Problem complexity calculation and evaluation method and system in major concept teaching
Through a method based on the large concept knowledge graph, problem feature definition is assigned to the problem and the problem complexity is evaluated using vector scalar functions, the problem of inaccurate and objective evaluation in the existing technology is solved, and more accurate and objective evaluation is achieved, and teaching decision-making is supported.
Patent Information
- Application Number
- CN202411862034.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-17
- Publication Date
- 2025-04-11
AI Technical Summary
When evaluating the complexity of problems in large concept teaching, the existing technology relies on teachers' experience and subjective judgment, lacks the idea based on large concept teaching, and links the complexity of problems with the concepts associated with them, resulting in inaccurate and objective enough.
Using a method based on a large concept knowledge graph, we use a method to obtain large concepts and small concepts associated with practical teaching problems, give problem feature definitions, and use vector scalar functions to map multidimensional features into a real number to evaluate the complexity of the problem.
It achieves a more accurate, comprehensive and objective assessment of problem complexity, reduces the dependence of teachers' subjective experience, and provides quantitative measurement standards to support teaching decisions.
Smart Images
Figure CN119809431A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of education and teaching, and in particular relates to a method and system for calculating and evaluating the complexity of problems in large-concept teaching. Background Art
[0002] In big concept teaching, emphasis is placed on implementing teaching by visualizing big concepts through a variety of real-life cases, among which questions can provide cases for concept teaching and are an important part of the implementation of big concept teaching. Complexity is one of the attributes of a question and can help with question recommendations. Existing methods for evaluating the complexity of a question either rely on the teacher's experience and judgment, which is too subjective, or do not link the complexity of a question with its associated concepts based on the idea of big concept teaching. Therefore, this patent introduces the calculation of problem complexity based on the big concept knowledge graph to quantify the calculation of problem complexity, aiming to evaluate problem complexity more accurately, comprehensively, and objectively, and to provide a basis for subsequent teachers to use questions to implement big concept teaching. Summary of the invention
[0003] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides a method and system for calculating and evaluating the complexity of problems in big concept teaching.
[0004] The present invention adopts the following technical solution: a method for calculating and evaluating the complexity of problems in big concept teaching, comprising the following steps: Obtain a large concept knowledge graph, and define the large concepts and small concepts with transfer value in the large concept knowledge graph as idea ; Define practical teaching problems based on big concepts as problem ; Get and problem There is a correlation idea , and classified into set I: ;right problem Give feature definition , which can be expressed as: ;in, n+1 is the number of features; Create scalar functions from vectors , the scalar function About A monotone increasing function is used to convert the multidimensional vector It is mapped to a real number, and the complexity of the actual teaching problem is evaluated according to the real number: the larger the real value, the higher the complexity of the corresponding actual teaching problem.
[0005] In a further embodiment, the generation process of the set I is as follows: Traverse the problemAll the adjacent points of , the adjacent points of large concepts and small concepts with migration value are updated to set I in the form of ideas.
[0006] In a further embodiment, the feature items include at least: the number of associated ideas , similarity of related ideas , whether the corresponding problem is interdisciplinary , whether the corresponding problem comes from a real scene , the overall complexity of the associated idea ; correspondingly, .
[0007] In a further embodiment, the number of associated ideas The calculation method is as follows: Creating a mapping function , the mapping function Related to existence idea The number N is monotonically increasing, and there is an upper bound value ; The mapping function It is expressed as: ; in, , so ; It is a pre-set hyperparameter, which indicates an upper limit on the number of nodes associated with a problem.
[0008] In a further embodiment, the similarity of the associated ideas The calculation process is as follows: Traverse and get each idea in set I, recorded as , get its adjacent points and add them to a set, record the set as set ;based on Calculate the similarity between the elements in set I: assumed are two elements in set I, and their corresponding neighbor node sets are and , we are and Calculating the similarity can get a value, recorded as: ; The similarity between two adjacent points By arranging, we can get the similarity matrix , , ; The similarity matrix Do the following to get the scalar value : ; For the scalar value Normalization is performed to obtain the "overlap of problem-related concepts", which is recorded as : ,but ; Building a mapping function , the mapping function and There is a monotonically decreasing mapping relationship between them, and there is an upper bound value , the mapping function It is expressed as: ;in, ,but .
