Integrated application of multi-modal interaction technology in high school mathematics teaching

Abstract

The invention provides an integrated application of a multi-modal interaction technology in senior high school mathematics teaching, and belongs to the technical field of intelligent teaching. Abstract knowledge is converted into vivid images and dynamic demonstration through multimedia resources, the learning effect is improved, for example, students are helped to establish spatial thinking when solid geometry is explained, and the teaching efficiency is improved. The virtual reality or augmented reality technology is introduced to create an immersive learning environment, enhance knowledge understanding and improve practical ability, the intelligent interaction device realizes real-time interaction and improves enthusiasm and initiative of students, convenient operation and efficient response enable learning to be smoother, the voice recognition technology assists the students, expression accuracy is improved, interestingness is increased, and learning efficiency is improved. The big data analysis can track the learning progress and behavior mode, provides a basis for teaching according to materials, and improves the teaching quality.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent teaching, and specifically relates to the integrated application of multi-modal interaction technology in high school mathematics teaching. Background Art

[0002] In today's education field, high school mathematics teaching faces many challenges. Traditional teaching methods mainly rely on blackboards, chalks and textbooks. This single teaching mode often fails to stimulate students' learning interests and initiatives. With the continuous development of technology, education is gradually seeking innovation and change to adapt to the learning needs and characteristics of students in the new era. On the one hand, high school mathematics knowledge is abstract and complex. Concepts such as functions and geometries are relatively difficult for students to understand. Under the traditional teaching mode, students can only understand these abstract concepts through static images and texts, lacking intuitive feelings and interactive experiences, resulting in poor learning effects. On the other hand, in the information age, students are exposed to more diverse information, and they also have higher expectations for learning methods. The single teaching mode is difficult to meet students' pursuit of diverse learning experiences, easily makes students feel bored in the learning process, and reduces their learning enthusiasm. At the same time, existing teaching technologies often have certain limitations in the application process. For example, although some multimedia teaching resources can provide certain visual and auditory stimuli, they lack in-depth interaction with students; the application of virtual reality and augmented reality technologies in the education field is not extensive and mature enough, with problems such as high content production costs and poor technology compatibility; the functions of intelligent interaction devices have not been fully explored, and their application scenarios in mathematics teaching are relatively limited; the application of speech recognition technology in mathematics teaching is not accurate and comprehensive enough to meet students' needs in solving mathematical problems and communication; the application of big data analysis in teaching is also in its infancy, lacking effective data collection and analysis methods, and it is difficult to truly achieve personalized teaching.

[0003] In summary, in order to improve the quality of high school mathematics teaching and stimulate students' learning interests and initiatives, there is an urgent need for a teaching method that can integrate multiple advanced technologies, that is, an integrated application method of multi-modal interaction technology in high school mathematics teaching. This method organically combines multiple technologies such as multimedia resources, virtual reality / augmented reality technology, intelligent interaction devices, speech recognition technology and big data analysis to provide students with a more rich, intuitive and interactive learning experience, meeting the needs of high school mathematics teaching in the new era. Summary of the Invention

[0004] The purpose of the present invention is to provide an integrated application of multi-modal interaction technology in high school mathematics teaching, aiming to solve the problems in the prior art.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] An integrated application of multimodal interaction technology in high school mathematics teaching includes the following steps:

[0007] Utilize multimedia resources such as animations and videos to visually display mathematical concepts and principles. The display degree D of the mathematical concepts and principles can be calculated by the formula D = k 1 ×M + k 2 ×V + k 3 ×T m where M is the richness of the multimedia resources (ranging from 0 to 10), V is the clarity of the video (ranging from 0 to 10), T m is the degree of fit between the multimedia resources and the teaching content (ranging from 0 to 10), and k 1 、k 2 、k 3 are weight coefficients (and k 1 + k 2 + k 3 = 1);

[0008] Introduce virtual reality (VR) or augmented reality (AR) technology to create an immersive mathematics learning environment. The immersion index I of the learning environment can be expressed as I = k 4 ×S + k 5 ×T + k 6 ×P e where S is the authenticity of the scene (ranging from 0 to 10), T is the complexity of the task (ranging from 0 to 10), P e is the satisfaction degree of the interactive experience of the environment (ranging from 0 to 10), and k 4 、k 5 、k 6 are weight coefficients (and k 4 + k 5 + k 6 = 1);

