q t =c t +μ t ·d t

[0009] Where q tis the question answered by the student at time step t, r t is the student's answer to the question, c t is the difficulty vector of question q t , μ t is the embedding vector of the knowledge point corresponding to question q t , d t is the difficulty vector of question q t , and f t is the change vector of the knowledge point corresponding to question q

[0010] The question-answer interaction pair is encoded as:

[0011] a t = e t + μ t · f t

[0012] where e t is the embedding vector of the question-answer interaction pair (q t , r t ), μ t is the difficulty vector of question q t , and f t is the change vector of the question-answer interaction pair (q t , r t );

[0013] 1.2) For each time step t, filter the last k practice records with the same knowledge point as question q ti from the historical practice records, and denote the filtered k questions as where μ ti is the difficulty vector of the question, and r ti is the student's answer to the question;

[0014] 1.3) Input the k practice records into a Gate Recurrent Unit (GRU) network; the formula is:

[0015]

[0016] where is the concatenation operation, μ ti is the difficulty vector of the i-th question in , and r ti is an all-1 vector or an all-0 vector with the same dimension as μ k . Finally, k output vectors [m1, m2,... mk] are obtained, and m k is taken as the learning ability m t of the student at time step t, i.e.:

[0017] m t = m k

[0018] Step 2: Knowledge state encoding

[0019] 2.1) Each student has a different feeling about the difficulty of the question. If the student's knowledge level has reached the requirements of the question, he will feel that the question is relatively easy; while for those who have not reached the requirements of the question, they will feel that the question is difficult. The subjective question difficulty of the student is defined as:

[0020]

[0021]

[0022]

[0023] where tanh is the tanh activation function, σ is the Sigmoid activation function, and are learnable weight parameters, b1 and b2 are bias vectors; q t is the embedding vector of question q t , h t-1 is the knowledge state of the student at the last time step, is the direct difference between q t and h t-1 , is the gate vector, which is used to retain or remove information in . Finally, through , the subjective question difficulty sd t of the student at time step t for question q t is obtained;

[0024] 2.2) Compare the learning ability of the student and the subjective question difficulty. If the subjective question difficulty is within the range of the student's learning ability, the student can understand the content contained in the question and learn more knowledge from this time; while if the subjective question difficulty is beyond the student's current ability, the student will gain less after finishing the question. The knowledge acquisition of the student after finishing the question is defined as:

[0025]

[0026]

[0027]

[0028]

[0029] Where tanh is the tanh activation function and σ is the sigmoid activation function. and These are learnable weight parameters, and b3 and b4 are bias vectors; a t The embedding vector of the question-answer interaction pair at time step t, m t The student is at time step t regarding the question q t The learning ability vector corresponding to the knowledge point. It is m t With sd t-1 The direct difference, It is a gated vector used to retain or remove. The information in the middle, through Obtain the student's level of knowledge acquisition (ka) t Ultimately, it was achieved through ka. t ·a t Calculate the students' knowledge acquisition

[0030] 2.3) Transfer the knowledge state h from the previous moment. t-1 Knowledge state acquired at time t Student learning ability m t The concatenated data is input into a fully connected network, and the knowledge state is updated through a gating mechanism; the formula is:

[0031]

[0032]

[0033] in This indicates a splicing operation. These are learnable weight parameters, b5 is the bias vector, and Γ is... t It is a gating value used for adaptive combination. and h t-1 h t This represents the student's knowledge status at time t.

[0034] 2.4) Use a multi-head attention mechanism to further calculate the correlation of knowledge states at different time steps and update the knowledge states; the formula is:

[0035] M=Norm(Q+MultiHead(Q,K,V))

[0036] H E =Norm(M+FFN(M))

[0037] Where M is the intermediate output value, and H is... Eis the updated knowledge state after attention mechanism, Norm is normalization operation, FFN is feedforward neural network, Q, K, V are vectors input into attention mechanism, whose values are knowledge states of student at each time step [h1, h2,..., h T ], MultiHead(Q, K, V) is multi-head attention; its formula is:

[0038] MultiHead(Q, K, V) = [head1,..., head h ]W o

[0039]

[0040]

[0041] where W o , is a learnable weight parameter, d k is the dimension of vectors in Q;

[0042] Step 3: Knowledge state extraction

[0043] 3.1) Input the question sequence into the Gate Recurrent Unit (GRU) to obtain the order and context information of the question sequence; its formula is:

[0044] p t = GRU(p t-1 , q t )

[0045] where q t is the embedding vector of question q t , p t is the embedding vector of the fusion of question order and context information.

