Student mathematical ability evaluation method based on time series regression and incremental learning model

Abstract

The application discloses a student mathematical ability evaluation method based on a time series regression and an incremental learning model, relates to the technical field of mathematical ability evaluation, and comprises the following steps: S1, establishing a mathematical question bank and performing ability dimension division, and recording the examination proportion of the ability dimension; S2, setting a dynamic data screening mechanism of a sliding window; S3, collecting student answering sequence data; S4, constructing a mathematical ability evaluation regression model based on the dynamic data screening mechanism of the sliding window and a time decay weight; S5, constructing a loss function of the mathematical ability evaluation regression model, and searching for the mathematical ability evaluation regression model parameters when the loss function reaches a minimum value by adopting a Bayesian optimization algorithm; and S6, performing real-time dynamic evaluation and diagnostic evaluation on the mathematical ability of students.The application has the characteristics of small calculation amount, low complexity, real-time incremental updating, strong interpretability and personalized analysis of learning paths, and can be applied to mobile terminal deployment under resource-limited conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mathematical ability evaluation, in particular to a student mathematical ability evaluation method based on time series regression and incremental learning model. BACKGROUND

[0002] In traditional education, the evaluation and accurate leak detection and repair of mathematical ability highly depend on the experience of famous teachers, and it is difficult to carry out on a large scale of students. Usually, it can only be realized in small class teaching or even 1 to 1 teaching. This mode is high in cost and scarce in resources. In recent years, the breakthrough progress of artificial intelligence technology provides a new path to solve the above-mentioned difficulties. The personalized diagnosis tool driven by machine learning algorithm makes it possible to "teach students according to their aptitude" on a large scale for the first time. However, the existing scheme is usually based on deep learning time series scheme, which is high in computational complexity and large in calculation amount, and depends on deep learning model, which usually needs to be retrained regularly (especially when the knowledge graph is updated). The heavy model leads to poor dynamic adaptability.

[0003] For example, CN 112001536A discloses a primary and secondary school mathematical ability point defect small sample high precision finding method based on machine learning. The scheme constructs the probability relationship between the ability points, generates the question bank and labels the ability, uses the method of RNN+SortNet for model training and ability point prediction, so as to find the ability defect point of mathematical subject. The shortcomings of this scheme are: 1. high computational complexity and large calculation amount; 2. the heavy model leads to poor dynamic adaptability, and lacks incremental updating mechanism; 3. the black box model of deep learning (neural network weight is not interpretable) has poor interpretability; 4. PyTorch needs to be used to realize model training and prediction, which is high in hardware equipment and resource consumption, and usually needs GPU server. SUMMARY

[0004] In order to solve the problems of high computational complexity, large calculation amount, poor dynamic adaptability, poor interpretability and high resource consumption of the existing mathematical ability evaluation method, the present application provides a student mathematical ability evaluation method based on time series regression and incremental learning model. The method has small calculation amount, low complexity, can be updated incrementally in real time, has strong interpretability and learning path individualization analysis characteristics, and can be applied to mobile terminal deployment under resource limited conditions in large scale real time evaluation scene, so as to solve the above problems.

[0005] The present application provides a student mathematical ability evaluation method based on time series regression and incremental learning model, which comprises the following steps:

[0006] S1, establishing a mathematical question bank and dividing the ability dimensions, labeling one or more ability dimensions for each question target and recording the examination proportion of the ability dimensions;

[0007] S2, set a dynamic data filtering mechanism of sliding window, for each ability dimension, according to the cumulative number of answers, get the window dynamic adjustment rule;

[0008] S3, collect student answer sequence data, including sequence number, question number, score rate, answer time and timestamp;

[0009] S4, based on the dynamic data filtering mechanism of sliding window and time decay weight, construct a mathematical ability evaluation regression model;

[0010] S5, construct the loss function of the mathematical ability evaluation regression model, and search for the mathematical ability evaluation regression model parameters when the loss function reaches the minimum value by using the Bayesian optimization algorithm;

[0011] S6, real-time dynamic evaluation and diagnostic evaluation of students' mathematical ability.

