CN109191345B - Cognitive diagnosis method for student cognitive process - Google Patents
Cognitive diagnosis method for student cognitive process Download PDFInfo
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Abstract
The invention discloses a cognitive diagnosis method for a student cognitive process, which comprises the following steps: constructing a multi-granularity representation model of knowledge points and exercises, constructing a academic state representation model of student nodes, and performing cognitive diagnosis analysis on the student nodes. The invention can use the knowledge map method to express the academic state of the student in a multi-granularity way, thereby analyzing the mastering degree of the corresponding knowledge points of the student according to the answering condition of the student aiming at different cognitive processes of the student.
Description
Technical Field
The invention relates to the field of education data mining, in particular to a multi-granularity cognitive diagnosis method for a student cognitive process.
Background
With the development of open education resource platforms such as a mullet course and the like, the promotion of 'internet + education' is highly concerned and valued at the national level. Educational researchers quantitatively evaluate the personalized differences and Cognitive levels of students through Cognitive diagnostics (Cognitive Diagnosis). Massive learning data of students exist on the Internet, and knowledge points related to most topics present different granularity levels. In the cognitive process of students, the requirements of the students on the granularity level of mastered knowledge points in different learning stages are different.
Therefore, the learning state of the student is tracked in real time by analyzing the real-time learning data, and personalized guidance and learning early warning are performed in a targeted manner, so that the method has important significance. At present, a DINA model based on a test question knowledge point association matrix is a mainstream cognitive diagnosis model, however, the existing method based on the test question knowledge point association matrix causes that the model cannot sufficiently express different granularities of knowledge points.
Based on the above situations, it is particularly important to design a reasonable multi-granularity cognitive diagnosis method facing the cognitive process of students.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a reasonable cognitive diagnosis method facing the cognitive process of students, so that the academic state of the students can be expressed in a multi-granularity mode by using a knowledge map, and the mastery degree of the knowledge points corresponding to the students can be analyzed according to the answering conditions of the students aiming at different cognitive processes of the students.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention relates to a cognitive diagnosis method for a student cognitive process, which is characterized by comprising the following steps of:
(1) constructing a multi-granularity representation model of knowledge points and exercises:
(1.1) setting the number of knowledge points as P, the number of exercises as Q and the number of students as M;
(1.2) creating a knowledge point node K ═ K1,K2,…,Kp,…,KPGet the question node J ═ J1,J2,…,Jq,…,JQThe student node I is { I ═ I }1,I2,…,Im,…,IM}; wherein, KpRepresents the p-th knowledge point node, JqRepresents the q-th problem node, ImRepresents the mth student node, P is 1,2, …, P, Q is 1,2, …, Q, M is 1,2, …, M;
(1.3) defining the p-th knowledge point node KpThe attributes of (1) include: knowledge point name KpName, detail KpContext, difficulty value KpDifficuty; thereby defining the attributes of the P knowledge point nodes;
define the qth problem node JqThe attributes of (1) include: exercise content JqName, problem option JqOption, exercise answer JqAn answer; thereby defining attributes of Q problem nodes;
define mth student node ImIs the name of the student ImName; thereby defining attributes of the M student nodes;
(1.4) setting attribute values of P knowledge point nodes, Q exercise nodes and M student nodes;
(1.5) if the p-th knowledge point node KpContaining the v-th knowledge point node KvThen, it represents the p-th knowledge point node KpAnd the v-th knowledge nodePoint KvThere is an edge in between, denoted L1(Kp,Kv) And L is1(Kp,Kv)＝1；
