Mathematics virtual-real fusion teaching system

Abstract

The invention discloses a mathematics virtual-real fusion teaching system. A scene construction module is used for constructing a virtual teaching scene by using a virtual reality technology according to teaching contents and learning requirements of students; the animation simulation module is used for creating a mathematical model and an animation in the virtual teaching scene by utilizing a three-dimensional modeling technology and an animation production technology; the data acquisition module is used for acquiring learning behavior data and physiological data of students through the intelligent teaching terminal and the wearable sensor to obtain learning feedback data; analyzing the learning feedback data by using a machine learning algorithm to obtain learning state data of the student; and the teaching feedback module is used for adjusting a teaching mode and a teaching scene in the virtual teaching scene according to the learning state data. Through virtual reality and augmented reality technologies, in combination with a highly vivid virtual teaching scene and an innovative interaction mode, mathematics learning is more vivid and interesting, and the learning interest of students is greatly improved.

Description

Technical Field

[0001] The invention relates to the field of virtual technology, in particular to a mathematics virtual-real fusion teaching system. Background Art

[0002] Traditional teaching is difficult to present abstract mathematical concepts intuitively. Mathematics is a highly abstract subject, and many concepts such as functions and properties of geometric figures are difficult for students to understand. In traditional classrooms, teachers usually explain these concepts through verbal explanations and simple graphic drawing, but this method cannot allow students to truly "see" and "touch" mathematical objects, and it is difficult to form a deep impression in students' minds. For example, when explaining solid geometry, it is difficult for students to imagine the shape and relationship of objects in three-dimensional space only through the display of plane figures, resulting in insufficient understanding of related knowledge. The traditional teaching process is relatively boring and lacks interactivity. Classes are often teacher-centered, and students passively listen and take notes, and rarely have the opportunity to actively participate in the teaching process. This one-way knowledge transmission method can easily make students feel tired and bored, reducing their enthusiasm for learning. Moreover, due to the lack of interaction, it is difficult for teachers to accurately understand students' learning situation and needs, and they cannot adjust teaching strategies in time, which further affects the teaching effect. Summary of the invention

[0003] The purpose of the present invention is to solve the above problems and to design a mathematics virtual-real fusion teaching system.

[0004] To achieve the above object, the technical solution of the present invention is that, further, in the above-mentioned mathematics virtual-reality fusion teaching system, the mathematics virtual-reality fusion teaching system includes the following modules:

[0005] The scene construction module is used to construct a virtual teaching scene using virtual reality technology according to the teaching content and students' learning needs;

[0006] An animation simulation module, used for creating mathematical models and animations in the virtual teaching scene by using three-dimensional modeling technology and animation production technology;

[0007] The data collection module is used to collect students' learning behavior data and physiological data through intelligent teaching terminals and wearable sensors to obtain learning feedback data;

[0008] A teaching analysis module is used to analyze the learning feedback data using a machine learning algorithm to obtain the student's learning status data;

[0009] The teaching feedback module is used to adjust the teaching method and teaching scene in the virtual teaching scene according to the learning status data.

[0010] Furthermore, in the above-mentioned mathematics virtual-real integration teaching system, the scene construction module includes the following submodules:

[0011] An acquisition submodule is used to acquire teaching content and students' learning needs, wherein the teaching content at least includes mathematical formulas and mathematical equations, and the learning needs at least include teaching arrangements and teaching progress;

[0012] The construction submodule is used to construct a virtual space of geometric shapes and a function image world of dynamic demonstration according to the teaching content to obtain an initial virtual scene;

[0013] The simulation submodule is used to use the Unity virtual reality engine to perform physical simulation of the light and shadow effects of the initial virtual scene to obtain a virtual teaching scene.

[0014] Furthermore, in the above-mentioned mathematics virtual-real integration teaching system, it is characterized in that the animation simulation module includes the following submodules:

[0015] A creation submodule is used to create a three-dimensional shape of a mathematical model using Maya three-dimensional modeling software, and adjust the material and texture of the three-dimensional shape;

[0016] A submodule is obtained, which is used to dynamically construct a function image according to a function formula by using a parametric modeling technology to obtain an image model.