[0009] In a further embodiment, whether the corresponding problem is interdisciplinary The calculation method is as follows: Get the "Is it interdisciplinary" attribute of the current problem and record the value of the attribute as , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value : ;in ,but .
[0010] In a further embodiment, whether the corresponding problem comes from a real scene The calculation method is as follows: Get the "scenario authenticity" attribute of the current problem and record the attribute value as , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value ; The mapping function It is expressed as: ,but .
[0011] In a further embodiment, the overall complexity of the associated idea The calculation process is as follows: Traverse each element in set I and read the attribute value of the interdisciplinary attribute "problem complexity" as , and the set is C(I), and ; Average the elements in C(I) to get the mean , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value ; The mapping function It is expressed as: ,but .
[0012] In a further embodiment, the scalar function The formula is as follows: ; In the formula is the evaluation value of the problem complexity, calculated as follows: ; , , , , is the weight parameter of the feature item; for The upper bound value of ; but , It is a normalized evaluation value of the problem complexity, and its value range is 0-100.
[0013] A system for calculating and evaluating the complexity of problems in big concept teaching, used to implement the calculation and evaluation method as described above, comprising: The first module is set to obtain the big concept knowledge graph, and the big concepts and small concepts with transfer value in the big concept knowledge graph are defined as idea ; Define practical teaching problems based on big concepts as problem ; The second module is set to problem Give feature definition , which can be expressed as: ;in, Represents feature items n The characteristic value of The third module is set up to create a scalar function for the vector , the scalar function About A monotone increasing function is used to convert the multidimensional vector It is mapped to a real number, and the complexity of the actual teaching problem is evaluated according to the real number: the larger the real value, the higher the complexity of the corresponding actual teaching problem.
[0014] Beneficial effects of the present invention: Taking into account that existing evaluation methods may not fully integrate the idea of big concept teaching, the present invention ensures the association between the calculation of problem complexity and concepts by introducing big concept knowledge graphs; at the same time, it helps to achieve more objective and quantitative evaluation, reduce the degree of reliance on teachers' subjective experience, and improve the objectivity of problem complexity evaluation; linear equations are used to calculate problem complexity, which provides a quantitative measurement standard for problem recommendation, making the calculation of problem complexity more accurate and comprehensive, thereby better supporting teaching decisions. DETAILED DESCRIPTION
[0015] The present invention will be further described below in conjunction with the embodiments.
[0016] Example 1 A method for calculating and evaluating the complexity of problems in big concept teaching includes the following steps: Obtain a large concept knowledge graph, and define the large concepts and small concepts with transfer value in the large concept knowledge graph as idea ; Define practical teaching problems based on big concepts as problem .
[0017] For example: In biology, "ecosystem" is a broad concept, and "the role of forest ecosystem" is a narrow concept, so the transferability of these two concepts is different.
[0018] Transferability mainly refers to whether a book can be transferred to different scenarios in daily life. For example, after establishing the concept of ecosystem, when transferring to business, a large industry can be regarded as an ecosystem for analysis, and each company has its own ecological position; when transferring to literary writing, the characters, things and relationships in a work can be regarded as an ecosystem, and these elements are also interconnected in the process of change like the ecosystem; and so on. After the big concept of ecosystem is established, there are many scenarios in learning and life where it can be transferred to and used. This is an example of the transferability of the big concept.
[0019] In contrast, as a small concept, "the role of forest ecosystems" is a small knowledge concept with relatively weak transferability outside of books.
[0020] Get and problem There is a correlation idea , and classified into set I: ;right problem Give feature definition ; The feature definition It is expressed as: ;in, Represents feature items n The characteristic value of Create scalar functions from vectors , the scalar function About A monotone increasing function is used to convert the multidimensional vector It is mapped to a real number, and the complexity of the actual teaching problem is evaluated according to the real number: the larger the real value, the higher the complexity of the corresponding actual teaching problem.