[0012] Preferably, the S1 comprises the following steps:

[0013] The mathematical ability is divided into a set of dimensions , each question in the mathematical question bank is marked with one or more ability labels, and for a certain dimension of mathematical ability , the examination proportion is recorded as .

[0014] Preferably, the S2 comprises the following steps:

[0015] For a certain dimension of mathematical ability , only the latest records are calculated, and the window dynamic adjustment rule is:

[0016]

[0017] Wherein, is the cumulative number of answers of the ability dimension , and is the window minimum value.

[0018] Preferably, the student answer sequence in S3 is as follows:

[0019]

[0020] Wherein, represents the sequence number of the answer sequence, represents the th question, represents the score rate of the th question, represents the time spent on answering the th question, represents the timestamp when the student finishes answering the i-th question.

[0021] Preferably, the S4 comprises the following steps:

[0022] S41, defining the time decay weight of the history record of the answering sequence of the student , wherein is the decay amount per unit time and , represents the normalized time interval of the current time and the answering time of the i-th question, represents the current timestamp, represents the decay period; S42, calculating the cumulative weighted score of all questions in the sliding window for each ability dimension;

[0023] S43, calculating the cumulative time penalty amount of all questions in the sliding window for each ability dimension;

[0024] S44, calculating the final ability evaluation value for each ability dimension.

[0025] Preferably, the S42 comprises the following steps:

[0026] For each question

[0027] , the score rate is distributed to each ability dimension according to the examination proportion of the ability dimension, denoted as , represents the examination proportion of the question on the mathematical ability type;

[0028] For a certain dimension of mathematical ability , the cumulative weighted score of all questions in the sliding window is as follows:

[0029]

[0030] wherein represents the score rate of the question on the mathematical ability type.

[0031] Preferably, the S43 comprises the following steps:

[0032] The reference time of the question time penalty term is:

[0033]

[0034] wherein ​​Indicates the median operation. Indicates all answered questions the number of students, Indicates the Students answer questions Time consuming, It means taking the arithmetic mean of the time taken by students to answer the questions in the last 100 times. Indicates the smoothing coefficient of the dynamic update of the original data, Indicates the smoothing coefficient for dynamic update of new answer record data;

[0035] For each question , the penalty for calculating the deviation of the answer time from the reference time is as follows:

[0036]

[0037] in, Indicates the title The standard deviation of the time taken to answer historical answers, is the time penalty coefficient;

[0038] Mathematical ability in a certain dimension , the cumulative time penalty for all questions in the sliding window is as follows:

[0039]

[0040] in, For the title Penalty for answering time deviating from the reference time.

[0041] Preferably, the final capability evaluation value in S44 is:

[0042]

[0043] The function .

[0044] Preferably, the S5 comprises the following steps:

[0045] S51. Regarding the topic , the probability that the student answers correctly is , the student's mathematical ability in a certain dimension The personalized reference truth value generated by the actual ability level is as follows:

[0046]

[0047] right Perform normalization to obtain the standardized personalized reference truth value:

[0048]

[0049] wherein, denotes a scaling factor, denotes a scaling center, denotes a done question the average score of all students in mathematical ability , denotes a done question the standard deviation of all students in mathematical ability ;

[0050] S52, define the loss function as follows:

[0051]

[0052] wherein, denotes the number of mathematical ability types, denotes the variance of the dimension prediction value of all students, is the total number of students, denotes the prediction value of the th student in mathematical ability , denotes the standardized value of the personalized reference pointer generated according to the actual ability level of the th student in mathematical ability , is the variance stability coefficient;

[0053] S53, taking the student answer sequence of a certain student as the training data set, using the Bayesian optimization algorithm to search for the mathematical ability evaluation regression model when the loss function reaches the minimum value, including the decay amount per unit time and the time penalty coefficient , and bringing into the mathematical ability evaluation regression model.

