Mathematical ability tracking and question recommendation method of adaptive IRT model

Abstract

The invention discloses a mathematical ability tracking and question recommendation method of a self-adaptive IRT model. The method comprises the following steps: S1, establishing a student mathematical exercise question bank and marking an initial difficulty coefficient; s2, establishing a student mathematical ability data file; s3, constructing a staged variable parameter IRT model, and carrying out student mathematical ability estimation; s4, the question matching degree in the candidate question set is calculated, and question recommendation is carried out; s5, obtaining a new answer record of the student, updating a mathematical ability data file of the student, and updating question parameters in real time; and S6, carrying out periodic global IRT model parameter calibration. According to the method, the parameter estimation and model precision is improved, the effect of balancing the precision and the speed is achieved, the student mathematical ability can be adaptively and dynamically estimated, and the real-time performance and the accuracy of student mathematical ability estimation are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of student ability prediction and question matching recommendation, and particularly relates to a mathematical ability tracking and question recommendation method of an adaptive IRT model. BACKGROUND

[0002] In the process of mathematics education and teaching, the student's mathematical ability level is usually evaluated by periodic tests (such as monthly exams), and then evaluated by test scores and school rankings. In the process of daily teaching and exercise, the same paper and the same questions are usually used. However, such traditional evaluation and exercise methods have the following defects: first, the frequency of periodic tests is usually low, lacking of data in daily life, and cannot reflect the real-time changes of student ability, and is easily affected by extreme values of a test, so the evaluation results will be affected by extreme values; second, in the process of question exercises, the difficulty of the questions is not different for students of different levels. For students with poor actual ability level, the difficulty of the exercises is too high, which will destroy the students' enthusiasm and confidence, and lead to a decline in learning interest. For students with high actual ability level, the difficulty of the exercises is too low, which will lead to a decrease in learning efficiency and waste of time.

[0003] In the evaluation of student mathematical ability, the traditional IRT model usually ignores the influence of question exposure on model parameters, resulting in systematic deviation in model prediction ability; at the same time, the traditional IRT model cannot be compatible with the evaluation difference between discrete scores (such as multiple-choice questions, true or false questions, etc.) and continuous scores (answer questions), and the forced normalization leads to information loss, precision decline or calculation increase.

[0004] For example, CN118734021A discloses an evaluation method for test attributes and student knowledge level, which constructs a hierarchical Bayesian IRT model based on 2PL-IRT, and estimates the hidden parameters by a sampling algorithm. This scheme ignores individual differences such as student learning rate and ability fluctuation variance, uses a static parameter estimation framework, and lacks an adaptive tracking mechanism for the dynamic change direction and rate of student ability; in addition, this scheme uses binary scores as statistical items, i.e. it uses a discrete score probability model, and does not process continuous score questions, which forces the continuous score to be processed as a binary score, resulting in loss of answer information and precision, thereby affecting the accurate evaluation of student ability. SUMMARY

[0005] In order to solve the problem that the conventional IRT model cannot adaptively and dynamically evaluate the student's mathematical ability, and cannot be compatible with the evaluation difference between discrete scores and continuous scores, thereby leading to low accuracy of student ability evaluation, the present application proposes a mathematical ability tracking and question recommendation method of an adaptive IRT model to solve the above problems.

[0006] The application discloses a mathematical ability tracking and question recommendation method of an adaptive IRT model, and comprises the following steps:

[0007] S1, establishing a student mathematical exercise question bank by grades and semesters, and marking initial difficulty coefficients for questions in the question bank;

[0008] S2, establishing a student mathematical ability data archive for storing data for evaluating the mathematical ability of the student;

[0009] S3, constructing a stage-variable parameter IRT model to estimate the mathematical ability of the student;

[0010] S4, calculating the matching degree of questions in a candidate question set, and recommending questions according to the matching degree of the questions;

[0011] S5, obtaining new answer records of the student, updating the student mathematical ability data archive, and updating the question parameters in real time;

[0012] S6, periodically calibrating global IRT model parameters.

