CN109919810B - Student modeling and personalized course recommendation method in online learning system - Google Patents
Student modeling and personalized course recommendation method in online learning system Download PDFInfo
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Abstract
The invention discloses a student modeling and personalized course recommendation method in an online learning system, which belongs to the field of education data mining, and mainly researches cognitive level modeling and personalized course recommendation of students; secondly, modeling an online course; and finally, carrying out personalized recommendation according to the cognitive level of the student and the characteristics of the online courses. The invention carries out personalized recommendation based on the cognitive level of the student and in combination with the characteristic indexes of the online courses, not only can help the user to carry out more accurate personalized course recommendation, but also ensures that the online course recommendation has more interpretability and acceptability.
Description
Technical Field
The invention belongs to the field of education data mining, and particularly relates to a student modeling and personalized course recommendation method in an online learning system.
Background
In recent years, large-scale Online Open Courses (MOOCs for short) represented by Coursera, udacity, edX and the like greatly promote the development of Online education, bring new important opportunities for universities and personal learning users, and greatly facilitate the acquisition of new knowledge by learners. Meanwhile, the continuously and rapidly growing mass learning resources often make learners have no place when facing 'information overload' and 'information lost'. How to accurately recommend learning resources for learners is an important research problem to be solved urgently. Most of the existing recommendation algorithms are modeled from a single dimension (learning behaviors or interest preferences of students), influence factors of the students and courses are not comprehensively considered, and the interpretability and the rationality of a recommendation result are still insufficient.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a student modeling and personalized course recommendation method in an online learning system, which is reasonable in design, overcomes the defects of the prior art and has a good effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a student modeling and personalized course recommendation method in an online learning system comprises the following steps:
step 1: modeling by students;
according to the course learning condition and the course hierarchical structure analysis diagram of the student, a DINA model is used for modeling the course mastery degree of the student, the course mastery condition of the student is obtained, and the cognitive ability of the student is further abstracted by an fuzzy analytic hierarchy process in combination with learning behaviors and interests;
step 2: modeling an online course;
modeling and quantifying the difficulty level of the courses by analyzing the characteristics of the courses on different online platforms;
and step 3: personalized recommendation of students;
and establishing a course implicit rating model, performing comprehensive sequencing and selecting corresponding courses according to the prediction rating and the difficulty degree of the courses to be recommended, and thus performing personalized online course Top-N recommendation on each student.
Preferably, in step 1, in the course master modeling process based on the DINA model, a set of students S = { S = { S = is given 1 ，S 2 ，...，S u }, test question set J = { J = 1 ，J 2 ，...，J v And student test question score matrix R = [ R uv ] U×V Wherein r is uv =1 student u answer right test question J v ，r uv =0 student u answer wrong test J v (ii) a For all knowledge points K = { K) examined in the test question set J 1 ，K 2 ，...，K k And the association condition of the test questions and the knowledge points is defined by a Q matrix: q = [ Q ] vk ] V×K Wherein q is vk =1 test question J v Examining knowledge points k, q vk =0 test question J v The knowledge point k is not examined;
modeling is carried out on students by combining a question making condition R matrix and a test question knowledge point association Q matrix of the students, and each student S u Described as a knowledge point mastery degree vector alpha u ＝{α u1 ，α u2 ，...，α uk Each one of themDimension corresponds to a knowledge point, α uk =1 represents the knowledge point k, α grasped by student u uk =0 represents the student u does not grasp the knowledge point k;
test question parameters including error rate and guess rate are introduced to model the answering condition of students in a real state; the mathematical expression of the model is:
(1)η uv =0 denotes student S u Test question J which cannot be answered correctly v If η uv =1 then considers student S u Can correctly answer the test question J v The concrete formula is as follows:
(2) Rate of failure s v : although all the required skill attributes of the test question are mastered, there still exists no answer to the test question J v Student s v That is, the probability in this case, a specific formula is defined as follows:
s v ＝P(R uv ＝0|μ uv ＝1)；
(3) Guess rate g v : although not all of the skill attributes required in the test question are mastered, there is a question J v Students who answer right g v That is, the probability in this case, a specific formula is defined as follows:
g v ＝P(R uv ＝1|μ uv ＝0)；
obtained by EM algorithm
And to
Estimating parameters of (2); student S u Knowledge point of (a) grasp vector α u By maximizing the student's trialThe question is determined by posterior probability, so that a binary knowledge point grasping vector of the student is obtained, and the following steps are included:
after the mastery degree of the students about the knowledge points is obtained, mapping each knowledge point to each chapter of the online course according to the knowledge structure level analysis chart of the course, and analyzing the mastery condition of the students on the chapters of the course, wherein each student S u Described as an on-line course chapter module mastery degree vector β u ＝{β u1 ，β u2 ，...，β ul Each dimension corresponding to a chapter, β, of the course ul Indicating how well the student u mastered the chapter 1.