[0054] Preferably, the S6 comprises the following steps:

[0055] S61, when a certain student generates a new answer record , for a certain dimension of mathematical ability , dynamically update the cumulative weighted score and the question cumulative time penalty amount :

[0056]

[0057]

[0058] wherein, denotes a memory decay factor, denotes a new question in the mathematical ability of the student, a reference time indicating a time penalty term of a new question, a historical answer record time consumption standard deviation of the new question, a score rate of the new question, a time consumption of answering the new question, a timestamp when the student finishes answering the new question, S62, dynamically updating the mathematical ability values of the student in each type according to S42-S44 in real time; S63, performing short board weighted fusion on the mathematical ability values in each type, and recording a mathematical ability comprehensive index of the student as:

[0059]

[0060] wherein,

[0061] a short board penalty coefficient, a minimum value in each type, a predicted value of the mathematical ability,

[0062] i.e. a predicted value of the first type of mathematical ability, a predicted value of the second type of mathematical ability, a predicted value of the nth type of mathematical ability; S64, diagnostic evaluation of the mathematical ability of the student, based on the answer sequence of the student, calculating the final ability evaluation value of each type of mathematical ability and the mathematical ability comprehensive index corresponding to each sequence element, and performing short board ability analysis. Advantages of the present application: 1. The window mechanism and time decay weight form a space-time double filtering to reduce the amount of calculation data, through a sliding window statistics and a regression model, a deep learning neural network is replaced, the calculation complexity is low, the calculation amount is small, and the application deployment of a mobile terminal in a limited computing power and resource is more suitable.

[0063] 2. The memory strength is controlled through a decay factor, and an incremental updating mechanism is designed based on the same, the data has strong dynamic adaptability, the influence of new answer records on overall ability evaluation can be included in the model and the result in real time, and the present application is especially suitable for large-scale real-time evaluation scenarios.

[0064]

[0065] 1. The window mechanism and time decay weight form a space-time double filtering to reduce the amount of calculation data, through a sliding window statistics and a regression model, a deep learning neural network is replaced, the calculation complexity is low, the calculation amount is small, and the application deployment of a mobile terminal in a limited computing power and resource is more suitable.

[0066] 2. The memory strength is controlled through a decay factor, and an incremental updating mechanism is designed based on the same, the data has strong dynamic adaptability, the influence of new answer records on overall ability evaluation can be included in the model and the result in real time, and the present application is especially suitable for large-scale real-time evaluation scenarios.

[0067] ​​​​​3. The essence of the ability evaluation is to observe the mapping relationship between the behavior (answering questions) and the potential characteristics (mathematical ability), and the final ability evaluation value in the model and the cumulative weighted score of the question , the cumulative time penalty amount The linear weighted statistical quantity mapping relationship is established, and the model has strong interpretability.

[0068] 4. In the model, the sliding window of each student in different ability dimensions, the standardized personalized reference true value and other statistical quantities are all different, and the personalized learning track can be reflected. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 The flow chart of the student mathematical ability evaluation method based on the time series regression and incremental learning model in the embodiment of the application is shown. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below with reference to the drawings and examples.

[0071] The embodiment of the present application discloses a student mathematical ability evaluation method based on a time series regression and incremental learning model, and the flow thereof is as shown in Figure 1 , including the following steps:

[0072] S1, a mathematical question bank is established and ability dimension division is performed, and the mathematical ability is divided into multiple types of mathematical ability (for example, basic operation ability, mathematical concept understanding, logical reasoning ability, spatial imagination ability, problem solving ability, mathematical modeling ability, etc.). The mathematical ability is divided into a set of dimensions , and one or more ability labels are marked on each question in the mathematical question bank. For a certain dimension of mathematical ability , the examination proportion is recorded as .