[0009] Combine intelligent interactive devices such as tablet computers and electronic whiteboards to achieve real-time interaction between students and teaching content. The interaction efficiency E can be determined by the formula E = k 7 ×R + k 8 ×P + k 9 ×F s where R is the response speed of the device (ranging from 0 to 10), P is the convenience of operation (ranging from 0 to 10), F s is the stability of the device (ranging from 0 to 10), and k 7 、k 8 、k 9 are weight coefficients (and k 7 + k 8 + k9 = 1);

[0010] Using speech recognition technology to assist students in answering math questions and communicating, the calculation formula for the speech recognition accuracy A is A = k 10 × C + k 11 × F + k 12 × L v , where C is the clarity of the speech, F is the optimization degree of the algorithm (value range is 0 to 10), L is the diversity of the speech samples (value range is 0 to 10), and k 10 , k 11 , k 12 are weight coefficients (and k 10 + k 11 + k 12 = 1);

[0011] Adopting big data analysis to track students' learning progress and behavior patterns, providing a basis for personalized teaching, the personalized teaching matching degree M p can be represented by M p = k 13 × G + k 14 × H + k 15 × B p , where G is the grasping accuracy of the learning progress (value range is 0 to 10), H is the analysis depth of the behavior pattern (value range is 0 to 10), B p is the matching degree of students' personal preferences (value range is 0 to 10), k 13 , k 14 , k 15 are weight coefficients (and k 13 + k 14 + k 15 = 1).

[0012] As a preferred solution of the present invention, the multimedia resources should be screened and produced according to the high school mathematics teaching syllabus and curriculum standards to ensure the accuracy and pertinence of the content. The screening and production of multimedia resources should follow the formula Q = k 16 × Z + k 17 × X + k 18 × N c , where Z is the degree of fit with the teaching syllabus (value range is 0 to 10), X is the degree of compliance with the curriculum standards (value range is 0 to 10), N c is the novelty of the content (value range is 0 to 10), k 16 , k 17 , k 18 are weight coefficients (and k 16 + k 17 + k 18 = 1).

[0013] As a preferred embodiment of the present invention, the learning environment created by the virtual reality (VR) or augmented reality (AR) technology should include scenarios and tasks related to high school mathematics courses to strengthen students' practical application abilities. The design of the scenarios and tasks should satisfy the relational expression L = k 19 ×Y + k 20 ×W + k 21 ×E s , where Y is the degree of association with the course (value range is 0 to 10), W is the practical value of the task (value range is 0 to 10), E s is the student participation rate (value range is 0 to 10), and k 19 , k 20 , k 21 are weight coefficients (and k 19 + k 20 + k 21 = 1).

[0014] As a preferred embodiment of the present invention, the operation interface of the intelligent interaction device should be simple and clear, facilitating students to quickly get started and operate, and having an anti-addiction function. The anti-addiction control coefficient F c can be expressed as F c = k 22 ×U + k 23 ×V'+ k 24 ×T l , where U is the strictness of the usage time limit (value range is 0 to 10), V' is the reminder frequency (value range is 0 to 10), T l is the effectiveness of the locking mechanism (value range is 0 to 10), and k 22 , k 23 , k 24 are weight coefficients (and k 22 + k 23 + k 24 = 1).

[0015] As a preferred embodiment of the present invention, the speech recognition technology should have error correction and prompting functions to help students correctly express their mathematical thinking. The effectiveness E v of error correction and prompting is calculated as E v = k 25 ×J + k 26 ×K + k 27 ×S p , where J is the accuracy rate of error correction (value range is 0 to 10), K is the appropriateness of prompting (value range is 0 to 10), S p is the fluency of speech interaction (value range is 0 to 10), and k 25 , k 26 , k27 is the weight coefficient (and k 25 + k 26 + k 27 = 1).