Preferably, in step 1, the cognitive ability of the student is mainly influenced by the learning behavior condition of the student and the learning achievement condition of the student, and the cognitive ability is specifically divided into the following three modules: functional dimensions, structural dimensions, method dimensions; the functional dimension mainly comprises the specific mastering conditions of the students on the course chapters; the structure dimension mainly comprises other modules of making homework, watching video, discussing, reading Wikipedia and browsing courses; the mode dimensions mainly include: a web page and a client; the fuzzy analytic hierarchy process specifically comprises the following steps:
step S1: on the basis of research, multi-dimensional classification is carried out on learning behaviors by combining an online course learning platform, and the classification is as follows:
(1) Learning behavior based on functional dimensions: the student can specifically master the situation of the course chapters;
(2) Learning behavior based on structural dimensions: making homework, watching video, discussing, reading wikipedia and browsing courses;
(3) Learning behavior based on mode dimension: a web page and a client;
step S2: establishing a student cognitive ability analysis system according to the following principles:
(1) Qualitative and quantitative combination: considering the universality of factors influencing a student cognitive ability analysis system, qualitative data and quantitative data are combined;
(2) Scientifically: the set indexes are limited, all factors cannot be taken into consideration, and the main aspects and essential characteristics are grasped according to the characteristics of cognitive ability, so that the cognitive ability is scientific;
(3) And (3) measuring the comparability: the data collection of the basic indexes must be given by objective data or expert scoring, so the establishment of the indexes must be measurable or comparable;
(4) Layering: subdividing the indexes into relevant levels according to the relevance of each index and the characteristics of an analytic hierarchy process;
and step S3: the student cognitive ability analysis system based on online course learning is established according to the student online course mastering condition and the student learning condition, and cognitive ability evaluation indexes are divided into three levels: the target layer, the standard layer and the index layer are established according to the following index system layers:
(1) And (4) target layer: cognitive ability E to be based on student online course learning behavior ij Setting as a target layer, wherein i represents students and j represents courses;
(2) A criterion layer: the criterion layer mainly comprises three modules: u shape 1 Learning behavior condition, U, based on functional dimension 2 Learning behavior situation and U based on structural dimensions 3 Learning behavior based on a mode dimension;
(3) An index layer: learning behavior condition U based on functional dimension 1 The following indexes are provided: situation U mastery in chapter I 11 Second chapter controls situation U 12 Chapter iii mastery of situation U 13 And so on; learning context U based on structural dimensions 2 The following indexes are provided: doing U 21 Video watching U 22 Forum discussion U 23 Wikipedia U for reading courses 24 Browsing other parts of the course U 25 (ii) a Mode dimension-based student basic learning condition U 3 The following indexes are provided: webpage U 31 Client U 32 。
The invention has the following beneficial technical effects:
according to the method, a large amount of data recorded in the teaching interaction process is mined, the learning mode, the learning interest and the learning ability of the student are modeled, the personalized cognitive ability model of the student is constructed, and accurate and interpretable personalized course recommendation can be generated according to the cognitive level of the student; meanwhile, online course modeling is carried out, and the accuracy and the adaptability of course recommendation are further improved by combining online course characteristics.
Drawings
FIG. 1 is a schematic diagram of a student cognitive ability analysis hierarchical structure model.
FIG. 2 is a flow chart of the method of the present invention.
FIG. 3 is a basic flow diagram of a matrix decomposition model.
Detailed Description
The invention is described in further detail below with reference to the following figures and embodiments:
1. brief introduction to the drawings
According to the invention, a large amount of data recorded in the teaching interaction process is mined, the learning mode, the learning interest and the learning ability of the student are modeled, the personalized cognitive ability model of the student is constructed, and the precise and interpretable personalized course recommendation can be generated according to the cognitive level of the student. Meanwhile, online course modeling is carried out, and the accuracy and the adaptability of course recommendation are further improved by combining the course characteristics.
2. Student cognitive competence modeling based on online course learning
2.1 course learning based on DINA (Deterministic Inputs, noise "And" gate model) model
In the field of education data mining, a DINA model is applied to the problem of personalized test question recommendation and achieves a good effect.
