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CN-121998507-A - Mathematical core literacy assessment method based on multi-feature fuzzy rank sum vector

CN121998507ACN 121998507 ACN121998507 ACN 121998507ACN-121998507-A

Abstract

The invention discloses a mathematical core literacy assessment method based on multi-feature fuzzy rank and vector, and belongs to the field of education assessment and education data mining. The method comprises the steps of constructing a high-speed mathematical core literacy index system comprising a plurality of first-level indexes and second-level indexes, collecting multiple examination data of students, calculating the score of each student on each second-level index, extracting multi-feature data, normalizing the multi-feature data to obtain normalized feature values, calculating fuzzy rank vectors of each student under each feature value based on the normalized feature values, wherein the fuzzy rank vectors represent membership degrees of the students on different sequencing results, and calculating single-feature fuzzy rank sum vectors and multi-feature fuzzy rank sum vectors. According to the invention, the scientificity and the accuracy of high-school mathematical core literacy evaluation are effectively improved by constructing the multi-feature data model and introducing the fuzzy rank vector ordering method.

Inventors

  • LIU GAOFENG

Assignees

  • 乐山师范学院

Dates

Publication Date
20260508
Application Date
20260128

Claims (10)

  1. 1. The mathematical core literacy assessment method based on the multi-feature fuzzy rank and vector is characterized by comprising the following steps of: S1, constructing a high-school mathematical core literacy index system comprising a plurality of primary indexes and secondary indexes; S2, collecting multiple examination data of students, calculating the score rate of each student on each secondary index, and extracting multi-feature data, wherein the multi-feature data comprise the minimum value, the mean value, the maximum value, the variance and the median of the score rate; s3, carrying out normalization processing on the multi-feature data to obtain normalized feature quantities; S4, calculating a fuzzy rank vector of each student under each characteristic quantity based on the normalized characteristic quantity, wherein the fuzzy rank vector represents membership degrees of the students on different sequencing results; S5, calculating a single-feature fuzzy rank sum vector and a multi-feature fuzzy rank sum vector, fusing multi-feature data through weighted summation, and dynamically weighting by adopting an empirical weight or entropy weight method; s6, comprehensively sequencing students based on the multi-feature fuzzy rank sum vector; and S7, carrying out core literacy grade assessment based on the comprehensive sequencing result and the numerical distribution of the multi-feature fuzzy rank sum vector, and outputting an assessment result and grade.
  2. 2. The mathematical core literacy assessment method based on multi-feature fuzzy rank and vector according to claim 1, wherein in step S1, the index system is based on "common high school mathematical course standard", including six primary indexes including mathematical abstraction, logical reasoning, mathematical modeling, visual imagination, mathematical operation and data analysis, each primary index being refined into two secondary indexes.
  3. 3. The mathematical core literacy assessment method based on the multi-feature fuzzy rank and vector according to claim 1, wherein in the step S2, the score rate is calculated by dividing the actual score of a student on a question corresponding to a certain index by the full score of the question corresponding to the index, and extracting minimum, mean and maximum feature quantities based on multiple examination data, the variance feature quantity is the square of the standard deviation of the multiple examination score rate, the median feature quantity is the intermediate value of the multiple examination score rates arranged in ascending order, and the average value of the two intermediate values is taken when the sample quantity is even.
  4. 4. The mathematical core literacy assessment method based on multi-feature fuzzy rank and vector according to claim 1, wherein in step S3, the normalization process adopts a Min-Max method to normalize feature quantity to [0,1] interval, and the calculation formula is: Wherein, the The original feature quantity is represented by a set of features, The normalized feature quantity is represented by i as index number, j as student number, and d as feature quantity number.
  5. 5. The mathematical core literacy assessment method based on multi-feature fuzzy rank and vector of claim 1, characterized in that in step S4 the calculation of fuzzy rank vector comprises calculating membership for rank order look likely result k: Wherein, the Representing the ranking ideal value; The fuzzy rank vector is expressed as: 。
  6. 6. the mathematical core literacy assessment method based on multi-feature fuzzy rank and vector of claim 1, characterized in that in step S5, a single feature fuzzy rank and vector The calculation formula of (2) is as follows: Wherein, the Is index weight, meets ; Multi-feature fuzzy rank sum vector The calculation formula of (2) is as follows: Wherein, the Is the weight of the characteristic quantity, satisfies 。
  7. 7. The mathematical core literacy assessment method based on multi-feature fuzzy rank sum vectors of claim 6, wherein weight setting comprises two ways: (1) Empirical weight Set to equal weights, i.e Wherein m is the index number, weight Empirically set, the weights of the minimum, mean, maximum, variance, and median feature amounts are 0.15, 0.4, 0.15, and 0.15, respectively; (2) And the entropy weight method is used for dynamically weighting, namely calculating the weight based on the information entropy of each characteristic quantity, and realizing objective distribution of the weight.
  8. 8. The mathematical core literacy assessment method based on multi-feature fuzzy rank and vector of claim 1, wherein in step S6, the comprehensive ordering is implemented by iteratively selecting students corresponding to a maximum value in the multi-feature fuzzy rank and vector, specifically comprising: initializing an alternative student set d= {1,2,..n }; For the rank position s (s=1 to n), calculate Wherein Blurring components of rank sum vectors for multiple features; Update d=d- { s k }, until all student ordering is complete.
  9. 9. The mathematical core literacy assessment method based on multi-feature fuzzy rank and vector of claim 7, wherein the step of calculating entropy weight method dynamic weights comprises: (1) Calculating the specific gravity of each student normalized feature quantity under the d feature quantity: Wherein, the N is the number of students for normalizing the feature quantity; (2) Calculating the information entropy of the d feature quantity: If it is Then ; (3) Calculating the weight of the d feature quantity: Satisfy the following requirements 。
  10. 10. The mathematical core literacy assessment method based on multi-feature fuzzy rank and vector of claim 1, characterized in that in step S7, the ranking employs a quantile method, the maximum component of the multi-feature fuzzy rank and vector is ranked by the following threshold: excellent that the maximum component is more than or equal to 0.22; Good that the maximum component is less than or equal to 0.18 and less than 0.22; Qualified: a maximum component of 0.14 <0.18; to be lifted, the maximum component is <0.14.