[0016] As a preferred embodiment of the present invention, the big data analysis result should generate a detailed report to provide reference for teachers to adjust teaching strategies and for students to formulate personalized learning plans. The detail level R d can be represented by R d = k 28 × L'+ k 29 × M'+ k 30 × R p where L' is the dimension of the data (the value range is from 0 to 10), M' is the depth of analysis (the value range is from 0 to 10), R p is the prediction accuracy (the value range is from 0 to 10), and k 28 , k 29 , k 30 are the weight coefficients (and k 28 + k 29 + k 30 = 1).

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] Intuitively demonstrating mathematical concepts and principles through multimedia resources such as animations and videos can transform abstract and complex high school mathematics knowledge into vivid images and dynamic demonstrations, making difficult-to-understand concepts such as functions and geometry more concrete and perceptible. Students no longer rely solely on static images and text, but can perceive mathematical knowledge from multiple dimensions, greatly improving learning effects. For example, when explaining solid geometry, animations can clearly show the graphic changes from different angles, helping students establish spatial thinking. Secondly, introducing virtual reality (VR) or augmented reality (AR) technology to create an immersive learning environment brings a brand-new learning experience to students. In such an environment, students seem to be in a real mathematical scene. By completing various tasks, they not only strengthen their understanding of knowledge but also improve their practical application abilities. For instance, when learning analytic geometry, students can personally construct curve equations in a virtual environment and feel the beauty of mathematics. Moreover, the use of intelligent interactive devices enables real-time interaction between students and teaching content. Students can quickly participate in classroom interactions through devices such as tablets and electronic whiteboards, enhancing their learning enthusiasm and initiative. At the same time, the convenient operation and high response speed of the devices also provide convenience for learning, making the learning process smoother. In addition, speech recognition technology assists students in answering mathematical questions and communicating. On the one hand, it improves the accuracy of students' expression of mathematical thinking, and on the other hand, it also increases the fun of learning. When students encounter problems, they can communicate with the system by voice and obtain timely feedback and guidance. Finally, the application of big data analysis can track students' learning progress and behavior patterns, providing a basis for personalized teaching. Teachers can understand the learning situation of each student according to the big data analysis results, formulate targeted teaching plans, truly achieve individualized instruction, and improve the overall teaching quality. Detailed implementation manners

[0019] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0020] Embodiment 1

[0021] The present invention provides the following technical solutions:

[0022] An integrated application of multi-modal interaction technology in high school mathematics teaching, characterized by including the following steps:

[0023] Using multimedia resources, such as animations, videos, etc., to intuitively demonstrate mathematical concepts and principles. The demonstration degree D of mathematical concepts and principles can be calculated by the formula D = k 1 ×M + k 2 ×V + k3 ×T m Calculated, where M is the richness of multimedia resources (ranging from 0 to 10), V is the clarity of the video (ranging from 0 to 10), and T m is the degree of fit between the multimedia resource and the teaching content (ranging from 0 to 10), k 1 、k 2 、k 3 are weight coefficients (and k 1 +k 2 +k 3 = 1);

[0024] Introduce virtual reality (VR) or augmented reality (AR) technology to create an immersive mathematics learning environment. The immersion index I of the learning environment can be expressed as I = k 4 ×S + k 5 ×T + k 6 ×P e , where S is the authenticity of the scene (ranging from 0 to 10), T is the complexity of the task (ranging from 0 to 10), and P e is the satisfaction degree of the interactive experience of the environment (ranging from 0 to 10), k 4 、k 5 、k 6 are weight coefficients (and k 4 +k 5 +k 6 = 1);

[0025] Combine intelligent interactive devices, such as tablets and electronic whiteboards, to achieve real-time interaction between students and teaching content. The interaction efficiency E can be determined by the formula E = k 7 ×R + k 8 ×P + k 9 ×F s , where R is the response speed of the device (ranging from 0 to 10), P is the convenience of operation (ranging from 0 to 10), and F s is the stability of the device (ranging from 0 to 10), k 7 、k 8 、k 9 are weight coefficients (and k 7 +k 8 +k 9 = 1);