[0046] 3.2) Extract the knowledge state according to the multi-head attention network; its formula is:

[0047] M1 = Norm(Q + MultiHead(Q, K, V))

[0048] M2 = Norm(H E + MultiHead(M1, M1, H E ))

[0049] H D = Norm(M2 + FFN(M2))

[0050] Wherein M1 and M2 are intermediate output values, Norm is a normalization operation, FFN is a feedforward neural network, Q, K, V are input attention mechanism vectors, the values of which are all [p1, p2,..., p T ] obtained in step 3.1, H E is the knowledge state obtained in step 2.4, H D =[h d1 , h d2 ,..., h dT ] is the final extracted knowledge state, MultiHead(Q, K, V) is a multi-head attention, and its formula is:

[0051] MultiHead(Q, K, V)=[head1,..., head h ]W o

[0052]

[0053]

[0054] Wherein W o , is a learnable weight parameter, d k is the dimension of the vector in Q.

[0055] Step 4: answer prediction

[0056] 4.1) The knowledge state h dt , learning ability m t and question embedding vector q t extracted at time t are spliced and input into a fully connected layer for prediction, and the formula is:

[0057]

[0058] Wherein represents a splicing operation, sigma is a Sigmoid activation function, is a learnable weight parameter, b6 is a bias vector, is the probability of the student answering the question correctly. The model training adopts a cross-entropy loss function.

[0059] Compared with the prior art, the present application solves the problem that the existing model only feeds back the student's test record as the knowledge mastery level, the learning ability information can be more detailed to model and analyze the student's knowledge acquisition and updating process, and the effect of answer prediction is effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1Model diagram for implementing the present application;

[0061] Figure 2 Adaptive sequence neural network module diagram. DETAILED DESCRIPTION

[0062] For the sake of understanding the present application, the present application is described in detail below in conjunction with the accompanying drawings, in which Figures 1-2 The data set is divided into training set, validation set and test set according to the ratio of 8:1:1 in the embodiment. The method comprises the following steps:

[0063] 1) Refer to Figure 1 (a) section, specifically including:

[0064] 1.1) Given the student's record χ = {(q1, r1), (q2, r2),..., (q T , r T )}, encode the question and question answer interaction pair, and encode the question at t time step as:

[0065] q t = c t + μ t · d t

[0066] Where q t is the question done by the student at t time step, r t is the student's answer, which is a binary variable with a value of 0 or 1, c t is the embedding vector of the knowledge point corresponding to the question q t , μ t is the difficulty vector of the question q t , and d t is the change vector of the knowledge point corresponding to the question q t ;

[0067] Encode the question-answer interaction pair as:

[0068] a t = e t + μ t · f t

[0069] Where e t is the embedding vector of the question-answer interaction pair (q t , r t ), μ t is the difficulty vector of the question q t , and f t is the change vector of the question-answer interaction pair (q t , r t );

[0070] 1.2) For each time step t, filter the last k times of practice records with question q t from the history, and record the filtered k questions as wherein μ ti is the difficulty vector of the question, r ti is the student's answer to the question. In the implementation process, the value of k is taken as 8;

[0071] 1.3) Input the 8 practice records into the Gate Recurrent Unit (GRU); the formula is:

[0072]

[0073] wherein is the splicing operation, μ ti is the difficulty vector of the i-th question in r ti is a full 1 vector or a full 0 vector with the same dimension as μ ti . Finally, 8 output vectors [m1, m2,... m8] are obtained, and m8 is taken as the learning ability m t of the student at time step t, that is:

[0074] m t = m8

[0075] 2) Refer to Figure 2 the adaptive sequence neural network module diagram, Figure 1 part (b), which specifically includes:

[0076] 2.1) Each student has different difficulty perception for the question. If the student's knowledge mastery level has reached the requirements of the question, the student will feel that the question is relatively easy; while for those students who have not reached the requirements of the question, the student will feel that the question is difficult, refer to Figure 2 part (a) defines the subjective question difficulty of the student as:

[0077]

[0078]

[0079]

[0080] wherein tanh is the tanh activation function, σ is the Sigmoid activation function, and are learnable weight parameters, b1 and b2 are bias vectors; q t is the question q tThe embedding vector, h t-1 It represents the student's knowledge state at the previous moment. It is q t with h t-1 The direct difference, It is a gated vector used to retain or remove. The information in the middle. Ultimately through Get the student's time step t for question q t The difficulty of the subjective questions is sd t ;

[0081] 2.2) Compare students' learning abilities with the difficulty of subjective questions. If the difficulty of the subjective questions is within the students' learning ability range, then the students can understand the content contained in the questions and learn more knowledge from this exercise; however, if the difficulty of the subjective questions exceeds the students' current abilities, then the students will gain less after completing the questions. (See also...) Figure 2 (b) Partially defines the knowledge acquired by students after completing the exercises as follows:

