Mathematics teaching system and method based on big data

Abstract

The invention relates to the technical field of data processing, in particular to a mathematical teaching system and method based on big data. The method comprises the steps that learning behavior data of students are collected and preprocessed, and preprocessed data are obtained; performing feature extraction and optimization on the preprocessed data through an adaptive multilayer nonlinear feature fusion and optimization algorithm to obtain comprehensive feature data; learning state analysis is carried out based on the comprehensive feature data, an analysis result is obtained, and personalized learning feedback is generated; based on personalized learning feedback, a learning path and learning content are automatically adjusted; and based on the learning path and the learning content, a personalized learning plan is pushed to the student through an intelligent recommendation algorithm, and mathematics teaching is realized. The technical problems that in a mathematics teaching system, student learning behavior data processing is not accurate enough, student learning state evaluation is not accurate, and the individuation degree of teaching plan making is low are solved.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to a mathematics teaching system and method based on big data. Background Art

[0002] At present, with the rapid development of information technology and big data, the education industry is gradually moving towards intelligent and personalized teaching models. In the traditional teaching system, students are usually in a unified teaching schedule and teaching methods, ignoring the existence of individual differences among students, which leads to significant differences in learning effects among different students. Therefore, how to provide students with personalized and customized learning experience has become a major challenge in the field of education.

[0003] With the popularity of online education and intelligent learning systems, more and more educational technologies are beginning to explore how to optimize learning paths and recommend appropriate learning resources with the help of advanced technologies such as data analysis, machine learning, and artificial intelligence. However, although some systems have attempted to make personalized recommendations for students, existing technologies still face many challenges, including the collection and processing of student learning behavior data, intelligent adjustment of learning paths, the accuracy of learning content recommendations, and how to improve the personalization of teaching plans.

[0004] Therefore, the above technology has the following technical problems: in the mathematics teaching system, the processing of student learning behavior data is not accurate enough, the assessment of student learning status is inaccurate, and the degree of personalization of teaching plan formulation is low. Summary of the invention

[0005] The present invention provides a mathematics teaching system and method based on big data to solve the technical problems in the mathematics teaching system, such as inaccurate processing of student learning behavior data, inaccurate evaluation of student learning status, and low personalization of teaching plan formulation.

[0006] The mathematics teaching system and method based on big data of the present invention specifically include the following technical solutions: The mathematics teaching method based on big data includes the following steps: S1. Collect students’ learning behavior data and preprocess them to obtain preprocessed data; extract and optimize the preprocessed data through adaptive multi-layer nonlinear feature fusion and optimization algorithm to obtain comprehensive feature data; analyze the learning status based on the comprehensive feature data to obtain analysis results and generate personalized learning feedback; S2. Based on personalized learning feedback, automatically adjust the learning path and learning content; based on the learning path and learning content, push personalized learning plans to students through intelligent recommendation algorithms to achieve mathematics teaching.

[0007] Preferably, the S1 specifically includes: The adaptive multi-layer nonlinear feature fusion and optimization algorithm extracts and optimizes features of pre-processed data by introducing multi-layer nonlinear fusion processing to obtain comprehensive feature data.

[0008] Preferably, the S1 specifically includes: In the process of implementing the adaptive multi-layer nonlinear feature fusion and optimization algorithm, feature engineering technology is used to perform preliminary feature extraction on the preprocessed data to obtain preliminary feature data, and the preliminary feature data is standardized to obtain standardized preliminary feature data; nonlinear transformation is introduced, and feature embedding is performed on the standardized preliminary feature data to obtain embedded feature data.

[0009] Preferably, the S1 specifically includes: Perform multi-layer nonlinear fusion processing on the embedded feature data, and apply a multi-layer fusion structure to perform weighted summation on the embedded feature data to obtain fused feature data. Preferably, S1 specifically includes: Genetic algorithms are introduced to perform feature selection and optimization on the fused feature data to obtain comprehensive feature data; based on the comprehensive feature data, learning status analysis is performed through a deep hierarchical neural network to obtain analysis results; based on the analysis results, personalized learning feedback is generated that includes students’ current learning status, degree of mastery, and areas that need improvement.