If the p-th knowledge point node KpDoes not contain the v-th knowledge point node KvThen let L1(Kp,Kv) 0; v ≠ P ≠ 1,2, …;
dividing the knowledge point nodes with mutually communicated edges into a knowledge cluster, thereby dividing all the knowledge point nodes into R knowledge clusters C ═ { C ═ C1,C2,…,Cr,…,CR}；CrRepresents the R-th knowledge cluster, R ═ 1,2, …, R;
(1.6) if the p-th knowledge point node KpBelonging to the r-th knowledge cluster CrAnd is the r-th knowledge cluster CrLeaf node of, and the qth problem node JqInvolving the p-th knowledge point node KpThen, it represents the q-th problem node JqAnd the p-th knowledge point node KpThere is an edge in between, denoted L2(Jq,Kp) And L is2(Jq,Kp) 1 is ═ 1; otherwise, let L2(Jq,Kp)＝0；
(1.7) if the p-th knowledge point node KpBelonging to the r-th knowledge cluster CrBut not the r-th knowledge cluster CrLeaf node of, and the ith knowledge point node KiIs the r-th knowledge cluster CrLeaf node of, and the p-th knowledge point node KpContaining the ith knowledge point node KiQ question node JqInvolving the p-th knowledge point node KpThen, the q-th problem node JqAnd the ith leaf node KiThere is an edge L in between2(Jp,Ki) And L is2(Jp,Ki) 1 is ═ 1; otherwise, let L2(Jq,Kp)＝0；
(1.8) if the mth student node ImNode J for completing q-th exerciseqThe answer of (1) indicates the mth student node ImAnd the q-th problem node JqThere is an edge L in between3(Im,Jq) And L is3(Im,Jq) 1, otherwise L3(Im,Jq)＝0；
Setting edge L3(Im,Jq) Has an attribute of L3(Im,Jq).ansmDenotes the mth student node ImQ question node JqThe answer of (1);
(1.9) setting edge L3(Im,Jq) Has an attribute of L3(Im,Jq) Flag, denoting the mth student node ImQ question node JqWhether the answer of (1) is correct; if L is3(Im,Jq).ansm＝JqAnswer, then order L3(Im,Jq) Otherwise let L be 13(Im,Jq).flag＝0；
(1.10) calculate and q problem node JqNumber n of student nodes with edgesqSo as to obtain the number n of student nodes with edges existing on all exercises J ═ n1,n2,…,nq,…,nQ}；
Calculate and q problem node JqNumber n of student nodes with edgesqMiddle, mth student node ImAnd the q-th problem node JqThere is an edge L in between3(Im,Jq) Property L of3(Im,Jq) Number of student nodes of 1 ═ flag
Thereby obtaining the number of the edges of the student nodes with the attribute of 1 which have edges with all the exercises J
(2) And constructing an mth student node ImThe academic state representation model:
(2.1) recreating the knowledge point node K ═ K1,K2,…,Kp,…,KPPoints J of exercise＝{J1,J2,…,Jq,…,JQAnd edges L between knowledge point nodes1Edges L between problem nodes and knowledge points2；
(2.2) defining the p-th knowledge point node KpThe attributes of (1) include: knowledge point name KpName, detail KpContext, mth student ImFor the p-th knowledge point node KpDegree of mastery Kp.cognitionm；
Define the qth problem node JqThe attributes of (1) include: exercise content JqName, problem option JqOption, exercise answer JqAnswer, mth student ImAnswer J ofq.ansmMth student ImAnswering time Jq.timem；
(2.3) setting attribute values of P knowledge point nodes, Q exercise nodes and M student nodes;
the mth student node ImFor the p-th knowledge point node KpDegree of mastery KpCognition is set to "-1"; thereby connecting the mth student node ImThe mastery degree of all knowledge point nodes is set to be '-1';
(3) mth student node ImCognitive diagnostic analysis of (1):
(3.1) setting the q-th problem node JqHas an initial difficulty coefficient of
Thereby setting the initial difficulty factors of all the exercises J to
(3.2) setting the total iteration number as T, setting the current iteration number as T, and initializing T to be 1;
(3.3) calculating the q-th problem node J by the formula (1)qIs adjusted by the coefficient wq', thereby obtaining the adjustment coefficients w' ═ w for all problems J1′,w2′,…,wq′,…,wQ′}：
(3.4) updating the q-th problem node J of the t-th iteration by the formula (2)qCoefficient of difficulty (c)
Thereby updating the difficulty coefficients of all the problems J of the t-th iteration
(3.5) assigning T +1 to T, judging whether T is equal to T or not, and if so, executing the step (3.6); otherwise, executing the step (3.4);
(3.6) making Condition S L3(Im,Jq)＝1∧{L3(Jq,Kp)＝1∨{L3(Jq,Ki)＝1∧KpComprising Ki}; condition S+Is L3(Im,Jq)＝1∧{L3(Im,Jq).flag＝1}∧{L3(Jq,Kp)＝1∨{L3(Jq,Ki)＝1∧KpComprising Ki}}；
