CN111538868A - Knowledge tracking method and exercise recommendation method - Google Patents
Knowledge tracking method and exercise recommendation method Download PDFInfo
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Abstract
The invention discloses a knowledge tracking method and a problem recommendation method, which improve the accuracy of knowledge tracking and the effect of subsequent application by improving a data processing mode, and particularly comprise the following steps: the learning migration is modeled by using a knowledge structure (represented by a graph structure), so that the effect of knowledge tracking is enhanced. In the modeling process, the influence of learning migration is quantified, so that the interpretability of the method is enhanced while the effect is improved; the knowledge tracking result can be used in subsequent application, and the application effect is improved.
Description
Technical Field
The invention relates to the technical field of machine learning and education data mining, in particular to a knowledge tracking method and a problem recommendation method.
Background
Knowledge Tracking (KT) is a technique for tracking the learning state of a student, which dynamically changes, during the learning process, based on the historical learning records of the student. Knowledge tracking is an indispensable loop in many intelligent educational applications. Education theory has proved that 'learning migration' plays a crucial role in human learning, but simultaneously indicates the complexity of the action mechanism, and no research can be carried out to effectively quantify the action. Although the action mechanism of "learning migration" is not clear at present, related studies prove that the action is hidden in the "knowledge structure". However, most of the previous researches neglect the influence of 'learning migration' hidden in the 'knowledge structure', and a small part of work just uses a limited method to model the influence of 'learning migration', so that the universality is poor.
Therefore, the prior art has defects and unreasonables in the data processing level, so that the accuracy of knowledge tracking and the effect of subsequent application are restricted.
Disclosure of Invention
The invention aims to provide a knowledge tracking method and a problem recommendation method, which can enhance the knowledge tracking effect and improve the effect of subsequent application.
The purpose of the invention is realized by the following technical scheme:
a knowledge tracking method, comprising:
collecting historical answer sequences generated in the process of doing questions by students and a graph structure formed by knowledge points and the relation of the knowledge points in the questions, wherein the graph structure is called a knowledge structure;
the method comprises the steps of obtaining a plurality of sub-knowledge structures only containing single type relations by segmenting a knowledge structure, extracting embedded vectors of the sub-knowledge structures by using a graph neural network, and finally obtaining the embedded vectors of the knowledge structure by combining the embedded vectors to quantify learning migration influence among knowledge points based on an attention mechanism;
the embedded vector of the knowledge structure is combined with the historical answering sequence, and then the learning state vector of the student is obtained through the LSTM network and the full connection layer.
A problem recommendation method utilizes the knowledge tracking method to realize knowledge tracking of students, generates a problem list according to knowledge tracking results and recommends the problem list to corresponding students.
According to the technical scheme provided by the invention, the accuracy of knowledge tracking and the effect of subsequent application are improved by improving the data processing mode, and specifically: the learning migration is modeled by using a knowledge structure (represented by a graph structure), so that the effect of knowledge tracking is enhanced. In the modeling process, the influence of learning migration is quantified, so that the interpretability of the method is enhanced while the effect is improved; the knowledge tracking result can be used in subsequent application, and the application effect is improved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
FIG. 1 is a stylized depiction of knowledge tracking provided by an embodiment of the present invention;
