A comprehensive knowledge tracing method with item difficulty enhancement

Abstract

The application discloses a comprehensive knowledge tracking method with enhanced test question difficulty, and comprises the following steps: a data set is formed by historical answering record data of students and corresponding test question data; a student's answering process psychological ability is initialized and defined; after data processing, the student's answering ability and the difficulty of test questions and knowledge points are obtained through evaluation; data is embedded and processed; finally, a knowledge tracking model is trained by using a deep learning method, the knowledge state of each student and the optimized psychological ability data of the student are obtained, and the performance of the student on future test questions is predicted through the knowledge state of the student and the psychological ability data of the student. The application comprehensively considers the difficulty of test questions, the answering ability and psychological ability of students and other factors, and is close to the learning process in a real educational background to obtain reasonable knowledge states, and finally, the answering performance of the student is accurately predicted according to the knowledge state of the student.

Description

Technical Field

[0001] This invention belongs to the fields of artificial intelligence and educational data, and in particular relates to a comprehensive knowledge tracking method that enhances the difficulty of test questions. Technical Background

[0002] The task of knowledge tracking is to use students' historical learning process interaction data to track and model the changes in students' knowledge status, that is, the degree of knowledge mastery, over time, in order to more accurately predict students' answer performance and knowledge mastery level in future learning. In recent years, knowledge tracking has received much attention due to its importance in education and has been widely used in intelligent tutoring systems, online education platforms, and personalized exercise recommendation systems.

[0003] There are many solutions for knowledge tracking, such as probabilistic graphical models and Bayesian models. With the rapid development of deep neural networks, models based on deep knowledge tracking have achieved excellent results. Examples include the DKT model, which first introduced deep learning into the knowledge tracking problem and used hidden layer states to represent knowledge states; the AKT model, which captures students' similar performance on similar questions through an attention mechanism; and the GKT model, which models knowledge states using graph neural networks. However, currently only a few methods consider the impact of question difficulty on students' knowledge acquisition. They merely use the percentage of students who answer questions correctly as the question difficulty, a crude approach that is unreasonable for some long-tailed questions. Secondly, different methods consider different factors when modeling the knowledge tracking process. Currently, there is no unified model that comprehensively considers multiple factors in the learning process, such as knowledge updating, forgetting, question relevance, and students' psychological abilities. Summary of the Invention

[0004] The purpose of this invention is to provide a comprehensive knowledge tracking method that enhances the difficulty of test questions. This method uses a thorough analysis of students' problem-solving abilities and the difficulty of test questions and knowledge points as important inputs, and accumulates the knowledge state when answering historical test questions related to the current test question through attention mechanisms. Considering the psychological abilities of students in the problem-solving process, it models the learning gains and forgetting mechanisms of students' learning process to more accurately predict student performance and track changes in students' knowledge mastery level.

[0005] A comprehensive knowledge tracking method with increased test difficulty, characterized by comprising:

[0006] The dataset consists of students' historical answer records and corresponding test questions. Initially, students' psychological ability data during the answering process is defined. After data processing, the students' answering abilities and the difficulty of the test questions and knowledge points are evaluated. The data is then embedded. Finally, a knowledge tracking model is trained using deep learning methods to obtain each student's knowledge status and optimized psychological ability data. Based on the students' knowledge status and psychological ability data, the model predicts the students' performance on future test questions.

[0007] Historical answer records include: question number, score for each question, and the knowledge points covered by each question;

[0008] For a dataset D of students' historical answer records, there is a set S = {s1, s2, ..., sn} containing I students. i , ..., s I} contains a set of J test questions, E = {e1, e2, ..., e}. j , ..., e J} and the set of knowledge points K = {k1, k2, ..., k m , ..., k M Each question is pre-labeled with the relevant knowledge points, and the connection between the questions and the knowledge points is represented by a Q matrix, where Q∈R. J×M The matrix consists of 0s and 1s, Q jm =1 indicates that question e j Knowledge point k involved m Conversely, it is not involved. The student's question-answering sequence is defined as x = {(e1, C1, r1), (e2, C2, r2), ..., (e...}. t C t r t One of the tuples (e) t C t r t ) represents a learning unit, where e t Representative question, C t Representative and test question e t The relevant set of knowledge points, r t The r represents whether the answer is correct or not. t ∈{0, 1}, where 1 represents a correct answer and 0 represents an incorrect answer.