(3.7) calculating the mth student node I by the formula (3)mTo the p-th knowledge point node KpDegree of mastery Kp.cognitionm：
Compared with the prior art, the invention has the beneficial effects that:
1. the invention adopts a knowledge map method to construct a multi-granularity representation model of knowledge points and exercises and a academic state representation model of students, thereby being capable of carrying out cognitive diagnosis analysis on the students and solving the problem of non-granularity hierarchy of the knowledge point nodes in the prior art, so that the academic state condition of the students can be analyzed in a multi-level and all-around way aiming at different cognitive processes of the students when the students are subjected to cognitive diagnosis;
2. for large-scale exercises, knowledge points and student data in an open education platform, the relationship among the data in the model is far less than the number of the data. In the prior art, a matrix representation method is used for representing knowledge points, exercise models and student state models, so that the matrix is sparse. The multi-granularity representation model of knowledge points and exercises and the academic state representation model of students are constructed based on the knowledge map method, so that the problem of data sparsity is relieved, and the spatial complexity of data is effectively reduced;
3. because the learning emphasis of the students and the granularity level of the mastered knowledge points are greatly different in different cognitive stages of the students, such as unit test, in-phase test and end-of-period test of the students, the multi-granularity representation model provided by the invention enables the knowledge points to be displayed in different granularity levels, so that the model can perform diagnosis and analysis aiming at different emphasis points of the students in different cognitive processes.
Drawings
FIG. 1 is a flow chart of a cognitive diagnosis method for student cognitive processes according to the present invention;
FIG. 2 is a schematic diagram of a multi-granular representation model of knowledge points, problems of the present invention;
FIG. 3 is a schematic diagram of a student academic state representation model of the present invention;
FIG. 4 is a schematic diagram of a problem, knowledge point matrix used by a conventional teacher;
FIG. 5 is a schematic diagram of a problem and knowledge point matrix oriented to the cognitive process of a student according to the present invention;
FIG. 6 is a diagram of the relationship of "sorted" knowledge clusters to problems 1,2 in an embodiment of the present invention.
Detailed Description
In this embodiment, a cognitive diagnosis method for a student cognitive process includes: firstly, constructing a multi-granularity representation model of knowledge points and exercises based on a knowledge graph method; secondly, constructing a student's academic state representation model based on the multi-granularity representation model of the knowledge points and the exercises; and thirdly, performing multi-granularity cognitive diagnosis analysis on the students according to the cognitive process of the students. The algorithm flow chart is shown in fig. 1. Specifically, the method comprises the following steps:
(1) constructing a multi-granularity representation model of knowledge points and exercises:
the relation between knowledge points and the relation between exercises and knowledge points are expressed by using a knowledge graph method. As shown in fig. 2, there are three types of nodes in the knowledge graph, which are knowledge point nodes, problem nodes, and student nodes; edges then indicate the existence of relationships between nodes.
(1.1) setting the number of knowledge points as P, the number of exercises as Q and the number of students as M;
(1.2) creating a knowledge point node K ═ K1,K2,…,Kp,…,KPGet the question node J ═ J1,J2,…,Jq,…,JQThe student node I is { I ═ I }1,I2,…,Im,…,IM}; wherein, KpRepresents the p-th knowledge point node, JqRepresents the q-th problem node, ImRepresents the mth student node, P is 1,2, …, P, Q is 1,2, …, Q, M is 1,2, …, M;
specifically, as shown in fig. 2, the rectangular nodes represent knowledge point nodes, the elliptical nodes represent problem nodes, and the pentagonal nodes represent student nodes.
