CN113033808A - Deep embedded knowledge tracking method based on exercise difficulty and student ability - Google Patents
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Abstract
The invention belongs to the field of knowledge tracking, and discloses a deep embedded knowledge tracking method based on exercise difficulty and student ability, which comprises the following steps of S1: the depth knowledge tracking model is further integrated with exercise difficulty characteristics and student ability characteristics; s2 predicts student performance: and (4) combining an attention mechanism, and predicting the student performance by using the depth knowledge tracking model constructed in the step one. Compared with the traditional knowledge tracking method, the method considers the influence of different exercise difficulty and student ability on the student answering situation, and enables the model to put more attention on the answer records with similar exercise difficulty and student ability through the attention mechanism, so that the prediction accuracy is improved. The method and the device not only improve the accuracy of knowledge tracking, but also can be used in subsequent problem recommendation application, and improve the application effect.
Description
Technical Field
The invention belongs to the field of knowledge tracking, and particularly relates to a deep embedded knowledge tracking method based on exercise difficulty and student ability.
Background
With the advent of the 2.0 era of education informatization, the rapid development of technologies such as educational big data, learning analysis, artificial intelligence, etc., and the recent rapid growth of the number of people who learn by using network resources, for example, large-scale online open courses (Couresra, EDX, MOOCs, etc.) platforms provide abundant high-quality learning resources for learners from all over the world, so that anyone in the world can learn without any obstacle. A large amount of educational resource data including user information data, learning data, examination data, user behavior data, and the like are accumulated through these platforms. These data all provide a data basis for educational assessment and intelligent tutoring in educational data mining.
However, in the face of increasing mass data information, it is difficult for learners to find information really helpful to themselves as if the information is a sea fishing needle, so that the explosive growth of the online learning resources also brings problems of information lost and overload to the learners, and prevents the learners from accurately positioning the learning resources suitable for themselves. Therefore, under the condition, a good knowledge tracking algorithm can track the mastery degree of the knowledge of the students, reliably predict the future performance of the students and improve the learning efficiency, not only can solve the problem of the individual requirements of the students, but also can effectively avoid the situations of information navigation and overload.
At present, the research of Knowledge tracking mainly comprises three models, namely Bayesian Knowledge Tracking (BKT), Dynamic Key Value Memory neural network (DKVMN) and Deep Knowledge Tracking (DKT). Bayesian knowledge tracking is to use Bayesian networks to model knowledge state changes in the learning process of students, but neglect the influence of the association between the exercise sequence and the exercises of the students on the prediction result. A dynamic key-value memory network (DKVMN), proposed by Irwin King in 2017 and used for knowledge tracking tasks, stores and updates the student's mastery level of the corresponding problem (i.e., the student's knowledge state) with one static matrix storing problem concept called a key and another dynamic matrix called a value. However, the conventional DKMMN only takes the exercise tag and the correctness tag as the input of a model, and ignores other information which is collected by an intelligent learning platform and is related to student exercise. Deep Knowledge Tracking (DKT) tracks the mastery degree of student knowledge by using a deep learning method, the existing deep knowledge tracking model is mainly realized based on RNN and LSTM, although the prediction precision is improved, only the answer sequence and answer result of students are adopted, and the influence of other characteristics on the learning process of the students, such as exercise difficulty and the self-ability of the students, is ignored, so that the further improvement of the model performance is influenced. In the actual situation, students with the same ability answer questions with different degrees of difficulty, and students with different abilities answer questions with the same degree of difficulty have distinct influences on the learning results of the students.
Disclosure of Invention
The invention aims to solve the technical problem that in the prior art, only the answer sequence and answer results of students are adopted, but the influence of the student ability and the exercise difficulty on the learning process of the students is neglected, so that the answer conditions of the students with different learning abilities when answering different exercise difficulties can not be distinguished, and the deep embedded knowledge tracking method based on the exercise difficulty and the student ability is provided.
