Student development comprehensive evaluation method based on multi-dimensional accomplishment indexes

Abstract

The invention relates to the technical field of education data analysis, and discloses a student development comprehensive evaluation method based on a multi-dimensional accomplishment index, and the method comprises the steps: obtaining the multi-dimensional performance data of a student, and constructing an N-dimensional state vector containing the position and speed; constructing an N-dimensional dynamic virtual potential energy field formed by superposing static potential energy representing an education target and dynamic potential energy reflecting individual history; simulating the evolution of an N-dimensional state vector in a field according to a kinetic equation in which dynamic inertial mass is introduced to generate a development trajectory; and finally, quantitatively analyzing the track characteristics, and outputting an evaluation result. According to the method, the historical intervention effect can be evaluated by comparing the actual trajectory with the reference trajectory, preferential selection can be carried out by simulating future trajectories under different interventions, and a basis is provided for formulating a personalized strategy. According to the method, the physical dynamics model is introduced into educational evaluation, dynamic, process and predictive evaluation is realized, static limitation of traditional evaluation is overcome, and evaluation is more scientific and objective and has prospective guiding significance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of educational data analysis, in particular to a student development comprehensive evaluation method based on multi-dimensional literacy indicators. BACKGROUND

[0002] In the current educational practice, the comprehensive evaluation of students is a key link in the process of teaching management and talent training. At present, the mainstream evaluation method mainly relies on a series of relatively static indicator sets. For example, the academic performance of students is measured by standardized academic test scores, course grade point average (GPA), and various competition awards; and a "comprehensive quality evaluation report" is formed by combining teacher comments, extracurricular activity participation records, and social practice experience. These methods can reflect the achievements of students at a certain stage to some extent.

[0003] However, these mainstream evaluation methods are essentially a measure of the performance of students at a specific time node. The evaluation can present the final results of students at a certain point in time, but it is difficult to reveal the process, speed and internal potential of achieving the results, so the evaluation presents the characteristics of stage and termination, and seriously lacks the continuity of the development process. Therefore, the present application proposes a student development comprehensive evaluation method based on multi-dimensional literacy indicators to solve the problems of the prior art. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application provides a student development comprehensive evaluation method based on multi-dimensional literacy indicators, which solves the problem that it is difficult to reveal the process, speed and internal potential of achieving the results, so the evaluation presents the characteristics of stage and termination, and seriously lacks the continuity of the development process.

[0005] To achieve the above purpose, the present application is realized by the following technical scheme: a student development comprehensive evaluation method based on multi-dimensional literacy indicators, comprising the following steps: S1: constructing a multi-dimensional literacy space and generating a state vector: An N-dimensional multi-dimensional literacy space is constructed, where N is a positive integer, each dimension corresponds to a preset literacy indicator, and an N-dimensional state vector representing the student's literacy level at time is generated according to the collected multi-dimensional performance data of the student , the N-dimensional state vector includes an N-dimensional position vector and an N-dimensional velocity vector ; Wherein, each component of the N-dimensional position vector represents the student's level in the i-th dimension of literacy; the N-dimensional velocity vector is the derivative of the N-dimensional position vector with respect to time, characterizing the rate of change of student's literacy level in each dimension.

[0006] S2: Constructing a virtual potential field: Within the N-dimensional literacy space, a virtual potential field is constructed which assigns a scalar potential value to each point (i.e. each possible N-dimensional position vector ) in the space.

[0007] S3: Establishing a dynamics equation: A dynamics equation is established to describe the evolution of the N-dimensional state vector over time, in which the evolution of the N-dimensional state vector is jointly determined by an internal field force and an external intervention force , the internal field force is determined by the negative gradient of the virtual potential field, an exemplary dynamics equation form is as follows: ; wherein, is the dynamic inertial mass; , is the gradient operator; is the rate of change of velocity over time; represents the internal force; represents the external force.

[0008] S4: Determining the development trajectory: According to the dynamics equation, and combined with an initial N-dimensional state vector , by solving the differential equation, the continuous development trajectory formed by the change of the N-dimensional position vector over time is determined.

[0009] S5: Generating a comprehensive evaluation result: Based on the morphology, trend, end position and other quantifiable geometric or physical characteristics of the development trajectory, a comprehensive evaluation result of student development is generated.

[0010] Preferably, the step of generating the N-dimensional state vector further comprises: collecting multi-source heterogeneous data reflecting student's literacy performance, such as academic performance, classroom performance, physical health test data, records of participating in social practice activities, etc.; pre-processing and normalizing the multi-source heterogeneous data to generate each component of the N-dimensional position vector .

[0011] Preferably, the virtual potential field is a dynamic total potential field which is composed of a static basic potential field and a dynamic path-dependent potential field Linear superposition: ; The value of the dynamic path-dependent potential field is determined by the development trajectory determined by the historical position of the N-dimensional state vector, i.e. , where represents a time variable, which refers to any past time point before time .

[0012] Preferably, the calculation step of the dynamic path-dependent potential field comprises: for any point in the N-dimensional multi-dimensional literacy space, the path-dependent potential value at time is determined by integrating the potential influence of all points on point on the historical development trajectory over time: ; wherein is a preset contribution function for describing the influence of historical positions on the current space point; is the instantaneous contribution to the total cumulative amount when the system state is at time variable ; indicates integration along the time variable .

[0013] Preferably, the dynamic inertia mass in the kinetic equation is a function of the dynamic path-dependent potential field, i.e. .

[0014] Preferably, the construction step of the static basic potential field comprises: constructing a target potential well potential ; and constructing a literacy coupling potential , and the target potential well potential and the literacy coupling potential are superimposed to form the basic potential field: .

[0015] Preferably, the step of constructing the target potential well potential comprises: taking the position of the target vector characterizing the educational target in the N-dimensional multi-dimensional literacy space as the potential minimum value center to construct the target potential well potential, and the target vector can be determined by calculating the centroid of one or more reference student group state vectors, and the value of the target potential well potential can be determined by a preset function, an example form of which is: ; wherein is a normal number, denotes the Euclidean distance; denotes the square of the Euclidean distance.