In course mastering situation modeling process based on DINA modelSet of student S = { S = { (S) } 1 ，S 2 ，...，S u Test question set J = { J = } 1 ，J 2 ，...，J v And student test question score matrix R = [ R uv ] U×V Wherein r is uv =1 student u answer right test question J v ，r uv =0 student u answer wrong test J v (ii) a For all knowledge points K = { K) examined in the test question set J 1 ，K 2 ，...，K k And the association condition of the test questions and the knowledge points is defined by a Q matrix: q = [ Q ] vk ] V×K Wherein q is vk =1 test question J v Examining knowledge points k, q vk =0 test question J v The knowledge points k are not examined, and the examination condition of the examination questions on the knowledge points is obtained by the labeling of experts in the education field. In order to obtain the learning state (individual state) and cognitive ability of the student, the method analyzes and diagnoses the course grasping condition of the student according to the DINA model and the course hierarchical structure. The DINA model models the students by combining the student question making condition R matrix and the test question knowledge point association Q matrix. Each student S u Described as a knowledge point mastery degree vector alpha u ＝{α u1 ，α u2 ，...，α uk In which each dimension corresponds to a knowledge point, α uk =1 denotes the knowledge point k, α grasped by student u uk =0 indicates that the student u does not grasp the knowledge point k.
TABLE 3-2Q matrix of topic and cognitive attributes
In the table, the knowledge points of each topic investigation are different, and 0 and 1 are respectively used to indicate whether the topic investigates the knowledge point, 1 indicates that the topic investigates the knowledge point, and 0 indicates that the topic is not investigated.
In addition, on the basis of a DINA model, test question parameters (error rate and guess rate) are introduced to model the answer condition of students in a real state. The mathematical expression of the model is:
(1)η uv =0 denotes that student Su cannot answer test question J correctly v If η uv =1 then considers student S u Can correctly answer the test question J v The concrete formula is as follows:
(2) Error rate s v : although all the required skill attributes of the test question are mastered, there still exists no answer to the test question J v Student of (1), s v That is, the probability in this case, a specific formula is defined as follows:
s v ＝P(R uv ＝0|μ uv ＝1)；
(3) Guess rate g v : while not all of the skill attributes required in the test question are mastered, there is a question J v Students who answer right g v That is, the probability in this case, the specific formula is defined as follows:
g v ＝P(R uv ＝1|μ uv ＝0)；
obtained by EM algorithm
And to
Estimating parameters of (2); student S u Knowledge point of (a) grasp vector α u The student test question score posterior probability is maximized to obtain the binary knowledge point grasping vector of the student, as follows:
after the mastery degree of the student on the knowledge points is obtained, the knowledge points are obtained according to the coursesThe structure level analysis graph maps each knowledge point to each section of the online course, the mastering condition of the student on the course sections can be analyzed, and each student S u Described as an on-line course chapter module mastery degree vector beta u ＝{β u1 ，β u2 ，...，β ul Each dimension corresponding to a chapter, β, of the course ul Indicating how mastery student u mastered chapter 1.
2.2 establishing student cognitive ability analysis model by fuzzy hierarchical comprehensive evaluation method
In the personalized course recommendation method based on cognitive diagnosis provided by the invention, the cognitive ability of a student is mainly influenced by the on-line course mastering condition of the student and the learning behavior condition of the student, the on-line course mastering condition of the student depends on the mastering conditions of all modules of the course, the learning condition of the student mainly comprises the interest direction of the student for selecting the on-line course, the learning time of the selected course, the learning mode of the on-line course, the mastering condition of the on-line course, whether to break the course and other factors.
On the basis of research, multi-dimensional classification is carried out on learning behaviors by combining an online course learning platform, and the classification is as follows:
1) Learning behavior based on functional dimensions: the course is divided into sections according to the main content and the logic structure between the contents, and students can study the course in a planned and sequential way. The content mastering condition of each chapter is closely related to the whole course learning condition and the cognitive level of students.
2) Learning behavior based on structural dimensions: the online course basic module is mainly based on the course learning mode designed by the online course producer, the uploader and the platform. For example, the MOOC sets a course module as the following parts: video viewing, discussion, practice problems, etc. The video watching behavior of the student judges whether to want or need to learn a certain video content according to the self-mastery condition of the student on the part of knowledge, and the active learning behavior is controlled by self-cognition of the student. The discussion is an interactive learning behavior: the mode of teaching knowledge students to accept knowledge by online course teachers is a learning mode, and communication during the learning process can also be regarded as a learning mode. In the daily learning environment, there are interactive behaviors between teachers and students, between students and learning resources. The method comprises interactive learning behaviors of issuing questions, answering questions, participating in topic discussions, browsing topic discussions and the like. The practice problem module is used for consolidating and checking the mastering condition of the learned content through a certain problem in the learning process. In the learning process, the note module can help students to collect, mark and annotate appointed learning resources, write electronic notes and the like, and the effect of assisting in improving efficiency can be achieved.
3) Learning behavior based on mode dimension: the basic learning behaviors based on the online platform mainly comprise some basic learning behaviors of students, such as learning interests and choices, whether the students have dropped lessons, online learning active time, learning resource acquisition modes and the like. The learning interest is the internal motivation of the students in the learning process, and the interest of the students can be accurately reflected according to the retrieval of the students and the online course selection behavior. Whether the student drops a course or not when the student carries out online course learning can directly reflect the activity degree and the interestingness of the student to the course, and certain influence is exerted on the cognitive level of the student. The online learning active time refers to the total active time for learning a certain online course when the course is selected. Learning resource acquisition is mainly in two ways under the current online course learning platform: the system comprises a webpage and a client, and different students select different learning modes according to their learning habits.
