Method for dynamically tracking knowledge change of student

Abstract

The invention discloses a method for dynamically tracking knowledge changes of students, and relates to the field of knowledge tracking in intelligent education. The method comprises the following steps: constructing a knowledge state model of students based on independent increment characteristics of student knowledge increase; constructing a meta-knowledge dictionary based on the knowledge points of the learning items, and constructing a Bayesian framework of question answering by the students according to the meta-knowledge dictionary and the knowledge state model of the students to obtain a loss function model of question answering by the students; and according to the answer data of the students and the loss function model of the questions answered by the students, obtaining a loss function result of the questions answered by the students by adopting an alternating direction multiplier method, and according to the loss function result of the questions answered by the students, updating the meta-knowledge dictionary and the knowledge states of the students by adopting a coordinate descent strategy. And the knowledge state change of the student is dynamically tracked. The method can effectively diagnose the current knowledge state of the student, does not need a large amount of offline training, and can adapt to a dynamically changing online learning environment.

Description

Technical Field

[0001] The present invention relates to the field of knowledge tracking in intelligent education, and in particular to a method for dynamically tracking changes in student knowledge. Background Art

[0002] Accurately assessing students' learning status is crucial for recommending resources that are suitable for their learning needs. Knowledge tracing technology is key to achieving this goal, which predicts students' future performance by analyzing their learning history. Methods based on traditional Bayesian knowledge tracing models simplify learners' knowledge status into binary form, while methods based on deep knowledge tracing models regard students' knowledge status as continuous and use recurrent neural networks to predict learners' performance.

[0003] At present, although the methods based on deep knowledge tracing models have made significant progress in knowledge tracing, they mainly focus on predicting learners' future learning performance, but fail to effectively diagnose students' current knowledge status. In addition, these methods often require a lot of offline training and are not suitable for dynamically changing online learning environments. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for dynamically tracking changes in student knowledge.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for dynamically tracking student knowledge changes, comprising the following steps: S1. Construct a student's knowledge status model based on the independent incremental characteristics of student knowledge growth; S2. Build a meta-knowledge dictionary based on the knowledge points of the learning project, and build a Bayesian framework for students to answer questions based on the meta-knowledge dictionary and the student's knowledge state model in step S1 to obtain a loss function model for students to answer questions; S3. According to the students' answer data and the loss function model of the students' answers in step S2, the alternating direction multiplication method is used to obtain the loss function results of the students' answers. According to the loss function results of the students' answers, the coordinate descent strategy is used to update the meta-knowledge dictionary and the students' knowledge status to dynamically track changes in the students' knowledge status.

[0006] Furthermore, in step S1, a knowledge state model of students is constructed based on the independent incremental characteristics of students' knowledge growth, which is expressed as: , , ; in: is the student's knowledge state at time t, is the student's knowledge state at time s, is a normal distribution with mean 0 and variance ts, The knowledge status of students, is the incremental distribution satisfied by the student's knowledge state, is the linear transformation matrix, is the normal distribution variance of X, X is the increment of students’ knowledge growth, is the transpose symbol, For students' knowledge status Transfer to The probability density function of is the exponential function symbol, For students at all times The knowledge state vector, For students at all times The knowledge state vector, For the time series i time, For the time series i +1 moment.

[0007] Furthermore, in step S2, a meta-knowledge dictionary is constructed based on the knowledge points of the learning project. The specific process is: the knowledge points of the learning project are divided into minimum knowledge point units, and the minimum knowledge point units are indivisible and only include one state of mastering or not mastering, and their linear combination is used to represent knowledge entities, and the minimum knowledge point units are numbered to construct a corresponding matrix to construct a meta-knowledge dictionary.

[0008] Furthermore, in step S2, based on the meta-knowledge dictionary and the student's knowledge state model in step S1, a Bayesian framework for students to answer questions is constructed, which is expressed as: , , , ; in: For a given dictionary matrix and students’ knowledge status , the students' answers to the questions y follow the mean , the variance is The normal distribution of The mean is , the variance is The normal distribution of is the dictionary matrix No.i List, The mean is 0 and the variance is The normal distribution of For students i row knowledge state vector, is a Laplace distribution with mean 0 and scale parameter b, is a normal distribution with mean 0 and variance ts, For students at all times The knowledge state vector, For students at all times The knowledge state vector, For the time series i time, For the time series i +1 moment.

