CN117216132B - Mathematical test question similarity judging method, system and application - Google Patents
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Abstract
The invention provides a method, a system and an application for judging similarity of mathematical test questions, which comprise the steps of establishing a keyword library and a homodromous word library, wherein the keyword library comprises a core keyword, a strong keyword and a weak keyword, and all have corresponding preset weight values. And establishing a mathematical symbol library, wherein the contained mathematical symbols are divided into N classes. And establishing a same-direction word library, wherein the same-direction words refer to the same or close relationship of corresponding knowledge points among the words. Identifying keywords of the test questions, calculating key word important coefficients of the test questions, and calculating the similarity of the test questions by combining the keyword homodromous degree and the mathematical symbol expression similarity, so as to judge the similarity of the two test questions. The method improves the generalization capability of the algorithm by introducing the co-directional words and the key word significant coefficients, and can be applied to calculation of the similarity of the mathematical test questions by combining the algorithm with the similarity of the mathematical symbol expression, so as to provide a more accurate test question similarity judging method.
Description
Technical Field
The invention relates to the technical field, in particular to a method, a system and application for judging similarity of mathematical test questions.
Background
The teaching informatization is not separated from the construction of a question bank center, the question bank center has an important function of automatically judging the similarity of the questions, the examination paper and the operation can be compiled in an auxiliary mode through the judgment of the similarity of the questions, the teaching efficiency is improved, the traditional similarity judging method is used for filtering and judging according to a large amount of manual labeling information, time and labor are wasted, a machine learning training method is also used, the accuracy of the similarity judgment is not high, the practical degree is difficult to achieve, and the similarity judging method is different from other subjects in mathematic experiments, contains various symbols and formulas, and is more difficult to judge the similarity in a simple text recognition mode.
Disclosure of Invention
The embodiment of the invention provides a mathematical test question similarity judging method, which solves the problems of time and labor waste and low accuracy of the current test question similarity judging method.
In a first aspect, a method for determining similarity of mathematical test questions is provided, including:
establishing a keyword library, wherein the keyword library comprises keywords extracted from knowledge points and/or mathematical test questions, the keywords are divided into core keywords, strong keywords and weak keywords, and the uncore keywords, the strong keywords and the weak keywords have corresponding preset weight values.
A mathematical symbol library is established, which comprises mathematical symbols extracted from mathematical test questions, wherein the mathematical symbols are divided into N classes.
The same-direction word library is established, and it is noted that the same-direction words are different from the approximate words, and the same-direction words refer to the same or close relationship of the corresponding knowledge points among the words, for example, sine and cosine are classified as the same-direction words, so that the algorithm has more generalization capability.
Identifying keywords of the test questions, calculating keyword emphasis coefficients of the test questions, and combining the keyword homodromous degree and the mathematical symbol expression similarity by using the keyword emphasis coefficients to calculate the similarity of the test questions so as to judge the similarity of the two test questions.
The test question similarity=keyword homodromous, keyword emphasis coefficient+mathematical symbol expression similarity (1-keyword emphasis coefficient).
The keyword importance factor = core keyword weight sum/all keyword weight sum. When the keyword emphasis coefficient is less than 0.6 and the keyword exists, the keyword emphasis coefficient is set to 0.6. When the keyword emphasis coefficient is greater than 0.8, the keyword emphasis coefficient is set to 0.8.
Keyword co-ordinates = same keyword weight sum/MAX (question 1 keyword weight sum, question 2 keyword weight sum).
And the numerical value of each sequence position of the characteristic sequence is expressed by 0 or 1, when mathematical symbols exist in the mathematical symbol types corresponding to the corresponding sequence positions of the two test questions, the numerical value of the sequence position is 1, and otherwise, the numerical value is 0, and the mathematical symbols express similarity = the same number/N of the characteristic sequence.
The method improves the generalization capability of the algorithm by introducing the homodromous words and the key word significance coefficients, combines the keyword homodromous degree and the mathematical symbol expression similarity by using the key word significance coefficients to calculate the test question similarity, can be applied to calculation of the mathematical test question similarity, and provides a more accurate test question similarity judging method.