[0016] Preferably, the step of constructing the literacy coupling potential includes: constructing the literacy coupling potential by a preset coupling function for characterizing the internal interaction relationship between different literacy dimensions. For example, a preset binary coupling function may be used to characterize the interaction relationship between the literacy of the i-th dimension and the literacy of the j-th dimension, and the values of the i-th dimension and the j-th dimension in the N-dimensional state vector are taken as inputs of the function to determine the literacy coupling potential between the two dimensions, and the total literacy coupling potential can be the sum of the coupling potentials of all dimension pairs: .

[0017] Preferably, the external intervention force vector is set to a zero vector, and the dynamic equation is solved to obtain a baseline natural trajectory in the case of no external intervention; the development trajectory determined by the actual external intervention force is compared and analyzed with the baseline natural trajectory to evaluate the actual effect of the external intervention force, and the evaluation result is taken as part of the comprehensive evaluation result.

[0018] Preferably, the method further includes the following steps: setting at least one assumed external intervention force vector ; taking the N-dimensional state vector at the current time as the initial condition, and iteratively calculating the N-dimensional state vector at time under the joint action of the internal field force and the assumed external intervention force vector to simulate one or more possible future development trajectories; and generating and outputting personalized development suggestions based on the one or more possible future development trajectories.

[0019] The present application provides a student development comprehensive evaluation method based on multi-dimensional literacy indicators. The present application has the following beneficial effects: 1. The present application converts the student development process into a continuous trajectory by establishing a dynamic equation describing the evolution of the N-dimensional state vector with time, which realizes dynamic and process display of the student literacy development, solves the limitation of traditional evaluation that can only provide discrete and static evaluation results, and can intuitively reveal the continuous process and trend of development, thereby providing a more comprehensive evaluation perspective.

[0020] ​​​​​2、 The present application realizes simulation and prediction of multiple possible development paths by introducing an assumed external intervention force vector in the kinetic equation and iteratively calculating the future state, which makes the evaluation system forward-looking and provides quantifiable decision basis for the formulation and selection of personalized education intervention measures, thereby scientifically selecting the best and improving the accuracy of guidance.

[0021] 3、 The present application generates a baseline natural trajectory without intervention by setting the external intervention force in the kinetic model to zero, and compares it with the actual development trajectory, which can quantitatively separate the net effect of external intervention. This design provides a framework for attribution analysis of education intervention measures, making the evaluation of the effectiveness of historical intervention measures no longer dependent on subjective judgment and more objective. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 is the overall flowchart of the present application; Figure 2 is the internal structure diagram of the data acquisition and state vector generation module of the present application; Figure 3 is the internal structure diagram of the dynamic virtual potential field construction module of the present application; Figure 4 is the internal structure diagram of the kinetic evolution and trajectory simulation module of the present application; Figure 5 is the internal structure diagram of the development trajectory analysis and evaluation output module of the present application. DETAILED DESCRIPTION

[0023] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the present application specification. Obviously, the described embodiments are only part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0024] Referring to the drawings Figure 1 , Figure 1 is the structure diagram of the student development comprehensive evaluation system according to an embodiment of the present application. The embodiment of the present application provides a student development comprehensive evaluation method based on multiple literacy indicators, which includes a data acquisition and state vector generation module 10, a dynamic virtual potential field construction module 20, a kinetic evolution and trajectory simulation module 30, and a development trajectory analysis and evaluation output module 40.

[0025] The data acquisition and state vector generation module 10 is configured to acquire multi-dimensional performance data of the student and generate an N-dimensional state vector for describing the state of the student's literacy. The dynamic virtual potential field construction module 20 is connected to the output end of the data acquisition and state vector generation module 10 and is configured to construct an N-dimensional virtual potential field. The dynamics evolution and trajectory simulation module 30 is connected to the output ends of the data acquisition and state vector generation module 10 and the dynamic virtual potential field construction module 20 and is configured to calculate the development trajectory of the student's literacy state over time according to a dynamics equation. The development trajectory analysis and evaluation output module 40 is connected to the output end of the dynamics evolution and trajectory simulation module 30 and is configured to analyze the generated development trajectory and output a comprehensive evaluation result or personalized development suggestion.

[0026] Specifically, the data acquisition and state vector generation module 10 is configured to construct an N-dimensional multi-dimensional literacy space and generate an N-dimensional state vector representing the literacy level of the student at a specific time. The module acquires multi-source heterogeneous data reflecting the literacy performance of the student, such as, but not limited to, academic achievement data, classroom performance records, physical health test data, and records of participation in social practice activities.

[0027] After acquiring the multi-source heterogeneous data, the data acquisition and state vector generation module 10 performs a preprocessing operation on the data, which includes normalizing the data from different sources and with different dimensions.

[0028] N-dimensional position vector consisting of N components, where each component corresponds to the student's literacy level in the i-th dimension at time and the i-th dimension normalized level value.

[0029] The data acquisition and state vector generation module 10 further generates an N-dimensional velocity vector and combines it with the N-dimensional position vector to form a complete N-dimensional state vector .

[0030] wherein: is an N-dimensional state vector representing the overall literacy state of the student at time t; is an N-dimensional position vector; is an N-dimensional velocity vector defined as the derivative of the N-dimensional position vector with respect to time, representing the rate of change of the student's literacy level in each dimension, and for discrete time points and ​The data collected, one way to calculate the N-dimensional velocity vector is to use finite difference method .

[0031] Finally, the data collection and state vector generation module 10 will generate N-dimensional state vector Output to the dynamics evolution and trajectory simulation module 30, as the initial conditions of the dynamics evolution.

[0032] Referring to the accompanying Figure 1 , dynamic virtual potential field construction module 20 input and data collection and state vector generation module 10 output end connection, dynamic virtual potential field construction module 20 function is to build a N-dimensional dynamic virtual potential field , N-dimensional dynamic virtual potential field for each position vector In time A scalar potential value, N-dimensional dynamic virtual potential field data is then output to the dynamics evolution and trajectory simulation module 30.