[0009] Furthermore, in step S2, the loss function model of the student answering the question is obtained, which is expressed as:

[0010] in: is the loss function for students answering questions, To obtain the minimum value, Representation Knowledge Dictionary and the state of knowledge Student answer data matrix The reconstruction error, is the Frobenius norm square loss function, For the student answer data matrix, is the dictionary matrix, The knowledge status of students, is the number of students, For tracking items, For students i +1 row knowledge state vector, For students i row knowledge state vector, is the dictionary matrix No. i OK.

[0011] Further, in step S3, according to the student's answer data and the loss function model of the student's answer question in step S2, the alternating direction multiplication method is used to obtain the loss function result of the student's answer question, including the following steps: A1. Using the alternating direction multiplier method, the meta-knowledge dictionary is updated with the student's knowledge state fixed, expressed as:

[0012] in: is the dictionary matrix The loss function is Representation Knowledge Dictionary and the state of knowledge Student answer data matrix The reconstruction error, is the Frobenius norm square loss function, For the student answer data matrix, is the dictionary matrix, The knowledge status of students, is the number of students, is the dictionary matrix No. i OK; A2. Using the alternating direction multiplier method, the student's knowledge state is updated under the condition of a fixed meta-knowledge dictionary, which is expressed as:

[0013] in: The state of knowledge for students The loss function is For students i +1 row knowledge state vector, For students i row knowledge state vector; A3. Calculate the first term of the loss function model for students’ answers, expressed as:

[0014] in: is the trace of the matrix, is the transpose symbol; A4. According to the updated meta-knowledge dictionary in step A1, the updated student's knowledge status in step A2, and the first item of the loss function model of the student's answer to the question in step A3, obtain the loss function result of the student's answer to the question.

[0015] Further, in step S3, according to the loss function result of the student's answer to the question, the coordinate descent strategy is used to update the meta-knowledge dictionary and the student's knowledge state, including the following steps: B1. According to the loss function result of the student's answer, determine the meta-knowledge dictionary and the student's knowledge state, expressed as: , , , , ; in: is the student's knowledge state at time t, is a function that returns the index position of the smallest element in an array. Answer the data matrix for students and dictionary representation The reconstruction error between is the student answer data matrix at time t, is the dictionary matrix at time t-1, The knowledge status of students, is the Frobenius norm square loss function, is the sparsity regularization parameter, is the temporal smoothness regularization parameter, is the student’s knowledge state at time t-1, is the dictionary matrix at time t, is the trace of the matrix, is the dictionary matrix, , , For the student answer data matrix, is the transpose symbol, To balance the weight, is the symbol of the objective function; B2. Use the coordinate descent strategy to update the knowledge dictionary and the student's knowledge status in step B1, expressed as: , ; in: is the value of the i-th column of the student’s knowledge state at time t, is the value of the i-th column of the student’s knowledge status at time t-1, is the outer product matrix of the knowledge dictionary at time t-1, is the matrix product of the knowledge dictionary and the student answer data matrix at time t-1, is the value of the jth column of the dictionary matrix at time t, is the value of the jth column of the dictionary matrix at time t-1, for The value of the jth row and jth column at time t, for The value of the jth column at time t, for The value of the j-th column of the transpose at time t.

[0016] The present invention has the following beneficial effects: (1) The present invention constructs a student's knowledge state model based on the independent incremental characteristics of the student's knowledge growth, then constructs a meta-knowledge dictionary based on the knowledge points of the learning project, and constructs a Bayesian framework for students to answer questions based on the meta-knowledge dictionary and the student's knowledge state model to obtain a loss function model for students to answer questions. Finally, based on the student's answer data and the loss function model for students to answer questions, the alternating direction multiplication method is used to obtain the loss function result of students to answer questions, and based on the loss function result of students to answer questions, the coordinate descent strategy is used to update the meta-knowledge dictionary and the student's knowledge state. The whole process can effectively diagnose the student's current knowledge state, does not require a large amount of offline training, and can adapt to the dynamically changing online learning environment; (2) The present invention constructs a meta-knowledge dictionary based on the knowledge points of the learning project. This process proposes a meta-knowledge dictionary theory for more detailed division of professional knowledge points. The theory assumes that there are indivisible minimum meta-knowledge point units, each of which has the same difficulty. The knowledge entity is regarded as a linear combination of these meta-knowledge points. The more meta-knowledge points it contains, the greater the difficulty of the knowledge entity. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The figure is a flowchart of a method for dynamically tracking changes in students' knowledge. DETAILED DESCRIPTION

[0018] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0019] like Figure 1 As shown, a method for dynamically tracking student knowledge changes includes steps S1-S3, which are as follows: S1. Construct a student's knowledge status model based on the independent incremental characteristics of student knowledge growth.