Preferably, the core keywords are keywords reflecting investigation knowledge points and reflecting the specificity of mathematical expression, and the weight value is 9. The strong keywords are keywords which are associated with knowledge points but cannot completely express the knowledge points, and the weight value is 4. The weak keywords are expression words which are irrelevant to knowledge points but are commonly used for the mathematical test questions, and the weight value is 1.
Preferably, the mathematical symbols are divided into 10 classes, including:
1) The single letter "x, y, z".
2) Single letter "A, B, C".
3) Double letter "AB, AC, AD, BC, BD, EF".
4) The single letters "k, m, n".
5) The single letters "a, b, c".
6) Symbol "=".
7) Symbols "+, -, ×, ≡).
8) Symbols "<, >,.
9) The symbols "≡e-.
10 Numerical values "3.14, pi".
The feature sequence is 10 digits, and the mathematical symbol expresses similarity=the same number of feature sequences/10.
Preferably, the method further comprises the step of judging the question type, and when the question types are inconsistent, the questions are directly judged to be dissimilar, and the similarity of the test questions is not calculated. The question types include proof questions, drawing questions, calculation questions, and other question types. Judging the question type by using the keywords, comprising:
1) The judging method of the proving questions comprises the following steps: if keywords such as ' proof, asking for evidence ' and testing evidence ' exist in the test question content, judging the test question as the proof question.
2) The calculation question judging method comprises the following steps: if keywords such as calculation, one calculation, oral calculation and written calculation exist at the front part of the test question content, the test question is judged to be a calculation question.
3) The drawing question judging method comprises the following steps: the keywords such as drawing, painting, drawing and drawing method exist in the test question content, and the keywords are drawing questions.
4) Question types other than proof questions, calculation questions and drawing questions are classified into other types of question types.
Preferably, for the test questions with graphics, the graphics are manually marked to give keywords expressing the graphics content, and the keywords are taken from the keyword library and the mathematical symbol library.
Preferably, when keywords of the test questions are identified, a keyword library is utilized to search whether keywords exist in the test questions, so that a keyword list of the content of the test questions is obtained. And after the keyword list of the two test questions is obtained, searching the same-direction words of the keywords through the same-direction word bank, and obtaining the same-direction word list of the keywords.
In a second aspect, a mathematical test question similarity determination system is provided, including:
the data acquisition module is used for acquiring the content of the test questions to be analyzed;
the data processing module is used for establishing a keyword library and comprises keywords extracted from knowledge points and/or mathematical test questions, wherein the keywords are divided into core keywords, strong keywords and weak keywords, and the core keywords, the strong keywords and the weak keywords all have corresponding preset weight values; establishing a mathematical symbol library which comprises mathematical symbols extracted from mathematical test questions; the mathematical symbols are divided into N classes; establishing a same-direction word library, wherein the same-direction words refer to the same or close relationship of corresponding knowledge points among the words; identifying keywords of the test questions, calculating key word important coefficients of the test questions, calculating similarity of the test questions by combining the keyword homodromous degree and the mathematical symbol expression similarity, and judging the similarity of the two test questions:
the test question similarity=keyword homodromous, keyword emphasis coefficient+mathematical symbol expression similarity (1-keyword emphasis coefficient);
the key word significant coefficient=core key word weight sum/all key word weight sum; when the key word significant coefficient is smaller than 0.6 and the key word exists, setting the key word significant coefficient to be 0.6; when the key word significant coefficient is larger than 0.8, setting the key word significant coefficient to be 0.8;
keyword co-directional degree=co-directional keyword weight sum/MAX (test question 1 keyword weight sum, test question 2 keyword weight sum);
and the numerical value of each sequence position of the characteristic sequence is expressed by 0 or 1, when mathematical symbols exist in the mathematical symbol types corresponding to the corresponding sequence positions of the two test questions, the numerical value of the sequence position is 1, and otherwise, the numerical value is 0, and the mathematical symbols express similarity = the same number/N of the characteristic sequence.
In a third aspect, a mathematical test question similarity determination apparatus is provided, including: memory, processor. The memory has executable code stored thereon, which when executed by the processor causes the processor to perform the mathematical test question similarity determination method of the first aspect.