fig. 2 is a block diagram of a knowledge tracking method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The inventionThe embodiment provides a knowledge tracing method, which is a formal description diagram of knowledge tracing as shown in fig. 1. For the knowledge tracking task, the objective is to (1) infer the student's answer situation at every moment in the past according to the student's answer sequence, and (2) simultaneously infer the student's performance in the future answer process. Giving students a historical response sequence Xt＝{xtT ∈ {0,1, …, T } }, where xt＝(et,rt)，rtShow student at exercise e at time ttThe above response scenario. r ist0 means that the student did not answer correctly at time t et(e.g. in FIG. 12)，r t1 means that the student correctly answered e at time tt(e.g. in FIG. 11、e3、e4). At each moment the student answers etOne or more knowledge points are associated and the association is represented by a Q-matrix (table Q-matrix at the top right of fig. 1). Note etThe set of knowledge points involved (examined) is ct＝{ct,1,ct,2…, any knowledge point in the set is a vertex on the knowledge structure G (v,). Knowledge Structure G (v,) (Knowledge Structure below the right part of fig. 1) consists of a set of vertices v ═ v1,v2,…,vMSet of relations (edges)
Composition, wherein M is the number of vertices and K is the number of relationship types; the knowledge structure comprises knowledge points and corresponding relations corresponding to all the exercises in the historical answering sequence. The points in each set of vertices represent a knowledge point. The relationship set comprises a plurality of types of relationships, and the ith type of relationship is recorded as
Each element represents a continuous edge. Some types of classes may be directed edges, such as predecessor successor relationships (arrow lines in the Knowledge Structure below the right part of fig. 1):
representing a vertex vxIs the vertex vzIn the ith relationship RiLower, by edge
Connecting; while other kinds of relationships may be undirected, such as a similar relationship (lines without arrows in the Knowledge Structure below the right part of FIG. 1):
representing a vertex vxIs the vertex vzSimilarly, the two are in the j-th relation RjLower, by edge
Are connected. Considering the student 'S historical answer sequence and knowledge structure comprehensively, one of the purposes of knowledge tracking is to deduce the knowledge state at every moment in the student' S answering process, i.e. S ═ S1,S2,…,ST(radar plot on the top left part of FIG. 1). Knowledge state S at any timetThe length is M, each dimension corresponds to a knowledge point, the value on each dimension is a continuous value between 0 and 1, the grasping condition of the knowledge point is represented, 0 is completely not grasped, and 1 is completely grasped. Meanwhile, another purpose of knowledge tracking is to guess the performance of students in the future answering process, namely answering e at the t +1 momentt+1In the case of (2), the conditional probability that the student correctly answers the question is P (r)t+1＝1|et+1,x1,…,t,G)。，x1,…,tIs equivalent to x1,x2,…,xt。
As shown in fig. 2, the model framework for knowledge tracking mainly includes the following steps:
firstly, data collection and preprocessing.
1. And (6) collecting data.
In the embodiment of the invention, the answer log records generated in the student question making process and the graph structure formed by knowledge points and the knowledge point relations in the exercises can be collected from the open source education platform data, and the graph structure is called as the knowledge structure.
2. And (4) preprocessing data.
1) Log sorting and ordering
In the embodiment of the invention, the logs are required to be sorted into answering sequences according to the student id, the session id and the answering time, the student id and the session id are the same in each answering sequence, and the answering sequences are arranged from front to back according to the answering time.
As previously described, the historical response sequence is represented as: xt＝{xtT ∈ {0,1, …, T } }, the answer record x at time Tt＝(et,rt)，rtShow student at exercise e at time ttThe above response condition; r ist0 means that the student did not answer correctly at time t et，r t1 indicates that the student correctly answers exercise e at time tt(ii) a Exercise etOne or more knowledge points are associated, and the association is represented by a Q-matrix. Exercise etThe associated knowledge point is denoted ct＝{ct,1,ct,2…, any knowledge point in the set is a vertex on the knowledge structure G (v,), and the knowledge point relationship forms a connecting edge in the knowledge structure G (v,); according to different relation categories of the knowledge points, the continuous edges are further divided into directed edges and undirected edges.
2) Removing conflicts in "knowledge Structure
There is a potential relationship conflict in the knowledge structure, and the subgraph formed by the directed relationship (such as the predecessor successor relationship) should be a directed acyclic graph, i.e. there should not be a cyclic structure (cyclic case) of a → b → c → a. In order to ensure that a subgraph formed by directed relationships is a directed acyclic graph, any edge in the ring is deleted for the ring condition.
And secondly, establishing a model structure.