[0073] S2, a dynamic data screening mechanism of a sliding window is set, and for each ability dimension, the window dynamic adjustment rule is obtained according to the cumulative answering quantity.

[0074] For a certain dimension of mathematical ability , only the latest records are limited to statistical calculation, and the window dynamic adjustment rule is:

[0075]

[0076] wherein, is the cumulative answering quantity of the ability dimension , and is the minimum window maintenance value, and in the embodiment of the present application The value can be 10.

[0077] S3, collect student answer sequence data, including sequence number, question number, score rate, answer time and timestamp.

[0078] A certain student's answer sequence is as follows:

[0079]

[0080] Among them, indicates the sequence number of the answer sequence, indicates the th question, indicates the score rate of the th question, indicates the time spent on answering the th question, indicates the timestamp when the student finishes answering the th question.

[0081] S4, based on the dynamic data filtering mechanism of the sliding window and the time decay weight, a mathematical ability evaluation regression model is constructed.

[0082] S41, define the time decay weight of the answer history record in the student answer sequence , wherein is the decay amount per unit time and , indicates the standardized time interval between the current time and the th question answer time, indicates the current timestamp, indicates the decay period.

[0083] S42, for each ability dimension, calculate the cumulative weighted score of all questions in the sliding window.

[0084] For each question , the score rate is distributed to each ability dimension according to the examination proportion of the ability dimension, denoted as , indicates the examination proportion of the question in the mathematical ability type;

[0085] For a certain dimension of mathematical ability , the cumulative weighted score of all questions in the sliding window is as follows:

[0086]

[0087] Among them, indicates the question In mathematical ability Score rate by type.

[0088] S43. For each ability dimension, calculate the cumulative time penalty for all questions in the sliding window.

[0089] Reference time for calculating the time penalty for the question:

[0090]

[0091] in, Indicates the median operation. Indicates all answered questions the number of students, Indicates the Students answer questions Time consuming, It means taking the arithmetic mean of the time taken by students to answer the questions in the last 100 times. Indicates the smoothing coefficient of the dynamic update of the original data, Indicates the smoothing coefficient for the dynamic update of new answer record data. The above expression means that when the number of answers to a question does not exceed 100, the median is taken as the reference time to avoid interference from extreme values. Otherwise, the exponentially weighted moving average is used to dynamically update the reference time.

[0092] For each question , the penalty for calculating the deviation of the answer time from the reference time is as follows:

[0093]

[0094] in, Indicates the title The standard deviation of the time taken to answer historical answers, is the time penalty coefficient;

[0095] Mathematical ability in a certain dimension , the cumulative time penalty for all questions in the sliding window is as follows:

[0096]

[0097] in, For the title Penalty for answering time deviating from the reference time.

[0098] S44. For each capability dimension, calculate the final capability assessment value.

[0099]

[0100] The function .

[0101] S5, construct a loss function of the mathematical ability evaluation regression model, and search for the mathematical ability evaluation regression model parameters when the loss function reaches the minimum value by using a Bayesian optimization algorithm.

[0102] S51, for the question , record the probability of the student answering correctly as , the value of which is equal to the ratio of the number of correct answers to the total number of answers, and the actual ability level of the student in the mathematical ability dimension generates a personalized reference true value as follows:

[0103]

[0104] Standardize to obtain a standardized personalized reference true value:

[0105]

[0106] wherein, denotes a scaling coefficient, denotes a scaling center, and in the present embodiment, an empirical value , , denotes the mean score of all students who have done the question in the mathematical ability dimension, denotes the standard deviation of the scores of all students who have done the question in the mathematical ability dimension;

[0107] S52, define the loss function as follows:

[0108]

[0109] wherein, denotes the number of mathematical ability types, denotes the variance of the dimension prediction value of all students, is the total number of students, denotes the prediction value of the th student in the mathematical ability dimension, denotes the standardized value of the personalized reference pointer generated according to the actual ability level of the th student in the mathematical ability dimension, is a variance stability coefficient.