[0010] Preferably, the S2 specifically includes: In the process of implementing the intelligent recommendation algorithm, the cognitive state function and the emotional state function are defined, and the cognitive state adjustment coefficient and the emotional state adjustment coefficient are introduced to construct a learning cognitive model and an emotional dynamic analysis model to obtain the cognitive state and the emotional state.

[0011] Preferably, the S2 specifically includes: A nonlinear spatiotemporal weight adjustment mechanism is introduced to dynamically adjust the spatiotemporal weight of the learning content based on the cognitive state and the recommended time point of the learning content. The specific formula is as follows: , in, It is the learning content exist The spatiotemporal weight of the moment; It is the learning content The initial importance coefficient of is the time decay factor; It is the learning content Recommended time point: is the influence coefficient of cognitive state on the spatiotemporal weight of learning content; is the total number of knowledge points; It is the nonlinear influence index of cognitive state on the spatiotemporal weight of learning content; is Students should always keep in mind the knowledge points cognitive state.

[0012] Preferably, the S2 specifically includes: Based on the spatiotemporal weight of the learning content, combined with cognitive state and emotional state, dynamic analysis is performed to generate the recommended priority of the learning content. The formula is as follows: , in, It is the learning content exist Recommendation priority at the moment; is the influence coefficient of emotional state on recommendation priority; It's a student emotional state at the moment; is the influence coefficient of learning progress on recommendation priority; It's a student Always check the knowledge points learning progress; is the nonlinear adjustment coefficient used to control the impact of learning progress; is the influence coefficient of cognitive status on recommendation priority; It's a student The cognitive state of the moment.

[0013] Preferably, the S2 specifically includes: The recommended priorities of learning contents are arranged from large to small, and personalized learning plans are pushed to students based on the recommended priorities of learning contents. Those with high recommendation priorities are studied first to achieve mathematics teaching.

[0014] The mathematics teaching system based on big data includes the following parts: Data collection module, intelligent processing and feature optimization module, learning status analysis and feedback module, personalized learning module, intelligent recommendation module; The data acquisition module is responsible for collecting students' learning behavior data and obtaining raw data containing learning behavior data; the raw data is transmitted to the intelligent processing and feature optimization module; The intelligent processing and feature optimization module preprocesses the original data to obtain preprocessed data; extracts and optimizes the preprocessed data through an adaptive multi-layer nonlinear feature fusion and optimization algorithm to obtain comprehensive feature data; and transmits the comprehensive feature data to the learning state analysis and feedback module; The learning status analysis and feedback module performs learning status analysis based on comprehensive feature data, obtains analysis results, and generates personalized learning feedback; the personalized learning feedback is transmitted to the personalized learning module; The personalized learning module automatically adjusts the learning path and content based on personalized learning feedback; and transmits the learning path and content to the intelligent recommendation module; The intelligent recommendation module pushes personalized learning plans to students based on learning paths and learning content through intelligent recommendation algorithms to improve learning efficiency.

[0015] The beneficial effects of the technical solution of the present invention are: 1. Through adaptive multi-layer nonlinear feature fusion and optimization algorithm, the key features of students' learning behavior are extracted. The expressive power of data is enhanced through embedded nonlinear transformation, and through genetic algorithm optimization, more accurate and discriminative comprehensive feature data is obtained, and more recognizable learning features are extracted, laying the foundation for the analysis of students' learning status. At the same time, the comprehensive feature data can better capture the potential patterns of students' learning and enhance the generalization ability and accuracy of the data.

[0016] 2. Based on comprehensive feature data, through deep hierarchical neural networks, the learning status of students in multiple dimensions is captured, including mastery, learning progress, weak links, etc., and a comprehensive assessment of the students' learning status is conducted to generate analysis results. The analysis results include students' learning status, mastery, existing weak links, and feasible improvement measures. Based on the analysis results, personalized learning feedback is generated, providing a scientific basis for the automatic adjustment of subsequent learning paths and learning content.

[0017] 3. By constructing a learning cognitive model and an emotional dynamic analysis model, we can capture students' mastery of knowledge points and pay attention to the impact of students' emotional fluctuations on learning; introduce an intelligent recommendation algorithm, combine the learning cognitive model, emotional dynamic analysis model and feedback data, dynamically adjust the learning content through time and space weights, and recommend personalized learning plans. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a structural diagram of the mathematics teaching system based on big data described in the present invention; Figure 2 This is a flow chart of the mathematics teaching method based on big data described in the present invention. DETAILED DESCRIPTION

[0019] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0021] The specific scheme of the mathematics teaching system and method based on big data provided by the present invention is described in detail below with reference to the accompanying drawings.