[0021] Problem complexity refers to the teaching elements involved in a problem. The more elements a problem involves, the more difficult it is for teachers to teach. It is also more difficult for students to learn and understand.
[0022] In this embodiment, the generation process of set I is as follows: traverse the problem All the adjacent points of , these critical points are big concepts or small concepts one by one, and these big concepts and small concepts are updated to the set I in the form of ideas.
[0023] In another embodiment, the feature items include at least: the number of associated ideas , similarity of related ideas , whether the corresponding problem is interdisciplinary , whether the corresponding problem comes from a real scene , the overall complexity of the associated idea ; correspondingly, .
[0024] Based on the above description, the number of associated ideas The calculation method is as follows: Creating a mapping function , the mapping function Related to existence idea The number N is monotonically increasing, and there is an upper bound value ; The mapping function It is expressed as: ; in, , so ; It is a pre-set hyperparameter, which indicates an upper limit on the number of nodes associated with a problem.
[0025] Similarity of related ideas The calculation process is as follows: Traverse and get each idea in set I, recorded as , get its adjacent points and add them to a set, record the set as set ;based on Calculate the similarity between the elements in set I: assumed are two elements in set I, and their corresponding neighbor node sets are and , we are and Calculating the similarity can get a value, recorded as: ; The similarity between two adjacent points By arranging, we can get the similarity matrix , , ; The similarity matrix Do the following to get the scalar value : ; For the scalar value Normalization is performed to obtain the "overlap of problem-related concepts", which is recorded as : ,but ; Building a mapping function , the mapping function and There is a monotonically decreasing mapping relationship between them, and there is an upper bound value , the mapping function It is expressed as: ;in, ,but .
[0026] Is the corresponding problem interdisciplinary? The calculation method is as follows: Get the "Is Crosscutting Problem" attribute of the current problem and record the value of the attribute as , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value : ;in ,but .
[0027] Whether the corresponding problem comes from a real scenario The calculation method is as follows: Get the "situation authenticity degree" attribute of the current problem and record the attribute value as , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value ; The mapping function It is expressed as: ,but .
[0028] The overall complexity of the associated idea The calculation process is as follows: Traverse each element in set I and count the attribute value of the interdisciplinary attribute "problem complexity" as , and the set is C(I), and ; Average the elements in C(I) to get the mean , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value ; The mapping function It is expressed as: ,but .
[0029] In summary, the scalar function The formula is as follows: ; In the formula is the evaluation value of the problem complexity, calculated as follows: ; , , , , is the weight parameter of the feature item; for The upper bound value of ; but , It is a normalized evaluation value of the problem complexity, and its value range is 0-100.
[0030] Example 2 This embodiment implements the method described in Embodiment 1 and discloses a system for calculating and evaluating the complexity of problems in big concept teaching, including: The first module is set to obtain the big concept knowledge graph, and the big concepts and small concepts with transfer value in the big concept knowledge graph are defined as idea ; Define practical teaching problems based on big concepts as problem ; The second module is set to problem Give feature definition , which can be expressed as: ;in, Represents feature items n The characteristic value of The third module is set up to create a scalar function for the vector , the scalar function About A monotone increasing function is used to convert the multidimensional vector It is mapped to a real number, and the complexity of the actual teaching problem is evaluated according to the real number: the larger the real value, the higher the complexity of the corresponding actual teaching problem.
Claims
1. A method for calculating and evaluating the complexity of problems in big concept teaching, characterized in that: The following steps are involved: Obtain a large concept knowledge graph, and define the large concepts and small concepts with transfer value in the large concept knowledge graph as idea ; Define practical teaching problems based on big concepts as problem ; Get and problem There is a correlation idea , and classified into set I: ;right problem Give feature definition , which can be expressed as: ;in, n+1 is the number of features; Create scalar functions from vectors , the scalar function About A monotone increasing function is used to convert the multidimensional vector It is mapped into a real number, and the complexity of the actual teaching problem is evaluated according to the real number: the larger the real value, the higher the complexity of the corresponding actual teaching problem.