[0009] Data on students' psychological abilities during the answering process includes;

[0010] Initialize a matrix The matrix, where each row represents a student's psychological ability to answer questions, i.e., student s. t Psychological abilities can be represented by vectors. To express.

[0011] The calculation of students' problem-solving abilities and the difficulty of test questions and knowledge points includes;

[0012] Student S i Problem-solving ability g i The calculation formula is as follows:

[0013]

[0014] Where E i It is student s i In the sequence of test questions during the learning process, e j E i Question j in the series, |E i | represents the length of the question sequence, J represents the number of questions, and r ij ∈{0,1} represents student s i Answer question e in the question sequence. j Correct or incorrect. The intuition behind the formula is that students who answer more questions and have a higher accuracy rate have better problem-solving abilities.

[0015] Question e j Difficulty ed j The calculation formula is as follows:

[0016]

[0017] Where S j Representative who answered question e j The student assembly, g i S represents j Students in i Among the problem-solving abilities, |S j | represents the length of the student set, I represents the total number of students, and r represents the length of the student set. ij ∈{0,1} represents student s i Answer question e j Correct or incorrect. The intuition behind the formula is for question e. j The higher the test-taking ability of students who answer incorrectly, and the fewer the number of students who answer the test, the greater the difficulty of the test.

[0018] Knowledge point k m Difficulty KD m The calculation formula is as follows:

[0019]

[0020] Where E m |E represents the set of test questions that cover this knowledge point. m | represents the length of the set, ed j E mThe difficulty of question j, i.e. the difficulty of the knowledge point, is calculated by averaging the difficulty of all questions involving that knowledge point.

[0021] Data embedding processing includes:

[0022] One-hot encoding is performed on the question set E, followed by the use of an embedding matrix. Perform an embedding operation on the question vector, where J represents the number of questions, and d e This represents the dimension of the question vector after embedding, followed by the question e for each learning unit. t Vectors can be used To express.

[0023] One-hot encoding is performed on the knowledge point set K, followed by the use of an embedding matrix. Perform an embedding operation on the question vector, where M represents the number of knowledge points, and d k This represents the dimension of the knowledge point vector after embedding. Then, for each knowledge point k... m We can use vector k m This indicates that the test question e for each interactive unit is... t The set of knowledge points involved C t This can be represented by the sum of the vectors of knowledge points in the set, i.e., the set of knowledge points C. t Vectors can be used To represent this, the formula is as follows:

[0024]

[0025] The difficulty level of the test questions is divided into n levels according to the range of maximum and minimum values, transforming the difficulty level from a scalar to a category. One-hot encoding is then applied to each difficulty category to obtain a question difficulty vector, which is then embedded using an embedding matrix. Perform an embedding operation on the question difficulty vector, where d l This represents the dimension of the question difficulty vector after embedding, i.e., question e. t The difficulty can be represented by vectors. The formula for classifying test difficulty levels is as follows:

[0026]

[0027] in This represents the maximum difficulty level among all questions. Represents the minimum difficulty level among all test questions, ed j Representative question e j Difficulty Representative question e jThe value after converting the difficulty into a category type;

[0028] The difficulty of knowledge points is divided into n levels according to the range of maximum and minimum values, transforming the difficulty from a scalar to a category. One-hot encoding is then performed on each difficulty category to obtain a knowledge point difficulty vector, which is then embedded using an embedding matrix. Perform an embedding operation on the question difficulty vector, where d l This represents the dimension of the question difficulty vector after embedding, i.e., knowledge point k. m The difficulty can be represented by vectors. The formula for classifying test difficulty levels is as follows:

[0029]

[0030] in This represents the highest difficulty level among all knowledge points. kd represents the minimum difficulty among all knowledge points. m Representing knowledge point k m The difficulty, kl m Representing knowledge point k m The value after converting the difficulty into a category type;

[0031] Questions for each interactive unit t The set of knowledge points involved C t The difficulty can be calculated by adding the difficulty vectors of the knowledge points and then taking the average, i.e., the set of knowledge points C. t The difficulty can be represented by vectors. To represent it. The formula for calculating the difficulty of a set of knowledge points is as follows:

[0032]

[0033] Where |c t | represents the length of the knowledge point set, kl m Represents c t Knowledge Point k m The difficulty vector;

[0034] Subsequently, by using the question vector e t The set of knowledge points related to the test questions, vector c t The difficulty vector of the test questions t The set of knowledge points related to the test questions and the difficulty vector cl t Connect them together and use a multilayer perceptron for deep fusion to obtain the complete embedded test question information.