[0022] See attached Figure 1 , which shows a structure diagram of a mathematics teaching system based on big data provided by an embodiment of the present invention, the system includes the following parts: Data collection module, intelligent processing and feature optimization module, learning status analysis and feedback module, personalized learning module, intelligent recommendation module; The data collection module is responsible for collecting students' learning behavior data through various channels (such as learning platforms, online test systems, student homework submissions, classroom interactive tools, etc.), including classroom interactions, homework scores, test results, learning time, etc., to obtain raw data containing learning behavior data; and transmit the raw data to the intelligent processing and feature optimization module; The intelligent processing and feature optimization module performs preprocessing such as cleaning, denoising, and standardization on the original data to obtain preprocessed data; through the adaptive multi-layer nonlinear feature fusion and optimization algorithm, the preprocessed data is subjected to feature extraction and optimization to obtain comprehensive feature data; the comprehensive feature data is transmitted to the learning state analysis and feedback module; The learning status analysis and feedback module analyzes the learning status based on the comprehensive feature data, obtains the analysis results, and generates personalized learning feedback including the student's current learning status, mastery level, and areas for improvement; and transmits the personalized learning feedback to the personalized learning module; The personalized learning module automatically adjusts the learning path and learning content based on personalized learning feedback to help students review and master knowledge more effectively; the learning path and learning content are transmitted to the intelligent recommendation module; The intelligent recommendation module pushes personalized learning plans to students through intelligent recommendation algorithms based on learning paths and learning content, thereby improving learning efficiency.

[0023] See attached Figure 2, which shows a flow chart of a mathematics teaching method based on big data provided by an embodiment of the present invention, the method comprising the following steps: S1. Collect students’ learning behavior data and preprocess them to obtain preprocessed data; extract and optimize the preprocessed data through adaptive multi-layer nonlinear feature fusion and optimization algorithm to obtain comprehensive feature data; analyze the learning status based on the comprehensive feature data to obtain analysis results and generate personalized learning feedback; Students' learning behavior data, including classroom interaction, homework grades, test results, study time, etc., are collected through various channels (such as learning platforms, online testing systems, student homework submissions, classroom interactive tools, etc.) to obtain raw data containing learning behavior data. The raw data is preprocessed such as cleaning, denoising, and standardization to obtain preprocessed data. The technical means used for the preprocessing are all existing technologies well known to technicians in this field and will not be elaborated here.

[0024] The adaptive multi-layer nonlinear feature fusion and optimization algorithm is used to extract and optimize the features of the preprocessed data to obtain comprehensive feature data; the adaptive multi-layer nonlinear feature fusion and optimization algorithm extracts and optimizes the features of the preprocessed data by introducing multi-layer nonlinear fusion processing to obtain comprehensive feature data, so as to improve the accuracy and generalization ability of the analysis of the student's learning status; the specific implementation process is as follows: First, the existing feature engineering technology is used to extract preliminary features from the preprocessed data to obtain preliminary feature data, and the preliminary feature data is standardized to obtain standardized preliminary feature data to ensure that the features are comparable in value. The standardized preliminary feature data is denoted as ,in Indicates The preliminary feature data after standardization, is the total number of preliminary feature data after standardization; Furthermore, feature embedding is performed on the standardized preliminary feature data, that is, the standardized preliminary feature data is mapped to a higher-dimensional feature space to obtain embedded feature data. By introducing nonlinear transformation, the standardized preliminary feature data is converted to a more expressive space, such as Map to The specific formula for spatial,feature embedding processing is: , in, It is the embedded feature data obtained after nonlinear transformation, which means converting the preliminary feature data after standardization into a new, high-dimensional feature space, aiming to capture more complex patterns; It is An activation function of a nonlinear transformation is used to make the preliminary feature data after standardization better adapt to the complex relationship in high-dimensional space, which is determined according to the specific scenario; It is The weight of a feature map determines the importance of the feature in the embedding process and is determined experimentally; is the total number of feature maps, that is, the total number of nonlinear functions used in the embedding process; Furthermore, the embedded feature data is subjected to multi-layer nonlinear fusion processing, and the multi-layer fusion structure is applied to perform weighted summation on the embedded feature data to obtain the fused feature data, thereby improving the ability of feature expression. The specific formula is as follows: , in, It is the fused feature data; It is The weighting coefficient of the layer is obtained according to the expert experience method; It is The embedded feature data is The weighting coefficient of layer characteristics is determined by experimental method; It is The nonlinear activation function of the layer is determined based on expert experience; It is Embedded feature data; is the total number of levels, and also the total number of feature data after the current fusion; Furthermore, in order to optimize the fused feature data, the existing genetic algorithm (GA) was introduced to select and optimize the fused feature data. Through the selection, crossover and mutation operations of the genetic algorithm, the feature set is continuously optimized to ensure that the final comprehensive feature data has high discrimination ability and low redundancy. The feature selection process is not only based on the adaptive adjustment of the genetic algorithm, but also combined with the external expert system scoring to evaluate the relevance and importance of each fused feature data. Through this iterative process, unimportant features can be continuously eliminated, and features that can effectively reflect the learning status of students can be strengthened, and finally comprehensive feature data can be obtained, providing the most powerful data support for subsequent learning status evaluation.