In a fourth aspect, an embodiment of the present invention provides a non-transitory machine-readable storage medium having executable code stored thereon, which when executed by a processor of an electronic device, causes the processor to at least implement the method for determining similarity of mathematical test questions in the first aspect.
In the embodiment of the invention, the method, the system and the application for judging the similarity of the mathematical test questions are provided, and have the following beneficial effects:
the generalization capability of the algorithm is improved by introducing the homodromous words and the keyword homodromous degrees, and the keyword homodromous degrees and the mathematical symbol expression similarity are combined by utilizing the keyword significance coefficients, so that the method can be applied to calculation of the mathematical test question similarity and provides a more accurate test question approximation degree judgment method;
the problem type judgment is introduced, the test questions of different problem types are directly judged to be inappropriately, and excessive approximate calculation is avoided, so that the speed of approximate judgment or the speed of obtaining the approximate problems can be improved;
the test questions with the graphics are manually marked, and meanwhile, the marked keywords are taken from a keyword library and a mathematical symbol library, so that the model can perform approximation analysis on the test questions with the graphics, and the application range of the model is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and do not constitute a limitation on the invention.
Wherein:
FIG. 1 is a partial list of junior middle school mathematics keywords;
FIG. 2 is a partial list of math similar words for junior middle school;
fig. 3 is a main flow of test question similarity determination.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The terminology used in the embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this application and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise, the "plurality" generally includes at least two.
The words "if", as used herein, may be interpreted as "at … …" or "at … …" or "in response to a determination" or "in response to a detection", depending on the context. Similarly, the phrase "if determined" or "if detected (stated condition or event)" may be interpreted as "when determined" or "in response to determination" or "when detected (stated condition or event)" or "in response to detection (stated condition or event), depending on the context.
The teaching informatization is not separated from the construction of a question bank center, the question bank center has an important function of automatically judging the similarity of the questions, the examination paper and the operation can be compiled in an auxiliary mode through the judgment of the similarity of the questions, the teaching efficiency is improved, the traditional similarity judging method is used for filtering and judging according to a large amount of manual labeling information, time and labor are wasted, a machine learning training method is also used, the accuracy of the similarity judgment is not high, the practical degree is difficult to achieve, and the similarity judging method is different from other subjects in mathematic experiments, contains various symbols and formulas, and is more difficult to judge the similarity in a simple text recognition mode.
Aiming at the problems, the invention provides a mathematical test question similarity judging method, which improves the generalization capability of an algorithm by introducing the homodromous words and the keyword homodromous degrees, combines with the key word significance coefficients and the mathematical symbol expression similarity, can be applied to calculation of the mathematical test question similarity, and provides a more accurate test question similarity judging method.
The implementation principles of the method, system, device and medium of the present invention are similar, and will not be described here again.
Having described the basic principles of the present invention, various non-limiting embodiments thereof are specifically described below, it being noted that the examples provided herein are merely illustrative for ease of understanding the spirit and principles of the present invention and embodiments of the present invention are not limited in this respect. Rather, embodiments of the invention may be applied to any system where applicable.
Embodiment one:
a method for judging similarity of mathematical test questions comprises the following steps:
establishing a keyword library, wherein the keyword library comprises keywords extracted from knowledge points and/or mathematical test questions, the keywords are divided into core keywords, strong keywords and weak keywords, and the core keywords, the strong keywords and the weak keywords all have corresponding preset weight values. In one embodiment, as shown in fig. 1, the core keywords are keywords reflecting the investigation knowledge points and reflecting the specificity of the mathematical expression, and the weight value is 9. The strong keywords are keywords which are associated with knowledge points but cannot completely express the knowledge points, and the weight value is 4. The weak keywords are expression words which are irrelevant to knowledge points but are commonly used for the mathematical test questions, and the weight value is 1.