[0013] Preferably, the S1 comprises the following steps:

[0014] A question unique number is j, a difficulty coefficient d i is marked for the question j in the question bank, and the exposure amount of the question j is N i ;

[0015] The IRT model parameters are initialized, including a discrimination coefficient a i , a difficulty parameter b i , a guessing probability c j and a probability weighting item index

[0016] Preferably, the IRT model parameter calculation formula is as follows:

[0017]

[0018]

[0019] a j The initial value is 1.

[0020] Preferably, the student mathematical ability data archive in the S2 comprises a student ability value θ, an ability value variance σ 2 , a learning rate η0, a question history record set and a recent question history set queue Q, and the length of the recent question history set queue Q is L.

[0021] The student unique number is i, when the i-th student has not answered the question, that is, the initial state of the student is: θ=0.5, σ 2= 1, η0= 0.1, and Q is an empty set.

[0022] Preferably, when the student initiates a question request, the student unique number i is obtained, the student mathematical ability data profile is queried, and the student answer history record is recorded as k represents the total number of answers of student i, and r is the score rate, The elements in the set are arranged in ascending order of timestamps.

[0023] Preferably, the S3 comprises the following steps:

[0024] S31, a staged variable parameter IRT model is established:

[0025]

[0026] wherein, P j represents the probability of the student answering the question j correctly;

[0027] S32, the student ability estimate value is calculated by maximizing the likelihood function:

[0028]

[0029] wherein, θ IRT represents the student ability estimate value, is the value of θ corresponding to the maximum value of the likelihood function l(θ), and r m represents the student answer history record , the score rate of the mth answer record in the set, is an exponential of a probability weighting item selected according to the question type, represents the probability weighting item of the mth answer record, P m represents the exposure amount N j of the question j corresponding to the mth answer record;

[0030] S33, for the latest answer history set queue Q i of the student i, the average score rate is recorded as The dynamic adaptive learning rate parameter is:

[0031]

[0032] wherein, r0 is the ideal correct rate, and h is the sensitivity coefficient.

[0033] S34, the latest ability estimate value of the student is calculated:

[0034] θ i,cur = θ IRT + η t · sign(θ IRT - θ i,prev ).

[0035] where θ i,prev denotes the last calculated stored ability estimate of student i, and sign(·) is the sign function.

[0036] Preferably, the S4 comprises the following steps:

[0037] S41, obtaining the unanswered questions in the question bank corresponding to the grade and semester of student i as the candidate question set;

[0038] S42, for each question j in the candidate question set, calculating the exposure quantity N j , selecting the corresponding stage variable IRT model, and substituting the latest ability estimate of the student θ i,cur ; j ;

[0039] S43, calculating the question matching degree F

[0040] F j =1-|P j -r0|;

[0041] S44, selecting the question with the maximum matching degree F j to recommend to the student.

[0042] Preferably, the S5 comprises the following steps:

[0043] updating the ability value θ of the student:

[0044] θ←θ i,cur ;

[0045] updating the variance σ 2 of the ability value:

[0046]

[0047] where Δθ0 is a preset ability mutation threshold;

[0048] updating the learning rate η0:

[0049] η0←η0(1+0.5σ 2 );

[0050] updating the new question record of the student to the question history record set and the recent question history set queue Q.

[0051] Preferably, the S5 comprises the following steps:

[0052] recording the score rate r m of the new question recordnew a probability-weighted item index according to the type of the question calculating the probability-weighted item

[0053] calculating the question parameter update amount:

[0054]

[0055] wherein, Δa j is the update amount of the discrimination coefficient, Δb j is the update amount of the difficulty parameter b j , Δc j is the update amount of the guessing probability, η a is the update rate of the discrimination coefficient, η b is the update rate of the difficulty parameter, and η c is the update rate of the guessing probability.

[0056] updating the difficulty coefficient:

[0057]

[0058] wherein, is the updated difficulty coefficient, is the difficulty parameter before updating, is the difficulty parameter after updating.

[0059] Preferably, the S6 comprises the following steps:

[0060] for each question j, periodically calibrate the difficulty parameter and the difficulty coefficient:

[0061]

[0062] wherein, is the calibrated difficulty parameter, is the calibrated difficulty coefficient, α is a preset calibration coefficient, θ i is the ability value of the student i, r j,i represents the score rate of the i-th student for the question j, represents the probability-weighted item of the i-th student for the question j.