[0035]

[0036] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0037] After one-hot encoding the test answers, use the embedding matrix. Perform an embedding operation on the question vector, where d a This represents the dimension of the response vector after embedding, followed by the response r for each learning unit. t Vectors can be used To express.

[0038] Knowledge tracing models include:

[0039] Attention mechanism module: Embeds the test information of the current learning unit into E t Multiply by matrix Get the query vector Embed the test question information from the previous learning unit into the vector set {E1, E2, ..., E...} t-1 The vectors within} are multiplied by the matrix respectively To the key vector set {K1,K2,…,K t-1} Interact each vector in the key vector set with q t Dot product and then divide We obtain set α t ={α t,1 ,α t,2 ,…,α t,t-1}, performing a softmax operation on the set α yields the attention score set α′. t ={α′ t,1 ,α′ t,2 ,…,α′ t,t-1} will α′ t The attention scores are multiplied by the knowledge state set {h1, h2, ..., h} respectively. t-1 The vectors in} yield the accumulated knowledge state. The calculation formula is as follows:

[0040]

[0041] Learning Module: Embedding Test Question Information in E t , Answer embedded a t and the status of knowledge mastery The learning gain lg can be obtained by modeling the learning gain using a fully connected layer. t :

[0042]

[0043] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0044] Considering that learning gain cannot be fully converted into an increase in student knowledge, a learning gate was designed. To control students' ability to transform:

[0045]

[0046] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0047] Then Multiply by lg t Achieve true learning gains (LG) t :

[0048]

[0049] Forgetting Mechanism Module: Forgetting occurs during the learning process, affecting the degree of knowledge mastery. Therefore, a forgetting gate is used. To simulate the forgetting effect:

[0050]

[0051] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0052] We can then use the Forgotten Gate Multiply by the previous knowledge point mastery status h t-1 Plus LG t Get the current knowledge mastery status h t :

[0053]

[0054] Prediction Module: In the prediction module, we project the information from the next question, the student's current knowledge level, and the student's psychological ability into the output layer through a fully connected layer to obtain the output vector y. t+1 :

[0055]

[0056] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0057] A fully connected layer is used as the output layer to output the final prediction of the correctness of the test question answer. The value is between 0 and 1 and a threshold is set. If the value is greater than the threshold, the answer is judged to be correct, otherwise it is incorrect.

[0058]

[0059] in It is a weight vector, b6∈R 1 It is a bias term.

[0060] During model training, the binary cross-entropy loss function is used to calculate the loss value for predicting whether the question answer is correct.

[0061] loss = BCEloss(y t+1 ,r t+1 )

[0062] Where r t+1 ∈{0,1} represents question e t+1 The true value of whether the answer is correct or not.

[0063] Compared with the prior art, the present invention has the following advantages:

[0064] The above-mentioned solution provided by the embodiments of the present invention proposes a formula that comprehensively considers students' problem-solving abilities as well as the difficulty of test questions and knowledge points. It accumulates the knowledge state when answering questions related to the current test question in the historical answer sequence through the attention module. In the context of considering psychological abilities, it models the learning benefits and knowledge forgetting mechanism of students in the learning process, and obtains the student's changing knowledge state that is consistent with the learning process.

[0065] This invention employs a deep knowledge tracing model to model the learning process of students during question-answering, tracking their constantly changing knowledge state. By comprehensively considering factors such as the difficulty of the questions, students' problem-solving abilities, and psychological capabilities, this invention closely resembles the learning process in a real educational context to obtain a reasonable knowledge state, and ultimately makes accurate predictions about students' answer performance based on their knowledge state. Attached Figure Description

[0066] Figure 1 This is a flowchart of the method proposed in this invention;

[0067] Figure 2 This is a model architecture diagram of the present invention; Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0069] The objective of this invention is achieved through the following technical solution:

[0070] A comprehensive knowledge tracking method with increased test difficulty includes the following:

[0071] A dataset consisting of students' historical answer interaction data and corresponding test question information data is obtained and preprocessed.