[0033] In one embodiment, the dynamic virtual potential field By a static base potential field And a dynamic path dependent potential field Linear superposition of: ; Wherein: Characterized by a base development environment that does not change over time, determined by the intrinsic relationship between the educational objectives and the dimension of literacy; Characterized by the influence of the individual historical development path of the student on the current development environment, which is the dynamic part of the time evolution; static base potential field Further composed of target potential well potential And literacy coupling potential Superposition: ; The construction of the target potential well potential First, you need to determine an N-dimensional target vector , N-dimensional target vector Is a point in the N-dimensional literacy space, representing the preset education training target, the determination method of N-dimensional target vector includes, but is not limited to, calculating the barycenter of the N-dimensional position vector of one or more benchmark student groups (such as the excellent student group of a certain year) that meet certain standards at the corresponding time, determine the N-dimensional target vector After that, the target potential well potential Can be calculated by the following formula: ; Where, Is a preset constant, used to adjust the strength of the potential well; represents the current position vector of the student represents the Euclidean distance between the target vector and the current position vector of the student.

[0034] represents the coupling potential of the literacy represents the intrinsic interaction relationship between different literacy dimensions, which is calculated by a pre-set coupling function and takes the values of different dimension components in the N-dimensional position vector as input.

[0035] In one embodiment, the total literacy coupling potential is the sum of the interaction potentials between all pairs of dimensions: where represents the binary coupling function that characterizes the interaction relationship between the th literacy dimension and the th literacy dimension. If the th literacy and the th literacy are mutually promoting, an exemplary function form is: where is a positive coupling coefficient. If the two are mutually inhibitory, the function form can be: .

[0036] represents the dynamic path-dependent potential field , which quantifies the influence of the student's historical development trajectory on his current state. The value of the dynamic path-dependent potential field is determined by accumulating the potential influences generated by all state points on the historical development trajectory. For a discrete time sequence, the calculation method is: ; where is the current time, is the position vector at the historical time ; is the time step; is a contribution function that characterizes the potential contribution of the historical position to any point in the space, where is the current time; is the position vector at the historical time ; is the time step; is the discrete summation symbol, which means that the value of an expression is added multiple times. An exemplary contribution function form is: ; where is a positive constant that represents the influence amplitude; is a time decay coefficient.​​ spatial influence radius; natural constant; state similarity factor; time decay factor.

[0037] Finally, the dynamic virtual potential field construction module 20 outputs the computed total potential field information (e.g., its gradient information at each point in space) to the dynamics evolution and trajectory simulation module 30 as the basis for computing the internal field forces.

[0038] Referring to the accompanying Figure 1 The input terminals of the dynamics evolution and trajectory simulation module 30 are connected to the output terminals of the data acquisition and state vector generation module 10 and the dynamic virtual potential field construction module 20, respectively.

[0039] The core function of the dynamics evolution and trajectory simulation module 30 is to compute the evolution of the N-dimensional state vector over time according to a predetermined dynamics equation, thereby generating one or more development trajectories. In one embodiment, the dynamics equation has the following form: where: is the N-dimensional position vector; is the external intervention force vector; is the internal field force; the gradient operator computes the rate of change of the potential field in the direction of the greatest change in space, with the negative sign indicating that the direction of the internal field force points to the direction of decreasing potential; is the dynamic inertial mass, which is used to represent the inertia of the student's development state, i.e., the degree to which its state vector resists change; represents the inertial term of the system; is the second-order derivative of the state vector with respect to time; is a vector representing the force from the external environment of the system.

[0040] In one specific embodiment, the dynamic inertial mass is a function of the dynamic path-dependent potential field An exemplary functional relationship is: where: is a basic inertial mass constant; is a predetermined normal number.

[0041] Since the dynamics equation is usually a complex nonlinear differential equation, the dynamics evolution and trajectory simulation module 30 uses a numerical integration method for iterative solution. Taking the Euler method as an example, given a time step ​​From the current state vector , the next time state vector is calculated as follows: Calculate the total force at time : ; Calculate the acceleration vector at time : ; Update the velocity vector: ; Update the position vector: .

[0042] By continuously repeating the above steps, a complete development trajectory composed of discrete state points can be generated. Other numerical methods, such as the Runge-Kutta method, can also be used to obtain more accurate solutions.

[0043] The dynamics evolution and trajectory simulation module 30 has two operating modes: Evaluation analysis mode: In this mode, the dynamics evolution and trajectory simulation module 30 sets the external intervention force vector to a zero vector, and then, with the N-dimensional state vector at a certain historical time as the initial condition, solves the dynamics equation by the aforementioned numerical method to obtain a baseline natural trajectory under no external intervention. This baseline natural trajectory is output to the development trajectory analysis and evaluation output module 40 together with the recorded actual development trajectory.

[0044] Prediction suggestion mode: In this mode, the dynamics evolution and trajectory simulation module 30 receives at least one hypothetical external intervention force vector , and the dynamics evolution and trajectory simulation module 30 takes the N-dimensional state vector at the current time as the initial condition, takes as the external intervention force in the dynamics equation, and performs forward iteration calculation to simulate a possible future development trajectory. If multiple different hypothetical external intervention force vectors are input, multiple corresponding future development trajectories will be simulated, and all simulated trajectories are output to the development trajectory analysis and evaluation output module 40.

[0045] Referring to the attached Figure 1, the input end of the development trajectory analysis and evaluation output module 40 is connected with the output end of the kinetic evolution and trajectory simulation module 30, the function of the evaluation output module 40 is to receive one or more development trajectory data generated by the kinetic evolution and trajectory simulation module 30 (which is essentially a set of N-dimensional state vectors sorted by time), and to perform quantitative analysis on it to generate a structured evaluation result, in an embodiment, the quantitative analysis is realized by feature extraction on the trajectory, specifically including calculating a set of quantifiable feature indicators, such as: the end position of the trajectory at the preset time point, the time required to reach the preset target area, the total length of the trajectory, and the separation degree of two different trajectories, etc., the evaluation output module 40 finally generates a comprehensive evaluation result or personalized development suggestion based on the feature indicators.