[0020] In an optional embodiment of the present invention, the present invention constructs a student's knowledge state model based on the independent incremental characteristics of the student's knowledge growth, which is expressed as: , , ; in: is the student's knowledge state at time t, is the student's knowledge state at time s, is a normal distribution with mean 0 and variance ts, The knowledge status of students, is the incremental distribution satisfied by the student's knowledge state, is the linear transformation matrix, is the normal distribution variance of X, X is the increment of students’ knowledge growth, is the transpose symbol, For students' knowledge status Transfer to The probability density function of is the exponential function symbol, For students at all times The knowledge state vector, For students at all times The knowledge state vector, For the time series i time, For the time series i +1 moment.

[0021] S2. Construct a meta-knowledge dictionary based on the knowledge points of the learning project. According to the meta-knowledge dictionary and the knowledge state model of the students in step S1, construct a Bayesian framework for students to answer questions to obtain a loss function model for students to answer questions.

[0022] In an optional embodiment of the present invention, the present invention constructs a meta-knowledge dictionary based on the knowledge points of the learning project. The specific process is: divide the knowledge points of the learning project into minimum knowledge point units, the minimum knowledge point units are indivisible and only include one state of mastering or not mastering, and their linear combination is used to represent knowledge entities, the minimum knowledge point units are numbered to construct a corresponding matrix to construct the meta-knowledge dictionary.

[0023] The present invention constructs a Bayesian framework for students to answer questions based on the meta-knowledge dictionary and the student's knowledge state model in step S1, which is expressed as: , , , ; in: For a given dictionary matrix and students’ knowledge status , the students' answers to the questions y follow the mean , the variance is The normal distribution of The mean is , the variance is The normal distribution of is the dictionary matrix No. i List, The mean is 0 and the variance is The normal distribution of For students i row knowledge state vector, is a Laplace distribution with mean 0 and scale parameter b, is a normal distribution with mean 0 and variance ts, For students at all times The knowledge state vector, For students at all times The knowledge state vector, For the time series i time, For the time series i +1 moment.

[0024] Specifically, the present invention obtains the posterior parameters of the student's answer to the question based on the Bayesian framework of the student's answer to the question, which is expressed as:

[0025] in: is the posterior distribution, which means that given the student answer data matrix and hyperparameters In the case of and students’ knowledge status The joint distribution of is the likelihood function of the student's answer, representing the given dictionary matrix and students’ knowledge status When the student answers the data matrix The probability of is the dictionary matrix The prior distribution of The state of knowledge for students The prior distribution of .

[0026] The present invention calculates the likelihood function of the student's answer, which is expressed as: ; in: Answer the data matrix for students The product of the likelihood functions of each row of student answers in , is the variance of the normally distributed observation noise corresponding to the observation model in A1, is the prior scale parameter of the knowledge state in A1, is the number of students, For students i Row knowledge state vector.

[0027] The present invention calculates the dictionary matrix The prior distribution of is expressed as:

[0028] in: is the dictionary matrix in A1 The variance of the normal distribution corresponding to the prior is, is the formula symbol for product, k is the number of knowledge points, is the dictionary matrix The jth knowledge point in .

[0029] The present invention calculates the knowledge status of students The prior distribution of is expressed as: .

[0030] The present invention updates the posterior parameters of the student's answer to the question as: .

[0031] The present invention simplifies the above formula, assuming that the time interval Δt=m is the same, and then simplifies the formula to: .

[0032] The present invention takes logarithms on both sides of the above formula and expresses it as: .

[0033] The present invention obtains the loss function model of the student's answer to the question from the above formula.

[0034] The present invention obtains the loss function model of students answering questions, which is expressed as:

[0035] in: is the loss function for students answering questions, To obtain the minimum value, Representation Knowledge Dictionary and the state of knowledge Student answer data matrix The reconstruction error, is the Frobenius norm square loss function, For the student answer data matrix, is the dictionary matrix, The knowledge status of students, is the number of students, For tracking items, For students i +1 row knowledge state vector, For students i row knowledge state vector, is the dictionary matrix No. i List.

[0036] S3. According to the students' answer data and the loss function model of the students' answers in step S2, the alternating direction multiplication method is used to obtain the loss function results of the students' answers. According to the loss function results of the students' answers, the coordinate descent strategy is used to update the meta-knowledge dictionary and the students' knowledge status to dynamically track changes in the students' knowledge status.