[0026] Apply speech recognition technology to assist students in answering math questions and communicating. The calculation formula for the speech recognition accuracy rate A is A = k 10 ×C + k 11 ×F + k 12 ×L v, where C is the clarity of speech, F is the optimization degree of the algorithm (the value range is from 0 to 10), and L v is the diversity of speech samples (the value range is from 0 to 10), k 10 , k 11 , k 12 are weight coefficients (and k 10 + k 11 + k 12 = 1);

[0027] By using big data analysis to track students' learning progress and behavior patterns, it provides a basis for personalized teaching. The personalized teaching matching degree M p can be represented by M p = k 13 × G + k 14 × H + k 15 × B p where G is the grasping accuracy of the learning progress (the value range is from 0 to 10), H is the analysis depth of the behavior pattern (the value range is from 0 to 10), and B p is the matching degree of students' personal preferences (the value range is from 0 to 10), k 13 , k 14 , k 15 are weight coefficients (and k 13 + k 14 + k 15 = 1).

[0028] In the specific embodiments of the present invention, multimedia resources such as animations and videos have the characteristics of vividness and can transform abstract and complex high school mathematics knowledge into intuitive images and dynamic demonstrations. For example, in function teaching, in the past, students could only understand the concepts and properties of functions through static book images and texts, which were often obscure and difficult to understand. Now, carefully made animations can clearly show the dynamic process of the function image changing with variables, presenting the changing trends of the function from different angles, making students seem to be in a dynamic mathematical world. This way makes the originally difficult-to-understand function concepts become more concrete and perceptible, greatly improving students' learning interest and understanding ability. In geometric teaching, especially in solid geometry, animations can show the shapes and characteristics of different geometric bodies from various angles, helping students establish spatial thinking. Students no longer rely solely on static images and texts, but can feel mathematical knowledge from multiple dimensions, laying a solid foundation for subsequent in-depth learning.

[0029] Specifically, multimedia resources should be screened and produced according to the high school mathematics teaching syllabus and curriculum standards to ensure the accuracy and pertinence of the content. The screening and production of multimedia resources should follow the formula Q = k 16 × Z + k 17 × X + k 18 × Nc , where Z is the degree of alignment with the teaching syllabus (ranging from 0 to 10), X is the degree of compliance with the curriculum standards (ranging from 0 to 10), N c is the novelty of the content (ranging from 0 to 10), k 16 、k 17 、k 18 are the weight coefficients (and k 16 +k 17 +k 18 = 1).

[0030] In this embodiment: on the one hand, ensuring the degree of alignment with the teaching syllabus enables the teaching content to closely revolve around the teaching objectives and not deviate from the teaching direction. When teachers screen resources, they will pay more attention to the correspondence between the resources and the knowledge points required by the syllabus, so that students can accurately master the key points and difficulties during the learning process. For example, in the teaching of the algebraic part, for specific formulas and theorems, the selected multimedia resources can help students understand their application scenarios and derivation processes through examples and demonstrations. On the other hand, ensuring the degree of compliance with the curriculum standards can improve the quality and standardization of teaching. The multimedia resources that comply with the curriculum standards are carefully considered in terms of the depth and breadth of the content and can meet the learning needs of students at different levels. At the same time, the novelty of the content is also crucial. Novel multimedia resources can attract students' attention and stimulate their learning enthusiasm. For example, using the latest animation production technology to present mathematical knowledge or combining it with real-life cases to let students feel the practicality and interest of mathematics.

[0031] Specifically, the learning environment created by virtual reality (VR) or augmented reality (AR) technology should include scenarios and tasks related to high school mathematics courses to strengthen students' practical application abilities. The design of the scenarios and tasks should meet the relationship L = k 19 ×Y + k 20 ×W + k 21 ×E s , where Y is the degree of association with the course (ranging from 0 to 10), W is the practical value of the task (ranging from 0 to 10), E s is the degree of student participation (ranging from 0 to 10), k 19 、k 20 、k 21 are the weight coefficients (and k 19 +k 20 +k 21 = 1).