[0046] When the kinetic evolution and trajectory simulation module 30 works in the evaluation analysis mode, the development trajectory analysis and evaluation output module 40 receives an actual development trajectory and a benchmark natural trajectory, the development trajectory analysis and evaluation output module 40 quantifies the actual effect of external intervention by calculating the separation degree between the two trajectories, one way to calculate the separation degree is the time-averaged Euclidean distance : ; wherein, is the position vector of the actual development trajectory, is the position vector of the benchmark natural trajectory, is the evaluation time period, is the time-averaged operator, is the instantaneous Euclidean distance, representing the straight-line distance between the points on the two trajectories at any time , the development trajectory analysis and evaluation output module 40 combines the calculated separation degree indicator and other data such as the end position of the two trajectories into a comprehensive evaluation result and outputs it.

[0047] When the kinetic evolution and trajectory simulation module 30 works in the prediction suggestion mode, the development trajectory analysis and evaluation output module 40 receives multiple future simulation development trajectories respectively corresponding to different hypothetical external intervention force vectors, the development trajectory analysis and evaluation output module 40 sorts these simulation trajectories according to one or more preset optimization criteria, non-limiting examples of the optimization criteria include: minimum arrival time: select the trajectory that enters the preset target area first; best end point proximity: at the end of the simulation, select the trajectory with the smallest Euclidean distance between the end position and the target vector .

[0048] After the sorting is completed, the development trajectory analysis and evaluation output module 40 identifies the assumed external intervention force vector corresponding to the optimal trajectory, and finally, the development trajectory analysis and evaluation output module 40 generates a personalized development suggestion that explicitly indicates the adoption of the external intervention measure associated with the optimal trajectory, and outputs the suggestion.

[0049] Referring to the accompanying drawings Figure 2 , the data collection and state vector generation module 10 of the present application comprises a data collection unit 11, a data preprocessing and normalization unit 12, and a state vector generation unit 13.

[0050] The data collection unit 11 serves as a data input interface and communicates with one or more external data source systems (non-limiting examples include student management systems, online learning management systems, physical health management systems, etc.) through a predetermined data interface (for example, by calling an API or executing a database query) to obtain original data records related to student literacy performance containing student identifiers and timestamps.

[0051] The output end of the data preprocessing and normalization unit 12 is connected to the input end of the state vector generation unit 13, and the function of the data preprocessing and normalization unit 12 is to sequentially perform data cleaning, data type conversion, and numerical normalization operations on the received multi-source heterogeneous original data, wherein data cleaning is used to handle missing values (for example, using mean filling) or outliers; data type conversion is used to quantize non-numeric data (such as descriptive grades "excellent") according to a predetermined mapping rule; finally, all dimensions of numerical data are normalized and the processed data is output to the state vector generation unit 13.

[0052] In one embodiment, the data preprocessing and normalization unit 12 uses the min-max normalization method to linearly map the original numerical value of each literacy dimension to the interval [0, 1]. The calculation formula is as follows: ; wherein: is the normalized numerical value of the dimension literacy; is the original numerical value of the dimension literacy; is the preset maximum value of the original numerical value of the dimension literacy; is the preset minimum value of the original numerical value of the dimension literacy, and the preset maximum value and minimum value The aptitude index can be determined according to its inherent scale (for example, the maximum value of a percentage test score is 100 and the minimum value is 0), or obtained by statistical analysis of historical data.

[0053] Finally, the data preprocessing and normalization unit 12 will generate a set of N normalized values for each student at a specific time point , which is output to the state vector generation unit 13.

[0054] Referring to the accompanying drawings Figure 2 , the input end of the state vector generation unit 13 is connected with the output end of the data preprocessing and normalization unit 12, and the output end of the state vector generation unit 13 is the output end of the entire data acquisition and state vector generation module 10. The state vector generation unit 13 receives a set of N normalized dimension aptitude index values output by the data preprocessing and normalization unit 12, and constructs and outputs an N-dimensional state vector representing the complete dynamics of the student according to these dimension aptitude index values.

[0055] In one specific embodiment, the N-dimensional state vector generation state vector generation unit 13 first receives N normalized values and constructs an N-dimensional position vector .

[0056] ; Subsequently, the state vector generation unit 13 calculates and generates an N-dimensional velocity vector based on the position vector data on the time series , since the student data is collected at discrete time points (for example, , the state vector generation unit 13 uses the backward finite difference method to approximately calculate the velocity vector at the current time , and the calculation formula is as follows: ; , where: is the N-dimensional velocity vector calculated at the current time ; is the N-dimensional position vector generated at the current time ; is the N-dimensional position vector generated at the previous data acquisition time ; and is the time interval between two consecutive data acquisition times, and for the initial time , since there is no data at the previous time, its initial velocity vector can be set to a zero vector.

[0057] Finally, the state vector generation unit 13 will generate an N-dimensional position vector and an N-dimensional velocity vector Combine them to form a complete N-dimensional state vector. : .

[0058] See attached document Figure 3 , Figure 3 This is an internal structural block diagram of a dynamic virtual potential energy field construction module 20 according to an embodiment of the present invention. The dynamic virtual potential energy field construction module 20 may include: a static basic potential energy field construction unit 21 and a dynamic path-dependent potential energy field construction unit 22. The static basic potential energy field construction unit 21 further includes a target potential well potential energy construction subunit 211 and a literacy coupling potential energy construction subunit 212.