[0017] Furthermore, in the above-mentioned mathematics virtual-real integration teaching system, the teaching analysis module includes the following submodules:

[0018] A data collection submodule is used to collect students' learning behavior data and academic performance data, and use the learning behavior data as an independent variable and the academic performance data as a dependent variable;

[0019] The model building submodule is used to assume that there is a linear relationship between the dependent variable and the independent variable, that is, y = β0 + β1x1 + β2x2 + ... + βx, where y is the dependent variable, x1, x2, ..., x are independent variables, and β0, β1, β2, ..., β are the parameters to be estimated;

[0020] The parameter estimation submodule is used to estimate the parameters β0, β1, β2, ..., β using the least squares method;

[0021] The model evaluation submodule is used to evaluate the performance of the regression model using the mean square error (MSE) to obtain the target regression model.

[0022] The prediction submodule is used to predict the learning performance according to the new learning behavior data of the students by using the target regression model.

[0023] Furthermore, in the above-mentioned mathematics virtual-real integration teaching system, the teaching analysis module also includes the following submodules:

[0024] A data preparation submodule is used to collect students' physiological data, normalize and denoise the physiological data in sequence, and divide the processed data into a training set, a validation set, and a test set;

[0025] A model building submodule, used to build a CNN convolutional neural network model, wherein the CNN convolutional neural network model includes at least a convolutional layer, a pooling layer, and a fully connected layer, wherein the convolutional layer is used to extract data features, the pooling layer is used to reduce the dimension of the data, and the fully connected layer is used to perform regression;

[0026] A model training submodule is used to train the CNN convolutional neural network model using a training set, continuously adjust the parameters of the model through a back propagation algorithm, and set the loss function to a cross entropy loss function;

[0027] A model evaluation submodule is used to evaluate the CNN convolutional neural network model using a validation set, adjust the hyperparameters of the model, and obtain a target CNN convolutional neural network model.

[0028] The prediction submodule is used to test the target CNN convolutional neural network model using a test set, evaluate the generalization ability of the model, input new physiological data into the target CNN convolutional neural network model, and obtain the student's fatigue state and concentration level.

[0029] Furthermore, in the above-mentioned mathematics virtual-real integration teaching system, the teaching feedback module includes the following submodules:

[0030] The extension submodule is used to add extension content and learning challenge content to the virtual teaching scene if students master the content quickly;

[0031] Add sub-modules to gradually increase the difficulty and complexity of teaching content according to the learning progress of students who are gradually improving;

[0032] Provide submodules for adjusting the teaching method and providing more explanations and examples if the students are in difficulty;

[0033] The adjustment submodule is used to automatically adjust the color and brightness in the virtual teaching scene according to the students' fatigue level.

[0034] Furthermore, in the above-mentioned mathematics virtual-reality fusion teaching system, a method for implementing the above-mentioned mathematics virtual-reality fusion teaching system is provided, and the method comprises the following steps:

[0035] According to the teaching content and students' learning needs, virtual reality technology is used to build virtual teaching scenes;

[0036] Using three-dimensional modeling technology and animation production technology to create mathematical models and animations in the virtual teaching scene;

[0037] Collect students’ learning behavior data and physiological data through intelligent teaching terminals and wearable sensors to obtain learning feedback data;

[0038] Analyze the learning feedback data using a machine learning algorithm to obtain the student's learning status data;

[0039] The teaching method and teaching scene in the virtual teaching scene are adjusted according to the learning status data.

[0040] Furthermore, in the above-mentioned mathematics virtual-reality fusion teaching system, a method for implementing the above-mentioned mathematics virtual-reality fusion teaching system is provided, and the method comprises the following steps:

[0041] Collecting students' learning behavior data and learning performance data, taking the learning behavior data as independent variables and the learning performance data as dependent variables;

[0042] Assume that there is a linear relationship between the dependent variable and the independent variable, that is, y = β0 + β1x1 + β2x2 + ... + βx, where y is the dependent variable, x1, x2, ..., x are independent variables, and β0, β1, β2, ..., β are the parameters to be estimated;

[0043] Estimate the parameters β0,β1,β2,...,β using the least squares method;

[0044] Use MSE mean square error to evaluate the performance of the regression model and obtain the target regression model;

[0045] The target regression model is used to predict the learning performance according to the students' new learning behavior data.