(1.3) defining the p-th knowledge point node KpThe attributes of (1) include: knowledge point name KpName, detail KpContext, difficulty value KpDifficuty; thereby defining the attributes of the P knowledge point nodes;
define the qth problem node JqThe attributes of (1) include: exercise content JqName, problem option JqOption, exercise answer JqAn answer; to thereby decideDefining attributes of Q problem nodes;
define mth student node ImIs the name of the student ImName; thereby defining attributes of the M student nodes;
(1.4) setting attribute values of P knowledge point nodes, Q exercise nodes and M student nodes;
(1.5) if the p-th knowledge point node KpContaining the v-th knowledge point node KvThen, it represents the p-th knowledge point node KpAnd the v-th knowledge point node KvThere is an edge in between, denoted L1(Kp,Kv) And L is1(Kp,Kv)＝1；
If the p-th knowledge point node KpDoes not contain the v-th knowledge point node KvThen let L1(Kp,Kv) 0; v ≠ P ≠ 1,2, …;
dividing the knowledge point nodes with mutually communicated edges into a knowledge cluster, thereby dividing all the knowledge point nodes into R knowledge clusters C ═ { C ═ C1,C2,…,Cr,…,CR}；CrRepresents the R-th knowledge cluster, R ═ 1,2, …, R;
because the knowledge point node may include a plurality of sub-knowledge points, the knowledge points and the sub-knowledge points included therein form a knowledge cluster of a tree structure, that is, a knowledge point structure of different granularity levels is formed. The minimum knowledge point in each knowledge cluster is called a leaf node, i.e. a sub-knowledge point in the knowledge cluster that cannot be further subdivided.
Specifically, as shown in FIG. 2, C1Including the node K with knowledge point1Six knowledge points, i.e. C, for a parent node1＝{K1,K3,K4,K5,K8,K9}；C2Including the node K with knowledge point2Three knowledge points, i.e. C, for a parent node2＝{K2,K6,K7}. Wherein, knowledge point node K1Containing knowledge point node K3、K4、K5I.e. L1(K1,K3)＝1，L1(K1,K4)＝1，L1(K1,K5) 1 is ═ 1; knowledge point node K4Containing knowledge point node K8、K9I.e. L1(K4,K8)＝1，L1(K4,K9) 1 is ═ 1; knowledge point node K2Containing knowledge point node K6、K7I.e. L1(K2,K6)＝1，L1(K2,K7) 1. However, knowledge point node K1Node K without knowledge point6And K8Then L is1(K1,K6)＝0，L1(K1,K8) The non-inclusive relationship of the remaining knowledge point nodes is the same as 0.
(1.6) if the p-th knowledge point node KpBelonging to the r-th knowledge cluster CrAnd is the r-th knowledge cluster CrLeaf node of, and the qth problem node JqInvolving the p-th knowledge point node KpThen, it represents the q-th problem node JqAnd the p-th knowledge point node KpThere is an edge in between, denoted L2(Jq,Kp) And L is2(Jq,Kp) 1 is ═ 1; otherwise, let L2(Jq,Kp)＝0；
Specifically, as shown in FIG. 2, a knowledge point node K3Is a knowledge cluster C1Leaf node of, knowledge point node K6、K7Is a knowledge cluster C2A leaf node of (1); exercise node J1Relating to a knowledge point node K3、K6Then exercise node J1And knowledge point node K3、K6There is an edge in between, i.e. L2(J1,K3)＝1、L2(J1,K6) 1. Knowledge point node K4Is not a knowledge cluster C1Leaf node of (1), then although problem node J1Relating to a knowledge point node K4But problem node J1And knowledge point node K4There is no edge in between, i.e. L2(J1,K4) The same applies to the rest of the similar cases as 0. Exercise node J1Node K without knowledge point5I.e. L2(J1,K5) The same applies to the rest of the similar cases as 0.
(1.7) if the p-th knowledge point node KpBelonging to the r-th knowledge cluster CrBut not the r-th knowledge cluster CrLeaf node of, and the ith knowledge point node KiIs the r-th knowledge cluster CrLeaf node of, and the p-th knowledge point node KpContaining the ith knowledge point node KiQ question node JqInvolving the p-th knowledge point node KpThen, the q-th problem node JqAnd the ith leaf node KiThere is an edge L in between2(Jp,Ki) And L is2(Jp,Ki) 1 is ═ 1; otherwise, let L2(Jq,Kp)＝0；
Since each problem involves one or more knowledge points, a student can only answer the problem correctly if he or she grasps all the knowledge points involved in the problem, and therefore, each problem node is associated with the smallest knowledge point it involves.
Specifically, as shown in FIG. 2, a knowledge point node K4Is not a knowledge cluster C1Leaf node of, knowledge point node K4Containing knowledge point node K8And K9And knowledge point node K8And K9Is a knowledge cluster C1Leaf node of (2), if problem node J1Relating to a knowledge point node K4Then exercise node J1And knowledge point node K8And K9There is an edge in between, i.e. L2(J1,K8)＝1，L2(J1,K9) 1. And 0 in the remaining cases.