[0110] S53, use the student answer sequence of a student as a training data set, and search for the mathematical ability evaluation regression model when the loss function reaches the minimum value by using a Bayesian optimization algorithm, including the decay amount per unit time and time penalty coefficient , and brought into the mathematical ability assessment regression model.

[0111] S6. Conduct real-time dynamic and diagnostic assessments of students’ mathematical abilities.

[0112] S61. When a student generates a new answer record When the mathematical ability of a certain dimension , dynamically update the cumulative weighted score and the cumulative time penalty for the question :

[0113]

[0114]

[0115] in, represents the memory decay factor, Indicates a new topic In mathematical ability The proportion of investigations by type, Indicates a new topic The reference time of the time penalty term, Indicates a new topic The standard deviation of the time taken to answer the historical answer records, Indicates a new topic The scoring rate, Indicates answering a new question Time consuming, Indicates that the student has finished answering a new question The timestamp of the time.

[0116] S62. Dynamically update the students' various types of mathematical ability values ​​in real time according to S42-S44.

[0117] S63. Weigh the weaknesses of each type of mathematical ability and combine them to get the comprehensive mathematical ability index of the student:

[0118]

[0119] in, Indicates the short board penalty coefficient, which can be set to 0.3 in this embodiment. Indicates the minimum value of each type. Indicates mathematical ability The predicted value of ,Right now represents the predicted value of Category 1 mathematical ability, represents the predicted value of Category 2 mathematical ability, Indicates the The predictive value of mathematical ability.

[0120] S64, the diagnostic evaluation of the mathematical ability of the student, based on the answer sequence of the student, calculates the final ability evaluation value of each type of mathematical ability at each sequence element and the mathematical ability comprehensive index, and the growth change analysis or visual display of the mathematical ability of the student can be carried out. At the same time, short board ability analysis can be carried out, and for a specific student, The size of the median value reflects the strength and weakness, and the aspect with the smallest value is the weakest short board link of the student. In addition, the sliding window, standardized personalized reference true value and other statistical quantities of different ability dimensions of the student can be visualized, which can reflect the personalized learning track.

[0121] The student mathematical ability evaluation method based on time series regression and incremental learning model has the characteristics of small calculation amount, low complexity, real-time incremental updating, strong interpretability and personalized learning path analysis, and can be suitable for mobile terminal application deployment in large-scale real-time evaluation scenarios under resource limited conditions.