In order to realize the task, the invention adopts the following technical scheme:
a deep embedded knowledge tracking method based on exercise difficulty and student ability comprises the following steps:
s1, constructing a depth knowledge tracking model: the depth knowledge tracking model is further integrated with exercise difficulty characteristics and student ability characteristics;
s2 predicts student performance: and (4) combining an attention mechanism, and predicting the student performance by using the depth knowledge tracking model constructed in the step one.
Optionally, S students i, Q exercises j, te (1,. T), S and Q are both natural numbers other than 0, and S1 specifically includes:
step 1: acquiring exercise difficulty characteristics and student ability characteristics, and calculating through historical answer records of students to obtain exercise difficulty values Difficulty (j) and student ability values Ability (i), wherein the exercise difficulty characteristics and the student ability characteristics are represented by the exercise difficulty values Difficulty (j) and the student ability values Ability (i);
step 2: embedding and coding according to the problem difficulty value Difficulty (j) and the student ability value Ability (i) to obtain a problem difficulty embedding vector detAnd student ability embedding vector set；
And step 3: student answering condition rtThe difficulty of exercise is embedded into vector detAnd student ability embedding vector setPerforming joint coding to obtain input vector
LSTM network obtains hidden learning state vector h of studentt；
And 4, step 4: according to attention weight alpha in predictiontThe depth knowledge tracking model is enabled to put attention on answer records with similar exercise difficulty and similar student ability, and the probability of answering the questions at the next moment by the students is predicted.
Optionally, the input vector
Obtained by the following formula:
wherein, detEmbedding vectors, se, for problem difficultytEmbedding vectors, r, for student abilitytRepresenting the answering condition of the students; problem difficulty embedding detAnd student ability embedding setIs coded as et；
Modeling the learning state of the student by using an LSTM network to obtain a hidden learning state vector h of the student at each momentt。
Optionally, the predicting student performance includes the following steps:
wherein the content of the first and second substances,
probability of answering the question for the student at the time of T + 1; w1，W2，b1，b2Is a model parameter; σ (x) is a sigmoid activation function;
the symbol represents a connection operation;
αt＝cos(eT+1,et)，etat the time of the t-th interaction, the problem difficulty and the student ability are embedded into the joint coding vector of the vector.
Optionally, the problem difficulty value difficulty (j) is obtained by the following formula:
wherein N isjIs a collection of students trying to answer problem j, xijIs the result of the first attempt by student i on problem j, if the total number of students answering problem j is less than 5, then the difficulty of this problem is defaulted to 0.5.
Optionally, the student ability value ability (i) is obtained by the following formula:
wherein Correct (ij) and Incorrect (ij) represent the probability that student i answered problem j correctly or incorrectly, where N isijRepresenting the number of times student i tries to answer problem j, ajtWhether student i answers question j correctly or incorrectly at the time of the tth time, 0 represents wrong answer, and 1 represents correct answer; if N is presentijLess than 5, then Difficulty (j) is used instead of ability (i).
Optionally, the problem difficulty is embedded into vector detObtained by the following method:
establishing a fully-connected neural network, inputting the network as a problem number j, outputting the network as problem difficulty Difficulty (j), and then randomly initializing det∈RKAs an embedded representation of the difficulty of the problem, automatically learning in the training process; the difficulty of the problem can be converted into an embedded matrix D e RQ×KWhere K is the dimension of the embedded vector and Q is the number of problems.
Optionally, the student ability is embedded in a vector setObtained by the following method:
establishing a full-connection neural network, inputting the number i of the student, outputting the number Abiliity (i) of the student, and randomly initializing set∈RKAs an embedded representation of student ability, automatic learning in the training process; the student ability can be converted into an embedded matrix A e RS×KAnd K is the dimension of the embedded vector, and S is the number of students.
Optionally, concealing student state vector htThe update process is as follows:
ht＝ot·tanh(ct)；
wherein it，ft，ot，ctRespectively, the weight matrix and offset in the input gate, the forgetting gate, the memory cell, the output gate of LSTM, and Z and b, respectively, of the corresponding gate.