(1.8) if the mth student node ImNode J for completing q-th exerciseqThe answer of (1) indicates the mth student node ImAnd the q-th problem node JqThere is an edge L in between3(Im,Jq) And L is3(Im,Jq) 1, otherwise L3(Im,Jq)＝0；
Setting edge L3(Im,Jq) Has an attribute of L3(Im,Jq).ansmDenotes the mth student node ImQ question node JqThe answer of (1);
specifically, as shown in FIG. 2, student node I1Completes the exercise node J1When answering, the student node I1And problem node J1There is an edge L in between3(I1,J1) I.e. L3(I1,J1) 1 is ═ 1; in the same way, L3(I2,J1)＝1、L3(I2,J2)＝1、L3(I3,J2) 1. Due to student node I1Unfinished problem node J2When answering, the student node I1And problem node J2There is no edge in between, i.e. L3(I1,J2) 0; in the same way, L3(I3,J1)＝0。
Respectively provided with sides L3(I1,J1)、L3(I2,J1)、L3(I2,J2)、L3(I3,J2) Property L of3(I1,J1).ans1、L3(I2,J1).ans2、L3(I2,J2).ans2、L3(I3,J2).ans3And student node I1、I2、I3The answers corresponding to the answering questions are assigned to the above four attribute values.
(1.9) setting edge L3(Im,Jq) Has an attribute of L3(Im,Jq) Flag, denoting the mth student node ImQ question node JqWhether the answer of (1) is correct; if L is3(Im,Jq).ansm＝JqAnswer, then order L3(Im,Jq) Otherwise let L be 13(Im,Jq).flag＝0；
Specifically, as shown in fig. 2, the sides L are provided respectively3(I1,J1)、L3(I2,J1)、L3(I2,J2)、L3(I3,J2) Property L of3(I1,J1).flag、L3(I2,J1).flag、L3(I2,J2).flag、L3(I3,J2) Flag. If student node I1Correctly answering exercise node J1I.e. L3(I1,J1).ans1＝J1Answer, then L3(I1,J1) 1, ═ flag; if student node I1Wrong answer exercise node J1I.e. L3(I1,J1).ans1≠J1Answer, then L3(I1,J1) Flag ═ 0; the same way can get the rest attribute values.
(1.10) calculate and q problem node JqNumber n of student nodes with edgesqSo as to obtain the number n of student nodes with edges existing on all exercises J ═ n1,n2,…,nq,…,nQ}；
Calculate and q problem node JqNumber n of student nodes with edgesqMiddle, mth student node ImAnd the q-th problem node JqThere is an edge L in between3(Im,Jq) Property L of3(Im,Jq) Number of student nodes of 1 ═ flag
Thereby obtaining the number of the edges of the student nodes with the attribute of 1 which have edges with all the exercises J
Specifically, as shown in FIG. 2, with problem node J1Number n of student nodes with edges12; the same can obtain n2＝2。
If L is3(I1,J1).flag＝1、L3(I2,J1).flag＝1、L3(I2,J2).flag＝0、L3(I3,J2) If flag is 1, then
(2) And constructing an mth student node ImThe academic state representation model:
the relation between the exercises answered by the students and knowledge points is expressed by using a knowledge graph method. As shown in fig. 3, there are two types of nodes in the knowledge graph, which are knowledge point nodes and problem nodes, respectively; edges then indicate the existence of relationships between nodes. Hypothesis construction student node I2Represents a model.
(2.1) recreating the knowledge point node K ═ K1,K2,…,Kp,…,KPGet the question node J ═ J1,J2,…,Jq,…,JQAnd edges L between knowledge point nodes1Edges L between problem nodes and knowledge points2；
The knowledge point nodes, problem nodes and edges between nodes shown in fig. 3 are multiplexed with the knowledge point nodes, problem nodes and edges between nodes shown in fig. 2.
