Student mathematical ability assessment method based on time sequence regression and incremental learning model

Abstract

The invention discloses a student mathematical ability assessment method based on a time sequence regression and incremental learning model, and relates to the technical field of mathematical ability assessment, and the method comprises the steps: S1, building a mathematical question bank, carrying out the ability dimension division, and recording the investigation proportion of the ability dimension; s2, setting a dynamic data screening mechanism of the sliding window; s3, collecting student answer sequence data; s4, constructing a mathematical ability assessment regression model based on a dynamic data screening mechanism of a sliding window and a time attenuation weight; s5, constructing a loss function of the mathematical ability assessment regression model, and searching by adopting a Bayesian optimization algorithm to obtain mathematical ability assessment regression model parameters when the loss function obtains a minimum value; and S6, carrying out real-time dynamic evaluation and diagnostic evaluation on the mathematical ability of the student. The method has the advantages of being small in calculation amount, low in complexity, capable of achieving real-time incremental updating, high in interpretability and capable of achieving personalized analysis of learning paths, and can adapt to mobile terminal application deployment under the condition that resources are limited.

Description

Technical Field

[0001] The present invention relates to the technical field of mathematical ability assessment, and in particular to a method for assessing students' mathematical ability based on time series regression and incremental learning models. Background Art

[0002] In traditional education, assessing mathematical ability and accurately identifying and addressing gaps relies heavily on the experience of renowned teachers, making it difficult to conduct on a large scale. This approach is typically only feasible in small classes or even one-on-one instruction, which is costly and resource-scarce. Recent breakthroughs in artificial intelligence (AI) technology have provided a new path to addressing this dilemma. Personalized diagnostic tools driven by machine learning algorithms have, for the first time, made it possible to provide tailored instruction to students' needs at scale. However, existing solutions, often based on deep learning time-series approaches, are computationally complex and computationally intensive. They rely on deep learning models and typically require periodic full retraining (especially when knowledge graphs are updated). These complex models often result in poor dynamic adaptability.

[0003] For example, CN 112001536A discloses a high-precision method for discovering extremely small samples of mathematical ability deficiencies in primary and secondary schools based on machine learning. This solution constructs probabilistic connections between ability points, generates a question bank and labels the abilities, and uses the RNN+SortNet method for model training and ability point prediction, thereby discovering ability deficiencies in mathematics. The disadvantages of this solution are: 1. High computational complexity and large amount of calculations; 2. The heavy model leads to poor dynamic adaptability and lacks an incremental update mechanism; 3. The black box model of deep learning (the neural network weights cannot be interpreted) has poor interpretability; 4. PyTorch is required to implement model training and prediction, which consumes a lot of hardware equipment and resources, and usually requires a GPU server. Summary of the Invention

[0004] In order to solve the problems of high computational complexity, large computational load, poor dynamic adaptability, poor interpretability and high resource consumption in existing mathematical ability assessment methods, the present invention proposes a student mathematical ability assessment method based on time series regression and incremental learning model. The method has small computational load, low complexity, can be updated incrementally in real time, and has the characteristics of strong interpretability and personalized analysis of learning paths. It can be suitable for mobile application deployment under resource-constrained conditions in large-scale real-time assessment scenarios to solve the above problems.

[0005] This application proposes a method for evaluating students' mathematical ability based on time series regression and incremental learning models, which includes the following steps: 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. 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. S3, collect students' answer sequence data, including sequence number, question number, score rate, answer time and timestamp; S4. Construct a mathematical ability assessment regression model based on a dynamic data screening mechanism of a sliding window and time decay weights; 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.

[0006] Preferably, 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 .

[0007] Preferably, said 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:

[0008] in, For the capability dimension The cumulative number of answers, Minimum hold value for the window.

[0009] Preferably, the student answering sequence in S3 is as follows:

[0010] 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.

[0011] Preferably, said 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; S43. For each ability dimension, calculate the cumulative time penalty for all questions in the sliding window; S44. For each capability dimension, calculate the final capability assessment value.

[0012] Preferably, the S42 includes the following steps: 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:

[0013] in, Indicates the title In mathematical ability Score rate by type.

[0014] Preferably, the S43 includes the following steps: The reference time for the time penalty item is:

[0015] 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:

[0016] 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:

[0017] in, For the title Penalty for answering time deviating from the reference time.

[0018] Preferably, the final capability evaluation value in S44 is:

[0019] The function .

[0020] Preferably, 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:

[0021] right Perform normalization to obtain the standardized personalized reference truth value:

[0022] 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:

[0023] 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.

[0024] Preferably, 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 :

[0025]

[0026] 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:

[0027] 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 class 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.

[0028] Beneficial effects of the present invention: 1. The window mechanism and time-decay weights form a spatiotemporal dual filter to reduce the amount of computational data. By using sliding window statistics and regression models, it replaces deep learning neural networks, achieving low computational complexity and small computational effort, making it more suitable for mobile application deployment when computing power and resources are limited.

[0029] 2. By controlling the memory strength through a decay factor and designing an incremental update mechanism based on this, data is highly adaptable and the impact of new answer records on overall ability assessment can be incorporated into the model and results in real time, making it particularly suitable for large-scale real-time assessment scenarios.

[0030] 3. The essence of ability assessment is the mapping relationship between observed behavior (answering questions) and potential traits (mathematical ability). The final ability assessment value in the model is and the cumulative weighted score of the question , cumulative time penalty A linearly weighted statistical mapping relationship is established, and the model is highly interpretable.