[0046] Furthermore, in the above-mentioned mathematics virtual-reality fusion teaching system, a method for implementing the above-mentioned mathematics virtual-reality fusion teaching system is provided, and the method comprises the following steps:

[0047] Collecting students' physiological data, normalizing and denoising the physiological data in turn, and dividing the processed data into a training set, a validation set, and a test set;

[0048] Construct a CNN convolutional neural network model, wherein the CNN convolutional neural network model includes at least a convolutional layer, a pooling layer, and a fully connected layer, wherein the convolutional layer is used to extract data features, the pooling layer is used to reduce the dimension of the data, and the fully connected layer is used to perform regression;

[0049] The CNN convolutional neural network model is trained using the training set, the parameters of the model are continuously adjusted through the back propagation algorithm, and the loss function is set to the cross entropy loss function;

[0050] The CNN convolutional neural network model is evaluated using a validation set, and the hyperparameters of the model are adjusted, wherein the hyperparameters include at least a learning rate, a convolution kernel size, and a number of layers, to obtain a target CNN convolutional neural network model;

[0051] The target CNN convolutional neural network model is tested using the test set to evaluate the generalization ability of the model, and new physiological data are input into the target CNN convolutional neural network model to obtain the student's fatigue status and concentration level.

[0052] Its beneficial effect lies in that, through the scene construction module, it is used to construct a virtual teaching scene using virtual reality technology according to the teaching content and the learning needs of students; the animation simulation module is used to create mathematical models and animations in the virtual teaching scene using three-dimensional modeling technology and animation production technology; the data acquisition module is used to collect students' learning behavior data and physiological data through intelligent teaching terminals and wearable sensors to obtain learning feedback data; the teaching analysis module is used to analyze the learning feedback data using machine learning algorithms to obtain students' learning status data; the teaching feedback module is used to adjust the teaching method and teaching scene in the virtual teaching scene according to the learning status data. Improve learning interest: 1. Through virtual reality and augmented reality technology, combined with highly realistic virtual teaching scenes and innovative interactive methods, mathematics learning is made more vivid and interesting, which greatly improves students' learning interest. 2. Enhance intuitiveness: present abstract mathematical concepts in an extremely intuitive and vivid form to help students better understand and master mathematical knowledge. 3. Strong interactivity: students and teachers can interact and communicate in real time through the interactive teaching platform. At the same time, innovative interactive methods such as gesture recognition technology make the learning process more natural and convenient, and improve teaching effects. 4. Personalized teaching: Provide students with highly personalized learning suggestions and teaching resources based on their learning situation, learning style, interests and hobbies to meet the learning needs of different students. 5. Real-time monitoring and feedback: Wearable sensors can monitor students' learning status in real time and accurately, and provide teachers with timely feedback to adjust teaching strategies. 6. Intelligent tutoring: Intelligent tutoring algorithms combine machine learning technology to provide students with more scientific and effective tutoring and suggestions to help students solve problems encountered in learning. 7. Learning progress management and evaluation: Teachers can comprehensively manage and monitor students' learning progress through the teaching management system, and the evaluation algorithm conducts a multi-dimensional evaluation of students' learning effects, providing reference for teaching and feedback for students. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the following detailed description of the preferred embodiment.The drawings are only for the purpose of illustrating the preferred embodiments and are not to be construed as limiting the invention.

[0054] Figure 1 It is a schematic diagram of a first embodiment of a mathematics virtual-real integration teaching system in an embodiment of the present invention;

[0055] Figure 2 A schematic diagram of a second embodiment of a mathematics virtual-real integration teaching system in an embodiment of the present invention;

[0056] Figure 3 It is a schematic diagram of a third embodiment of a mathematics virtual-reality fusion teaching system in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0058] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a", "an", "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0059] The present invention will be described in detail below in conjunction with the accompanying drawings. Figure 1 As shown, a mathematics virtual-real integration teaching system includes the following modules:

[0060] The scene construction module is used to construct a virtual teaching scene using virtual reality technology according to the teaching content and students' learning needs;

[0061] Specifically, this embodiment also includes an acquisition submodule, which is used to obtain teaching content and students' learning needs, the teaching content at least includes mathematical formulas and mathematical equations, and the learning needs at least include teaching arrangements and teaching progress; a construction submodule, which is used to construct a virtual space of geometric shapes and a dynamically demonstrated function image world according to the teaching content to obtain an initial virtual scene; a simulation submodule, which is used to use the Unity virtual reality engine to perform physical simulation of light and shadow effects on the initial virtual scene to obtain a virtual teaching scene.