(2.2) defining the p-th knowledge point node KpThe attributes of (1) include: knowledge point name KpName, detail KpContext, mth student ImFor the p-th knowledge point node KpDegree of mastery Kp.cognitionm；
Define the qth problem node JqThe attributes of (1) include: exercise content JqName, problem option JqOption, exercise answer JqAnswer, mth student ImAnswer J ofq.ansmMth student ImAnswering time Jq.timem；
With knowledge points and exercisesCompared with a multi-granularity representation model, in the academic state graph of students, each knowledge point node is added with a student node I except the name and the detailed content of the knowledge point2The degree of mastery attribute of the knowledge point nodes; in addition to storing question information and answers in each question node, a student node I is added2The answer and the answer time attribute.
(2.3) setting attribute values of P knowledge point nodes, Q exercise nodes and M student nodes;
the mth student node ImFor the p-th knowledge point node KpDegree of mastery KpCognition is set to "-1"; thereby connecting the mth student node ImThe mastery degree of all knowledge point nodes is set to be '-1';
(3) mth student node ImCognitive diagnostic analysis of (1):
(3.1) setting the q-th problem node JqHas an initial difficulty coefficient of
Thereby setting the initial difficulty factors of all the exercises J to
The knowledge point and problem matrix used in the conventional cognitive diagnosis process is shown in fig. 4, and the knowledge point mastering conditions of different granularity levels cannot be embodied. Because the cognition process of each student is different at present, the requirement of the student in the learning stage of the new knowledge point on the granularity level mastered by the knowledge point is thinner, and the requirement of the student in the combing and reviewing stage of the knowledge point on the granularity level mastered by the knowledge point is thicker. Therefore, in the multi-granularity representation model constructed by the invention, the required granularity level (as shown in fig. 5) can be selected in a targeted manner according to different requirements of different students on the granularity level, so that the initial difficulty coefficient of the problem can be set for the student more specifically.
Specifically, the contribution of the invention on multiple granularity levels is shown in fig. 6, where problem 1 and problem 2 both examine the mastery degree of the student on the knowledge points related to the ranking algorithm, however, problem 1 is a practice problem in the learning stage of the ranking algorithm, and the knowledge points should be divided into finer granularities, i.e., { "hill ranking basic concept", "hill ranking time complexity" }, so as to emphatically examine the mastery condition of the student on each sub-knowledge point. Problem 2 is an examination problem in an end-of-term examination, and since there are many knowledge points involved in the end-of-term examination paper, if a fine-grained knowledge point partitioning method is used, the complexity of model solution is too high, and therefore, a coarser-grained knowledge point partitioning can be obtained by using a parent node of leaf nodes in a knowledge cluster. For example, the coarse-grained division of problem 2 can be { "hill sort", "bubble sort", "quick sort", "heap sort" }; and if the finest granularity division is used, the basic concept, the algorithm description and the stability of each sort algorithm are taken as knowledge points related to the problem, so that the model has higher time complexity in solving. Based on the method, the individual analysis can be carried out on students in different cognitive processes according to the method provided by the invention, and the initial difficulty coefficients of all exercises are formulated.
Suppose problem node J shown in FIG. 31、J2Respectively is
(3.2) setting the total iteration number as T, setting the current iteration number as T, and initializing T to be 1;
for simplicity, assume that the total number of iterations T is 3.
(3.3) calculating the q-th problem node J by the formula (1)qIs adjusted by the coefficient wq', thereby obtaining the adjustment coefficients w' ═ w for all problems J1′,w2′,…,wq′,…,wQ′}：
Problem node J shown in FIG. 31Adjustment coefficient of
Exercise node J2Adjustment coefficient of
(3.4) updating the q-th problem node J of the t-th iteration by the formula (2)qCoefficient of difficulty (c)
Thereby updating the difficulty coefficients of all the problems J of the t-th iteration
(3.5) assigning T +1 to T, judging whether T is equal to T or not, and if so, executing the step (3.6); otherwise, executing the step (3.4);
as shown in FIG. 3, by iterating T times, the problem node J shown in FIG. 4 can be obtained1、J2Coefficient of difficulty (c)
It can be seen that the answer question node J1All students correctly answer the question, question node J1The difficulty coefficient is greatly reduced; because the answer question node J2If the student has correct answer and wrong answer, the problem node J2The difficulty factor of (2) is reduced.