Students continuously acquire new knowledge through learning, and the knowledge state, namely the mastery degree of the knowledge, is continuously changed in learning. In the process of student learning, learning migration is an important factor. Learning migration describes the process of migrating existing knowledge to new knowledge by students, i.e. learning of new knowledge points is affected by mastered knowledge points. Educational theory has demonstrated that this effect is important and difficult to quantify. At present, educational experts indirectly describe the influence mainly by means of labeling a knowledge structure, but the quantification of the influence still is a problem to be solved urgently. Most of the previous knowledge tracking research works ignore the influence of learning migration hidden in a knowledge structure and only utilize the answering sequence information of students; little work is also just a limited method to model the influence of learning migration by using knowledge structures, and the universality is poor. In fact, there are difficulties and challenges to use a knowledge structure heterogeneous graph network containing a plurality of different relationships for quantifying learning migration impact and enhancing knowledge tracking effect: (1) how to characterize the knowledge structure of the heterogeneous graph network; (2) how to quantify the influence of learning migration between knowledge points; (3) in the knowledge tracking process, the influence brought by learning migration is fully considered, so that the model effect is enhanced.
In order to solve the above challenges, better utilize the knowledge Structure to quantify the learning migration impact, and finally enhance the knowledge tracking effect, the embodiment of the present invention designs two modules, a Structure embedding module (Structure embedding Layer) and a Sequence module (Sequence Layer). The structure embedding module is responsible for quantifying learning migration influence by using the knowledge structure and generating knowledge structure embedding vectors. The sequence module further considers the structure vector obtained by the structure embedding module on the basis of modeling the student answering sequence in the traditional mode, thereby enhancing the knowledge tracking effect.
1. The structure is embedded in the module.
As shown in part (b) of fig. 2, in the structure embedding module, the knowledge structure is segmented by the relationship type to obtain a plurality of sub-knowledge structures only containing relationships of a single type, the embedded vectors of the sub-knowledge structures are extracted by using a graph neural network, and the learning migration influence between knowledge points is quantified based on an attention mechanism by combining each embedded vector, so that the embedded vectors of the knowledge structure are finally obtained.
1) And (5) segmenting a knowledge structure.
The knowledge structure G (v,) is segmented, and a plurality of sub-knowledge structures containing only single type relations are obtained:
each sub-knowledge structure
The same vertex set is owned as the knowledge structure G (v), but its relationship type is only one of the "knowledge structure" relationship types, K being 1,2, …, K, where K is the relationship type number.
2) And (5) mapping a neural network.
In the embodiment of the invention, the embedded vector of each sub-knowledge structure is extracted by using a graph convolution neural network based on message propagation to obtain
The algorithm is as follows:
v referred to in the above code is equivalent to v in the text1,v2,…,vMFor ease of representation, corner labels are omitted from the code.
3) Quantization of the transition layer
The quantization migration layer is realized based on an attention mechanism, and an embedded vector of each sub knowledge structure is obtained
Then, the influence of learning migration between knowledge points is quantified by combining each embedded vector by using a quantization migration layer.
As shown in fig. 2 (d), first, the embedded vectors of the knowledge structures are summed:
wherein ,
representing a kth sub-knowledge structure embedding vector
Vector of middle knowledge point v
The f-th element of (1);
the summation result of the vectors of the knowledge points v which represent the embedding of K sub-knowledge structures into the vectors is obtained;
represents K
The result of the summation of (a) and (b),
is composed of
The f-th element of (1);
then, a self-normalized dot-product attention layer (scaled dot-product attention) is used to quantify the learning migration between knowledge points, as shown in part (e) of fig. 2, i.e., the sub-graph vector to be summed
As Q, K, V in the attention algorithm, i.e.
Thereby obtaining knowledge point embedding vectors after influence of attention mechanism quantitative learning migration:
wherein ,
representing the summed vector
Knowledge point embedding vector after influence of attention mechanism quantitative learning migration, dvIs that
The vector length of (2).