Secondly, a student cognitive ability analysis system is established according to the following principle, and through analysis of learning behaviors of students, the students can realize that different learning behaviors influence the cognitive ability of the students at different angles and degrees. The construction of the student cognitive ability analysis system based on online course learning not only reflects key points and key influence factors of the student cognitive ability, but also accords with reality, comprehensiveness and a system. The student cognitive ability analysis system is established according to the on-line course mastering condition of students and the basic learning condition of students, the student cognitive ability analysis system not only has a plurality of related factors, but also has more complex index calculation and wider related range, so when the comprehensive evaluation model is established, the principle is followed as follows:
(1) Qualitative and quantitative combination: considering the universality of factors influencing a student cognitive ability analysis system, qualitative data and quantitative data are combined;
(2) Scientifically: the set indexes are limited, all factors cannot be taken into consideration, and the main aspects and essential characteristics are grasped according to the characteristics of cognitive ability, so that the cognitive radio system has scientificity;
(3) Comparability as measured: the data collection of the basic indicators must be given by objective data or expert scoring, so the establishment of the indicators must be quantifiable or comparable;
(4) Layering: according to the relevance of each index and the characteristics of the analytic hierarchy process, the indexes are subdivided into relevant levels, so that the expert can conveniently evaluate the indexes.
Finally, a student cognitive ability analysis system based on online course learning is established according to the student online course mastering condition and the student learning condition, and cognitive ability evaluation indexes are divided into three levels: a target layer, a criteria layer, and an index layer. The established index system is layered as follows:
(1) Target layer: cognitive ability E to be based on student online course learning behavior ij Setting as a target layer, wherein i represents students and j represents courses;
(2) A criterion layer: the criterion layer mainly comprises three modules: u shape 1 Learning behavior condition based on functional dimension, U 2 Learning behavior situation and U based on structural dimensions 3 Learning behavior based on a mode dimension;
(3) An index layer: learning behavior condition U based on functional dimension 1 The following indexes are provided: situation U mastered in chapter I 11 Second chapter controls situation U 12 Third chapter U grasp situation 13 And so on. Learning condition U based on structural dimensions 2 The following indexes are provided: doing U 21 And video watching U 22 Forum discussion U 23 Wikipedia U for reading courses 24 Browsing other parts of the course U 25 (ii) a Mode dimension-based student basic learning condition U 3 The following indexes are provided: webpage U 31 Client U 32 。
The established index system is shown in fig. 1.
2.3 implementation of student cognitive competence analysis System
(1) Rating set V of evaluations
An evaluation set is a set of various total evaluation results that may be made by an expert, scholarly or staff member who gives an evaluation to an evaluated object, usually with V = { V = 1 ，v 2 ，...，v m Denotes from v 1 To v m Each rating corresponding to a fuzzy subset. In the cognitive ability evaluation of students, the number m of evaluation grades is 5, namely, the cognitive ability of online learning behaviors of students is evaluated in five grades, and m is generally an odd number. V = { V = 1 ，v 2 ，...，v m The evaluation set of the model is {2,4,6,8, 10}, where good, general, poor, and bad } respectively, with 10 as the highest value and 2 division intervals for each rank.
(2) Weight of evaluation index factor
Calculating the weight W of each index by adopting an analytic hierarchy process, and constructing a judgment matrix according to a 1-9 proportional scale method shown in the table 3-3 to obtain judgment matrices E and U 1 ，U 2 ，U 3 . The function of the judgment matrix is to compare the relative importance of the elements in the same layer under the element constraint of the upper layer. Calculating the maximum eigenvalue and eigenvector of the total judgment matrix, and performing consistency check to obtain judgment matrix W E ，
Tables 3-3 significance Scale
(3) Establishing a fuzzy evaluation matrix R and single-factor evaluation
The single-factor fuzzy evaluation refers to evaluating the independent membership degree of an evaluation set through index factors, and the method is used for calculating a single-factor evaluation matrix. The single factor set evaluation is a fuzzy mapping from U to F (V). For example, a single factor evaluation of one factor: the degree of membership u of each evaluation level is given in the evaluation set V i And the degree of membership r of the jth element ij Recorded in V. The single-factor evaluation fuzzy set may be represented as R i ＝{r i1 ，r i2 ，...，r im }. Wherein, i belongs to (1,2.. Multidot., n), and j belongs to (1,2.. Multidot., m). After calculating the single factor evaluation set of each factor, the single factor evaluation sets of n factors are formed into a matrix, i.e.
And the evaluation matrix is formed into a matrix in sequence to obtain a comprehensive evaluation matrix, namely a comprehensive evaluation matrix R.