[0032] In this embodiment: First, the authenticity of the scenario enables students to feel as if they are in a real mathematics scenario, greatly enhancing the immersion in learning. When learning analytic geometry, students can enter a virtual space through VR or AR technology, construct curve equations by themselves, and experience the beauty of mathematics. This immersive experience not only strengthens students' understanding of knowledge but also improves their practical application ability. For example, when learning solid geometry, students can observe the characteristics of different geometric bodies in a virtual three-dimensional space, perform operations such as angle measurement and volume calculation, so as to understand the properties of geometric bodies more deeply. Second, the complexity of the tasks is reasonably designed, which can stimulate students' desire for challenge and exploration spirit. Teachers can set tasks of different difficulties according to students' learning progress and ability levels, so that each student can grow in challenges. Finally, students' participation has also been greatly improved. In this immersive learning environment, students are no longer passive recipients of knowledge, but actively participate in the learning process, actively exploring and discovering the mysteries of mathematics.

[0033] Specifically, the operation interface of the intelligent interaction device should be simple and clear, convenient for students to quickly get started, and have an anti-addiction function. The anti-addiction control coefficient F c can be expressed as F c = k 22 ×U + k 23 ×、V′ + k 24 ×T l , where U is the strictness of the usage time limit (the value range is 0 to 10), V′ is the reminder frequency (the value range is 0 to 10), T l is the effectiveness of the locking mechanism (the value range is 0 to 10), k 22 、k 23 、k 24 are weight coefficients (and k 22 + k 23 + k 24 = 1).

[0034] In this embodiment: The fast response speed of the device enables students to receive timely feedback during use, improving learning efficiency. When students submit answers or perform operations through devices such as tablets and interactive whiteboards, the system can respond quickly, allowing students to experience the fluency of learning. For example, in classroom interaction sessions, students can answer questions and participate in discussions quickly without being affected by device lag, which may dampen their enthusiasm for learning. Secondly, the high convenience of operation enables students to get started easily without spending too much time learning complex operation methods. The simple and clear operation interface allows students to focus on the learning content rather than being troubled by cumbersome operations. Moreover, the stability of the device is also crucial. A stable intelligent interaction device can ensure the smooth progress of the teaching process without interrupting teaching due to device failures. For example, during online tests or group cooperative learning, the stability of the device can ensure that students can complete tasks smoothly and obtain a good learning experience.

[0035] Specifically, the speech recognition technology should have error correction and prompting functions to help students correctly express their mathematical thinking. The effectiveness E v of error correction and prompting is calculated as v E = k 25 × J + k 26 × K + k 27 × S p , where J is the accuracy rate of error correction (the value range is from 0 to 10), K is the appropriateness of prompting (the value range is from 0 to 10), S p is the fluency of speech interaction (the value range is from 0 to 10), and k 25 , k 26 , k 27 are weight coefficients (and k 25 + k 26 + k 27 = 1).

[0036] In this embodiment: On the one hand, accurate speech recognition can improve the accuracy of students' expression of mathematical thinking. During the process of solving math problems and communicating, students may affect their learning outcomes due to unclear or incorrect expressions. The speech recognition technology can accurately recognize students' speech, correct incorrect expressions in a timely manner, and provide appropriate prompts. For example, when students use incorrect terms or concepts when describing math problems, the system can promptly remind them to correct, helping them better express their thinking. On the other hand, the speech recognition technology increases the fun of learning. Students can communicate with the system through speech and obtain timely feedback and guidance. This interactive method makes the learning process more vivid and interesting. For example, during the learning process, students can ask questions by voice, and the system will answer the questions in voice, as if there is a private tutor guiding beside. At the same time, the speech recognition technology can also promote the development of students' oral expression ability and thinking ability, and improve the comprehensive quality of students.

[0037] Specifically, the big data analysis results should generate a detailed report to provide reference for teachers to adjust teaching strategies and for students to formulate personalized learning plans. The detail level R d can be represented by R d = k 28 ×L′ + k 29 ×M′ + k 30 ×R p where L′ is the dimension of the data (the value range is from 0 to 10), M′ is the depth of analysis (the value range is from 0 to 10), R p is the prediction accuracy (the value range is from 0 to 10), and k 28 、k 29 、k 30 are weight coefficients (and k 28 + k 29 + k 30 = 1).