[0063] Advantages of the present application:

[0064] 1. The present application dynamically selects the model according to the stage of the question exposure amount, can reduce the systematic deviation caused by the inapplicable model, and improves the precision of parameter estimation.

[0065] 2. The application introduces a probability weighting item index, which integrates continuous score information into a discrete probability framework by weighting the index with a score rate, thereby significantly improving the accuracy of the model while maintaining computational efficiency.

[0066] 3. The application can update the active tracking change direction and consider the recent change trend of mathematical ability, thereby balancing precision and speed.

[0067] 4. The application establishes an adaptive learning rate mechanism, which dynamically adjusts the learning rate parameter through the variance of student ability and the recent correct answer rate, thereby adaptively and dynamically estimating the student's mathematical ability, improving the real-time and accuracy of the student's mathematical ability estimation. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 A flowchart of the mathematical ability tracking and question recommendation method of the adaptive IRT model of the embodiments of the application. DETAILED DESCRIPTION

[0069] To make the purpose, technical solutions and advantages of the application clearer, the application is further described in detail below with reference to the drawings and examples.

[0070] The embodiments of the application disclose a mathematical ability tracking and question recommendation method of an adaptive IRT model, the flow of which is shown in Figure 1 , including the following steps:

[0071] S1, establish a student math exercise question bank by grade and semester, and mark the initial difficulty coefficient of the questions in the question bank.

[0072] Let the unique number of the question be j, and the difficulty coefficient of question j in the question bank be d j , and the exposure amount of question j be N j . Initialize the IRT model parameters, including the discrimination coefficient a j (initial value 1), the difficulty parameter b j , the guessing probability c j and the probability weighting item index

[0073]

[0074] S2, establish a student mathematical ability data archive for storing data for evaluating the student's mathematical ability.

[0075] The student mathematical ability data archive includes the student ability value θ, the ability value variance σ 2 , the learning rate η0, and the answer history record set The length L of the recent answer history set queue Q is a preset parameter. In this embodiment, the value is L = 0.5. The student is uniquely numbered i. When the i-th student has not answered the question, the initial state of the student is: θ = 0.5, σ 2 =1, v0=0.1, and Q are both empty sets.

[0076] When a student initiates a question request, obtain the student's unique number i, query the student's mathematical ability data file, and record the student's answer history as k represents the total number of questions answered by student i, r is the score rate, The elements are sorted in ascending order by timestamp.

[0077] S3. Construct a staged variable parameter IRT model to estimate students' mathematical ability.

[0078] S31. Establish a phased variable parameter IRT model:

[0079]

[0080] Among them, P j represents the probability that the student answers question j correctly.

[0081] S32, using the maximum likelihood function to calculate the estimated value of student ability, the estimated value of student ability θ IRT The value of θ corresponding to the maximum value of the likelihood function l(θ) is:

[0082]

[0083] Among them, r m Indicates that the student's answer history is The score rate of the mth answer record, is the probability weighted item index selected according to the question type, Represents the probability weighted item of the mth answer record, P m Indicates the exposure N of question j according to the mth answer record j Select the IRT model.

[0084] S33, calculate the dynamic adaptive learning rate parameter. For student i's recent answer history set queue Q i , the average score is The dynamic adaptive learning rate parameters are:

[0085]

[0086] Here, r0 is the ideal accuracy (the value is 0.75 in this embodiment), and h is the sensitivity coefficient (the value is 0.2 in this embodiment).

[0087] S34, calculate the latest ability estimate of the student:

[0088] θ i,cur ← θ IRT + η t · sign(θ IRT - θ i,prev );

[0089] where θ i,prev represents the last calculated and stored ability estimate of student i, and sign(·) is a sign function,

[0090] S4, calculate the matching degree of the questions in the candidate question set, and recommend questions according to the matching degree of the questions.

[0091] S41, obtain the unanswered questions in the question bank corresponding to the grade and semester of student i as the candidate question set.