[0072] The formula calculates students' problem-solving abilities and the difficulty of test questions and knowledge points, initializes and generates students' psychological ability matrix, and embeds the data.

[0073] The attention mechanism is used to calculate the cumulative knowledge point status of historical questions related to the current question.

[0074] Knowledge gain is calculated by accumulating knowledge point status, embedding current test question information, embedding test question answers, and calculating psychological abilities.

[0075] By accumulating knowledge point states, embedding current test questions, embedding answers, and calculating psychological abilities, the knowledge states that have been forgotten are combined with knowledge gains to form new knowledge states.

[0076] Predicting answers to test questions based on students' current knowledge level, information embedded in the next test question, and psychological abilities.

[0077] The formulas used in the above method to calculate students' problem-solving abilities and the difficulty of test questions and knowledge points are as follows:

[0078] Student S i Problem-solving ability g i The calculation formula is as follows:

[0079]

[0080] Where E i It is student s i In the sequence of test questions during the learning process, |E i | represents the length of the question sequence, r ij The question e in the sequence represents j Whether the answer is correct or not, J represents the total number of questions, r ij ∈{0,1} represents student s i Answer question e in the question sequence. j Correct or incorrect.

[0081] Question e j Difficulty ed j The calculation formula is as follows:

[0082]

[0083] Where S j Representative who answered question e j Student set, |S j | represents the length of the student set, g i S represents j middle school students i The problem-solving ability, where I represents the total number of students, r ij ∈{0,1} represents student s i Answer question e j Correct or incorrect.

[0084] Knowledge point k m Difficulty KD m The calculation formula is as follows:

[0085]

[0086] Where E m |E represents the set of test questions that cover this knowledge point. m | represents the length of the question set, ed j E m Middle school test question e j The difficulty level, i.e. the difficulty of a knowledge point, is calculated by averaging the difficulty of all questions related to that knowledge point.

[0087] The method and formula for calculating the cumulative knowledge point status of historical questions related to the current question using the attention mechanism described above are as follows:

[0088] An attention score is obtained by calculating the similarity between the current question and the question information in the historical interaction sequence. The attention score is then multiplied by the previous knowledge point state to obtain the cumulative current knowledge point state.

[0089] The calculation formula is as follows:

[0090]

[0091] Where, {h1,h2,…,h t-1} represents the set of knowledge states, {α′ t,1 ,α′ t,2 ,…,α′ t,t-1} represents the set of attention scores. This represents the cumulative knowledge point status obtained through calculation.

[0092] The methods and formulas for calculating knowledge gain through accumulating knowledge point status, embedding current test question information, embedding test question answers, and psychological ability are as follows:

[0093] The learning gain lg can be obtained by modeling the learning gain using a fully connected layer. t :

[0094]

[0095] Where W2 is the weight matrix and b2 is the bias term.

[0096] Considering that learning gains cannot be fully converted into an increase in student knowledge, through learning gates To control students' ability to transform:

[0097]

[0098] Where W3 is the weight matrix and b3 is the bias term.

[0099] Will Multiply by lg t Achieve true learning gains (LG) t :

[0100]

[0101] The above method, which calculates the knowledge state after knowledge forgetting by accumulating knowledge point states, embedding current test questions, embedding answers, and using psychological abilities, and combines these with knowledge gains to form a new knowledge state, uses the following methods and formulas:

[0102] Forgetting can occur during the learning process, affecting the degree of knowledge mastery. Using a forgetting gate can address this. To simulate the forgetting effect:

[0103]

[0104] Where W4 is the weight matrix and b4 is the bias term.

[0105] By using the forget gate Multiply by the previous knowledge point mastery status h t-1 Plus LG t Get the current knowledge mastery status h t :

[0106]

[0107] The method and formula for predicting test answers based on students' current knowledge status, information embedded in the next test question, and psychological abilities are as follows:

[0108] We project the information embedded in the test question, the student's current mastery of the knowledge points, and the student's psychological ability into the output layer through a fully connected layer to obtain the output vector y. t+1 :

[0109]

[0110] Where W5 is the weight matrix and b5 is the bias term.