[0031] 4. In the model, each student’s different ability dimensions have different sliding windows, standardized personalized reference truth values, and other statistics, which can reflect personalized learning trajectories. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of a method for evaluating students' mathematical abilities based on temporal regression and incremental learning models according to an embodiment of the present invention. DETAILED DESCRIPTION

[0033] In order to make the objectives, technical solutions and advantages of this application more clear, the application is further described in detail below with reference to the accompanying drawings and examples.

[0034] The embodiment of the present application discloses a method for evaluating students' mathematical ability based on time series regression and incremental learning model. The process is as follows: Figure 1 As shown, the following steps are included: S1. Establish a math question bank and divide it into various types of math abilities (such as basic calculation ability, understanding of math concepts, logical reasoning ability, spatial imagination ability, problem-solving ability, mathematical modeling ability, etc.). Divide math abilities 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 .

[0035] S2. Set up a dynamic data screening mechanism for the sliding window. For each ability dimension, obtain dynamic window adjustment rules based on the cumulative number of answers.

[0036] 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:

[0037] in, For the capability dimension The cumulative number of answers, is the minimum hold value of the window. In this embodiment, The possible value is 10.

[0038] S3. Collect students’ answer sequence data, including sequence number, question number, score rate, answering time and timestamp.

[0039] The sequence of a student's answers is as follows:

[0040] 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.

[0041] S4. Based on the dynamic data screening mechanism of sliding window and time decay weight, a mathematical ability assessment regression model is constructed.

[0042] 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, Indicates the decay period.

[0043] S42. For each ability dimension, calculate the cumulative weighted scores of all questions in the sliding window.

[0044] 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:

[0045] in, Indicates the title In mathematical ability Score rate by type.

[0046] S43. For each ability dimension, calculate the cumulative time penalty for all questions in the sliding window.

[0047] Reference time for calculating the time penalty for the question:

[0048] 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. For each question , the penalty for calculating the deviation of the answer time from the reference time is as follows:

[0049] 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:

[0050] in, For the title Penalty for answering time deviating from the reference time.

[0051] S44. For each capability dimension, calculate the final capability assessment value.

[0052]

[0053] The function .

[0054] S5. Construct a loss function for the mathematical ability assessment regression model, and use the Bayesian optimization algorithm to search for the mathematical ability assessment regression model parameters when the loss function reaches the minimum value.

[0055] S51. Regarding the topic , the probability that the student answers correctly is , its value is equal to the ratio of the number of correct answers to the total number of answers, which indicates the mathematical ability of the student in a certain dimension. The personalized reference truth value generated by the actual ability level is as follows:

[0056] right Perform normalization to obtain the standardized personalized reference truth value:

[0057] in, represents the scaling factor, Indicates the zoom center, which can be an empirical value in this embodiment , , Indicates that all students who have done this question have a certain level of mathematical ability. The mean score of Indicates that all students who have done this question have a certain level of mathematical ability. The standard deviation of scores; S52. Define the loss function as follows:

[0058] 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.

[0059] 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.

[0060] S6. Conduct real-time dynamic and diagnostic assessments of students’ mathematical abilities.

[0061] 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 :

[0062]

[0063] 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.

[0064] S62. Dynamically update the students' various types of mathematical ability values ​​in real time according to S42-S44.

[0065] S63. Weigh the weaknesses of each type of mathematical ability and combine them to get the comprehensive mathematical ability index of the student:

[0066] 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.

[0067] S64, diagnostic assessment of students' mathematical ability, based on the student's answer sequence, calculates the final ability assessment value and comprehensive index of each type of mathematical ability corresponding to each sequence element, and can analyze or visualize the growth and change of each type of mathematical ability and overall mathematical ability of students. At the same time, it can also analyze the weak points of ability. For specific students, The numerical value reflects the strength of a student's ability, with the smallest numerical value representing the student's weakest link. Furthermore, statistical data such as sliding windows across different ability dimensions and standardized, personalized reference values ​​can be visualized to reflect personalized learning trajectories.

[0068] The student mathematical ability assessment method based on time series regression and incremental learning model proposed in this application has the characteristics of small computational complexity, low complexity, and real-time incremental update. It also has the characteristics of strong interpretability and personalized analysis of learning paths. It is suitable for mobile application deployment under resource-constrained conditions in large-scale real-time assessment scenarios.

[0069] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention 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. 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. S3, collect students' answer sequence data, including sequence number, question number, score rate, answer time and timestamp; S4. Construct a mathematical ability assessment regression model based on a dynamic data screening mechanism of a sliding window and time decay weights; 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: 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 the proportion of its investigation as .

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 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.

4. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 3 is characterized in that: The student answer sequence described in S3 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.

5. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 4 is characterized in that: 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; S43. For each ability dimension, calculate the cumulative time penalty for all questions in the sliding window; S44. For each capability dimension, calculate the final capability assessment value.

6. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 5 is characterized in that: The S42 includes the following steps: 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 by type.

7. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 6 is characterized in that: The S43 includes the following steps: The reference time for the question 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 answering time deviating from the reference time.

8. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 7 is characterized in that: The final capability assessment value stated in S44 is: The function .

9. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 8 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.

10. The method for evaluating students' mathematical ability based on time series regression and incremental learning model according to claim 9 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 The timestamp of the time; 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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