[0025] Further, entering the multi-level nonlinear learning state evaluation stage, in order to fully explore the temporal, hierarchical and nonlinear structural relationships contained in the comprehensive feature data, a deep hierarchical neural network composed of a multilayer perceptron (MLP), a deep neural network (DNN) and a long short-term memory network (LSTM) is used to evaluate the students' learning status. The technical purpose of this stage is to integrate the advantages of different types of neural networks, simultaneously model students' learning behaviors in both space and time dimensions, comprehensively and accurately predict students' current learning status, and extract potential cognitive trends and learning bottlenecks. The input of the entire evaluation process is the comprehensive feature data obtained after processing by the adaptive multi-layer nonlinear feature fusion and optimization algorithm; first, the comprehensive feature data is input into the multilayer perceptron (MLP) to preliminarily identify the high-order nonlinear mapping relationship between the comprehensive feature data, obtain high-order feature data, and use the high-order feature data as the output of the multilayer perceptron MLP. The function of the multilayer perceptron MLP structure is to quickly extract local correlations and nonlinear combination patterns from the comprehensive feature data, and establish a preliminary judgment on the performance of each student on each knowledge point; Next, the high-order feature data extracted by the multi-layer perceptron MLP is used as an intermediate representation and input into a deep neural network (DNN) for deeper feature modeling. The structure of a deep neural network DNN is similar to that of a multi-layer perceptron MLP, but contains more hidden layers (the specific number of layers is determined according to the specific scenario) and a larger representation capacity, which can capture more complex interactions between high-order feature data. This process captures the high-order collaborative features of learning behavior through nonlinear combinations, and uses the high-order collaborative features as the output of the deep neural network DNN; After the deep neural network DNN, in order to further introduce the temporal dynamic characteristics of student behavior, the high-order collaborative features are serialized and input into the long short-term memory network (LSTM) for sequence modeling; the long short-term memory network LSTM can process learning behavior data with time dependence, model the characteristic change trend of students at multiple time points (such as different learning stages), and identify the sequence vector that can represent the evolution trajectory of the learning state. The introduction of the long short-term memory network LSTM can understand the long-term changes in students' learning status and judge whether their mastery ability has a trend of continuous improvement or whether it has regressed at certain stages.

[0026] Finally, the sequence vector output by the long short-term memory network LSTM is sent to a prediction layer, such as the Softmax layer (used to classify students' learning status, such as excellent, good, medium, and poor), or a regression layer (predicting specific mastery rate values) to obtain analysis results. The analysis results are a comprehensive assessment of the students' learning status at the current stage, including a quantitative analysis of the students' overall knowledge mastery, existing weak links, and ability improvement trends; After the learning status assessment is completed and the analysis results are obtained, personalized learning feedback including the student's current learning status, mastery level and areas for improvement is generated based on the analysis results. Specifically, in terms of the student's current learning status, if the student scores high in all dimensions, the personalized learning feedback will point out that the student has mastered most of the knowledge and can apply it to practical problems; if the score in a certain dimension is low, the personalized learning feedback will point out the areas where the student needs to improve; in terms of mastery level, if the student scores high in the "Geometry" section but needs to improve in the "Algebra" section, the personalized learning feedback will specifically point out the learning status of the algebra section and give the specific content that needs to be reviewed; for areas that need improvement, if the student answers questions incorrectly in the "Function" section for many times, the personalized learning feedback will emphasize that this part is the student's current weakness and recommend reviewing the relevant content of this knowledge point.