[0059] The target potential well construction subunit 211 functions to construct a target potential well in the N-dimensional literacy space to characterize the overall development goal. : The first step is to determine the N-dimensional target vector. ; In one specific embodiment, the target vector is determined by statistically calculating the N-dimensional position vector of a preset benchmark student group. For example, if M students who meet specific criteria are selected to form a benchmark group, the target vector can be calculated as the centroid of the N-dimensional position vector of this group. ;in: It is the total number of students in the baseline student group; It is the first in the benchmark group N-dimensional position vectors of each student; This is the average factor; It is the summation symbol, for from arrive Perform a traversal, that is, traverse every student in the baseline group.

[0060] The second step is to construct the potential energy function of the target potential well. The target potential well potential energy construction sub-unit 211 uses the determined N-dimensional target vector. The location is constructed at the minimum point of the potential energy function, which in one embodiment takes the form of an anisotropic quadratic function: ;in: It is a vector at any position. The One component; It is the target vector The One component; It is a pre-defined positive constant, called the first positive constant. The potential well stiffness coefficient of the dimension; This is the summation of N-dimensional components, which represents the summation of the system from the Nth dimension. Dimension to the The potential energy contribution generated by each dimension of the dimensional array is summed up to obtain the total potential well energy.

[0061] The target potential well potential energy construction subunit 211 will use the potential energy function The calculation results or their parameters (e.g., all) and Output the value of (the value).

[0062] See attached document Figure 3 The static basic potential energy field construction unit 21 also includes a literacy coupling potential energy construction subunit 212. The function of the literacy coupling potential energy construction subunit 212 is to construct literacy coupling potential energy to characterize the intrinsic interaction relationship between different literacy dimensions in the N-dimensional literacy space. .

[0063] In one specific embodiment, the literacy coupling potential energy construction subunit 212 converts the total literacy coupling potential energy Defined as all different dimension pairs The sum of the potential energy of the interactions between them is calculated using the following formula: ;in: and They are N-dimensional position vectors The The and the first One component; It is a pre-defined binary coupling function used to quantize the first... Dimensional literacy and the first The interaction between dimensional literacy.

[0064] Binary coupling function The specific form is based on the first Dimensions and the The type of relationship between dimensional competencies (e.g., synergistic or mutually inhibiting) determines the relationship. For a synergistic relationship, an exemplary functional form is: ;in, It is a preset, positive positive number, called the cooperative coupling coefficient.

[0065] For a mutually inhibiting relationship, an exemplary functional form is: ;in, It is a preset, positive positive constant, called the suppression coupling coefficient. In this functional form, when and When the values of both the two dimensions increase, a positive potential energy term will be generated, thus having a lifting effect on the total potential energy of the system.

[0066] In one embodiment, the coupling coefficients of all pairs of dimensions (e.g., the above-mentioned and ) are stored in a coupling matrix , the value of the matrix element characterizes the coupling strength and type (positive value means inhibition, negative value means synergy) between the th dimension and the th dimension, and the matrix is a symmetric matrix (i.e., ), the diagonal element is 0.

[0067] After the total aptitude coupling potential energy is calculated by the aptitude coupling potential energy construction subunit 212, it is outputted.

[0068] Referring to the accompanying drawings, the dynamic virtual potential field construction module 20 further comprises a dynamic path-dependent potential field construction unit 22, the input end of the dynamic path-dependent potential field construction unit 22 is used for receiving student historical development trajectory data, i.e., a time-ordered sequence of N-dimensional position vectors Figure 3 . The function of the dynamic path-dependent potential field construction unit 22 is to construct a time-evolving, dynamic path-dependent potential field based on the historical trajectory data, and output the data of the potential field.

[0069] In one specific embodiment, the dynamic path-dependent potential field construction unit 22 calculates the path-dependent potential field at the current time by accumulating the potential energy effects generated at all discrete time points on the student historical trajectory, and the calculation formula is as follows: ; wherein: is any point in the N-dimensional aptitude space; is the current time; is the N-dimensional position vector at the historical time ; is the th time step; is a contribution function, which is used to quantify the potential energy contribution of the state at the historical time to the current time space point .

[0070] The contribution function ​​​One exemplary form is a Gaussian function, which is expressed as: wherein: is a constant number; is a spatial point is the Euclidean distance between the historical trajectory point is a state similarity factor; is a time decay factor; is an exponential function with a natural constant as the base; is a time decay coefficient; is a spatial influence radius.

[0071] Finally, the dynamic path-dependent potential field construction unit 22 superimposes the calculated and the output of the static basic potential field construction unit 21 to form a complete dynamic virtual potential field The complete potential field information is output to the dynamics evolution and trajectory simulation module 30.

[0072] Referring to the accompanying Figure 4 , Figure 4 is an internal structure block diagram of the dynamics evolution and trajectory simulation module 30 according to an embodiment of the present application. The dynamics evolution and trajectory simulation module 30 can include a core dynamics equation unit 31 and a trajectory solving and simulation unit 32.

[0073] The core dynamics equation unit 31 receives potential field data from the dynamic virtual potential field construction module 20 at the input end. The function of the core dynamics equation unit 31 is to establish an N-dimensional vector differential equation that describes the law of evolution of the N-dimensional position vector over time.

[0074] In a specific embodiment, the core dynamics equation is established as follows: The left side term of this equation represents the acceleration of the student literacy state, where is the dynamic inertial mass, is an N-dimensional acceleration vector.

[0075] The first term on the right side of the equation is an internal field vector which is uniquely determined by the dynamic virtual potential field The core dynamics equation unit 31 obtains this internal field by calculating the negative gradient of the dynamic virtual potential field at the position , and the calculation formula is: ​ ;in, It is an N-dimensional gradient operator, defined as follows: Therefore, the intrinsic field force vector Each component The calculation method is as follows .

[0076] The second term on the right-hand side of the equation is the vector of the external intervention force. This vector is an N-dimensional vector. This is used to quantify the impact of external interventions on students across various competency dimensions. Each component of this vector... Characterization in time Apply to the The type and intensity of external interventions in dimensional literacy, for example, an intensive tutoring program for mathematical ability, can be set as an external intervention force vector that is non-zero only on the dimensional components of the corresponding mathematical ability.