(3.6) making Condition S L3(Im,Jq)＝1∧{L3(Jq,Kp)＝1∨{L3(Jq,Ki)＝1∧KpComprising Ki}; condition S+Is L3(Im,Jq)＝1∧{L3(Im,Jq).flag＝1}∧{L3(Jq,Kp)＝1∨{L3(Jq,Ki)＝1∧KpComprising Ki}}；
The meaning of condition S is: student node ImAnswer knowledge point node KpProblem node J involvedqOr answer the knowledge point node KiProblem node J involvedqAnd knowledge point node KpContaining knowledge point node Ki。
Condition S+The meaning of (A) is: student node ImCorrectly answer the knowledge point node KpProblem node J involvedqOr correctly answer the knowledge point node KiProblem node J involvedqAnd knowledge point node KpContaining knowledge point node Ki。
As shown in fig. 3, condition S is: for student node I2Answer and knowledge point node K4Contained knowledge point node K8、K9Problem node J involved1(ii) a Condition S+Comprises the following steps: for student node I2Correctly answer and knowledge point node K4Contained knowledge point node K8、K9Problem node J involved1(ii) a The student node I can be obtained by the same method2Conditions for other knowledge point nodes.
(3.7) calculating the mth student node I by the formula (3)mTo the p-th knowledge point node KpDegree of mastery Kp.cognitionm：
From this, student node I can be obtained2For knowledge point node K4Degree of mastery of
As shown in FIG. 6, with "The basic concept knowledge points of Hill ordering are taken as examples, and the associated problems are problem 1 and problem 2 according to the formula
The mastery condition of the student on the knowledge point at this stage can be calculated. If the student is assumed to be in the end stage of the learning period and needs to have global mastery on the "sorted" knowledge points, the mastery condition of the student on the "exchange sorting" type granularity knowledge points in this stage should be analyzed. Using the "exchange sorting" knowledge point as an example, the associated problem is problem 2, and then the formula is followed
The mastering condition of the knowledge point at the end stage of the student can be calculated.
Claims (1)
1. A cognitive diagnosis method for cognitive processes of students is characterized by comprising the following steps:
(1) constructing a multi-granularity representation model of knowledge points and exercises:
(1.1) setting the number of knowledge points as P, the number of exercises as Q and the number of students as M;
(1.2) creating a knowledge point node K ═ K1,K2,…,Kp,…,KPGet the question node J ═ J1,J2,…,Jq,…,JQThe student node I is { I ═ I }1,I2,…,Im,…,IM}; wherein, KpRepresents the p-th knowledge point node, JqRepresents the q-th problem node, ImRepresents the mth student node, P is 1,2, …, P, Q is 1,2, …, Q, M is 1,2, …, M;
(1.3) defining the p-th knowledge point node KpThe attributes of (1) include: knowledge point name KpName, detail KpContext, difficulty value KpDifficuty; thereby defining the attributes of the P knowledge point nodes;
define the qth problem node JqThe attributes of (1) include: exercise content JqName, studyQuestion item JqOption, exercise answer JqAn answer; thereby defining attributes of Q problem nodes;
define mth student node ImIs the name of the student ImName; thereby defining attributes of the M student nodes;
(1.4) setting attribute values of P knowledge point nodes, Q exercise nodes and M student nodes;
(1.5) if the p-th knowledge point node KpContaining the v-th knowledge point node KvThen, it represents the p-th knowledge point node KpAnd the v-th knowledge point node KvThere is an edge in between, denoted L1(Kp,Kv) And L is1(Kp,Kv)＝1；
If the p-th knowledge point node KpDoes not contain the v-th knowledge point node KvThen let L1(Kp,Kv) 0; v ≠ P ≠ 1,2, …;
dividing the knowledge point nodes with mutually communicated edges into a knowledge cluster, thereby dividing all the knowledge point nodes into R knowledge clusters C ═ { C ═ C1,C2,…,Cr,…,CR}；CrRepresents the R-th knowledge cluster, R ═ 1,2, …, R;