[0062] Animation simulation module, which is used to create mathematical models and animations in virtual teaching scenes using 3D modeling technology and animation production technology;

[0063] Specifically, this embodiment also includes a creation submodule, which is used to use Maya three-dimensional modeling software to create a three-dimensional shape of a mathematical model and adjust the material and texture of the three-dimensional shape; an acquisition submodule, which is used to use parametric modeling technology to dynamically construct a function image according to a function formula to obtain an image model.

[0064] The data collection module is used to collect students' learning behavior data and physiological data through intelligent teaching terminals and wearable sensors to obtain learning feedback data;

[0065] Specifically, in this embodiment, the intelligent teaching terminal can record students' learning behavior data such as answering time, accuracy, and number of operations. At the same time, wearable sensors, such as smart bracelets and smart glasses, can collect students' physiological data such as heart rate, body temperature, and attention. These data are transmitted to the server of the teaching system in real time via Bluetooth or wireless network for storage and processing. In order to ensure the accuracy and reliability of the data, data verification and encryption technology are used to prevent data from being tampered with or lost during transmission.

[0066] The teaching analysis module is used to analyze learning feedback data using machine learning algorithms to obtain students’ learning status data;

[0067] Specifically, the present embodiment also includes a data preparation submodule, which is used to collect students' physiological data, normalize and denoise the physiological data in turn, and divide the processed data into a training set, a validation set, and a test set; a model construction submodule, which is used to construct a CNN convolutional neural network model, the CNN convolutional neural network model includes at least a convolutional layer, a pooling layer, and a fully connected layer, the convolutional layer is used to extract data features, the pooling layer is used to reduce the dimension of the data, and the fully connected layer is used for regression; a model training submodule, which is used to train the CNN convolutional neural network model using the training set, continuously adjust the parameters of the model through the back propagation algorithm, and set the loss function to the cross entropy loss function; a model evaluation submodule, which is used to evaluate the CNN convolutional neural network model using the validation set, adjust the hyperparameters of the model, and the hyperparameters include at least the learning rate, the convolution kernel size, and the number of layers to obtain the target CNN convolutional neural network model; a prediction submodule, which is used to test the target CNN convolutional neural network model using the test set, evaluate the generalization ability of the model, input the new physiological data into the target CNN convolutional neural network model, and obtain the student's fatigue state and concentration level.

[0068] Specifically, the present embodiment also includes a data collection submodule, which is used to collect students' learning behavior data and learning performance data, and uses the learning behavior data as the independent variable and the learning performance data as the dependent variable; a model building submodule, which is used to assume that there is a linear relationship between the dependent variable and the independent variable, that is, y = β0 + β1x1 + β2x2 + ... + βx, where y is the dependent variable, x1, x2, ..., x are independent variables, and β0, β1, β2, ..., β are parameters to be estimated; a parameter estimation submodule, which is used to estimate parameters β0, β1, β2, ..., β using the least squares method; a model evaluation submodule, which is used to evaluate the performance of the regression model using the MSE mean square error to obtain a target regression model; a prediction submodule, which is used to use the target regression model to predict the academic performance based on the students' new learning behavior data.

[0069] The teaching feedback module is used to adjust the teaching methods and teaching scenes in the virtual teaching scene according to the learning status data.

[0070] Specifically, the present embodiment also includes an expansion submodule, which is used to add expansion content and learning challenge content to the virtual teaching scene if the student is a quick master; an increase submodule, which is used to gradually increase the difficulty and complexity of the teaching content according to the learning progress of students who are gradually improving; a provision submodule, which is used to adjust the teaching method of the system and provide more explanations and examples if the student is in a difficult situation; and an adjustment submodule, which is used to automatically adjust the color and brightness in the virtual teaching scene according to the student's fatigue level.