[0111] A fully connected layer is used as the output layer to output the final prediction y of the correctness of the test questions. t+1 The value is between 0 and 1, and a threshold is set. If the value is greater than the threshold, the answer is considered correct; otherwise, it is considered incorrect.

[0112]

[0113] Where W6 is the weight vector and b6 is the bias term.

[0114] E in the above formula t Represents embedded test information, E t+1 Represents the embedding of information from the next question, α t Represents embedded answers, p t Represents the vector of psychological abilities, h represents the accumulated knowledge mastery status t-1 Represents the mastery status of knowledge points at the previous moment, h t This represents the current mastery status of the knowledge point; σ represents the activation function sigmoid. This represents a splicing operation.

[0115] Specifically, embodiments of the present invention provide a comprehensive knowledge tracking method with enhanced test question difficulty, such as... Figure 1 As shown, it mainly includes:

[0116] Step 1: Obtain and preprocess a dataset consisting of students' historical answer interaction data and corresponding test question information data. The historical answer interaction data includes each student's answer to the test questions during their learning process, and the test question information data includes the knowledge points involved in each test question.

[0117] Preprocessing operations include data cleaning and representing the data in the dataset using a uniform mathematical form: For a dataset D of students' historical answer records, there is a set S = {s1, s2, ..., s...} containing I students. i ,…,s I} contains a set of J test questions, E = {e1, e2, ..., e} j ,…,e J} and the set of knowledge points K = {k1,k2,…,k m ,…,kM Each question is pre-labeled with the relevant knowledge points, and the connection between the questions and the knowledge points is represented by a Q matrix, where Q∈R. J×M The matrix consists of 0s and 1s, Q jm =1 indicates that question e j Knowledge point k involved m Conversely, it is not involved. The student's interactive sequence of answers is defined as x={(e1,C1,r1),(e2,C2,r2),…,(e t C t ,r t One of the tuples (e) t C t ,r t ) represents a learning unit, where e t Representative question, C t Representative and test question e t The relevant set of knowledge points, r t The r represents whether the answer is correct or not. t ∈{0,1}, where 1 represents a correct answer and 0 represents an incorrect answer.

[0118] Step 2: Calculate students' problem-solving abilities and the difficulty of test questions and knowledge points using formulas, generate students' psychological ability matrix, and embed the data.

[0119] Student S i The formula for calculating problem-solving ability is as follows:

[0120]

[0121] Where E i It is student s i In the sequence of test questions during the learning process, e j E i Question j in the series, |E i | represents the length of the question sequence, J represents the number of questions, and r ij ∈{0,1} represents student s i Answer question e in the question sequence. j Correct or incorrect;

[0122] Question e j Difficulty ed j The calculation formula is as follows:

[0123]

[0124] Where S j Representative who answered question e j The student assembly, g i S represents j Students ini Among the problem-solving abilities, |S j | represents the length of the student set, I represents the total number of students, and r represents the length of the student set. ij ∈{0,1} represents student s i Answer question e j Correct or incorrect; knowledge point k m Difficulty KD m The calculation formula is as follows:

[0125]

[0126] Where E m |E represents the set of test questions that cover this knowledge point. m | represents the length of the set, ed j E m The difficulty of question j, i.e. the difficulty of the knowledge point, is calculated by averaging the difficulty of all questions involving that knowledge point.

[0127] Generating a student's psychological ability matrix and embedding the data includes: initializing a matrix The matrix, where each row represents a student's psychological ability to answer questions, i.e., student s. t Psychological abilities can be represented by vectors. To express.

[0128] One-hot encoding is performed on the question set E, followed by the use of an embedding matrix. Perform an embedding operation on the question vector, where J represents the number of questions, and d e This represents the dimension of the question vector after embedding, followed by the question e for each learning unit. t Vectors can be used To express.