(4) Fuzzy comprehensive evaluation of evaluation index
According to the membership principle, the weight vectors of all indexes of the index layers in the fuzzy evaluation matrix of the criterion layer formed by the evaluation results of all the indexes can obtain the evaluation results of all the factors on the criterion layer, and then according to the evaluation results of the criterion layer, the evaluation results of the target layer are recurred upwards according to the membership principle. According to the actual situation and the advantages and disadvantages of each model, the invention adopts a weighted average algorithm, and each membership degree r of the model is divided into two groups ij All are taken into account, i.e. the influence of all factors is reflected to the rating comment v j Comprehensive degree of membership s of j . And synthesizing the fuzzy weight vector W and the fuzzy relation matrix R by using a weighted average fuzzy operator to obtain a fuzzy comprehensive evaluation result vector S of each evaluated object. The model of fuzzy comprehensive evaluation is as follows:
B＝W*R＝(b 1 ，b 2 ，...，b m )
wherein the synthesis operation of generalized fuzzy matrices is represented, i.e.
Herein, the
Representing a fuzzy and operation in a broad sense,
the generalized fuzzy OR operation is represented by the formula to become a comprehensive evaluation model which can be recorded as a model
Selected for use herein
To calculate the comprehensive degree of membership, i.e.
2.4 student cognitive ability evaluation results and analysis
Through the analysis, the cognitive ability quantitative values of the students can be obtained, the final cognitive ability quantitative values are greatly floated due to obvious differences in the aspects of learning behaviors, learning habits, learning interests and the like of the students, and extreme conditions with large errors such as extremely high or extremely low cognitive level analysis can be caused if the original values are directly used for analysis. Therefore, the data needs to be normalized, i.e., scaled to fall within a small specific interval. The method selects min-max standardization, and is linear transformation of the original data, so that the result is mapped to [0,1 ]]And (4) interval. Raw cognitive ability data { x } is calculated by the following formula 1 ，x 2 ，...，x n And (4) carrying out transformation:
new sequence y 1 ，y 2 ，...，y n ∈[0，1]。
3. Problem definition and method holistic framework
3.1 problem definition there are two basic elements (use and item) in the course recommendation model proposed in this application, where the user represents a registered student and the item represents an online course in the MOOC. S = { S } used herein 1 ，S 2 ，...，S u Represents a set of users, using C = { C = } 1 ，C 2 ，...，C m Represents a curriculum set. The relationship between the test question and the knowledge point is defined by the Q matrix: q = [ Q ] vk ] V×K The scores of the students on the test questions are defined by an R matrix: r = [ R ] uv ] U×V . Let K = { K 1 ，K 2 ，...，K k }，Ch＝{Ch 1 ，Ch 2 ，...，Ch l Are the knowledge point set and chapter set, respectively. Given a set S, a set C, a set K, a set Ch, a matrix Q and a matrix R, the main research problems of the application are as follows: (1) how cognitive ability modeling is performed; (2) How to perform personalized online course recommendation based on cognitive level; the course mastery questions in the personalized course recommendation method may be defined as follows:
f：(S，C，J，R，Q，K，Ch)→L C
TABLE 3-1 symbols and descriptions relating to course recommendation questions
3.2 Algorithm framework
The overall flow of the personalized course recommendation method based on cognitive modeling is shown in fig. 2. It can be seen from the figure that the recommendation method is mainly divided into 3 steps:
step 1: analyzing the cognitive ability of the students;
according to the course learning condition and the course hierarchical structure analysis diagram of the student, a DINA model is used for modeling the course mastery degree of the student, the course mastery condition of the student is obtained, and the learning behavior interest is combined to further abstract the cognitive ability of the student through an fuzzy analytic hierarchy process;
step 2: modeling an online course;
modeling and quantifying the difficulty level of the courses by analyzing the characteristics of the courses on different online platforms;
and 3, step 3: personalized recommendation of students;
and establishing a course implicit rating model, comprehensively sequencing and selecting corresponding courses according to the prediction rating and the difficulty degree of the courses to be recommended, and thus performing personalized online course Top-N recommendation on each student.
4 Online course modeling
In a plurality of online course learning platforms, such as MOOC, internet cloud courses and the like, the contents, forms and difficulty degrees of different courses are different, and in an online course personalized recommendation system, the testability characteristic of the online course is a necessary factor to be considered when course recommendation is carried out and is also a necessary basis when the recommendation system is carried out. The difficulty degree and the association degree of the courses are analyzed, the individual recommendation can be performed from more angles and in a multi-dimensional all-round manner in the individual recommendation, the cognitive level of students is considered, the comprehensive analysis is performed by combining the characteristics of the courses, and therefore the recommendation accuracy is improved.