[0071] Specifically, in this embodiment, if the student is a quick master, some expansive content and challenges can be added to the virtual teaching scene to stimulate the student's learning potential. For example, some difficult math problems or projects are provided for students to explore. For students who are gradually improving, the difficulty and complexity of the teaching content can be gradually increased according to their learning progress. For example, tasks of different difficulty levels are set in the virtual scene for students to complete step by step. If the student is in a difficult type, the system can adjust the teaching method and provide more explanations and examples. In the virtual teaching scene, some prompts and guidance can be added to help students understand mathematical concepts. At the same time, a virtual teaching assistant can be arranged to answer questions for students at any time. In addition, according to the student's physiological state data, such as fatigue level, the system can automatically adjust the color and brightness of the virtual teaching scene to relieve the student's visual fatigue. If the student is not focused, sound prompts or animation effects can be used to attract the student's attention and improve the learning effect.

[0072] Its beneficial effect lies in that the scene construction module is used to construct a virtual teaching scene using virtual reality technology according to the teaching content and the learning needs of students; the animation simulation module is used to create mathematical models and animations in the virtual teaching scene using three-dimensional modeling technology and animation production technology; the data acquisition module is used to collect students' learning behavior data and physiological data through intelligent teaching terminals and wearable sensors to obtain learning feedback data; the teaching analysis module is used to analyze the learning feedback data using machine learning algorithms to obtain students' learning status data; the teaching feedback module is used to adjust the teaching methods and teaching scenes in the virtual teaching scene according to the learning status data. Improve learning interest: 1. Through virtual reality and augmented reality technology, combined with highly realistic virtual teaching scenes and innovative interactive methods, mathematics learning is made more vivid and interesting, which greatly improves students' learning interest. 2. Enhance intuitiveness: Abstract mathematical concepts are presented in an extremely intuitive and vivid form to help students better understand and master mathematical knowledge. 3. Strong interactivity: Students and teachers can interact and communicate in real time through the interactive teaching platform. At the same time, innovative interactive methods such as gesture recognition technology make the learning process more natural and convenient, and improve teaching effectiveness. 4. Personalized teaching: Provide students with highly personalized learning suggestions and teaching resources based on their learning situation, learning style, interests and hobbies to meet the learning needs of different students. 5. Real-time monitoring and feedback: Wearable sensors can monitor students' learning status in real time and accurately, and provide teachers with timely feedback to adjust teaching strategies. 6. Intelligent tutoring: Intelligent tutoring algorithms combine machine learning technology to provide students with more scientific and effective tutoring and suggestions to help students solve problems encountered in learning. 7. Learning progress management and evaluation: Teachers can comprehensively manage and monitor students' learning progress through the teaching management system, and the evaluation algorithm conducts a multi-dimensional evaluation of students' learning effects, providing reference for teaching and feedback for students.

[0073] In this embodiment, please refer to Figure 2 In a second embodiment of a mathematics virtual-real integration teaching system according to an embodiment of the present invention, the teaching analysis module includes the following submodules:

[0074] The data collection submodule is used to collect students’ learning behavior data and academic performance data, with the learning behavior data as the independent variable and the academic performance data as the dependent variable;

[0075] The model building submodule is used to assume that there is a linear relationship between the dependent variable and the independent variable, that is, y = β0 + β1x1 + β2x2 + ... + βx, where y is the dependent variable, x1, x2, ..., x are independent variables, and β0, β1, β2, ..., β are the parameters to be estimated;

[0076] The parameter estimation submodule is used to estimate the parameters β0, β1, β2, ..., β using the least squares method;

[0077] The model evaluation submodule is used to evaluate the performance of the regression model using the mean square error (MSE) to obtain the target regression model.

[0078] The prediction submodule is used to predict the learning performance based on the students' new learning behavior data using the target regression model.

[0079] In this embodiment, please refer to Figure 3 In a third embodiment of a mathematics virtual-real integration teaching system according to an embodiment of the present invention, the teaching analysis module further includes the following submodules:

[0080] The data preparation submodule is used to collect students' physiological data, normalize and denoise the physiological data in turn, and divide the processed data into training set, validation set and test set;

[0081] The model building submodule is used to build a CNN convolutional neural network model. The CNN convolutional neural network model includes at least a convolutional layer, a pooling layer, and a fully connected layer. The convolutional layer is used to extract data features, the pooling layer is used to reduce the dimension of the data, and the fully connected layer is used for regression.