Then, a feedforward neural network is used for further extracting knowledge structure information on the basis of an embedded vector generated by a self-normalized point-multiplied attention layer, and a final embedded vector of a knowledge structure is obtained by adding a residual connection; the FFN layer is composed of two layers of feedforward neural networks, and the middle hidden layer uses a RELU activation function:
wherein ,
to represent
Inputting the vector obtained after the input FFN first layer feedforward neural network,
an embedded vector, W, representing a knowledge point v in the resulting knowledge structure1、b1、W2、b2Is a parameter to be learned, W is a weight term, and b is a bias term; LayerNorm TableLayer regularization layer, like softmax of the previous formula, is a common notation in the art.
2. And a sequence module.
Since the learning migration effect existing between knowledge points can affect the cognitive process of students, the learning migration effect should be taken into consideration when modeling the student response sequence. Therefore, on the basis of the traditional modeling mode, the knowledge structure embedded vector is combined with the student answering sequence, and the learning state vector of the student is obtained through the LSTM network and the full connection layer. As shown in part (a) of fig. 2, the following is specific:
as previously described, problem e for time ttIts associated knowledge point vector is ct＝{ct,1,ct,2,…}，ctIs a vector of length M, whose mth element indicates problem etWhether the mth knowledge point is examined. c. C t,m1 denotes the exercise etThe mth knowledge point is examined, otherwise, none is found. Then, the constructed concept incidence matrix is used
To construct a vector of associated knowledge points
wherein ,
wherein ,
in the above formula, the first and second carbon atoms are,
to represent
The s-th element of (c)t,sRepresenting a knowledge point vector ctThe s-th vector of c t,s1 denotes the exercise etCorresponding knowledge points are investigated;
record x of answers for time ttVectorizing by using one-hot encoding to obtain response vector
wherein ,
is that
The j' th element of (1).
Using an embedding layer to carry out dimension compression on the response vector so as to reduce the calculation amount and obtain the response embedding vector:
wherein ,WeIs an embedded layer weight matrix;
associating knowledge point vectors
And-answering embedded vectors
Splicing to obtain a response vector containing learning migration information:
as shown in part (c) of fig. 2, the learning state hidden vector h ═ { h } for each time of the student is calculated using LSTM (long short term memory network)1,h2…, each time step is inputted with a response vector containing learning migration information, the t-th time step, the hidden vector h of LSTMtThe update is as follows:
it＝σ(Wxixt′+Whiht-1+bi)
ft＝σ(Wxfxt′+Whfht-1+bf)
ot＝σ(Wxoxt′+Whoht-1+bo)
ct＝ftct-1+ittanh(Wxcxt′+Whcht-1+bc)
ht＝ottanhct
wherein ,it,ft,ot,ctThe input gate, the forgetting gate, the memory cell and the output gate of the LSTM respectively, and the weight matrix and the offset in the corresponding gate of W and b respectively; taking the input gate as an example, Wxi、WhiRespectively, an input response vector xt', and the previous time hidden vector ht-1Weight of (a), biIs the polarization of the input gate;
implicit vector htAs an intermediate quantity, o is calculated in the above mannertI.e. learning state hidden vector, using a full-connected layer to obtain the learning state vector S of the student from the learning state hidden vectort：
St＝σ(Wosot+bs)。
wherein ,Wos、bsIs a parameter to be learned, and sigma is a sigmoid activation function;
then, the probability that the student answers the exercise at the next moment can be utilized by using the obtained learning state vector:
wherein ,St,s’Represents a learning state vector StThe s' th element in (a); c. Ct+1Shows the exercise e at time tt+1Associated knowledge point vector, ct+1,s’Denotes ct+1The s' th vector of (1), c t+1,s’1 represents that the corresponding knowledge point is considered; p (r)t+11) problem e representing the time when the student answers pair t +1t+1The probability of (c).