Through research on learning resource difficulty by researchers, we can analyze the difficulty of online courses based on the following three aspects: content difficulty, organization difficulty, and presentation form. The content difficulty of the online course mainly comprises the breadth and depth of the course specific knowledge; the organization difficulty of the online courses is derived from the organization mode and the relevance among knowledge, the presentation forms of the online courses are presented in the forms of videos, test questions, discussions and the like on all learning platforms, and the presentation modes of the courses are approximately the same.
According to the factors influencing the difficulty of the online course and the specific characteristics of the course, the quantitative method for the difficulty index of the online course can be obtained:
(1) Density of knowledge points s den : each class is divided into a plurality of chapters according to the theme of the coursek i Total number N, knowledge points associated with the subject of each chapter are subdivided into each section j i K th, k i The number of segments included in a chapter is denoted as c 1 (k i ) Then the total number of the lessons is
Hence knowledge of the point density s den Can be measured by the number of chapters contained in the course, S den The larger the learning difficulty is, the larger the knowledge point density contained in the course is, the larger the learning difficulty is; knowledge point density S den Can be expressed as:
(2) Knowledge point depth S dep : the hierarchical diagram of the curriculum knowledge structure system can be made according to the structural analysis, and any knowledge point j can be calculated according to the hierarchical structure between the knowledge points i Number of layers c 2 (j i ) It is also understood that the number of relevant knowledge points that need to be learned in advance to learn this knowledge point. If the course has M knowledge points, the depth S of the knowledge points dep Can be expressed as:
(3) The total time length T of the course: the presentation form of the online course is in the forms of videos, test questions and the like on each learning platform, and the longer the total duration of the course is, the more time and energy are consumed for mastering the course, so the more the content of the course is, the greater the difficulty is; the total lesson duration T may be expressed as:
T＝T video +T problem (4-3)；
personalized course recommendation based on student cognitive level
5.1 implicit Scoring model for Online course learning
The rating types of a user can be divided into explicit ratings and implicit ratings. Explicit rating means that the user explicitly gives a rating of the item, the most common examples being user rating on Taobao and rating buttons on MOOC websites, and the star rating system of video platforms. Implicit rating is that we do not let the user explicitly give a rating of an item, but rather obtain preference information by observing their behavior. One example is that by observing and analyzing the user's click records on the New York Times website, a reasonable favorite model can be carved out for the user-he does not like entertainment news, but focuses on sports news; if a user sees two articles in succession: experience with cook university and cook skill, she is likely learning to cook; if she clicks on the iPhone's advertisement, it indicates that she is likely to be interested in this product.
Through the analysis of the learning behaviors of different online learning platforms, an author finds that the online learning platforms are greatly different from common electronic commerce, and some platforms are provided with modules for directly grading or evaluating the levels of online courses, such as an internet cloud classroom; some platforms are not provided with corresponding modules, such as MOOC. In view of this situation, the processing method for implicit rating data in e-commerce recommendation systems is obviously not applicable here. However, it has been found through research that even in a learning platform provided with a course evaluation module, students who learn courses on the platform are not all willing to evaluate, objectively evaluate, and accurately evaluate. Thus, this section presents an implicit scoring model based on online course learning. The student's evaluation of the course is not to be derived from the interest in the course, the learning behavior about the course, and the knowledge and skills that the student mastered from through the course. Therefore, the cognitive ability based on the online course can more accurately reflect the objective scoring and evaluation of the course. Through the analysis of cognitive abilities based on student online course learning, the implicit rating of a course can be accurately determined.
5.2 personalized course recommendation based on probability matrix decomposition Algorithm
The probability matrix decomposition algorithm is applied to the personalized course recommendation system, and improved optimization is carried out by combining with an online course implicit scoring model.
In the probability matrix decomposition, the user potential feature matrix and the project potential feature matrix are assumed to be subject to Gaussian distribution, the user potential feature matrix and the project potential feature matrix are obtained by learning the known score values in the user-project score matrix, and then unknown values in the user-project score matrix are predicted through the user potential feature matrix and the project potential feature matrix.
Assuming that there are N users and M articles in the system and the dimension of the feature vector is K, all users can be represented by K × N user potential feature matrix U, and some articles are represented by K × M article potential feature matrix V, so that the N × M scoring matrix R is represented by N × K U T Multiplying with K multiplied by V of M; the training matrix decomposition model is to find the optimal approximate value of the dimension K under the given loss function, so that U is enabled to be obtained T * V is closest to the observed nxm scoring matrix.