[0038] In this embodiment: First, by collecting data on students' classroom interactions, homework completion, test performance, etc., the big data analysis system can comprehensively understand the learning situation of each student. For example, by analyzing data such as students' participation in classroom interactions and the accuracy of their answers to questions, it is possible to understand students' mastery of knowledge points and learning attitudes. Second, multi-dimensional analysis can deeply explore students' learning behavior patterns and weak links in knowledge mastery. For instance, by analyzing the types and frequencies of errors in students' homework completion, it can be found which knowledge points students have difficulty understanding, thus providing targeted teaching suggestions for teachers. Finally, the detailed reports generated from the analysis results provide a basis for teachers to formulate personalized teaching plans. Teachers can, based on the learning situation of each student, push targeted learning resources and practice questions, truly achieving individualized teaching. This personalized teaching method can improve students' learning effects, stimulate students' learning interests and initiatives, and thus enhance the overall teaching quality.

[0039] The working principle and usage process of the present invention:

[0040] In the teaching preparation stage, teachers, according to the teaching syllabus and curriculum standards, carefully select and produce multimedia resources, including animations, videos, etc. These resources should ensure a high degree of richness, clarity, and relevance to the teaching content. For example, for the explanation of the function concept, vivid animations are produced to show the dynamic process of the function image changing with variables, enabling students to intuitively feel the properties of the function. Then, virtual reality or augmented reality technology is introduced to design scenarios and tasks closely related to high school mathematics courses. For example, in solid geometry teaching, a virtual three-dimensional space is created where students can observe the characteristics of different geometric bodies. By completing specific tasks such as measuring angles and calculating volumes, they can deepen their understanding and mastery of knowledge. During the classroom teaching process, intelligent interactive devices such as tablet computers and electronic whiteboards are used to achieve real-time interaction between students and teaching content. Students can submit answers and participate in discussions through the devices, and teachers can also timely understand students' learning situations and adjust the teaching progress. At the same time, speech recognition technology plays an auxiliary role. When students answer math questions or communicate, the system can accurately recognize speech, correct incorrect expressions, and provide appropriate hints, increasing the fun and accuracy of learning. After class, the big data analysis system starts to work, tracking students' learning progress and behavior patterns. By collecting data on students' classroom interactions, homework completion, test performance, etc., multi-dimensional analysis is carried out. The analysis results generate detailed reports, providing teachers with the learning situations of each student, including weak links in knowledge mastery, learning habits, etc. Teachers, based on these reports, formulate personalized teaching plans for students, push targeted learning resources and practice questions, truly achieving individualized teaching and improving the overall teaching quality. Such an operation process organically combines a variety of advanced technologies, bringing new changes and improvements to high school mathematics teaching.

[0041] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An integrated application of multimodal interaction technology in high school mathematics teaching, characterized in that: The following steps are involved: Use multimedia resources, such as animations and videos, to intuitively display mathematical concepts and principles. The degree of display of mathematical concepts and principles can be expressed by the formula D = k1×M+k2×V+k3×T m The calculation results show that M is the richness of multimedia resources (ranging from 0 to 10), V is the clarity of the video (ranging from 0 to 10), and T m is the fit between multimedia resources and teaching content (the value range is 0 to 10), k1, k2, k3 are weight coefficients (and k1+k2+k3=1); Introduce virtual reality (VR) or augmented reality (AR) technology to create an immersive mathematics learning environment. The immersion index I of the learning environment can be expressed as I = k4×S+k5×T+k6×P e , where S is the realism of the scene (ranging from 0 to 10), T is the complexity of the task (ranging from 0 to 10), and P e is the interactive experience satisfaction of the environment (the value range is 0 to 10), k4, k5, k6 are weight coefficients (and k4+k5+k6=1); Combined with intelligent interactive devices, such as tablet computers and electronic whiteboards, real-time interaction between students and teaching content is achieved. The interaction efficiency E can be expressed by the formula E = k7 × R + k8 × P + k9 × F s Determine, where R is the response speed of the device (ranging from 0 to 10), P is the convenience of operation (ranging from 0 to 10), and F s is the stability of the equipment (the value range is 0 to 10), k7, k8, k9 are weight coefficients (and k7+k8+k9=1); Using speech recognition technology to assist students in solving math problems and communicating, the formula for calculating the speech recognition accuracy A is A=k 10 ×C+k 11 ×F+k 12 ×L v , where C is the clarity of speech, F is the optimization degree of the algorithm (the value range is 0 to 10), L v k is the diversity of speech samples (ranging from 0 to 10) 10 , k 11 , k 12 is the weight coefficient (and k 10 +k 11 +k 12 =1); Using big data analysis to track students' learning progress and behavior patterns, providing a basis for personalized teaching, personalized teaching matching degree M p Available M p =k 13 ×G+k 14 ×H+k 15 ×B p Indicates that G is the accuracy of learning progress (ranging from 0 to 10), H is the depth of analysis of behavior patterns (ranging from 0 to 10), and B p is the matching degree of students’ personal preferences (ranging from 0 to 10), k 13 , k 14 , k 15 is the weight system (and k 13 +k 14 +k 15 =1).