Optionally, the depth knowledge tracking model is also trained, and the loss function during training is as follows:
wherein r istShowing the real answering situation at the time t,
showing the predicted answer situation at time t.
Compared with the prior art, the invention has the following technical characteristics:
the existing knowledge tracking method is mostly modeled only according to the answer sequence and answer results of students, and the influence of the student ability and exercise difficulty on the learning effect is not considered, so that the algorithm adds two characteristics of exercise difficulty and student ability in a deep knowledge tracking model.
The invention calculates the exercise difficulty and student ability, and uses the neural network to carry out embedded coding and reconstruct the model input.
The invention adds an attention mechanism during prediction, so that the model puts more attention on answer records with similar exercise difficulty and student ability.
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The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure without limiting the disclosure. In the drawings:
FIG. 1 is a flow chart of a method for deep embedded knowledge tracking based on problem difficulty and student ability;
FIG. 2 is a model diagram of a deep-embedding knowledge tracking method based on problem difficulty and student ability.
Detailed Description
The technical scheme of the invention is specifically explained by combining the attached drawings and the specific implementation mode, the invention mainly reforms the original deep knowledge tracking model, the original deep knowledge tracking model only focuses on the student answering situation, namely modeling is carried out according to the student answering sequence and answering result, the invention also introduces the exercise difficulty characteristic and the student ability characteristic at the same time, a new training set (namely the input vector of the model) is formed by jointly coding the student answering situation embedded vector, the exercise difficulty embedded vector and the student ability embedded vector to train the deep knowledge tracking model, the prediction accuracy of the model is improved, then the attention mechanism is added in the later prediction stage, even if the deep knowledge tracking model puts more attention on the answering records with similar exercise difficulty characteristic and/or similar student ability characteristic, the accuracy of predicting the probability of the student answering the question at the next moment is further improved.
The specific scheme comprises the following steps:
FIG. 1 shows a basic flow of a deep-embedding knowledge tracking method based on problem difficulty and student ability. As can be seen from fig. 1, the method mainly includes two stages of modeling and prediction:
a modeling stage: the student ability and the exercise difficulty are embedded and coded, the obtained embedded codes are combined with the student answering conditions, the input vectors are coded again to replace the original one-hot codes, the new input vectors not only carry out natural clustering on the student ability and the exercise difficulty, the relation between variables is kept, the dimensionality is reduced, and the model processing is more convenient.
A prediction stage: the model can predict the performance of each student in future interaction according to the historical answer records of the students.
Further, the knowledge tracking task is defined as follows:
a total of S students i, Q exercises j, S and Q are all natural numbers which are not 0; expressing the answer records of each student as
Wherein
Shows the answer records of the ith student at the time t,
is a correct/incorrect binary result, a 1 indicates a pair, and a 0 indicates a mistake. Recording one-time interaction of student i due to consideration of student ability and exercise difficulty
Is shown as
Wherein setIndicating the learning ability of student i to answer at time t, detIndicating the difficulty of the problem answered by the student at time t. Given a set of interaction sequences s { (e) of a student from time 1 to time T1,r1),(e2,r2),...,(eT,rT) Predicting the interaction e of the student at the moment T +1T+1Performance of (1)
Referring to FIG. 2: the invention also discloses a deep embedded knowledge tracking method based on exercise difficulty and student ability, which comprises the following steps:
step 1: acquiring exercise difficulty characteristics and student ability characteristics, and calculating through historical answer records of students to obtain exercise difficulty values Difficulty (j) and student ability values Ability (i);
step 2: embedding and coding according to the problem difficulty value Difficulty (j) and the student ability value Ability (i) to obtain a problem difficulty embedding vector detAnd student ability embedding vector set；
And step 3: student answering condition rtThe difficulty of exercise is embedded into vector detAnd student ability embedding vector setPerforming joint coding to obtain input vector
LSTM network obtains hidden learning state vector h of studentt；
And 4, step 4: according to attention weight alpha in predictiont(calculation of attention weight α according to equation (8)tJudging the similarity degree according to the attention weight, namely obtaining the answer records with similar exercise difficulty and similar student ability), so that the deep knowledge tracking model puts attention on the answer records with similar exercise difficulty and similar student ability, and predicts the probability of the student answering to the next moment.