[0027] S2. Based on personalized learning feedback, automatically adjust the learning path and learning content; based on the learning path and learning content, push personalized learning plans to students through intelligent recommendation algorithms to achieve mathematics teaching.

[0028] Automatically adjust the learning path and content based on personalized learning feedback; for example, if a student is weak in a certain math knowledge point, the learning path will be adjusted to emphasize the review of this knowledge point and recommend related learning content, including courseware, exercises, explanation videos, etc. The automatic adjustment of learning content is based on personalized learning feedback and dynamic changes in combination with students' learning in various fields. For example, the content repetition in the field where students have a higher level of mastery is reduced to avoid excessive redundant learning, while strengthening training for students' weak links. While adjusting the learning content, the student's learning progress is also taken into account to ensure that the recommended content neither exceeds the student's current learning ability nor is it too simple.

[0029] Furthermore, based on the learning path and learning content, personalized learning plans are pushed to students through intelligent recommendation algorithms to achieve mathematics teaching. The intelligent recommendation algorithm introduces a learning cognitive model and an emotional dynamic analysis model, as well as a nonlinear spatiotemporal weight adjustment mechanism. It introduces the cognitive state and emotional state (such as anxiety, interest, etc.) involved in the student learning process as new variables, and dynamically adjusts the learning content in combination with spatiotemporal weights to provide students with more accurate and personalized learning resource recommendations. The specific implementation process is as follows: Step 1: Construct a learning cognitive model and an emotional dynamic analysis model; In order to better understand the students' learning status, we first construct a learning cognitive model and an emotional dynamic analysis model to obtain the students' cognitive status and emotional status; The students' cognitive status Indicates that students The degree of mastery of knowledge points at all times, and the emotional state represents the student's learning interest or emotional fluctuation; define the cognitive state function and emotional state function , which are used to reflect students' cognitive state and emotional state and their impact on learning outcomes. The formula is as follows: , , in, is the first cognitive state adjustment coefficient, used to control the cognitive state function Cognitive state The contribution degree is obtained based on the expert experience method; and They respectively represent the influence of students’ cognitive state and affective state on learning effect, which are obtained according to the expert experience method; It's a student The familiarity of the learning content at any time indicates the degree of students' understanding of a certain knowledge point, which is quantified through tests and generally ranges from 0 to 1; It is the perceived difficulty of the learning content, which is used to describe the challenge of the learning content to students. It is usually obtained through the difficulty assessment of the course content by the course designer, and the range is generally 0 to 1; is the second cognitive state adjustment coefficient, used to control the subfunction Cognitive state The contribution degree is obtained based on the expert experience method; Indicates the influence of students' emotional state on cognitive state, adjusts students' cognitive level based on students' emotional fluctuations, and is obtained according to expert experience method; It is the students' emotional feedback (positive influence) on learning activities. It is used to quantify students' emotional response to learning content, such as students' interest or satisfaction in learning. Its value range is -1 to 1, with negative values ​​indicating negative emotions and positive values ​​indicating positive emotions. It is obtained through experiments. It is the emotional stability of students’ emotions, which is used to measure the fluctuation of students’ emotions. It is predicted by existing psychological models or emotional computing models. The higher the emotional stability, the smaller the emotional fluctuation and the less impact on the cognitive state of learning. is the first affective state adjustment coefficient, used to control the affective state function Emotional state The contribution degree is obtained based on the expert experience method; It is the students' emotional acceptance of the current learning content, which is used to reflect the students' emotional attitude towards the learning content, whether they are interested, whether they feel happy, etc. The range is -1 to 1. Negative values ​​indicate that they do not like the content, and positive values ​​indicate that they like the content. It is obtained through experiments; It indicates the emotional stability of students during the learning process. It is used to describe the stability of students' emotions. It is obtained through existing psychological measurement tools and reflects the degree of students' emotional fluctuations. is the second emotional state adjustment coefficient, used to control the sub-function Emotional state The contribution degree is obtained based on the expert experience method; It is another part of the students' emotional state, indicating the impact of learning content on students' emotions, obtained according to the expert experience method; It is the positive feedback of students' emotions, indicating the positive impact of certain behaviors in the learning process (such as task completion, goal achievement, etc.) on students' emotions. It ranges from 0 to 1. The larger the value, the stronger the positive impact. It is obtained through experiments. It is the negative feedback of students' emotions, indicating the negative feedback influence of emotions, such as low mood or dissatisfaction with learning content, which is quantified by students' emotional fluctuation data, ranging from 0 to 1; The cognitive state function , emotional state function , sub-function and subfunctions All are designed based on expert experience, psychology and educational behavior theory to ensure compliance with the basic theoretical logic in the fields of cognitive psychology, educational behavior and human-computer emotional interaction; The cognitive state function Used to characterize students in time The degree of mastery of a certain knowledge point depends not only on the students' familiarity with the learning content, but also on the students' , and also affected by the perceived difficulty of the learning content According to Bloom's cognitive goal taxonomy theory, the speed at which students' mastery of difficult knowledge decreases is nonlinear. Therefore, a reasonable expression should be able to reflect: when students are familiar with the learning content, High, perceived difficulty of learning content When the difficulty level of the learning content is low, the mastery level is high; when the difficulty level of the learning content is high When it is higher, the growth of mastery is related to the familiarity of the learning content. More sensitive; in terms of the difficulty of learning content In higher regions, the rate of increase in mastery tends to decrease.