(1.6) if the p-th knowledge point node KpBelonging to the r-th knowledge cluster CrAnd is the r-th knowledge cluster CrLeaf node of, and the qth problem node JqInvolving the p-th knowledge point node KpThen, it represents the q-th problem node JqAnd the p-th knowledge point node KpThere is an edge in between, denoted L2(Jq,Kp) And L is2(Jq,Kp) 1 is ═ 1; otherwise, let L2(Jq,Kp)＝0；
(1.7) if the p-th knowledge point node KpBelonging to the r-th knowledge cluster CrBut not the r-th knowledge cluster CrLeaf node of, and the ith knowledge point node KiIs the r-th knowledge cluster CrLeaf node of, and the p-th knowledge point node KpContaining the ith knowledge point node KiThe q thExercise node JqInvolving the p-th knowledge point node KpThen, the q-th problem node JqAnd the ith leaf node KiThere is an edge L in between2(Jp,Ki) And L is2(Jp,Ki) 1 is ═ 1; otherwise, let L2(Jq,Kp)＝0；
(1.8) if the mth student node ImNode J for completing q-th exerciseqThe answer of (1) indicates the mth student node ImAnd the q-th problem node JqThere is an edge L in between3(Im,Jq) And L is3(Im,Jq) 1, otherwise L3(Im,Jq)＝0；
Setting edge L3(Im,Jq) Has an attribute of L3(Im,Jq).ansmDenotes the mth student node ImQ question node JqThe answer of (1);
(1.9) setting edge L3(Im,Jq) Has an attribute of L3(Im,Jq) Flag, denoting the mth student node ImQ question node JqWhether the answer of (1) is correct; if L is3(Im,Jq).ansm＝JqAnswer, then order L3(Im,Jq) Otherwise let L be 13(Im,Jq).flag＝0；
(1.10) calculate and q problem node JqNumber n of student nodes with edgesqSo as to obtain the number n of student nodes with edges existing on all exercises J ═ n1,n2,…,nq,…,nQ}；
Calculate and q problem node JqNumber n of student nodes with edgesqMiddle, mth student node ImAnd the q-th problem node JqThere is an edge L in between3(Im,Jq) Property L of3(Im,Jq) Number of student nodes of 1 ═ flag
Thereby obtaining the number of the edges of the student nodes with the attribute of 1 which have edges with all the exercises J
(2) And constructing an mth student node ImThe academic state representation model:
(2.1) recreating the knowledge point node K ═ K1,K2,…,Kp,…,KPGet the question node J ═ J1,J2,…,Jq,…,JQAnd edges L between knowledge point nodes1Edges L between problem nodes and knowledge points2；
(2.2) defining the p-th knowledge point node KpThe attributes of (1) include: knowledge point name KpName, detail KpContext, mth student ImFor the p-th knowledge point node KpDegree of mastery Kp.cognitionm；
Define the qth problem node JqThe attributes of (1) include: exercise content JqName, problem option JqOption, exercise answer JqAnswer, mth student ImAnswer J ofq.ansmMth student ImAnswering time Jq.timem；
(2.3) setting attribute values of P knowledge point nodes, Q exercise nodes and M student nodes;
the mth student node ImFor the p-th knowledge point node KpDegree of mastery KpCognition is set to "-1"; thereby connecting the mth student node ImThe mastery degree of all knowledge point nodes is set to be '-1';
(3) mth student node ImCognitive diagnostic analysis of (1):
(3.1) setting the q-th problem node JqHas an initial difficulty coefficient of
Thereby setting the initial difficulty factors of all the exercises J to
(3.2) setting the total iteration number as T, setting the current iteration number as T, and initializing T to be 1;
(3.3) calculating the q-th problem node J by the formula (1)qIs adjusted by the coefficient wq', thereby obtaining the adjustment coefficients w' ═ w for all problems J1′,w2′,…,wq′,…,wQ′}：
(3.4) updating the q-th problem node J of the t-th iteration by the formula (2)qCoefficient of difficulty (c)
Thereby updating the difficulty coefficients of all the problems J of the t-th iteration
(3.5) assigning T +1 to T, judging whether T is equal to T or not, and if so, executing the step (3.6); otherwise, executing the step (3.4);
(3.6) making Condition S L3(Im,Jq)＝1∧{L3(Jq,Kp)＝1∨{L3(Jq,Ki)＝1∧KpComprising Ki}; condition S+Is L3(Im,Jq)＝1∧{L3(Im,Jq).flag＝1}∧{L3(Jq,Kp)＝1∨{L3(Jq,Ki)＝1∧KpComprising Ki}}；
(3.7) calculating the mth student node I by the formula (3)mTo the p-th knowledge point node KpDegree of mastery Kp.cognitionm：
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