The expression of the above formula means that the probability of answering the question at the time t +1 is equal to the cumulative multiplication of the knowledge mastery degree on the knowledge points examined at the time t + 1. For example, at time t + 1, the topic looks at knowledge points 1 and 3, then P (r)t+1＝1)＝St,1·St,3。
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 student user portrayal, adaptive learning and the like. Taking the exercise recommendation method as an example, knowledge tracking of students can be realized according to the scheme, an exercise list is generated according to knowledge tracking results, and the exercise list is recommended to corresponding students. Taking the user portrait as an example, knowledge tracking can be realized according to the scheme, and the mastery degree of the knowledge points of the user at each moment is obtained, so that the mastered knowledge points, the mastered weak knowledge points and the like of the user are found out, and the user portrait is formed.
Through the above description of the embodiments, it is clear to those skilled in the art that the above embodiments can be implemented by software, and can also be implemented by software plus a necessary general hardware platform. With this understanding, the technical solutions of the embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a usb disk, a removable hard disk, etc.), and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods according to the embodiments of the present invention.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (9)
1. A method of knowledge tracking, comprising:
collecting historical answer sequences generated in the process of doing questions by students and a graph structure formed by knowledge points and the relation of the knowledge points in the questions, wherein the graph structure is called a knowledge structure;
the method comprises the steps of obtaining a plurality of sub-knowledge structures only containing single type relations by segmenting a knowledge structure, extracting embedded vectors of the sub-knowledge structures by using a graph neural network, and finally obtaining the embedded vectors of the knowledge structure by combining the embedded vectors to quantify learning migration influence among knowledge points based on an attention mechanism;
the embedded vector of the knowledge structure is combined with the historical answering sequence, and then the learning state vector of the student is obtained through the LSTM network and the full connection layer.
2. A knowledge tracking method as claimed in claim 1, wherein the historical response sequence is represented by: xt＝{xtT ∈ {0,1, …, T } }, the answer record x at time Tt＝(et,rt)，rtShow student at exercise e at time ttThe above response condition; r ist0 means that the student did not answer correctly at time t et，rt1 indicates that the student correctly answers exercise e at time tt(ii) a Exercise etOne or more knowledge points are associated, and the association is represented by a Q-matrix.
3. A method for tracking knowledge as claimed in claim 1 or 2 in which problem etThe associated knowledge point is denoted ct＝{ct,1,ct,2…, any knowledge point in the set is a knowledge structure
The relation of the top point and the knowledge point forms a knowledge structure
The connecting edge of (1); according to different relation categories of the knowledge points, the continuous edges are further divided into directed edges and undirected edges.
4. The knowledge tracking method of claim 3, wherein processing the knowledge structure to remove knowledge point relationship conflicts existing in the knowledge structure before segmenting the knowledge structure comprises: directed edges form a directed acyclic graph, and if a loop result exists in the graph, any edge in the loop structure is deleted.
5. A knowledge tracking method as claimed in claim 3, characterized in that for the knowledge structure
And performing segmentation to obtain a plurality of sub-knowledge structures only containing single type relations:
each sub-knowledge structure
Possession and knowledge structure
The same vertex set, K ═ 1,2, …, K, where K is the relationship type number.
6. The knowledge tracking method of claim 1, wherein the extracting of the embedded vectors of the sub-knowledge structures by using the neural network of the graph, and then quantifying learning migration influence among the knowledge points based on an attention mechanism by combining the embedded vectors to finally obtain the embedded vectors of the knowledge structures comprises:
extracting the embedded vector of each sub-knowledge structure by using a graph convolution neural network based on message propagation to obtain
Wherein K is the number of relationship types;
quantifying learning migration effects between knowledge points based on an attention mechanism in conjunction with individual embedded vectors: first, the embedded vectors of the knowledge structures are summed:
wherein ,
representing a kth sub-knowledge structure embedding vector
The vector of the medium knowledge point v,
vector representing knowledge point v in K sub-knowledge structure embedded vectors
The sum of the results;
then, self-normalized point-by-attention layers are used for quantifying learning migration among knowledge points, namely adding up sub-graph vectors
As Q, K, V in the attention algorithm, i.e.