[0037] In an optional embodiment of the present invention, the present invention uses an alternating direction multiplier method to obtain a loss function result of the student's answer question based on the student's answer data and the loss function model of the student's answer question in step S2, including the following steps: A1. Using the alternating direction multiplier method, the meta-knowledge dictionary is updated with the student's knowledge state fixed, expressed as:

[0038] in: is the dictionary matrix The loss function is Representation Knowledge Dictionary and the state of knowledge Student answer data matrix The reconstruction error, is the Frobenius norm square loss function, For the student answer data matrix, is the dictionary matrix, The knowledge status of students, is the number of students, is the dictionary matrix No. i List; A2. Using the alternating direction multiplier method, the student's knowledge state is updated under the condition of a fixed meta-knowledge dictionary, which is expressed as:

[0039] in: The state of knowledge for students The loss function is For students i +1 row knowledge state vector, For students i row knowledge state vector; A3. Calculate the first term of the loss function model for students’ answers, expressed as:

[0040] in: is the trace of the matrix, is the transpose symbol; A4. According to the updated meta-knowledge dictionary in step A1, the updated student's knowledge status in step A2, and the first item of the loss function model of the student's answer to the question in step A3, obtain the loss function result of the student's answer to the question.

[0041] The present invention uses a coordinate descent strategy to update the meta-knowledge dictionary and the student's knowledge state according to the loss function result of the student's answer to the question, including the following steps: B1. According to the loss function result of the student's answer, determine the meta-knowledge dictionary and the student's knowledge state, expressed as: , , , , ; in: is the student's knowledge state at time t, is a function that returns the index position of the smallest element in an array. Answer the data matrix for students and dictionary representation The reconstruction error between is the student answer data matrix at time t, is the dictionary matrix at time t-1, The knowledge status of students, is the Frobenius norm square loss function, is the sparsity regularization parameter, is the temporal smoothness regularization parameter, is the student’s knowledge state at time t-1, is the dictionary matrix at time t, is the trace of the matrix, is the dictionary matrix, , , For the student answer data matrix, is the transpose symbol, To balance the weight, is the symbol of the objective function; B2. Use the coordinate descent strategy to update the knowledge dictionary and the student's knowledge status in step B1, expressed as: , ; in: is the value of the i-th column of the student’s knowledge state at time t, is the value of the i-th column of the student’s knowledge status at time t-1, is the outer product matrix of the knowledge dictionary at time t-1, is the matrix product of the knowledge dictionary and the student answer data matrix at time t-1, is the value of the jth column of the dictionary matrix at time t, is the value of the jth column of the dictionary matrix at time t-1, for The value of the jth row and jth column at time t, for The value of the jth column at time t, for The value of the j-th column of the transpose at time t.

[0042] Specifically, in order to allow knowledge increment to be represented on expert concepts, the present invention assumes that expert concepts can be linearly combined by a subset of meta-knowledge. The present invention defines the relationship matrix between items and expert concepts, and then obtains the knowledge dictionary and the knowledge state of the student on the expert concepts, which is expressed as: , , ; in: For the knowledge dictionary on expert concepts, is the relationship matrix between items and expert concepts, The knowledge status of students on the concept of expert.

[0043] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0044] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0045] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0046] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0047] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for dynamically tracking student knowledge changes, characterized in that: The following steps are involved: S1. Construct a student's knowledge status model based on the independent incremental characteristics of student knowledge growth; S2. Build a meta-knowledge dictionary based on the knowledge points of the learning project, and build a Bayesian framework for students to answer questions based on the meta-knowledge dictionary and the student's knowledge state model in step S1 to obtain a loss function model for students to answer questions; S3. According to the students' answer data and the loss function model of the students' answers in step S2, the alternating direction multiplication method is used to obtain the loss function results of the students' answers. According to the loss function results of the students' answers, the coordinate descent strategy is used to update the meta-knowledge dictionary and the students' knowledge status to dynamically track changes in the students' knowledge status.

2. The method for dynamically tracking student knowledge changes according to claim 1, characterized in that: In step S1, the student's knowledge state model is constructed based on the independent incremental characteristics of the student's knowledge growth, which is expressed as: ， ， in: is the student's knowledge state at time t, is the student's knowledge state at time s, is a normal distribution with mean 0 and variance ts, The knowledge status of students, is the incremental distribution satisfied by the student’s knowledge state, is the linear transformation matrix, is the normal distribution variance of X, X is the increment of students’ knowledge growth, is the transpose symbol, For students' knowledge status Transfer to The probability density function of is the exponential function symbol, For students at all times The knowledge state vector, For students at all times The knowledge state vector, For the time series i time, For the time series i +1 moment.