[0077] The core dynamic equation unit 31 outputs the established complete dynamic equations, with all parameters defined, to the trajectory solving and simulation unit 32.

[0078] See attached document Figure 4 In establishing the core dynamic equations, the core dynamic equation unit 31 introduces dynamic inertial mass. This scalar parameter.

[0079] In one specific embodiment, dynamic inertial mass It is not a pre-set constant, but a function that depends on the student's historical development trajectory. Core dynamic equation unit 31 establishes dynamic inertial mass. With dynamic path-dependent potential field This property is achieved through the functional relationship between them, using a dynamic path-dependent potential field. The value is calculated and provided by the dynamic path-dependent potential field building unit 22, and an exemplary functional relationship is as follows: ;in: It is in time When the student's position vector is The dynamic inertial mass value at that time; It is a preset, positive-zero fundamental inertial mass constant; It is a preset path influence coefficient, greater than or equal to zero, used to adjust the intensity of the influence of historical development trajectory on the magnitude of inertial mass; It is the dynamic path-dependent potential field at the student's current position. and time The absolute value of the potential energy.

[0080] The core dynamics equation unit 31 re-computes the value of the dynamic inertial mass at each time step, based on the current position vector and time, and applies it to the dynamics equation, passing the complete, parameterized equation to the trajectory solving and simulation unit 32.

[0081] Referring to the drawings Figure 4 , the dynamics evolution and trajectory simulation module 30 further includes a trajectory solving and simulation unit 32, which is connected to the output of the core dynamics equation unit 31. The trajectory solving and simulation unit 32 receives the N-dimensional second-order vector differential equation, fully parameterized, established by the core dynamics equation unit 31, as well as an N-dimensional state vector as the initial condition for the solution. The function of the trajectory solving and simulation unit 32 is to solve the differential equation using a numerical integration method, with a pre-determined time step , and thereby generate a time-evolving trajectory consisting of discrete state points.

[0082] In one specific embodiment, the trajectory solving and simulation unit 32 uses the velocity Verlet algorithm for numerical integration, starting from the state vector at the current time , to compute the state vector at the next time . The detailed steps are as follows: 1. Compute the acceleration at the current time: first, compute the total force and the dynamic inertial mass based on the position and the current time , and thereby obtain the current acceleration vector .

[0083] ; 2. Compute the position at the next time: directly compute the position vector at the next time using the position, velocity, and acceleration at the current time.

[0084] ; 3. Compute the acceleration at the next time: re-compute the total force and the dynamic inertial mass based on the newly computed position vector and the next time , and thereby obtain the acceleration vector at the next time .

[0085] ; ​4. Calculate the velocity at the next time step: Using the velocity at the current time step, and the average of the acceleration at the current time step and the acceleration at the next time step, calculate the velocity vector at the next time step. .

[0086] ; Trajectory solving and simulation unit 32 executes steps 1 to 4 above in a loop, starting from the initial time. Initially, a series of state vectors are generated sequentially { The set of these vectors constitutes a complete, discretized development trajectory.

[0087] See attached document Figure 4 The trajectory solving and simulation unit 32 has an evaluation and analysis operation mode. In this evaluation and analysis mode, the trajectory solving and simulation unit 32 first receives a specified historical time. And the actual N-dimensional state vector recorded from the data acquisition and N-dimensional state vector generation module 10 at that time. .

[0088] Subsequently, the trajectory solving and simulation unit 32 performs a crucial parameter setting on the core dynamic equations: from historical time... up to the current time Throughout the entire simulation time interval, the external intervention force vector will be... Forced to be an N-dimensional zero vector, that is, for any They all .

[0089] After the parameter settings are completed, the trajectory solving and simulation unit 32 will generate the historical state vector. As initial conditions for numerical solution, and by invoking the aforementioned numerical solution method (e.g., the velocity Verlet algorithm), from... Start with time step Iterate forward until the current time. .

[0090] Through the above calculation process, the trajectory solving and simulation unit 32 generates a simulated "baseline natural trajectory", which consists of a series of N-dimensional state vectors. constitute.

[0091] See attached document Figure 4 The trajectory solving and simulation unit 32 also has a prediction suggestion operation mode. In the prediction suggestion mode, the trajectory solving and simulation unit 32 first receives a current N-dimensional state vector as the starting point of the simulation. , the current N-dimensional state vector is generated by the data acquisition and N-dimensional state vector generation module 10 according to the latest data, at the same time, the trajectory solving and simulation unit 32 also receives a set of P different assumed external intervention force vectors , each vector represents a preset intervention strategy from the current time to a preset future time .

[0092] In a specific embodiment, these assumed external intervention force vectors can be constructed as vectors that remain constant within the simulation time interval , for example, a vector may only have a normal value in the dimension component corresponding to "logical reasoning ability", and other components are zero, which represents a single-point intervention strategy focusing on improving logical reasoning ability, another vector may have non-zero values in multiple dimension components, representing a balanced intervention strategy in multiple aspects.

[0093] The trajectory solving and simulation unit 32 then performs a loop calculation process, the number of iterations is , in the th iteration: set the initial condition of the numerical solution to the current state vector ; in the core dynamic equation, set the external intervention force term to the th assumed intervention force vector ; call the aforementioned numerical solution method, iterate from , with a time step , until the future time ; this iteration generates a complete future simulation development trajectory corresponding to the intervention strategy ; when the loop process is completed, the trajectory solving and simulation unit 32 generates different future simulation development trajectories; finally, the trajectory solving and simulation unit 32 outputs these future simulation development trajectories and their respective assumed external intervention force vectors as a data set to the development trajectory analysis and evaluation output module 40.

[0094] Referring to the accompanying Figure 5 , Figure 5 is the internal structure block diagram of the development trajectory analysis and evaluation output module 40 according to an embodiment of the present application, the development trajectory analysis and evaluation output module 40 can include: a trajectory feature extraction unit 41, a trajectory evaluation and sorting unit 42, and a visualization and report generation unit 43.