The problem difficulty feature Difficulty (j) is obtained by the formula (1):
wherein N isjIs a collection of students trying to answer problem j, xijIs the result of the first attempt by student i on problem j (0 for making a mistake and 1 for making a pair), if the total number of students answering problem j is less than 5, then the difficulty of this problem is 0.5 by default.
Then establishing a full-connection neural network, inputting the network as a problem number j, outputting the network as problem difficulty Difficulty (j), and then randomly initializing det∈RKAs an embedded representation of the difficulty of the problem, it will learn automatically during the training process. Thus, the problem difficulty can be converted into an embedded matrix D e RQ×KWhere K is the dimension of the embedded vector and Q is the number of problems.
Further, the student ability characteristic ability (i) is obtained by formula 2:
wherein Correct (ij) and Incorrect (ij) represent the probability that student i answered problem j correctly or incorrectly, where N isijRepresenting the number of times student i tries to answer problem j, ajtWhether student i answered question j correctly or incorrectly at time t, 0 for wrong answer and 1 for correct answer. If N is presentijLess than 5, then Difficulty (j) is used instead of ability (i).
Then, a full-connection neural network is also established, the input of the network is the student number i, the output of the network is the student ability (i), and se is randomly initialized at the same timet∈RKAs an embedded representation of the student's ability, it will automatically learn during the training process. The student ability can be converted into an embedded matrix A e RS×KAnd K is the dimension of the embedded vector, and S is the number of students.
At each time step T ∈ (1.,. T.), the input of the network is the problem difficulty embedding detAnd student ability embedding setOf (e) joint codingt：
Wherein
Symbol representing the operation of two vectors connectedDo this.
The correct answer (1) and the wrong answer (0) have different influences on the student state in the learning process, so that the student answer condition value rtExpansion into a joint coded vector e embedded with problem difficulty and student abilityt0 vectors with the same dimension are input into the vector
Expressed as:
wherein
The symbol represents the operation of connecting two vectors, rtAnd (4) representing whether the student answers correctly or not when the student answers the question at the t-th interaction, wherein 0 represents that the student answers wrongly and 1 represents that the student answers the question.
Finally obtaining the combined student answer sequence
Then, the LSTM network is used for modeling the learning state of the student to obtain the hidden learning state h of the student at each momentt。
Further, the hidden student state vector htThe update process is as follows:
ht＝ot·tanh(ct) (5)；
wherein it，ft，ot，ctRespectively, the weight matrix and offset in the input gate, the forgetting gate, the memory cell, the output gate of LSTM, and Z and b, respectively, of the corresponding gate.
Further, σ (x) is sigmoid nonlinear activation function:
further, tanh (x) is also a nonlinear activation function:
after all parameters are initialized, modeling of the exercise process of each student from step 1 to T is started, and the performance of the student at step T +1 is predicted. As students with similar learning ability can obtain similar answers when answering questions with similar difficulty, an attention mechanism is added in the prediction process, and the model can put attention in student answer records with similar learning ability and similar exercise difficulty.
Further, the attention mechanism implementation process comprises the following steps:
step a: calculating the attention weight α according to equation (8)t：
αt＝cos(eT+1,et) (8)；
Wherein e istWhen the user interacts for the t time, the exercise difficulty and the student ability are embedded into a joint coding vector of the vector;
step b: at step T +1, the student status is the weighted sum of all historical student statuses in the process. Defining an attention mechanics birth state vector h according to equation (9)att：
Step c: after the attention mechanical state is obtained in the T +1 step, combining the input e of the current T +1 stepT+1And (3) predicting the performance of the student at the step T +1 according to the formula (10):
wherein, W1，W2，b1，b2Is the model parameter, σ (x) is the sigmoid activation function,
the symbol indicates the operation of the connection,
the probability of answering the topic at time T +1 for the student.