[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, and various changes and improvements can be made without departing from the spirit and scope of the present application. 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. A method for evaluating students' mathematical ability based on time series regression and incremental learning model, characterized by: The following steps are involved: S1. Establish a math question bank and divide it into ability dimensions. Label each question with one or more ability dimension labels and record the assessment proportion of the ability dimension. Said S1 comprises the following steps: Divide mathematical ability into A collection of dimensions , mark each question in the math question bank with one or more ability labels, for a certain dimension of math ability , record its inspection proportion as ; S2. Set up a dynamic data screening mechanism for the sliding window. For each ability dimension, dynamically adjust the window based on the cumulative number of answers. The S2 comprises the following steps: Mathematical ability in a certain dimension , limited to the most recent The statistics of records are calculated and the window dynamic adjustment rules are as follows: in, For the capability dimension The cumulative number of answers, Minimum hold value for the window; S3, collect students' answer sequence data, including sequence number, question number, score rate, answer time and timestamp; The student answer sequence is as follows: in, The serial number indicating the answer sequence, Indicates the A question, Indicates the The scoring rate of the question, Indicates answer The time taken to answer the question, Indicates that the student has finished answering the The timestamp when the question was asked; S4. Construct a mathematical ability assessment regression model based on a dynamic data screening mechanism of a sliding window and time decay weights; The S4 comprises the following steps: S41. Define the time decay weight of the student's answer history in the answer sequence ,in is the attenuation per unit time and , Indicates the current time and The standardized time interval between the time it takes to answer a question. Indicates the current timestamp, represents the decay period; S42. For each ability dimension, calculate the cumulative weighted scores of all questions in the sliding window; For each question , the scoring rate According to the proportion of the ability dimension, it is allocated to each ability dimension, recorded as , Indicates the title In mathematical ability The proportion of investigation by type; Mathematical ability in a certain dimension , the cumulative weighted scores of all questions in the sliding window are as follows: in, Indicates the title In mathematical ability Score rate on type; S43. For each ability dimension, calculate the cumulative time penalty for all questions in the sliding window; The reference time for the time penalty item is: in, Indicates the median operation. Indicates all answered questions the number of students, Indicates the Students answer questions Time consuming, It means taking the arithmetic mean of the time taken by students to answer the questions in the last 100 times. Indicates the smoothing coefficient of the dynamic update of the original data, Indicates the smoothing coefficient for dynamic update of new answer record data; For each question , the penalty for calculating the deviation of the answer time from the reference time is as follows: in, Indicates the title The standard deviation of the time taken to answer historical answers, is the time penalty coefficient; Mathematical ability in a certain dimension , the cumulative time penalty for all questions in the sliding window is as follows: in, For the title Penalty for deviation of answer time from the reference time; S44. For each capability dimension, calculate the final capability evaluation value; The final capability assessment values ​​are: The function ; S5. Construct a loss function for the mathematical ability assessment regression model, and use a Bayesian optimization algorithm to search for the mathematical ability assessment regression model parameters when the loss function reaches a minimum value; S6. Conduct real-time dynamic and diagnostic assessments of students’ mathematical abilities.

2. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 1 is characterized in that: The S5 comprises the following steps: S51. Regarding the topic , the probability that the student answers correctly is , the student's mathematical ability in a certain dimension The personalized reference truth value generated by the actual ability level is as follows: right Perform normalization to obtain the standardized personalized reference truth value: in, represents the scaling factor, Indicates the zoom center, Indicates that you have done the question All students have good mathematical skills The mean score of Indicates that you have done the question All students have good mathematical skills The standard deviation of scores; S52. Define the loss function as follows: in, Indicates the number of mathematical ability types, represents the variance of the predicted values ​​of all students in the dimension, is the total number of students, Indicates the students in mathematics ability The predicted value of Indicates that according to students in mathematics ability Normalized values ​​of personalized reference indicators generated based on actual ability levels, is the variance stability coefficient; S53, the student's answer sequence As a training data set, the Bayesian optimization algorithm is used to search for the mathematical ability evaluation regression model when the loss function reaches the minimum value, including the attenuation per unit time. and time penalty coefficient , and brought into the mathematical ability assessment regression model.

3. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 2 is characterized in that: The S6 comprises the following steps: S61. When a student generates a new answer record When the mathematical ability of a certain dimension , dynamically update the cumulative weighted score and the cumulative time penalty for the question : in, represents the memory decay factor, Indicates a new topic In mathematical ability The proportion of investigations by type, Indicates a new topic The reference time of the time penalty term, Indicates a new topic The standard deviation of the time taken to answer the historical answer records, Indicates a new topic The scoring rate, Indicates answering a new question Time consuming, Indicates that the student has finished answering a new question Timestamp when S62, dynamically update the math ability values ​​of students in various categories in real time according to S42-S44; S63. Weigh the weaknesses of each type of mathematical ability and combine them to get the comprehensive mathematical ability index of the student: in, represents the short board penalty coefficient, Indicates the minimum value of each type, Indicates mathematical ability The predicted value of ,Right now represents the predicted value of Category 1 mathematical ability, represents the predicted value of Category 2 mathematical ability, Indicates the Predictive value of mathematical ability; S64. Diagnostic assessment of students' mathematical abilities. Based on the student's answer sequence, the final ability assessment value and comprehensive mathematical ability index of each type of mathematical ability corresponding to each sequence element are calculated, and weak point ability analysis is performed at the same time.

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