[0030] Therefore, the cognitive state function It can be defined as: , in, Indicates the student's current familiarity with the learning content, with higher values ​​indicating greater familiarity; Indicates the subjective difficulty perception of a knowledge point, the higher the value, the more difficult it is; is the weight coefficient, which is used to control the nonlinear inhibitory strength of the difficulty perception of the learning content on the degree of mastery. , set by expert experience method; It is the difficulty threshold, which indicates the difficulty threshold that students can bear, and is set based on grade or stage. The above formula is an asymmetric sigmoid correction function, which ensures that the mastery level will not be overestimated when students are familiar with the learning content but the difficulty is also high; The emotional state function Express students in time The influence of emotional state on learning effect is affected by emotional acceptance and emotional stability Educational psychology believes that high acceptance but low stability (i.e., large emotional fluctuations) will weaken the sustained interest in learning content, so: , in, is the students’ emotional acceptance of the learning content. ; It is the emotional stability of students. The higher the level, the more stable it is. ; , is the adjustment coefficient, which is used to control the adjustment sensitivity of emotional acceptance and emotional stability, and is determined according to the expert experience method. In the above formula It is used to reflect students' emotional attitude towards learning content and has an emotional saturation effect. It is a fast-growing function that reflects that high stability enhances the credibility of emotional expression. The product of the two constitutes the final emotional response intensity. The sub-function Used to model the modifying effect of emotion on cognition. According to cognitive load theory and emotion-cognition coupling effect, students’ emotional feedback on learning activities It promotes cognitive development and emotional stability It can alleviate the interference of negative emotions. Therefore, the sub-function The composition is as follows: , in, Indicates students’ emotional feedback on learning activities. ; Indicates the emotional stability of students' emotions, ; It is used to adjust the reinforcement weight of emotional stability on cognitive gain, which is determined according to the expert experience method. The above function means that positive emotions plus high emotional stability can improve cognitive state together, while negative emotions are more likely to lead to cognitive collapse under low stability. The square root function avoids over-amplifying the influence of high stability. The sub-function It is used to simulate the impact of learning events on emotional states. It is an emotional regulation function based on positive and negative feedback. Emotional fluctuations should have a competitive relationship between positive and negative terms, that is, positive feedback raises emotions, and negative feedback suppresses emotions; sub-function The composition is as follows: , in, It is the positive feedback of students' emotions, such as task completion and improved grades. ; It is the negative feedback of students' emotions, such as failure in answering questions and disappointment. ; is a small constant used to prevent the denominator from being zero. The above function is a two-variable logarithmic competition function, whose value changes with the positive feedback of students' emotions. Increase and grow, with the negative feedback of students' emotions Increase and decrease. If positive and negative emotions are balanced (e.g. ), the output is ;like , indicating that the emotion tends to be positive; conversely, the emotion tends to be negative. This function has the effect of suppressing extreme emotional changes to avoid over-responding to short-term emotional disturbances; Step 2: Construct a nonlinear spatiotemporal weight adjustment mechanism; In order to accurately adjust the spatiotemporal weight of learning content according to students’ cognitive and emotional states, a nonlinear spatiotemporal weight adjustment mechanism is introduced; the nonlinear spatiotemporal weight adjustment mechanism dynamically adjusts the spatiotemporal weight of learning content according to students’ learning states (cognitive and emotional states) at different time points and the recommended time points of learning content. The formula is as follows: , in, It is the learning content exist The spatiotemporal weight of the moment; It is the learning content The initial importance coefficient reflects the priority of the learning content itself, which is set by experts or based on the criteria of course design; It is the time decay factor, which is used to control the decay rate of the importance of learning content over time and is set according to the update frequency of the subject content; It is the learning content The recommended time point is the reference point in the time decay factor, which is used to indicate the recommended time for the learning content; is the influence coefficient of cognitive state on the spatiotemporal weight of learning content, determined according to the expert experience method; is the total number of knowledge points; It is the nonlinear influence index of cognitive state on the spatiotemporal weight of learning content. It is used to control the nonlinear influence of the sum of students' cognitive states of all knowledge points in learning content recommendation. It is determined according to the expert experience method. is Students should always keep in mind the knowledge points cognitive state; Step 3: Combine cognitive state and emotional state to conduct dynamic analysis and generate personalized learning recommendations; Based on the spatiotemporal weight of learning content, combined with cognitive state and emotional state, generate recommendation priorities for learning content , the formula is as follows: , in, is the influence coefficient of emotional state on recommendation priority. A larger value indicates that the emotional state has a greater impact on the recommendation priority, and vice versa. It is obtained by experimental method; It is the influence coefficient of learning progress on recommendation priority, which is used to quantify the influence of learning progress on recommendation priority and is determined according to the expert experience method; It's a student Always pay attention to a certain knowledge point The learning progress is represented by a value between 0 and 1, where 0 means no learning and 1 means complete mastery. It is directly obtained through self-tests, correctness of exercises and other indicators; is the nonlinear adjustment coefficient used to control the influence of learning progress, obtained according to the experimental method; is the influence coefficient of cognitive status on recommendation priority, which is determined according to the expert experience method; The recommended priorities of the learning contents are arranged from large to small, and then personalized learning plans are pushed to students based on the recommended priorities of the learning contents, that is, the contents with high recommendations are studied first to achieve mathematics teaching.