In an embodiment, the keyword library establishment method may be:
1) Extracting core keywords from mathematical knowledge points, such as triangle congruence, sector statistical diagram, parity and the like, according to the teaching outline;
2) Keywords which can express the specificity of the mathematical test questions, such as denominators, axisymmetry, shortest paths and the like, are analyzed and summarized from the test question content;
3) Decomposing a core keyword containing a plurality of words into a plurality of strong keywords, such as decomposing triangle congruent into triangle and congruent two strong keywords;
4) The mathematical common expression words which are irrelevant to knowledge points are summarized from the analysis of the test question content, and the words are used as weak keywords, such as 'observation', 'process', 'every', 'all', and the like;
5) The weight value of the core keyword is set to be 9, the weight of the strong keyword is set to be 4, and the weight of the weak keyword is set to be 1.
A mathematical symbol library is established, which comprises mathematical symbols extracted from mathematical test questions, wherein the mathematical symbols are divided into N classes. In an embodiment, a feature sequence with a length of N is formed by N types of mathematical symbols, and a value of each sequence position of the feature sequence is expressed by 0 or 1, when two test questions have mathematical symbols in the mathematical symbol types corresponding to the corresponding sequence positions, the value of the sequence position is 1, otherwise, the value of the sequence position is 0.
The same-direction word library is established, and it is noted that the same-direction words are different from the approximate words, and the same-direction words refer to the same or close relationship of the corresponding knowledge points among the words, for example, sine and cosine are classified as the same-direction words, so that the algorithm has more generalization capability. In one embodiment, the keyword library table is analyzed to list words capable of reflecting the same direction of the mathematical expression as the same direction keywords, such as "cross, intersect, intersection", "sine, cosine, tangent, cotangent, cos, sin, tan, cot", etc., as shown in fig. 2.
And identifying keywords of the test questions, and optionally, searching whether keywords exist in the test questions by utilizing a keyword library when the keywords of the test questions are identified, so as to obtain a keyword list of the content of the test questions. And after the keyword list of the two test questions is obtained, searching the same-direction words of the keywords through the same-direction word bank, and obtaining the same-direction word list of the keywords.
And calculating the key word significance coefficient of the test question, wherein the key word significance coefficient reflects the expression degree of the key word in the test question content, and the lower the significance coefficient is, the more the key word cannot reflect the investigation knowledge point and the solution idea of the test question.
And combining the keyword homodromous and the mathematical symbol expression similarity by using the keyword emphasis coefficient to calculate the similarity of the test questions, so as to judge the similarity of the two test questions.
In an embodiment, the test question similarity=keyword co-direction degree, keyword emphasis coefficient+mathematical symbol expression similarity (1-keyword emphasis coefficient).
Wherein the keyword emphasis coefficient=core keyword weight sum/all keyword weight sum. When the keyword emphasis coefficient is less than 0.6 and the keyword exists, the keyword emphasis coefficient is set to 0.6. When the key word significant coefficient is larger than 0.8, the key word significant coefficient is set to 0.8, so that the self-adaptive dynamic weighting coefficient is realized.
Keyword co-ordinates = same keyword weight sum/MAX (question 1 keyword weight sum, question 2 keyword weight sum).
The mathematical symbols express similarity=the same number of feature sequences/N, and in a specific embodiment, the mathematical symbols are divided into 10 classes, including:
1) The single letter "x, y, z".
2) Single letter "A, B, C".
3) Double letter "AB, AC, AD, BC, BD, EF".
4) The single letters "k, m, n".
5) The single letters "a, b, c".
6) Symbol "=".
7) Symbols "+, -, ×, ≡).
8) Symbols "<, >,.
9) The symbols "≡e-.
10 Numerical values "3.14, pi".
The characteristic sequence is 10 digits, the numerical value of each sequence position of the characteristic sequence is expressed by 0 or 1, when two test questions exist in mathematical symbol types corresponding to the corresponding sequence positions, the numerical value of the sequence position is 1, otherwise, the numerical value is 0, and the mathematical symbol expression similarity=the same number/10 of the characteristic sequence.
The method improves the generalization capability of the algorithm by introducing the homodromous words and the key word significant coefficients, combines the keyword homodromous degree and the mathematical symbol expression similarity by utilizing the key word significant coefficients, and can be applied to calculation of the mathematical test question similarity to provide a more accurate test question similarity judging method.
In addition, in order to reduce unnecessary computation, in another embodiment, a question type judgment is introduced, when the question types are inconsistent, the questions are directly judged to be dissimilar, and the similarity of the questions is not computed. The question types include proof questions, drawing questions, calculation questions, and other question types.