Specifically, the loss function during training is:
wherein r istShowing the real answering situation at the time t,
showing the predicted answer situation at time t.
Example 1:
the data set selected in the embodiment is real-world public data sets ASSISTMENTs, which is a free learning platform and is used for arranging mathematical assignments and classroom assignments for students and providing feedback information for teachers. Assistmetents 2009-2010 is a data set collected by assistmetents intelligent tutoring system. This online data set is publicly available and has been widely used by researchers working with knowledge tracking. In this example, we performed experiments using data from 2009-2010. This data set had 338,001 answer records, including 4,216 students and 24,896 subjects. In the experiment, the number of hidden units of the LSTM network is set to 16, and when the Adam algorithm is used for model training, the initial learning rate is set to 0.01, and the learning attenuation rate is set to 0.0005. The number of iterations was set to 500. Implemented using a Tensorflow framework, the runtime environment is an ubuntu server.
The task of predicting student performance is considered a classification question in which correct answers by students are positive examples and incorrect answers are negative examples. And selecting an area AUC under the ROC curve as an evaluation index, wherein the value range of the AUC is 0-1, 0.5 represents that a prediction result is random, and the larger the value is, the better the performance is.
TABLE 1 ASSISTMENTS 2009-2010 data set Performance prediction results of each model student
Compared with other knowledge tracking models, the deep embedding knowledge tracking method based on the problem difficulty and the student ability has higher prediction precision on the problem of predicting the future performance of the student. As shown in table 1, when 80% of the sequences in the dataset were selected as training data and the remainder as test data, the AUC values of the deep-embedding knowledge tracking method (DKT-DAA) based on problem difficulty and student ability were increased by 19%, 14%, 10% respectively over baseline methods BKT, PFA, DKT, DKVMN.
The method considers two characteristics of exercise difficulty and student ability, integrates an attention mechanism, further considers the similarity between interaction records with similar exercise difficulty and student ability, and captures important characteristics influencing the learning state of students. The deep embedding knowledge tracking method based on the problem difficulty and the student ability improves the knowledge tracking effect.
In addition, after the knowledge tracking method provided by the embodiment of the invention realizes knowledge tracking of students, the knowledge tracking method can be used in other technical application layers, such as intelligent education fields of personalized learning route recommendation, intelligent learning situation analysis and the like. Taking exercise recommendation as an example, knowledge tracking of students can be realized according to the scheme, the predicted student exercise accuracy is obtained according to the knowledge tracking result, and exercises in a certain range are recommended to the students according to the probability, so that individuation of the learning process is realized. By taking intelligent learning situation analysis as an example, knowledge tracking can be achieved according to the scheme to obtain the exercise mastering conditions of students, so that a teacher can be helped to master the learning requirements of individual students more accurately, more professional guidance opinions are provided for reasonably planning teaching resources and selecting a proper teaching mode, and the precision of the teaching process is realized.
Claims (10)
1. A deep embedded knowledge tracking method based on exercise difficulty and student ability is characterized by comprising the following steps:
s1, constructing a depth knowledge tracking model: the depth knowledge tracking model is further integrated with exercise difficulty characteristics and student ability characteristics;
s2 predicts student performance: and (4) combining an attention mechanism, and predicting the student performance by using the depth knowledge tracking model constructed in the step one.
2. The method for tracking deeply embedded knowledge based on problem difficulty and student ability according to claim 1, wherein S students i, Q problems j, te e (1,. T), S and Q are both natural numbers other than 0, and S1 specifically comprises:
step 1: acquiring exercise difficulty characteristics and student ability characteristics, and calculating through historical answer records of students to obtain exercise difficulty values Difficulty (j) and student ability values Ability (i);
step 2: embedding and coding according to the problem difficulty value Difficulty (j) and the student ability value Ability (i) to obtain a problem difficulty embedding vector detAnd student ability embedding vector set；
And step 3: student answering condition rtThe difficulty of exercise is embedded into vector detAnd student ability embedding vector setTo carry outJoint coding to obtain input vector
LSTM network obtains hidden learning state vector h of studentt；
And 4, step 4: according to attention weight alpha in predictiontThe depth knowledge tracking model is enabled to put attention on answer records with similar exercise difficulty and similar student ability, and the probability of answering the questions at the next moment by the students is predicted.