[0129] One-hot encoding is performed on the knowledge point set K, followed by the use of an embedding matrix. Perform an embedding operation on the question vector, where M represents the number of knowledge points, and d k This represents the dimension of the knowledge point vector after embedding. Then, for each knowledge point k... m We can use vector k m This indicates that the test question e for each interactive unit is... t The set of knowledge points involved C t This can be represented by the sum of the vectors of knowledge points in the set, i.e., the set of knowledge points C. t Vectors can be used To represent this, the formula is as follows:

[0130]

[0131] The difficulty level of the test questions is divided into n levels according to the range of maximum and minimum values, transforming the difficulty level from a scalar to a category. One-hot encoding is then applied to each difficulty category to obtain a question difficulty vector, which is then embedded using an embedding matrix. Perform an embedding operation on the question difficulty vector, where d l This represents the dimension of the question difficulty vector after embedding, i.e., question e. t The difficulty can be represented by vectors. The formula for classifying test difficulty levels is as follows:

[0132]

[0133] in This represents the maximum difficulty level among all questions. Represents the minimum difficulty level among all test questions, ed j Representative question e j Difficulty Representative question e j The difficulty value is converted into a category type; the difficulty of each knowledge point is divided into n levels according to the maximum and minimum value range, thus transforming the difficulty from a scalar to a category. One-hot encoding is then performed on the knowledge point difficulty categories to obtain a knowledge point difficulty vector, which is then used with an embedding matrix. Perform an embedding operation on the question difficulty vector, where d l This represents the dimension of the question difficulty vector after embedding, i.e., knowledge point k. m The difficulty can be represented by vectors. The formula for classifying test difficulty levels is as follows:

[0134]

[0135] in This represents the highest difficulty level among all knowledge points. kd represents the minimum difficulty among all knowledge points. m Representative knowledge point k m The difficulty, kl m Representative knowledge point k m The value after converting the difficulty into a category type;

[0136] Questions for each interactive unit t The set of knowledge points involved C t The difficulty can be calculated by adding the difficulty vectors of the knowledge points and then taking the average, i.e., the set of knowledge points C. t The difficulty can be represented by vectors. To represent it. The formula for calculating the difficulty of a set of knowledge points is as follows:

[0137]

[0138] Where |c t | represents the length of the knowledge point set, kl m Represents c t Knowledge Point k m The difficulty vector;

[0139] Subsequently, by using the question vector e t The set of knowledge points related to the test questions, vector c t The difficulty vector of the test questions t The set of knowledge points related to the test questions and the difficulty vector cl t Connect them together and use a multilayer perceptron for deep fusion to obtain the complete embedded test question information.

[0140]

[0141] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0142] After one-hot encoding the test answers, use the embedding matrix. Perform an embedding operation on the question vector, where d a This represents the dimension of the response vector after embedding, followed by the response r for each learning unit. t Vectors can be used To express.

[0143] Step 3: Utilize attention mechanisms to calculate the cumulative knowledge point status of historical questions related to the current question. Specific modules include... Figure 2 As shown.

[0144] Attention mechanism module: Embeds the test information of the current learning unit into E t Multiply by matrix Get the query vector Embed the test question information from the previous learning unit into the vector set {E1, E2, ..., E...} t-1 The vectors within} are multiplied by the matrix respectively To the key vector set {K1,K2,…,K t-1} Interact each vector in the key vector set with q t Dot product and then divide We obtain set α t ={α t,1 ,α t,2 ,…,α t,t-1}, performing a softmax operation on the set α yields the attention score set α′. t ={α′ t,1 ,α′ t,2 ,…,α′ t,t-1} will α′ t The attention scores are multiplied by the knowledge state set {h1, h2, ..., h} respectively. t-1 The vectors in} yield the cumulative knowledge state. The calculation formula is as follows:

[0145]

[0146] Step 4: Calculate knowledge gain through accumulated knowledge point status, embedding current test question information, embedding test question answers, and psychological ability calculations. Specific modules include... Figure 2 As shown.

[0147] Learning Module: Embedding Test Question Information in E t , Answer embedded a t and the status of knowledge mastery The learning gain can be obtained by modeling it using a fully connected layer:

[0148]

[0149] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0150] Considering that learning gain cannot be fully converted into an increase in student knowledge, a learning gate was designed. To control students' ability to transform:

[0151]

[0152] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0153] Then Multiply by lg t Achieve true learning gains (LG) t :

[0154]

[0155] Step 5: By accumulating knowledge point states, embedding current test questions, embedding answers, and calculating psychological abilities, the knowledge states that have undergone knowledge forgetting are combined with knowledge gains to form new knowledge states. Specific modules include... Figure 2 As shown.