Specifically, the method for judging the question type by using the keywords comprises the following steps:
1) The judging method of the proving questions comprises the following steps: if keywords such as ' proof, asking for evidence ' and testing evidence ' exist in the test question content, judging the test question as the proof question.
2) The calculation question judging method comprises the following steps: if keywords such as calculation, one calculation, oral calculation and written calculation exist at the front part of the test question content, the test question is judged to be a calculation question.
3) The drawing question judging method comprises the following steps: the keywords such as drawing, painting, drawing and drawing method exist in the test question content, and the keywords are drawing questions.
4) Question types other than proof questions, calculation questions and drawing questions are classified into other types of question types.
In other embodiments, for test questions with graphics, the graphics are manually marked to give keywords that express the graphics content, which are taken from the keyword library and the mathematical symbol library.
Embodiment two:
as shown in fig. 3, the following test question similarity determination steps are obtained according to the first embodiment:
s10, importing a key word stock, a same-direction word stock and a mathematical symbol stock, wherein the key word stock, the same-direction word stock and the mathematical symbol stock are classified into three types of primary mathematics, junior middle school mathematics and senior high school mathematics;
s20, preprocessing the test question contents to be compared, removing formatted data and image link data, and adding keywords for explaining images to the tail of the question stem contents;
s30, identifying the question type, if the question type is a proof question, a calculation question and a drawing question, judging whether the question type is consistent, if not, directly giving a dissimilar judgment result;
s40, extracting keywords from the stems, calculating the importance coefficients of the keywords, and correspondingly listing similar words;
s50, extracting mathematical symbol expression characteristics from the content of the stem, and calculating mathematical symbol expression similarity;
s60, firstly calculating the keyword homodromous and mathematical symbol expression similarity, and then combining the keyword homodromous and mathematical symbol expression similarity by using the keyword emphasis coefficient;
and S70, judging whether the two test questions are similar according to the similarity threshold, wherein the similarity threshold is 0.8 through a test, and of course, in other embodiments, other values can be adopted.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. The method for judging the similarity of the mathematical test questions is characterized by comprising the following steps of:
establishing a keyword library, wherein the keyword library comprises keywords extracted from knowledge points and/or mathematical test questions, the keywords are divided into core keywords, strong keywords and weak keywords, and the core keywords, the strong keywords and the weak keywords all have corresponding preset weight values;
establishing a mathematical symbol library, wherein the mathematical symbol library comprises mathematical symbols extracted from mathematical test questions, and the mathematical symbols are divided into N classes;
establishing a same-direction word library, wherein the same-direction words refer to the same or close relationship of corresponding knowledge points among the words;
identifying keywords of the test questions, calculating keyword emphasis coefficients of the test questions, and calculating the similarity of the test questions by combining the keyword homodromous degree and the mathematical symbol expression similarity by using the emphasis coefficients, so as to judge the similarity of the two test questions:
the test question similarity=keyword homodromous, keyword emphasis coefficient+mathematical symbol expression similarity (1-keyword emphasis coefficient);
the key word significant coefficient=core key word weight sum/all key word weight sum; when the key word significant coefficient is smaller than 0.6 and the key word exists, setting the key word significant coefficient to be 0.6; when the key word significant coefficient is larger than 0.8, setting the key word significant coefficient to be 0.8;
keyword co-directional degree=co-directional keyword weight sum/MAX (test question 1 keyword weight sum, test question 2 keyword weight sum);
and the numerical value of each sequence position of the characteristic sequence is expressed by 0 or 1, when mathematical symbols exist in the mathematical symbol types corresponding to the corresponding sequence positions of the two test questions, the numerical value of the sequence position is 1, and otherwise, the numerical value is 0, and the mathematical symbols express similarity = the same number/N of the characteristic sequence.
2. The method for judging the similarity of mathematical test questions as claimed in claim 1, wherein the core keywords are keywords reflecting investigation knowledge points and reflecting the specificity of mathematical expression, and the weight value is 9; the strong keywords are keywords which are associated with knowledge points but cannot completely express the knowledge points, and the weight value is 4; the weak keywords are expression words which are irrelevant to knowledge points but are commonly used for the mathematical test questions, and the weight value is 1.