3. The method of claim 1 or 2, wherein the input vector is a deep embedded knowledge tracking method based on difficulty of problem and student ability
Obtained by the following formula:
wherein, detEmbedding vectors, se, for problem difficultytEmbedding vectors, r, for student abilitytRepresenting the answering condition of the students; problem difficulty embedding detAnd student ability embedding setIs coded as et；
Modeling the learning state of the student by using an LSTM network to obtain a hidden learning state vector h of the student at each momentt。
4. The method for tracking deeply embedded knowledge based on difficulty of problem and ability of student according to claim 1 or 2, wherein said predicting student performance comprises the steps of:
wherein the content of the first and second substances,
probability of answering the question for the student at the time of T + 1; w1，W2，b1，b2Is a model parameter; σ (x) is a sigmoid activation function;
the symbol represents a connection operation;
αt＝cos(eT+1,et)，etat the time of the t-th interaction, the problem difficulty and the student ability are embedded into the joint coding vector of the vector.
5. The method for deep embedded knowledge tracking based on problem difficulty and student ability according to claim 1 or 2, wherein the problem difficulty value difficullty (j) is obtained by the following formula:
wherein N isjIs a collection of students trying to answer problem j, xijIs the result of the first attempt by student i on problem j, if the total number of students answering problem j is less than 5, then the difficulty of this problem is defaulted to 0.5.
6. The method for tracking deeply embedded knowledge based on difficulty of problem and ability of student according to claim 1 or 2, wherein the ability value Ability (i) of student is obtained by the following formula:
wherein Correct (ij) and Incorrect (ij) represent the probability that student i answered problem j correctly or incorrectly, where N isijRepresenting the number of times student i tries to answer problem j, ajtWhether student i answers question j correctly or incorrectly at the time of the tth time, 0 represents wrong answer, and 1 represents correct answer; if N is presentijLess than 5, then Difficulty (j) is used instead of ability (i).
7. The method for tracking deeply embedded knowledge based on problem difficulty and student ability according to claim 1 or 2, wherein the problem difficulty embedding vector detObtained by the following method:
establishing a fully-connected neural network, inputting the network as a problem number j, outputting the network as problem difficulty Difficulty (j), and then randomly initializing det∈RKAs an embedded representation of the difficulty of the problem, automatically learning in the training process; the difficulty of the problem can be converted into an embedded matrix D e RQ×KWhere K is the dimension of the embedded vector and Q is the number of problems.
8. The method for tracking deeply embedded knowledge based on difficulty of problem and ability of student as claimed in claim 1 or 2, wherein said student ability embedding vector setObtained by the following method:
establishing a full-connection neural network, inputting the number i of the student, outputting the number Abiliity (i) of the student, and randomly initializing set∈RKAs an embedded representation of the ability of the student,automatic learning in the training process; the student ability can be converted into an embedded matrix A e RS×KAnd K is the dimension of the embedded vector, and S is the number of students.
9. The method of claim 1 or 2, wherein the student state vector h is hiddentThe update process is as follows:
ht＝ot·tanh(ct)；
wherein it，ft，ot，ctRespectively, the weight matrix and offset in the input gate, the forgetting gate, the memory cell, the output gate of LSTM, and Z and b, respectively, of the corresponding gate.
10. The method for tracking deeply embedded knowledge based on problem difficulty and student ability according to claim 1 or 2, characterized in that the deep knowledge tracking model is further trained, and the loss function during training is:
wherein r istShowing the real answering situation at the time t,
showing the predicted answer situation at time t.
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