[0082] The model training submodule is used to train the CNN convolutional neural network model using the training set, continuously adjust the parameters of the model through the back propagation algorithm, and set the loss function to the cross entropy loss function;

[0083] The model evaluation submodule is used to evaluate the CNN convolutional neural network model using the validation set, adjust the model's hyperparameters, which include at least the learning rate, convolution kernel size, and number of layers, and obtain the target CNN convolutional neural network model;

[0084] The prediction submodule is used to test the target CNN convolutional neural network model using the test set, evaluate the generalization ability of the model, input new physiological data into the target CNN convolutional neural network model, and obtain the student's fatigue status and concentration level.

[0085] Specifically, in the mathematics classroom in this embodiment, the teacher first displays the mathematical animation in the virtual teaching resource library through the teaching projector to introduce the teaching content of this class. Then, the students wear virtual reality helmets and enter a highly realistic virtual teaching scene for learning. In the virtual teaching scene, students can interact with various sophisticated mathematical models through the operating handle. At the same time, the dynamic light and shadow effects and physical simulation technology make students feel as if they are in a real environment. Teachers can use augmented reality devices to superimpose virtual mathematical content on the actual teaching scene, and ensure the precise matching of virtual content with the actual scene through high-precision image recognition algorithms and real-time tracking algorithms. Students can interact with virtual mathematical content in augmented reality through gesture recognition technology, and learn mathematical knowledge more naturally and conveniently. Students and teachers can interact in real time through the interactive teaching platform, asking questions, answering questions, and discussing. The virtual learning community provides students with a platform for exchanging learning experiences and sharing learning resources, which enhances students' learning motivation and participation. During the learning process, wearable sensors monitor students' learning status and physiological data in real time, and the data analysis module conducts in-depth analysis of these data to provide teachers with teaching references. If students are found to be distracted or tired, teachers can take corresponding measures, such as adjusting the teaching rhythm, arranging rest time, etc. After class, students can use the intelligent teaching terminal to review online and submit homework. The intelligent tutoring module will provide students with highly personalized tutoring and suggestions based on their answers and learning characteristics to help them consolidate their knowledge. The evaluation module will conduct a multi-dimensional evaluation of students' learning effects, generate detailed learning reports, and provide feedback to teachers and students.

[0086] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A mathematics virtual-real fusion teaching system, characterized in that: The mathematics virtual-real integration teaching system includes a scene construction module, an animation simulation module, a data acquisition module, a teaching analysis module, and a teaching feedback module, wherein: The scene construction module is used to construct a virtual teaching scene using virtual reality technology according to the teaching content and students' learning needs; An animation simulation module, used for creating mathematical models and animations in the virtual teaching scene by using three-dimensional modeling technology and animation production technology; The data collection module is used to collect students' learning behavior data and physiological data through intelligent teaching terminals and wearable sensors to obtain learning feedback data; A teaching analysis module is used to analyze the learning feedback data using a machine learning algorithm to obtain the student's learning status data; The teaching feedback module is used to adjust the teaching method and teaching scene in the virtual teaching scene according to the learning status data.

2. A mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The scene construction module includes the following submodules: An acquisition submodule is used to acquire teaching content and students' learning needs, wherein the teaching content at least includes mathematical formulas and mathematical equations, and the learning needs at least include teaching arrangements and teaching progress; The construction submodule is used to construct a virtual space of geometric shapes and a function image world of dynamic demonstration according to the teaching content to obtain an initial virtual scene; The simulation submodule is used to use the Unity virtual reality engine to perform physical simulation of the light and shadow effects of the initial virtual scene to obtain a virtual teaching scene.

3. A mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The animation simulation module includes the following submodules: A creation submodule is used to create a three-dimensional shape of a mathematical model using Maya three-dimensional modeling software, and adjust the material and texture of the three-dimensional shape; A submodule is obtained, which is used to dynamically construct a function image according to a function formula by using a parametric modeling technology to obtain an image model.