2. The integrated application of a multimodal interaction technology in high school mathematics teaching according to claim 1 is characterized by: The multimedia resources should be selected and produced according to the high school mathematics teaching syllabus and curriculum standards to ensure the accuracy and pertinence of the content. The selection and production of multimedia resources should follow the formula Q = k 16 ×Z+k 17 ×X+k 18 ×N c , where Z is the degree of fit with the syllabus (ranging from 0 to 10), X is the degree of conformity with the curriculum standards (ranging from 0 to 10), and N c is the novelty of the content (ranging from 0 to 10), k 16 , k 17 , k 18 is the weight coefficient (and k 16 +k 17 +k 18 =1).

3. The integrated application of a multimodal interaction technology in high school mathematics teaching according to claim 2 is characterized by: The learning environment created by the virtual reality (VR) or augmented reality (AR) technology should include scenes and tasks related to high school mathematics courses to enhance students' practical application ability. The design of scenes and tasks should satisfy the relationship L = k 19 ×Y+k 20 ×W+k 21 ×E s , where Y is the relevance to the course (ranging from 0 to 10), W is the practical value of the task (ranging from 0 to 10), and E s is the student's participation (ranging from 0 to 10), k 19 , k 20 , k 21 is the weight coefficient (and k 19 +k 20 +k 21 =1).

4. The integrated application of multimodal interaction technology in high school mathematics teaching according to claim 3 is characterized by: The operation interface of the intelligent interactive device should be concise and clear, convenient for students to quickly get started, and have an anti-addiction function. The anti-addiction control coefficient F c It can be expressed as F c =k 22 ×U+k 23 ×V′+k 24 ×T l , where U is the strictness of the usage time limit (ranging from 0 to 10), V′ is the reminder frequency (ranging from 0 to 10), T l is the effectiveness of the locking mechanism (ranging from 0 to 10), k 22 , k 23 , k 24 is the weight coefficient (and k 22 +k 23 +k 24 =1).

5. The integrated application of multimodal interaction technology in high school mathematics teaching according to claim 4 is characterized by: The speech recognition technology should have error correction and prompt functions to help students express mathematical thinking correctly. The effectiveness of error correction and prompts v The calculation formula is E v =k 25 ×J+k 26 ×K+k 27 ×S p , where J is the accuracy of error correction (ranging from 0 to 10), K is the appropriateness of the prompt (ranging from 0 to 10), S p is the fluency of voice interaction (ranging from 0 to 10), k 25 , k 26 , k 27 is the weight coefficient (and k 25 +k 26 +k 27 =1).

6. The integrated application of multimodal interaction technology in high school mathematics teaching according to claim 5 is characterized by: The big data analysis results should generate a detailed report to provide a reference for teachers to adjust teaching strategies and develop personalized learning plans for students. The level of detail of the report should be R d Available R d =k 28 ×L′+k 29 ×M′+k 30 ×R p Indicates, where L′ is the dimension of the data (ranging from 0 to 10), M′ is the depth of analysis (ranging from 0 to 10), and R p is the accuracy of the prediction (ranging from 0 to 10), k 28 , k 29 , k 30 is the weight coefficient (and k 28 +k 29 +k 30 =1).