[0156] Forgetting Mechanism Module: Forgetting occurs during the learning process, affecting the degree of knowledge mastery. Therefore, a forgetting gate is used. To simulate the forgetting effect:

[0157]

[0158] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0159] We can then use the Forgotten Gate Multiply by the previous knowledge point mastery status h t-1 Plus LG t Get the current knowledge mastery status h t :

[0160]

[0161] Step 6: Predict the student's answers to the test questions based on their current knowledge level, the information embedded in the next test question, and their psychological abilities. Specific modules include... Figure 2 As shown.

[0162] Prediction Module: In the prediction module, we project the information from the next question, the student's current knowledge level, and the student's psychological ability into the output layer through a fully connected layer to obtain the output vector y. t+1 :

[0163]

[0164] in This represents a splicing operation. It is a weight matrix. It is a bias term.

[0165] A fully connected layer is used as the output layer to output the final prediction of the correctness of the test question answer. The value is between 0 and 1 and a threshold is set. If the value is greater than the threshold, the answer is judged to be correct, otherwise it is incorrect.

[0166]

[0167] in It is a weight vector, b6∈R 1 It is a bias term.

[0168] During model training, the binary cross-entropy loss function is used to calculate the loss value for predicting whether the question answers are right or wrong:

[0169] loss = BCEloss(y t+1 ,rt+1 )

[0170] Where r t+1 ∈{0,1} represents question e t+1 The true value of whether the answer is correct or not.

Claims

1. A comprehensive knowledge tracking method with increased test difficulty, characterized in that, include: The dataset consists of students' historical answer records and corresponding test questions. Initially, students' psychological ability data during the answering process is defined. After data processing, the students' answering ability and the difficulty of the test questions and knowledge points are evaluated. The data is embedded. Finally, a knowledge tracking model is trained using deep learning methods to obtain each student's knowledge status and optimized psychological ability data. Based on the students' knowledge status and psychological ability data, the performance of students on future test questions is predicted. Initialize and define the student's psychological ability data during the question-answering process, specifically including: The formula calculates students' problem-solving abilities and the difficulty of test questions and knowledge points, initializes and generates students' psychological ability matrix, and embeds the data. After data processing, an evaluation is conducted to obtain students' answering abilities, as well as the difficulty of the test questions and knowledge points, specifically including: student Problem-solving ability The calculation formula is as follows: in Students The sequence of test questions in the learning process represent The first in question, Represents the length of the question sequence. Represents the number of test questions. On behalf of students Answer the questions in the question sequence. Correct or incorrect; Test Questions Difficulty The calculation formula is as follows: in Representative who has answered the test questions The students gathered. represent Students The ability to solve problems, among which Represents the length of the student set. Represents the total number of students. On behalf of students Answer the questions Correct or incorrect; Knowledge Points Difficulty The calculation formula is as follows: in This represents a set of test questions that cover this knowledge point. Represents the length of the set. represent Middle school exam questions The difficulty of the test questions, i.e. the difficulty of the knowledge points, is calculated by averaging the difficulty of all test questions involving that knowledge point. Knowledge tracing models include: Attention mechanism module: embeds test information from the current learning unit. Multiply by matrix Get the query vector This embeds information about the questions preceding the current learning unit into a vector set. The vectors within are multiplied by the matrix respectively to key vector set Each vector in the key vector set is compared with... Dot product and then divide Get the set ,right The attention score set is obtained by performing a softmax operation on the set. Will The attention scores are multiplied by the set of knowledge states respectively. The vector in the vector yields the accumulated knowledge state. The calculation formula is as follows: Learning Module: Embedding Test Question Information , Answer Embedded and accumulated knowledge status The learning gain is obtained by modeling the learning gain through a fully connected layer. : in This represents a splicing operation. It is a weight matrix. It is a bias term; A learning gate was designed. To control students' ability to transform: in This represents a splicing operation. It is a weight matrix. It is a bias term; Then Multiply Achieve real learning gains : Forgetting mechanism module: using a forgetting gate To simulate the forgetting effect: in This represents a splicing operation. It is a weight matrix. It is a bias term; Then we used the Forgotten Gate Multiply by the previous knowledge mastery status Plus Get the current mastery status of knowledge points : Prediction Module: In the prediction module, we project the information from the next question, the student's current knowledge level, and the student's psychological ability into the output layer through a fully connected layer to obtain the prediction vector. : in This represents a splicing operation. It is a weight matrix. It is a bias term; A fully connected layer is used as the output layer to output the final prediction of the correctness of the test question answer. The value is between 0 and 1 and a threshold is set. If the value is greater than the threshold, the answer is judged to be correct, otherwise it is incorrect. in It is a weight vector. It is a bias term; During model training, the binary cross-entropy loss function is used to calculate the loss value for predicting whether the question answer is correct. ; in Representative test questions The true value of whether the answer is correct or not.