4. A mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The teaching analysis module includes the following submodules: A data collection submodule is used to collect students' learning behavior data and academic performance data, and use the learning behavior data as an independent variable and the academic performance data as a dependent variable; The model building submodule is used to assume that there is a linear relationship between the dependent variable and the independent variable, that is, y = β0 + β1x1 + β2x2 + ... + βx, where y is the dependent variable, x1, x2, ..., x are independent variables, and β0, β1, β2, ..., β are the parameters to be estimated; The parameter estimation submodule is used to estimate the parameters β0, β1, β2, ..., β using the least squares method; The model evaluation submodule is used to evaluate the performance of the regression model using the mean square error (MSE) to obtain the target regression model. The prediction submodule is used to predict the learning performance according to the new learning behavior data of the students by using the target regression model.

5. A mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The teaching analysis module also includes the following submodules: A data preparation submodule is used to collect students' physiological data, normalize and denoise the physiological data in sequence, and divide the processed data into a training set, a validation set, and a test set; A model building submodule, used to build a CNN convolutional neural network model, wherein the CNN convolutional neural network model includes at least a convolutional layer, a pooling layer, and a fully connected layer, wherein the convolutional layer is used to extract data features, the pooling layer is used to reduce the dimension of the data, and the fully connected layer is used to perform regression; A model training submodule is used to train the CNN convolutional neural network model using a training set, continuously adjust the parameters of the model through a back propagation algorithm, and set the loss function to a cross entropy loss function; A model evaluation submodule is used to evaluate the CNN convolutional neural network model using a validation set, adjust the hyperparameters of the model, and obtain a target CNN convolutional neural network model. The prediction submodule is used to test the target CNN convolutional neural network model using a test set, evaluate the generalization ability of the model, input new physiological data into the target CNN convolutional neural network model, and obtain the student's fatigue state and concentration level.

6. A mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The teaching feedback module includes the following submodules: The extension submodule is used to add extension content and learning challenge content to the virtual teaching scene if students master the content quickly; Add sub-modules to gradually increase the difficulty and complexity of teaching content according to the learning progress of students who are gradually improving; Provide submodules for adjusting the teaching method and providing more explanations and examples if the students are in difficulty; The adjustment submodule is used to automatically adjust the color and brightness in the virtual teaching scene according to the students' fatigue level.

7. A method for implementing a mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The method comprises the following steps: According to the teaching content and students' learning needs, virtual reality technology is used to build virtual teaching scenes; Using three-dimensional modeling technology and animation production technology to create mathematical models and animations in the virtual teaching scene; Collect students’ learning behavior data and physiological data through intelligent teaching terminals and wearable sensors to obtain learning feedback data; Analyze the learning feedback data using a machine learning algorithm to obtain the student's learning status data; The teaching method and teaching scene in the virtual teaching scene are adjusted according to the learning status data.

8. A method for implementing a mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The method comprises the following steps: Collecting students' learning behavior data and learning performance data, taking the learning behavior data as independent variables and the learning performance data as dependent variables; Assume that there is a linear relationship between the dependent variable and the independent variable, that is, y = β0 + β1x1 + β2x2 + ... + βx, where y is the dependent variable, x1, x2, ..., x are independent variables, and β0, β1, β2, ..., β are the parameters to be estimated; Estimate the parameters β0,β1,β2,...,β using the least squares method; Use MSE mean square error to evaluate the performance of the regression model and obtain the target regression model; The target regression model is used to predict the learning performance according to the students' new learning behavior data.

9. A method for implementing a mathematics virtual-real fusion teaching system as claimed in claim 1, characterized in that: The method comprises the following steps: Collecting students' physiological data, normalizing and denoising the physiological data in turn, and dividing the processed data into a training set, a validation set, and a test set; Construct a CNN convolutional neural network model, wherein the CNN convolutional neural network model includes at least a convolutional layer, a pooling layer, and a fully connected layer, wherein the convolutional layer is used to extract data features, the pooling layer is used to reduce the dimension of the data, and the fully connected layer is used to perform regression; The CNN convolutional neural network model is trained using the training set, the parameters of the model are continuously adjusted through the back propagation algorithm, and the loss function is set to the cross entropy loss function; The CNN convolutional neural network model is evaluated using a validation set, and the hyperparameters of the model are adjusted, wherein the hyperparameters include at least a learning rate, a convolution kernel size, and a number of layers, to obtain a target CNN convolutional neural network model; The target CNN convolutional neural network model is tested using the test set to evaluate the generalization ability of the model, and new physiological data are input into the target CNN convolutional neural network model to obtain the student's fatigue status and concentration level.

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