3. The method for determining similarity of mathematical test questions of claim 1, wherein the mathematical symbols are divided into 10 classes, comprising:
1) Single letter "x, y, z";
2) Single letter "A, B, C";
3) Double letter "AB, AC, AD, BC, BD, EF";
4) Single letter "k, m, n";
5) Single letter "a, b, c";
6) Symbol "=";
7) Symbols "+, -, ×,";
8) Symbols "<, > or less than or equal to, <";
9) Symbols "≡e,", n ", u";
10 Numerical values "3.14, pi";
the feature sequence is 10 digits, and the mathematical symbol expresses similarity=the same number of feature sequences/10.
4. The method for judging the similarity of mathematical test questions according to claim 1, further comprising judging the question types, and when the question types are inconsistent, directly judging the questions as dissimilar, and not calculating the similarity of the test questions; the question types comprise proof questions, drawing questions, calculation questions and other question types; judging the question type by using the keywords, comprising:
1) The judging method of the proving questions comprises the following steps: judging that the test questions are proof if keywords such as proof, asking for evidence and testing evidence exist in the test question content;
2) The calculation question judging method comprises the following steps: if keywords such as calculation, calculation one calculation, oral calculation and written calculation exist at the front part of the test question content, judging the test question as a calculation question;
3) The drawing question judging method comprises the following steps: keywords such as drawing, painting, drawing and drawing method exist in the test question content, and the keywords are drawing questions;
4) Question types other than proof questions, calculation questions and drawing questions are classified into other types of question types.
5. The method according to claim 1, wherein, for the test questions with graphics, the graphics are manually marked to give keywords expressing the graphics content, the keywords are taken from the keyword library and the mathematical symbol library.
6. The method for judging the similarity of the mathematical test questions according to claim 1, wherein when the keywords of the test questions are identified, a keyword library is used for searching whether the keywords exist in the test questions so as to obtain a keyword list of the test question contents; and after the keyword list of the two test questions is obtained, searching and judging the same-directional words of the keyword list through the same-directional word library, and obtaining the same-directional word list.
7. A mathematical test question similarity determination system, comprising:
the data acquisition module is used for acquiring the content of the test questions to be analyzed;
the data processing module is used for establishing a keyword library and comprises keywords extracted from knowledge points and/or mathematical test questions, wherein the keywords are divided into core keywords, strong keywords and weak keywords, and the core keywords, the strong keywords and the weak keywords all have corresponding preset weight values; establishing a mathematical symbol library which comprises mathematical symbols extracted from mathematical test questions; the mathematical symbols are divided into N classes; establishing a same-direction word library, wherein the same-direction words refer to the same or close relationship of corresponding knowledge points among the words; identifying keywords of the test questions, calculating keyword emphasis coefficients of the test questions, and calculating the similarity of the test questions by combining the keyword homodromous degree and the mathematical symbol expression similarity by using the keyword emphasis coefficients, so as to judge the similarity of the two test questions:
the test question similarity=keyword homodromous, keyword emphasis coefficient+mathematical symbol expression similarity (1-keyword emphasis coefficient);
the key word significant coefficient=core key word weight sum/all key word weight sum; when the key word significant coefficient is smaller than 0.6 and the key word exists, setting the key word significant coefficient to be 0.6; when the key word significant coefficient is larger than 0.8, setting the key word significant coefficient to be 0.8;
keyword co-directional degree=co-directional keyword weight sum/MAX (test question 1 keyword weight sum, test question 2 keyword weight sum);
and the numerical value of each sequence position of the characteristic sequence is expressed by 0 or 1, when mathematical symbols exist in the mathematical symbol types corresponding to the corresponding sequence positions of the two test questions, the numerical value of the sequence position is 1, and otherwise, the numerical value is 0, and the mathematical symbols express similarity = the same number/N of the characteristic sequence.
8. A mathematical test question similarity judging apparatus, comprising: a memory, a processor; the memory has stored thereon executable code which, when executed by the processor, causes the processor to perform the mathematical test question similarity determination method of any one of claims 1 to 6.
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