[0095] The trajectory feature extraction unit 41 receives one or more development trajectories from the trajectory solving and simulation unit 32 at its input end. Each trajectory is a time series composed of N-dimensional state vectors. }

[0096] In one specific embodiment, the trajectory feature extraction unit 41 calculates at least the following four types of feature indicators: 1. Goal Achievement Metric: This metric is used to quantify the trajectory's achievement at the end time. The degree of closeness between the current state and the preset development goal can be calculated in one exemplary way: by calculating the trajectory endpoint position vector. With the target vector Negative Euclidean distance between : .

[0097] 2. Development Balance Indicator: An exemplary calculation method is to calculate the endpoint position vector. The reciprocal of the standard deviation of each component value : ;in It is the average value of all components of the endpoint position vector.

[0098] 3. Development efficiency indicators: An exemplary calculation method is to calculate the straightness of the trajectory. That is, the ratio of the straight-line distance from the starting point to the ending point of the trajectory to the actual arc length of the trajectory: .

[0099] 4. Development Stability Index: An exemplary calculation method is to calculate the root mean square value of the acceleration magnitude over the entire trajectory. The reciprocal: ;in That is the total duration.

[0100] For each input trajectory, the trajectory feature extraction unit 41 calculates the aforementioned set (or other preset) feature indicators and combines them into a feature vector, for example... .

[0101] See attached document Figure 5 The development trajectory analysis and evaluation output module 40 also includes a trajectory evaluation and ranking unit 42. The input end of the trajectory evaluation and ranking unit 42 is connected to the output end of the trajectory feature extraction unit 41. The trajectory evaluation and ranking unit 42 receives one or more sets of trajectory feature vectors output by the trajectory feature extraction unit 41. Its function is to calculate a comprehensive evaluation score for each trajectory according to a preset evaluation model, and rank multiple trajectories based on the score.

[0102] In one embodiment, the trajectory evaluation and ranking unit 42 employs a linear weighted summation method to calculate the overall evaluation score Q of each trajectory, which is calculated as follows: wherein: is the total dimension of the feature vector, is the preset weight coefficient of the th feature index, all weight coefficients are non-negative numbers, and satisfy These weight coefficients can be configured according to the specific training objectives and value orientation.

[0103] is the normalized value of the th feature index, in order to eliminate the influence of different feature index factors due to different dimension and numerical range, the trajectory evaluation and ranking unit 42 first performs maximum-minimum normalization processing on each component of the received feature vector , and maps it to the interval .

[0104] The workflow of the trajectory evaluation and ranking unit 42 is adjusted according to the number and type of trajectories it receives: In the evaluation analysis mode: the trajectory evaluation and ranking unit 42 receives two feature vectors corresponding to the actual development trajectory and the benchmark natural trajectory, respectively, and calculates the overall evaluation scores and for the two trajectories, then quantifies and evaluates the overall benefit of the external intervention measures implemented in the historical period by calculating the difference or the ratio between the two.

[0105] In the prediction suggestion mode: the trajectory evaluation and ranking unit 42 receives feature vectors corresponding to future simulated development trajectories, and calculates the overall evaluation score for each trajectory. Subsequently, the trajectory evaluation and ranking unit 42 ranks the trajectories in descending order according to the calculated scores.

[0106] Finally, the trajectory evaluation and ranking unit 42 outputs the calculated overall evaluation scores and ranking results, together with the original trajectory data and feature vectors, to the visualization and report generation unit 43.

[0107] Referring to the attached Figure 5The development trajectory analysis and evaluation output module 40 further comprises a visualization and report generation unit 43, the input end of which is connected with the output end of the trajectory evaluation and ranking unit 42, and the function of the visualization and report generation unit 43 is to present the analysis and evaluation results in the form of graphical and textual reports that are easy for human users to understand.

[0108] In one specific embodiment, the visualization and report generation unit 43 generates at least the following visualizations and report contents: 1. N-dimensional trajectory dimension reduction visualization: The visualization and report generation unit 43 uses principal component analysis dimension reduction technology to project the N-dimensional trajectory data (i.e. the sequence of position vectors) into a two-dimensional or three-dimensional space for visualization. In the generated graph, multiple trajectories (e.g. actual trajectory and benchmark trajectory, or multiple predicted trajectories) can be plotted simultaneously and distinguished using different colors or line types. In addition, the starting point, ending point and preset N-dimensional target vector of the trajectory are also explicitly marked in the graph. the corresponding position in the dimension reduction space.

[0109] 2. Multidimensional literacy radar chart: To achieve visualization, the visualization and report generation unit 43 generates a multidimensional literacy radar chart, in which each radial axis corresponds to a literacy dimension, and the value on the axis represents the normalized literacy level of that dimension, to visually show the literacy state distribution of the student at a specific time point.

[0110] Subsequently, the visualization and report generation unit 43 integrates the radar chart, trajectory dimension reduction chart, etc. into a report together with various quantitative indicators. The comprehensive analysis report at least includes: overall evaluation giving a comprehensive evaluation score Q and ranking; itemized details of characteristic index values such as target achievement, development balance, development efficiency and development stability in table form; and explanatory text automatically generated according to the evaluation results. Finally, the visualization and report generation unit 43 outputs this comprehensive analysis report with graphs and texts, providing decision-making basis for decision-makers to formulate or adjust the training plan.

[0111] Referring to the accompanying drawings Figure 1 , Figure 1 is a total block diagram of the method implementation process according to an embodiment of the present application. The overall implementation process of the method provided by the present application is described as follows: Generating an initial state vector: At the beginning of the method, the data acquisition and state vector generation module 10 first performs operations. The data acquisition and state vector generation module 10 acquires the original data of the student in N literacy dimensions, processes the data through the data preprocessing and normalization unit 12, and constructs an N-dimensional state vector representing the current state of the student by the state vector generation unit 13 The N-dimensional state vector contains the information of students' "position" and "velocity" of each dimension at the current time, which is used as the initial condition for all subsequent dynamic simulations.