Thereby obtaining knowledge point embedding vectors after influence of attention mechanism quantitative learning migration:
wherein ,
representing the summed vector
Knowledge point embedding vector after influence of attention mechanism quantitative learning migration, dvIs that
The length of the vector of (a) is,
representing knowledge structure
Each node corresponds to a knowledge point;
then, a feedforward neural network is used for further extracting knowledge structure information on the basis of an embedded vector generated by a self-normalized point-multiplied attention layer, and a final embedded vector of a knowledge structure is obtained by adding a residual connection; the FFN layer is composed of two layers of feedforward neural networks, and the middle hidden layer uses a RELU activation function:
wherein ,
to represent
Inputting the vector obtained after the input FFN first layer feedforward neural network,
an embedded vector, W, representing a knowledge point v in the resulting knowledge structure1、b1、W2、b2Is the LayerNorm to be learned parameter representing the layer regularization layer.
7. The knowledge tracking method of claim 3, wherein the step of combining the embedded vector of the knowledge structure with the historical answering sequence and obtaining the learning state vector of the student through the LSTM network and the full connection layer comprises the following steps:
by constructed concept incidence matrix
To construct a vector of associated knowledge points
wherein ,
an embedded vector representing the resulting knowledge structure,
representing knowledge structure
Each node corresponds to a knowledge point; concept correlation matrix
The s element of
Expressed as:
wherein ,ct，sRepresenting a knowledge point vector ctThe s-th vector of ct，s1 denotes the exercise etCorresponding knowledge points are investigated;
record x of answers for time ttVectorizing by using one-hot code to obtain answering vector
wherein ,
is that
The j' th element of (a);
using an embedding layer to carry out dimension compression on the response vector to obtain a response embedding vector:
wherein ,WeIs an embedded layer weight matrix;
associating knowledge point vectors
And-answering embedded vectors
Splicing to obtain a response vector containing learning migration information:
learning state hidden vector h ═ h for each moment of the student by using LSTM1，h2…, each time step is inputted with a response vector containing learning migration information, the t-th time step, the hidden vector h of LSTMtThe update is as follows:
it＝σ(Wxixt′+Whiht-1+bi)
ft＝σ(Wxfxt′+Whfht-1+bf)
ot＝σ(Wxoxt′+Whoht-1+bo)
ct＝ftct-1+ittanh(Wxcxt′+Whcht-1+bc)
ht＝ottanhct
wherein ,it，ft，ot，ctThe input gate, the forgetting gate, the memory cell and the output gate of the LSTM respectively, and the weight matrix and the offset in the corresponding gate of W and b respectively;
calculate o in the above mannertI.e. learning state hidden vector, using a full-connected layer to obtain the learning state vector S of the student from the learning state hidden vectort：
St＝σ(Wosot+bs)
wherein ,Wos、bsIs the parameter to be learned, and σ is the sigmoid activation function.
8. A method for knowledge tracking according to claim 1 or 7, the method further comprising: and (3) utilizing the obtained learning state vector to determine the probability of the student answering the exercise at the next moment:
wherein ,St,s’Represents a learning state vector StThe s' th element in (a); c. Ct+1Shows the exercise e at time tt+1Associated knowledge point vector, ct+1,s’Denotes ct+1The s' th vector of (1), ct+1,s’1 represents that the corresponding knowledge point is considered; p (r)t+11) problem e representing the time when the student answers pair t +1t+1The probability of (c).
9. A problem recommendation method is characterized in that the knowledge tracking method of any one of claims 1 to 8 is used for realizing knowledge tracking of students, and a problem list is generated according to knowledge tracking results and recommended to the corresponding students.
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