Description

Mathematical core literacy assessment method based on multi-feature fuzzy rank sum vector Technical Field The invention relates to education assessment and education data mining, in particular to a mathematical core literacy assessment method based on multi-feature fuzzy rank and vector. Background In the current background of high school education reform, core literacy has become an important direction for course reform and teaching evaluation. The standard of general high school mathematics course (revised in 2017 edition 2020) clearly indicates that mathematics teaching is to promote the culture of the mathematics core literacy of students so as to realize the comprehensive and individual development of the students. Therefore, how to scientifically and equitably evaluate the achievement condition of students in the aspect of mathematical core literacy becomes a key problem in teaching reform and education evaluation. Especially, under the background that big data and education measurement methods are continuously evolved, a mathematical core literacy evaluation technology with objectivity, comprehensiveness and accuracy is developed, and the method has important significance for promoting education high-quality development. Existing research on core literacy assessment mainly focuses on constructing an assessment index system and ranking students using traditional methods of weighted average, rank sum ratio, and the like. These methods are generally based on scores of students in a certain dimension, such as a mean score, ignoring the volatility and extremum features of the score, and cannot fully reflect the stability and potential of the student's ability. Meanwhile, most of the existing sorting methods adopt hard sorting (namely unique determination of a ranking), and sorting misjudgment is easy to be caused under the condition that student results are close or performances are changeable. In addition, some studies have attempted to introduce fuzzy mathematical methods to deal with uncertainties, but lack systematic modeling under student multidimensional data features. Therefore, the current method has three general disadvantages, namely single dimension of evaluation data, difficulty in comprehensively reflecting student characteristics, rigidity of a sorting mode, difficulty in embodying uncertainty among sorting, and lack of a fusion analysis mechanism for multi-characteristic data. These deficiencies limit the scientificity and differentiation of the evaluation method. Disclosure of Invention The invention aims to provide a high-middle mathematics core literacy evaluation method based on a multi-feature fuzzy rank vector. The method comprises the steps of firstly constructing six core literacy and subordinate secondary indexes thereof according to mathematical course standards, collecting multiple examination data of students, constructing a multi-feature data set through the minimum value, the average value and the maximum value of score rates, then using fuzzy rank vectors to represent sequencing membership degrees of the students on the indexes, and further fusing the multi-feature fuzzy rank vectors to form a comprehensive evaluation result. The method gives consideration to the stability, the bottom line and the potential of the student capability, breaks through the limitation of the traditional evaluation method in sequencing expression and information utilization, and has stronger discriminant and fairness. The technical scheme is that the mathematical core literacy assessment method based on the multi-feature fuzzy rank and vector comprises the following steps: step 1, constructing a core literacy index system (1) Index source According to the general high school course standard (the revised in the year 2020 of 2017 edition), six core literacy is selected as indexes, namely mathematical abstraction, logical reasoning, mathematical modeling, visual imagination, mathematical operation and data analysis, and the indexes are collectively called as first-level indexes. (2) Index refinement The invention refines 6 first-level indexes into 2 second-level indexes respectively on the basis of six-size core literacy indexes, as shown in figure 1. The mathematical symbols of the 6 primary indicators and the 12 secondary indicators are shown in fig. 5. Step 2, constructing characteristic data (1) Index quantization Collecting student answer data through staged examination (such as monthly examination and in-stage examination), establishing a 'question-index' mapping relation table, attributing each test question to a corresponding index, and calculating the score rate of the student under each index, wherein the score rate is equal to the actual score of the student in a question corresponding to a certain index divided by the full score of the question corresponding to the index. For example, assuming that 10 total tests are performed, the actual score, the full score, and the score rate correspon