2. According to the method for calculating and evaluating the complexity of problems in big concept teaching in claim 1, it is characterized by: The generation process of the set I is as follows: Traverse the problem All the adjacent points of , the adjacent points of large concepts and small concepts with migration value are updated to set I in the form of ideas.
3. The method for calculating and evaluating the complexity of problems in big concept teaching according to claim 1 is characterized in that: The feature items include at least: the number of associated ideas , similarity of related ideas , whether the corresponding problem is interdisciplinary , whether the corresponding problem comes from a real scene , the overall complexity of the associated idea ; correspondingly, .
4. The method for calculating and evaluating the complexity of problems in big concept teaching according to claim 3 is characterized in that: The number of associated ideas The calculation method is as follows: Creating a mapping function , the mapping function Related to existence idea The number N is monotonically increasing, and there is an upper bound value ; The mapping function It is expressed as: ； in, , so ; It is a pre-set hyperparameter, which indicates an upper limit on the number of nodes associated with a problem.
5. The method for calculating and evaluating the complexity of problems in big concept teaching according to claim 3 is characterized in that: The similarity of the associated ideas The calculation process is as follows: Traverse and get each idea in set I, recorded as , get its adjacent points and add them to a set, record the set as set ;based on Calculate the similarity between the elements in set I: assumed are two elements in set I, and their corresponding neighbor node sets are and , we are and Calculating the similarity can get a value, recorded as: ; The similarity between two adjacent points By arranging, we can get the similarity matrix , , ; The similarity matrix Do the following to get the scalar value : ; For the scalar value Normalization is performed to obtain the "overlap of problem-related concepts", which is recorded as : ,but ; Building a mapping function , the mapping function and There is a monotonically decreasing mapping relationship between them, and there is an upper bound value , the mapping function It is expressed as: ;in, ,but .
6. The method for calculating and evaluating the complexity of problems in big concept teaching according to claim 3 is characterized in that: Is the corresponding problem interdisciplinary? The calculation method is as follows: Get the "Is it interdisciplinary" attribute of the current problem and record the value of the attribute as , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value : ;in ,but .
7. The method for calculating and evaluating the complexity of problems in big concept teaching according to claim 3 is characterized in that: Whether the corresponding problem comes from a real scenario The calculation method is as follows: Get the "scenario authenticity" attribute of the current problem and record the attribute value as , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value ; The mapping function It is expressed as: ,but .
8. The method for calculating and evaluating the complexity of problems in big concept teaching according to claim 3 is characterized in that: The overall complexity of the associated idea The calculation process is as follows: Traverse each element in set I and read the attribute value of the interdisciplinary attribute "problem complexity" as , and the set is C(I), and ; Average the elements in C(I) to get the mean , ; Creating a mapping function , the mapping function and It forms a monotonically increasing relationship and has an upper bound value ; The mapping function It is expressed as: ,but .
9. The method for calculating and evaluating the complexity of problems in big concept teaching according to claim 3 is characterized in that: Scalar functions The formula is as follows: ； In the formula is the evaluation value of the problem complexity, calculated as follows: ; , , , , is the weight parameter of the feature item; for The upper bound value of ; but , It is a normalized evaluation value of the problem complexity, ranging from 0 to 100.
10. A system for calculating and evaluating the complexity of problems in big concept teaching, used to implement the calculation and evaluation method as claimed in any one of claims 1 to 9, characterized in that: include: The first module is set to obtain the big concept knowledge graph, and the big concepts and small concepts with transfer value in the big concept knowledge graph are defined as idea ; Define practical teaching problems based on big concepts as problem ; The second module is set to problem Give feature definition , which can be expressed as: ;in, Represents feature items n The characteristic value of The third module is set up to create a scalar function of the vector , the scalar function About A monotone increasing function is used to convert the multidimensional vector It is mapped into a real number, and the complexity of the actual teaching problem is evaluated according to the real number: the larger the real value, the higher the complexity of the corresponding actual teaching problem.