[0112] Building dynamic virtual potential field: Then, the dynamic virtual potential field building module 20 builds the potential field for the dynamic evolution based on the preset training target and the historical development trajectory of the student. The static basic potential field building unit 21 first establishes a static basic potential field that does not change with time The static basic potential field is superimposed by a "target potential well" pointing to the preset development target and a "coupling potential" describing the internal interaction between each dimension of literacy, and at the same time, the dynamic path-dependent potential field building unit 22 generates a dynamic potential field that evolves with time and has lower potential on the historical path according to the historical N-dimensional position vector sequence of the student The two parts of potential are finally superimposed to form a complete dynamic virtual potential field .

[0113] Solving the dynamic equation and simulating the trajectory: The dynamic evolution and trajectory simulation module 30 is the core calculation engine of the whole method. The core dynamic equation unit 31 first establishes an N-dimensional vector differential equation The force in the equation is determined by the gradient of the built potential field and the external intervention force vector , and a dynamic inertia mass related to the path-dependent potential field is also introduced Then, the trajectory solving and simulation unit 32 sets the corresponding external intervention force according to the user's specific needs (evaluation analysis or prediction suggestion) , and uses the numerical integration algorithm (such as the velocity Verlet algorithm) to solve the equation with the generated current state vector as the initial condition, to generate one or more discrete development trajectories.

[0114] Analyzing and evaluating the trajectory and generating the report: Finally, the development trajectory analysis and evaluation output module 40 interprets and presents the simulation trajectories generated in the previous steps. The trajectory feature extraction unit 41 first calculates multi-dimensional feature indicators such as target achievement, development balance, efficiency and stability from each trajectory, the trajectory evaluation and sorting unit 42 calculates a comprehensive evaluation score for each trajectory according to these feature indicators and preset weights, and sorts the predicted trajectories generated by different intervention schemes. Finally, the visualization and report generation unit 43 integrates all quantitative results into an intuitive and easy-to-understand analysis report in the form of dimensionality reduction trajectory chart, radar chart and comprehensive analysis text, and outputs it.

[0115] By repeatedly executing the above steps, the present application can continuously track the dynamic development of students and provide them with data-driven and personalized development evaluation and decision-making suggestions.

Claims

1. A comprehensive evaluation method for student development based on multi-dimensional literacy indicators, characterized in that, The method comprises the following steps: constructing an N-dimensional multidimensional literacy space, and generating an N-dimensional state vector representing the literacy level of a student at a certain time according to the collected multidimensional performance data of the student; in the N-dimensional multidimensional literacy space, a virtual potential field is constructed, which gives each point in the space a potential value; a dynamic equation describing the evolution of the N-dimensional state vector over time is established, in which the evolution of the N-dimensional state vector is affected by the internal field force and the external intervention force, and the internal field force is determined by the gradient of the virtual potential field; determining the development trajectory formed by the change of the N-dimensional state vector over time according to the dynamic equation; generating a comprehensive evaluation result of the student's development based on the development trajectory.

2. The method for comprehensive evaluation of student development based on multi-dimensional literacy indicators according to claim 1, characterized in that, The step of generating the N-dimensional state vector further comprises: collecting multi-source heterogeneous data reflecting the literacy performance of the student; normalizing the multi-source heterogeneous data to generate each component of the N-dimensional state vector. 3.The method of claim 1, wherein, The virtual potential field is a dynamic total potential field, which is superimposed by a static basic potential field and a dynamic path-dependent potential field; The value of the dynamic path-dependent potential field is determined by the development trajectory determined by the historical position of the N-dimensional state vector. 4.The method of claim 3, wherein, The calculation step of the dynamic path-dependent potential field comprises: for any point in the N-dimensional multidimensional literacy space, the path-dependent potential value is determined by integrating or summing the potential effects of all N-dimensional state vectors on the historical development trajectory over time. 5.The method of claim 3, wherein, The dynamic equation includes a dynamic inertial mass, which is a function of the dynamic path-dependent potential field. 6.The method of claim 3, wherein, The construction step of the static basic potential field comprises: the position of the target vector representing the educational target in the N-dimensional multidimensional literacy space is set as the center of potential energy minimum, and a target potential well potential is constructed; a preset coupling function is used to construct a literacy coupling potential, which represents the internal interaction relationship between different literacy dimensions. The target potential well potential and the literacy coupling potential are superimposed to form the basic potential field.

7. The method for comprehensive evaluation of student development based on multi-dimensional literacy indicators according to claim 6, characterized in that, The step of constructing the target potential well potential comprises: the target vector is determined by calculating the centroid of one or more reference student group state vectors, and the Euclidean distance between the N-dimensional state vector and the target vector is taken as the input of the preset function to obtain the value of the target potential well potential, which is the target potential well potential. 8.The method of claim 6, wherein, The construction step of the literacy coupling potential comprises: a preset binary coupling function is used to represent the internal interaction relationship between different literacy dimensions, and the values of at least two different dimension components in the N-dimensional state vector are taken as the input of the function to obtain the value of the literacy coupling potential, which is the literacy coupling potential. 9.The multi-dimensional literacy index based student development comprehensive evaluation method according to claim 1, wherein, The method further comprises the following steps: set the external intervention force to zero and solve the dynamic equation to obtain a baseline natural trajectory without external intervention; The development trajectory is compared with the benchmark natural trajectory to evaluate the actual effect of the external intervention force and as part of the comprehensive evaluation result. 10.The method of claim 1, wherein, Further comprising the following steps: Setting at least one assumed external intervention force; Using the N-dimensional state vector at the current time as the initial condition, calculating the N-dimensional state vector at the future time under the joint action of the internal field force and the assumed external intervention force vector, thereby simulating one or more possible future development trajectories; Generating personalized development suggestions and outputting based on the one or more possible future development trajectories.

Images