[0082]

[0083]

[0084]

[0085]

[0086] Where tanh is the tanh activation function and σ is the sigmoid activation function. and These are learnable weight parameters, and b3 and b4 are bias vectors; a t The embedding vector of the question-answer interaction pair at time step t, m t The student is at time step t regarding the question q t The learning ability vector corresponding to the knowledge point. It is m t With sd t-1 The direct difference, It is a gated vector used to retain or remove. The information in the middle, through Obtain the student's level of knowledge acquisition (ka) t Ultimately, it was achieved through ka. t .a t Calculate the students' knowledge acquisition

[0087] 2.3) Transfer the knowledge state h from the previous moment. t-1 Knowledge state acquired at time t Student learning ability mt concatenated into the input full connection network to update the knowledge state through the gating mechanism; see Figure 2 (c) part of the formula is:

[0088]

[0089]

[0090] wherein denotes the concatenation operation, is a learnable weight parameter, b5 is a bias vector, and t is the gating value, used for adaptive combination and h t-1 , h t is the knowledge state of the student at the current t time step;

[0091] 2.4) see Figure 1 (b) part, using multi-head attention mechanism to further calculate the correlation of knowledge states at different time steps and update the knowledge state; the formula is:

[0092] M = Norm(Q + MultiHead(Q, K, V))

[0093] H E = Norm(M + FFN(M))

[0094] wherein M is the intermediate output value, H E is the updated knowledge state after attention mechanism, Norm is the normalization operation, FFN is the feedforward neural network, Q, K, V are vectors input into the attention mechanism, and the values are the knowledge states of the student at each time step [h1, h2,..., h T ], MultiHead(Q, K, V) is the multi-head attention; the formula is:

[0095] MultiHead(Q, K, V) = [head1,..., head h ]W o

[0096]

[0097]

[0098] wherein W o , is a learnable weight parameter, and dk is the dimension of the vector in Q;

[0099] 3) see Figure 1(c) a portion, specifically including

[0100] 3.1) Obtain the order and context information of the question sequence in the Gate Recurrent Unit (GRU); the formula is:

[0101] p t =GRU(p t-1 ,q t )

[0102] where q t is the embedding vector of question q t , p t is the embedding vector of the fusion of question order and context information.

[0103] 3.2) Extract knowledge state according to multi-head attention network; the formula is:

[0104] M1=Norm(Q+MultiHead(Q,K,V))

[0105] M2=Norm(H E +MultiHead(M1,M1,H E ))

[0106] H D =Norm(M2+FFN(M2))

[0107] where M1 and M2 are intermediate output values, Norm is a normalization operation, FFN is a feedforward neural network, Q, K, V are input attention mechanism vectors, the values are all [p1, p2,..., p T ] obtained in step 3.1, H E is the knowledge state obtained in step 2.4, H D =[h d1 , h d2 ,..., h aT ] is the final extracted knowledge state, MultiHead(Q, K, V) is multi-head attention; the formula is:

[0108] MultiHead(Q, K, V) = [head1,..., head h ]W o

[0109]

[0110]

[0111] where W​o , are learnable weight parameters, d k is the dimension of the vector in Q.

[0112] 4) Refer to Figure 1 (d) part, specifically including:

[0113] 4.1) The knowledge state h dt , learning ability m t input prediction module, and the question embedding vector q t concatenated together and input into the full connection layer for prediction; the formula is:

[0114]

[0115] wherein represents the concatenation operation, and σ is the Sigmoid activation function, is a learnable weight parameter, and b6 is a bias vector, is the probability of the student answering the question correctly. The training of the model uses the cross-entropy loss function.