[0092] S42, for each question j in the candidate question set, calculate the probability P j that student i answers question j correctly according to the exposure N i,cur and the latest ability estimate θ i,cur of student i (i.e., let θ = θ j ) by selecting the corresponding stage variable IRT model.

[0093] S43, calculate the matching degree of the question:

[0094] F j = 1 - |P j - r0|;

[0095] S44, select the question with the maximum matching degree F j from the candidate question set as the recommended question, and push it to the student.

[0096] S5, obtain the new answer record of the student, update the student's mathematical ability data file, and update the question parameters in real time.

[0097] Updating the student's mathematical ability data file includes the following steps:

[0098] updating the student's ability value θ to θ i,cur calculated in S34:

[0099] θ ← θ i,cur ;

[0100] updating the ability value variance σ 2 :

[0101]

[0102] wherein, Δθ0 is a preset ability mutation threshold, and in the embodiment, the value is 0.5.

[0103] The learning rate η0 is updated as follows:

[0104] η0←η0(1+0.5σ 2 );

[0105] The new answer record of the student is updated to the answer history record set and the recent answer history set queue Q.

[0106] The real-time updating of the question parameter includes the following steps:

[0107] The score rate r m of the new answer record is recorded as follows: new The probability weighting term index is selected according to the question type, and the probability weighting term is calculated as follows:

[0108] The corresponding segmented probability model P j is selected according to the question exposure amount N j , the partial derivative of the question parameter is calculated according to the likelihood function expression l(θ), and the question parameter update amount is calculated as follows:

[0109]

[0110] wherein, Δa j is the update amount of the discrimination coefficient, Δb j is the update amount of the difficulty parameter b j , Δc j is the update amount of the guessing probability, η a is the update rate of the discrimination coefficient, η b is the update rate of the difficulty parameter, η c is the update rate of the guessing probability, η a , η b , and η c are preset values, and in the embodiment, the values are η a = 0.05, η b = 0.01, and η c = 0.001.

[0111] The difficulty coefficient is updated, and the update formula is as follows:

[0112]

[0113] wherein, is the updated difficulty coefficient, is the difficulty parameter before updating, and ​The updated difficulty parameter.

[0114] S6, periodically calibrating global IRT model parameters.

[0115] For each question j, the difficulty parameter is calibrated periodically (in this embodiment, daily at midnight):

[0116]

[0117] wherein, is the calibrated difficulty parameter, and a is a preset calibration coefficient, which in this embodiment takes a value of 0.2, and θ i is the ability value of student i, and r j,i represents the score rate of the i-th student for question j, represents the probability weighting item of the i-th student for question j.

[0118] Then, the difficulty coefficient is calibrated according to the difficulty parameter

[0119]

[0120] wherein, is the calibrated difficulty coefficient.

[0121] The mathematical ability tracking and question recommendation method of the adaptive IRT model provided in the embodiments of the present application takes into account the evaluation accuracy and efficiency, dynamic real-time tracking of mathematical ability, and question matching recommendation. The exposure amount driven model switching reduces systematic bias and improves model accuracy; the question type adaptive weighting index embeds the answer information under the continuous score model into the discrete score model, improving model accuracy while reducing computational load and improving efficiency; the sign function guidance and adaptive learning rate updating mechanism are added, realizing real-time and accurate tracking of students' mathematical ability and personalized question recommendation.

[0122] The above shows and describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above embodiments, and the above embodiments and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection of the present application is defined by the appended claims and their equivalents.​

Claims

1. The method of mathematical ability tracking and question recommendation based on the adaptive IRT model is characterized by: The following steps are involved: S1. Establish a math exercise question bank for students by grade and semester, and mark the initial difficulty coefficient for the questions in the question bank; S2. Establish a student mathematics ability data archive to store data for evaluating students’ mathematics abilities; S3, construct a staged variable parameter IRT model to estimate students’ mathematical ability; S4. Calculate the topic matching degree in the candidate topic set and recommend topics based on the topic matching degree; S5. Obtain the student's new answer record, update the student's mathematical ability data file, and update the question parameters in real time; S6. Perform periodic global IRT model parameter calibration.

2. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 1, characterized in that: Said S1 comprises the following steps: Assume the unique number of the question is j, and mark the difficulty coefficient of question j in the question bank as d j , record the exposure of topic j as N j ; Initialize IRT model parameters, including the discrimination coefficient a j , difficulty parameter b j , guess probability c j and probability-weighted term index 3. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 2, characterized in that: The IRT model parameter calculation formula is as follows: a j The initial value is 1.

4. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 3, characterized in that: The student mathematics ability data file described in S2 includes student ability value θ, ability value variance σ 2 , learning rate η0, answer history collection And the recent answer history set queue Q, the length of the recent answer history set queue Q is L; The student's unique number is i. When the i-th student has not answered the question, the student's initial state is: θ = 0.5, σ 2 =1,η0=0.1, and Q are both empty sets.

5. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 4, characterized in that: When a student initiates a question request, obtain the student's unique number i, query the student's mathematical ability data file, and record the student's answer history as k represents the total number of questions answered by student i, r is the score rate, The elements are sorted in ascending order by timestamp.

6. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 5, characterized in that: The S3 includes the following steps: S31. Establish a phased variable parameter IRT model: Among them, P j represents the probability that the student answers question j correctly; S32. Calculate the estimated value of student ability using the maximized likelihood function: Among them, θ IRT Represents the estimated value of student ability, which is the value of θ corresponding to the maximum value of the likelihood function l(θ), r m Indicates that the student's answer history is The score rate of the mth answer record, is the probability weighted item index selected according to the question type, Represents the probability weighted item of the mth answer record, P m Indicates the exposure N of question j according to the mth answer record j The selected IRT model; S33, for student i's recent answer history set queue Q i , the average score is The dynamic adaptive learning rate parameters are: Among them, r0 is the ideal accuracy rate, is the sensitivity coefficient; S34. Calculate the student's latest ability estimate: i i,cur =θ IRT +n t ·sign(θ IRT -θ i,prev ); Among them, θ i,prev represents the ability estimate of student i calculated and stored last time, and sign(·) is the sign function.

7. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 6, characterized in that: The S4 comprises the following steps: S41. Obtain unanswered questions in the question bank corresponding to the grade and semester of student i as a set of candidate questions; S42, for each topic j in the candidate topic set, according to the exposure N j Select the corresponding stage-varying parameter IRT model and substitute the student's latest ability estimate θ i,cur Calculate the probability P that a student answers question j correctly j ; S43. Calculate the matching degree of the question: F j =1-|P j -r0|; S44. Select matching degree F j The biggest topic is recommended to students.

8. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 7, characterized in that: Updating the student mathematics ability data file described in S5 includes the following steps: Update student ability value θ: θ←θ i,cur ; Update capability value variance σ 2 : Among them, Δθ0 is the preset capacity mutation threshold; Update the learning rate η0: η0←η0(1+0.5σ 2 ); Update the student's new answer record to the answer history collection And the recent answer history collection queue Q.

9. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 8, characterized in that: The real-time updating of the topic parameters in S5 includes the following steps: Record the score rate r of the new answer record m =r new , probability weighted item index selected according to question type Calculate probability weighted terms Calculate the updated amount of question parameters: Where Δa i is the update amount of the discrimination coefficient, Δb i is the difficulty parameter b i The update amount, Δc i is the update amount of guess probability, η a is the update rate of the discrimination coefficient, η b is the update rate of the difficulty parameter, η c is the update rate of the guess probability; Update difficulty coefficient: in, is the updated difficulty coefficient, is the difficulty parameter before the update, is the updated difficulty parameter.

10. The method for tracking mathematical ability and recommending questions based on the adaptive IRT model according to claim 9, characterized in that: The S6 comprises the following steps: For each question j, the difficulty parameter and difficulty coefficient are periodically calibrated: in, is the difficulty parameter after calibration, is the difficulty coefficient after calibration, α is the preset calibration coefficient, θ i is the ability value of student i, r i,i represents the score rate of the i-th student for question j, Represents the probability weighted term of the i-th student for question j.

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