Based on the above description, we can derive the basic flow of the matrix decomposition model as shown in fig. 3:
r ii represents the scoring of item j by user i, U belongs to R D×N And V ∈ R D×M Representing a user latent feature matrix and an item latent feature matrix. One row u in the matrix i And v j Representing potential feature vectors for user i and item j. Using a linear probability model with gaussian observation noise, the conditional probability distribution that can define an observation score is:
N(x|μ，σ 2 ) Denotes mean μ and variance σ 2 If user I has scored item j, then I ij The value is 1, otherwise 0. In addition, a gaussian prior with a mean of 0 is assumed for each user vector and item vector:
where C is a constant. The posterior probability, i.e. the likelihood (here, the log of the likelihood) is maximized in the case of fixed parameters (observed noise variance and prior variance), and then the loss function in the learning process can be obtained by deformation:
wherein the content of the first and second substances,
according to the basic matrix decomposition algorithm, the method needs to optimize the loss function, and the deformation is simplified into:
wherein the content of the first and second substances,
based on the formula (4-2), in combination with the student cognition level-based on-line course implicit scoring model, the final loss function is in the form of:
by the SGD random gradient descent method, by
Solving for U i ，V j Can obtain the optimal solution of the formula.
By modeling the online course, the difficulty measurement vector dif of the course can be obtained i ＝(S den ，S dep And T), comprehensively evaluating the difficulty characteristics of the online courses by a factor analysis method, and selecting the courses within the corresponding difficulty range according to the prediction scores of the courses, thereby improving the prediction accuracy and individuation.
The method includes the steps that personalized recommendation is carried out by combining course difficulty, comparison is carried out mainly through the difficulty degree of courses learned by students, one or more courses (called history optimal courses) with high implicit scores are selected from the courses learned by the students, difficulty vectors x of all the courses are analyzed, and the similarity between the courses and the difficulty vectors of the courses to be recommended is calculated. Therefore, a pearson correlation coefficient calculation method is introduced. The pearson correlation coefficient is generally used to calculate the closeness of the connection between two distance variables, and takes a value between [1 and 1], and the pearson correlation coefficient between vectors x and y is calculated by the formula:
wherein S is x ，S y Is the sample standard deviation of x and y. In the coefficient range [ -1,1]The larger the absolute value is, the stronger the correlation is, and the less the negative correlation is for recommendation.
The course difficulty similarity of the M candidate recommended courses and the history optimal course can be calculated through the formula, and the course adaptive recommendation sequence based on the difficulty can be obtained according to the size sequence of the M candidate recommended courses.
The method has the advantages that the courses to be recommended need to be comprehensively evaluated by combining the course difficulty degree characteristics, namely the courses to be recommended are comprehensively sequenced. The method and the device use the idea of sequencing according to the total score to comprehensively sequence the prediction scores and the difficulty degree of the courses. In order to determine the optimal weight value, firstly, weight =0.5 (weight is less than or equal to 1) is set as the initial weight of the prediction score, 1-weight is set as the initial weight of the course difficulty degree, then the growth gradient of weight is set as d =0.01, the model is trained, and the optimal weight value is judged according to the recommended accuracy.
6. To summarize
The invention mainly researches cognitive level modeling and personalized course recommendation of students. Firstly, judging the knowledge mastering state of a student based on a cognitive diagnosis model, analyzing the learning behavior of the student by using data on a system platform, and further modeling the cognitive ability of the student by integrating the course mastering condition; secondly, modeling an online course; and finally, carrying out personalized recommendation according to the cognitive level of the student and the characteristics of the online courses. The traditional collaborative filtering algorithm mainly depends on a single comprehensive score, and utilizes the comprehensive score to mine the interest of the user. However, a large number of studies show that a recommendation algorithm that only considers a single composite score does not well characterize the user's interest model. The personalized recommendation is carried out based on the cognitive level of the student and combined with the characteristic indexes of the online courses, so that the user can be helped to carry out more accurate personalized course recommendation, and the online course recommendation is more interpretable and acceptable.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (2)
1. The student modeling and personalized course recommendation method in the online learning system is characterized by comprising the following steps: the method comprises the following steps:
step l: modeling by students;
according to the course learning condition and the course hierarchical structure analysis chart of the student, a DINA model is used for modeling the course mastery degree of the student, the course mastery condition of the student is obtained, and the learning behavior and the interest are combined, so that the cognitive ability of the student is further abstracted through an fuzzy analytic hierarchy process;
and 2, step: modeling an online course;
modeling and quantifying the course difficulty degree through analyzing the course characteristics on different online platforms;
and step 3: personalized recommendation of students;
establishing a course implicit rating model, performing comprehensive sequencing and selecting corresponding courses according to the prediction rating and the difficulty degree of the courses to be recommended, and thus performing personalized online course Top-N recommendation on each student;