Claims

1. A knowledge tracking and predicting method based on students' knowledge states and learning abilities, the method comprising the following steps: Step 1: Calculate students' learning abilities 1.1) Given a student's record of work on problems χ = {(q1, r1), (q2, r2),..., (q T , r T )}, encode the problems and problem-answer interaction pairs, encode a problem at time step t as: q t = c t + μ t · d t Where q t It represents the questions the student answers at time step t, r t c is a binary variable representing the student's answers, with a value of either 0 or 1. t The question is q t The embedding vector of the corresponding knowledge point, μ t The question is q t The difficulty vector, d t The question is q t The change vector of the corresponding knowledge point; Encode the title answer interaction pair as: a t = e t + μ t · f t where e t is the embedding vector of the question-answer interaction pair (q t , r t ), μ t is the difficulty vector of the question q t , and f t is the change vector of the question-answer interaction pair (q t , r t ); 1.2) For each time step t, filter out the last k times of doing the question q t from the history of doing the questions, and record the k questions as where μ ti is the difficulty vector of the question, r ti is the student's answering situation; 1.3) inputting the k exercise records into a gated recurrent unit network (GRU); The formula is: in It's a splicing operation, μ ti yes The difficulty vector of the i-th question, r ti Is with μ ti Vectors consisting entirely of 1s or 0s with the same dimension; ultimately, k output vectors [m1, m2, ... m] are obtained. k ], m k The student's learning ability at time step t t ,Right now: m t = m k Step 2: Knowledge state encoding 2.1) Each student has a different perception of the difficulty of the question. If the student's knowledge level has reached the requirements of the question, the student will feel that the question is relatively easy. For those students who have not reached the requirements of the question, they will feel that the question is difficult. Define the subjective question difficulty of the student as: where tanh is the tanh activation function, σ is the Sigmoid activation function, and are learnable weight parameters, b1 and b2 are bias vectors; q t is the embedding vector of question q t , h t-1 is the student's knowledge state at the previous time step, is the direct difference between q t and h t-1 , is the gating vector, which is used to retain or remove information in h ; finally, through the subjective question difficulty sd t of the student at time step t for question q t is obtained; 2.2) Compare the student's learning ability and subjective question difficulty. If the subjective question difficulty is within the student's learning ability, the student can understand the content contained in the question and learn more knowledge from this time. If the subjective question difficulty is beyond the student's current ability, the student's gain after completing the question will be correspondingly less. Define the knowledge acquisition of the student after completing the question as: Where tanh is the tanh activation function and σ is the sigmoid activation function. and These are learnable weight parameters, and b3 and b4 are bias vectors; a t The embedding vector of the question-response interaction pair at time step t, m t The student is at time step t regarding the question q t The learning ability vector corresponding to the knowledge point. It is m t With sd t-1 The direct difference, It is a gated vector used to retain or remove. The information in the middle, through Obtain the student's level of knowledge acquisition (ka) t Ultimately through ka t ·a t Calculate the students' knowledge acquisition 2.3) Update the knowledge state h t-1 at time t Student learning ability m t Concatenate the input into a fully connected network, and update the knowledge state through the gating mechanism. The formula is: wherein denotes a concatenation operation, are learnable weight parameters, b5is a bias vector, and t is a gating value for adaptive combination and h t-1 , h t is the student's knowledge state at the current time t; 2.4) Use multi-head attention mechanism to further calculate the correlation of knowledge state at different time steps, update knowledge state; The formula is: M = Norm(Q + MultiHead(Q, K, V)) H E = Norm(M + FFN(M)) where M is the intermediate output value, H E is the updated knowledge state after attention mechanism, Norm is the normalization operation, FFN is the feed-forward neural network, Q, K, V are vectors input to the attention mechanism, whose values are the knowledge states of the student at each time step [h1, h2,..., h T ], MultiHead(Q, K, V) is the multi-head attention; The formula is: MultiHead(Q, K, V) = [head1,..., head h ]W o where W o , are learnable weight parameters, d k is the dimension of the vectors in Q; Step 3: Knowledge state extraction 3.1) Obtain the topic sequence In the gated recurrent unit (GRU), the order and context information of the topic sequence are obtained. The formula is: p t = GRU(p t-1 , q t ) where q t is the embedding vector for the question q t p t is the embedding vector that fuses the question order and context information; 3.2) Extract knowledge state according to multi-head attention network; The formula is: M1 = Norm(Q + MultiHead(Q, K, V)) M2 = Norm(H E + MultiHead(M i , M1, H E )) H D = Norm(M2 + FFN(M2)) Where M1 and M2 are intermediate output values, Norm is the normalization operation, FFN is the feedforward neural network, and Q, K, and V are the vectors input to the attention mechanism, with values ​​of [p1, p2, ..., p] obtained in step 3.

1. T ], H E H represents the knowledge state obtained in step 2.

4. D =[h d1 h d2 , ..., h dT [] represents the final extracted knowledge state, and MultiHead(Q, K, V) represents multi-head attention; The formula is: MultiHead(Q, K, V) = [head1,..., head h ]W o where W o , are learnable weight parameters, d k is the dimension of the vectors in Q; Step 4: Answer prediction 4.1) The knowledge state h extracted at time t dt , learning ability m t , and the question embedding vector q t are concatenated and input into a fully connected layer for prediction. The formula is: wherein denotes a concatenation operation, σ is a Sigmoid activation function, are learnable weight parameters, b6is a bias vector, is the predicted probability of a student answering a question correctly.

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