2. The comprehensive knowledge tracking method for increasing the difficulty of test questions according to claim 1, characterized in that, The dataset, consisting of students' historical answer records and corresponding test questions, includes: question number, test score, and the knowledge points covered by each question; Given a dataset D of students' historical answer records, containing a set of I students... It contains a set of J test questions. and a collection of knowledge points Each question is pre-marked with the relevant knowledge points, and the connection between the questions and these knowledge points is shown through... Represented using matrices, The matrix consists of 0s and 1s. Indicates test questions Knowledge points involved Conversely, this does not apply, where the student's question-answering interaction sequence is defined as x. One of the tuples Represents a learning unit, in which Representative test questions, Representatives and test questions A collection of relevant knowledge points This indicates whether the answer is correct or not. 1 represents a correct answer, and 0 represents an incorrect answer.

3. The comprehensive knowledge tracking method for increasing the difficulty of test questions according to claim 1, characterized in that, Data embedding processing includes: One-hot encoding is performed on the question set E, followed by the use of an embedding matrix. Perform an embedding operation on the question vector, where J represents the number of questions. This represents the dimension of the question vector after embedding, followed by the questions for each learning unit. Use vectors To indicate; One-hot encoding is performed on the knowledge point set K, followed by the use of an embedding matrix. The question vector is embedded, where M represents the number of knowledge points. This represents the dimension of the knowledge point vector after embedding, followed by each knowledge point. Using vectors This indicates the number of questions in each interactive unit. The set of knowledge points involved The set of knowledge points is represented by the sum of the vectors of the knowledge points in the set, i.e., the set of knowledge points. Using vectors To represent this, the formula is as follows: The difficulty of the test questions is divided into the range of maximum and minimum values. The difficulty level is divided into tiers, transforming the scalar difficulty into categorical categories. One-hot encoding of the difficulty categories yields a difficulty vector, which is then used with an embedding matrix. The question difficulty vector is embedded, where This represents the dimension of the question difficulty vector after embedding, i.e., the question difficulty. Difficulty using vectors The formula for classifying the difficulty value of test questions into category values ​​is as follows: in This represents the maximum difficulty level among all questions. This represents the minimum difficulty level among all test questions. Representative test questions The difficulty Representative test questions The value after converting the difficulty into a category type; The difficulty of knowledge points is divided into ranges of maximum and minimum values. The difficulty level is categorized into scalar values ​​and then converted into categories. One-hot encoding is performed on each category to obtain a difficulty vector, which is then used with an embedding matrix. The question difficulty vector is embedded, where This represents the dimension of the question difficulty vector after embedding, i.e., the knowledge points. Difficulty using vectors The formula for classifying the difficulty value of knowledge points into category values ​​is as follows: in This represents the highest difficulty level among all knowledge points. This represents the minimum difficulty level among all knowledge points. Representative knowledge points The difficulty Representative knowledge points The value after converting the difficulty into a category type; Questions for each interactive unit The set of knowledge points involved The difficulty level is calculated by adding the difficulty vectors of the knowledge points and then taking the average, which is the set of knowledge points. Difficulty using vectors The formula for calculating the difficulty of a set of knowledge points is as follows: in Representative knowledge point set Length, Chinese knowledge points The difficulty vector; Subsequently, by using the question vector The set of knowledge points related to the test questions (vector) Question Difficulty Vector The set of knowledge points related to the test questions and the difficulty vector Connect them together and use a multilayer perceptron for deep fusion to obtain the complete embedded test question information. : in This represents a splicing operation. It is a weight matrix. It is a bias term; After one-hot encoding the test answers, use the embedding matrix. Perform an embedding operation on the question vector, where This represents the dimension of the response vector after embedding, followed by the response for each learning unit. Use vectors To express.

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