3. The method for dynamically tracking student knowledge changes according to claim 1, characterized in that: In step S2, a meta-knowledge dictionary is constructed based on the knowledge points of the learning project. The specific process is: the knowledge points of the learning project are divided into minimum knowledge point units, the minimum knowledge point units are indivisible and only include one state of mastering or not mastering, and their linear combination is used to represent knowledge entities, the minimum knowledge point units are numbered to construct a corresponding matrix to construct a meta-knowledge dictionary.

4. The method for dynamically tracking student knowledge changes according to claim 1, characterized in that: In step S2, based on the meta-knowledge dictionary and the student's knowledge state model in step S1, a Bayesian framework for students to answer questions is constructed, which is expressed as: ， ， ， in: For a given dictionary matrix and students’ knowledge status , the students' answers to the questions y follow the mean , the variance is The normal distribution of The mean is , the variance is The normal distribution of is the dictionary matrix No. i List, The mean is 0 and the variance is The normal distribution of For students i row knowledge state vector, is a Laplace distribution with mean 0 and scale parameter b, is a normal distribution with mean 0 and variance ts, For students at all times The knowledge state vector, For students at all times The knowledge state vector, For the time series i time, For the time series i +1 moment.

5. The method for dynamically tracking student knowledge changes according to claim 1, characterized in that: In step S2, the loss function model of the student answering the question is obtained, which is expressed as: in: is the loss function for students answering questions, To obtain the minimum value, Representation Knowledge Dictionary and the state of knowledge Student answer data matrix The reconstruction error, is the Frobenius norm square loss function, For the student answer data matrix, is the dictionary matrix, The knowledge status of students, is the number of students, For tracking items, For students i +1 row knowledge state vector, For students i row knowledge state vector, is the dictionary matrix No. i OK.

6. The method for dynamically tracking student knowledge changes according to claim 1, characterized in that: In step S3, according to the student's answer data and the loss function model of the student's answer question in step S2, the alternating direction multiplication method is used to obtain the loss function result of the student's answer question, including the following steps: A1. Using the alternating direction multiplier method, the meta-knowledge dictionary is updated with the student's knowledge state fixed, expressed as: in: is the dictionary matrix The loss function is Representation Knowledge Dictionary and the state of knowledge Student answer data matrix The reconstruction error, is the Frobenius norm square loss function, For the student answer data matrix, is the dictionary matrix, The knowledge status of students, is the number of students, is the dictionary matrix No. i OK; A2. Using the alternating direction multiplier method, the student's knowledge state is updated under the condition of a fixed meta-knowledge dictionary, which is expressed as: in: The state of knowledge for students The loss function is For students i +1 row knowledge state vector, For students i row knowledge state vector; A3. Calculate the first term of the loss function model for students’ answers, expressed as: in: is the trace of the matrix, is the transpose symbol; A4. According to the updated meta-knowledge dictionary in step A1, the updated student's knowledge status in step A2, and the first item of the loss function model of the student's answer to the question in step A3, obtain the loss function result of the student's answer to the question.

7. The method for dynamically tracking student knowledge changes according to claim 1, characterized in that: In step S3, according to the loss function result of the student's answer to the question, the coordinate descent strategy is used to update the meta-knowledge dictionary and the student's knowledge state, including the following steps: B1. According to the loss function result of the student's answer, determine the meta-knowledge dictionary and the student's knowledge state, expressed as: ， ， ， ， in: is the student's knowledge state at time t, is a function that returns the index position of the smallest element in an array. Answer the data matrix for students and dictionary representation The reconstruction error between is the student answer data matrix at time t, is the dictionary matrix at time t-1, The knowledge status of students, is the Frobenius norm square loss function, is the sparsity regularization parameter, is the temporal smoothness regularization parameter, is the student’s knowledge state at time t-1, is the dictionary matrix at time t, is the trace of the matrix, is the dictionary matrix, , , For the student answer data matrix, is the transpose symbol, To balance the weight, is the symbol of the objective function; B2. Use the coordinate descent strategy to update the knowledge dictionary and the student's knowledge status in step B1, expressed as: ， in: is the value of the i-th column of the student’s knowledge state at time t, is the value of the i-th column of the student’s knowledge status at time t-1, is the outer product matrix of the knowledge dictionary at time t-1, is the matrix product of the knowledge dictionary and the student answer data matrix at time t-1, is the value of the jth column of the dictionary matrix at time t, is the value of the jth column of the dictionary matrix at time t-1, for The value of the jth row and jth column at time t, for The value of the jth column at time t, for The value of the j-th column of the transpose at time t.

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