in step 1, in the course master situation modeling process based on the DINA model, a set of students S = { S =isgiven 1 ，S 2 ，...，S u Test question set J = { J = } 1 ，J 2 ，...，J v And student test question score matrix R = [ R uv ] U×v Wherein r is uv =1 student u answer right test question J v ，r uv =0 student u answer wrong test J v (ii) a For all knowledge points K = { K) examined in the test question set J 1 ，K 2 ，...，K k And the association condition of the test questions and the knowledge points is defined by a Q matrix: q = [ Q ] vk ] v×K Wherein q is vk =1 test question J v Examining knowledge points k, q vk =0 test question J v The knowledge point k is not examined;
modeling is carried out on students by combining a question making condition R matrix and a test question knowledge point association Q matrix of the students, and each student S u Described as a knowledge point mastery degree vector alpha u ＝{α u1 ，α u2 ，...，α uk Each of which corresponds to a knowledge point, α uk =1 represents the knowledge point k, α grasped by student u uk =0 represents the student u does not grasp the knowledge point k;
test question parameters including error rate and guess rate are introduced to model the answering condition of students in a real state; the mathematical expression of the model is:
(1)η uv =0 for student S u Test question J unable to be answered correctly v If η uv =1 then considers student S u Can correctly answer the test question J v The concrete formula is as follows:
(2) Error rate s v : although all the required skill attributes of the test question are mastered, there still exists no answer to the test question J v Student s v That is, the probability in this case, the specific formula is defined as follows:
s v ＝P(R uv ＝0|μ uv ＝1)；
(3) Guess rate g v : although not all of the skill attributes required in the test question are mastered, there is a question J v Students who answer right g v That is, the probability in this case, a specific formula is defined as follows:
g v ＝P(R uv ＝1|μ uv ＝0)；
obtained by EM algorithm
And to
Estimating parameters of (2); student S u Knowledge point of (a) grasp vector α u By maximisingThe student test question score is determined by posterior probability, so that a binary knowledge point grasping vector of the student is obtained, and the method is as follows:
after the mastery degree of the students about the knowledge points is obtained, mapping each knowledge point to each chapter of the online course according to the knowledge structure level analysis chart of the course, and analyzing the mastery condition of the students on the chapters of the course, wherein each student S u Described as an on-line course chapter module mastery degree vector beta u ＝{β u1 ，β u2 ，...，β ul Each dimension corresponding to a chapter, β, of the course ul Indicating how well the student u mastered the chapter l.
2. The method for student modeling and personalized course recommendation in an online learning system as claimed in claim 1, wherein: in step 1, the cognitive ability of the student is mainly influenced by the learning behavior condition of the student and the learning achievement condition of the student, and the cognitive ability is specifically divided into the following three modules: functional dimensions, structural dimensions, method dimensions; the functional dimension mainly comprises the specific mastering conditions of the students on the course chapters; the structure dimension mainly comprises other modules of making homework, watching video, discussing, reading Wikipedia and browsing courses; the mode dimensions mainly include: a web page and a client; the fuzzy analytic hierarchy process specifically comprises the following steps:
step S1: on the basis of research, multi-dimensional classification is carried out on learning behaviors by combining an online course learning platform, and the classification is as follows:
(1) Learning behavior based on functional dimensions: the student can specifically master the situation of the course chapters;
(2) Learning behavior based on structural dimensions: making homework, watching video, discussing, reading wikipedia and browsing courses;
(3) Learning behavior based on mode dimension: a web page and a client;
step S2: establishing a student cognitive ability analysis system according to the following principles:
(1) Qualitative and quantitative combination: considering the universality of factors influencing a student cognitive ability analysis system, qualitative data and quantitative data are combined;
(2) Scientifically: the set indexes are limited, all factors cannot be taken into consideration, and the main aspects and essential characteristics are grasped according to the characteristics of cognitive ability, so that the cognitive radio system has scientificity;
(3) And (3) measuring the comparability: the data collection of the basic index must be given by objective data or expert scoring, so the establishment of the index must be measurable or comparable;
(4) Layering: subdividing the indexes into related levels according to the correlation of each index and the characteristics of an analytic hierarchy process;
and step S3: the student cognitive ability analysis system based on online course learning is established according to the student online course mastering condition and the student learning condition, and cognitive ability evaluation indexes are divided into three levels: the target layer, the standard layer and the index layer are established according to the following index system layers:
(1) Target layer: cognitive ability E to be based on student online course learning behavior ij Setting as a target layer, wherein i represents students and j represents courses;
(2) A criterion layer: the criterion layer mainly comprises three modules: u shape 1 Learning behavior condition based on functional dimension, U 2 Learning behavior situation and U based on structural dimensions 3 Learning behavior based on a mode dimension;
(3) An index layer: learning behavior condition U based on functional dimension 1 The following indexes are provided: situation U mastery in chapter I 11 Second chapter controls situation U 12 Third chapter U grasp situation 13 And so on; learning context U based on structural dimensions 2 The following indexes are provided: doing U 21 Video watching U 22 Forum discussion U 23 Wikipedia U for reading courses 24 Browsing other parts of the course U 25 (ii) a Mode dimension-based student basic learning condition U 3 The following indexes are provided: webpage U 31 Client U 31 。
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