[0031] In summary, the mathematics teaching system and method based on big data has been completed.

[0032] The order of the embodiments of the invention is for description only and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0033] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0034] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. The mathematics teaching method based on big data is characterized by: The following steps are involved: S1. Collect students’ learning behavior data and preprocess them to obtain preprocessed data; Through the adaptive multi-layer nonlinear feature fusion and optimization algorithm, the pre-processed data is subjected to feature extraction and optimization to obtain comprehensive feature data; Analyze learning status based on comprehensive feature data, obtain analysis results and generate personalized learning feedback; S2. Automatically adjust learning paths and content based on personalized learning feedback; Based on learning paths and learning content, personalized learning plans are pushed to students through intelligent recommendation algorithms to achieve mathematics teaching.

2. The mathematics teaching method based on big data according to claim 1 is characterized in that: The S1 specifically includes: The adaptive multi-layer nonlinear feature fusion and optimization algorithm extracts and optimizes features of pre-processed data by introducing multi-layer nonlinear fusion processing to obtain comprehensive feature data.

3. The mathematics teaching method based on big data according to claim 2 is characterized in that: The S1 specifically includes: In the process of implementing the adaptive multi-layer nonlinear feature fusion and optimization algorithm, feature engineering technology is used to perform preliminary feature extraction on the preprocessed data to obtain preliminary feature data, and the preliminary feature data is standardized to obtain standardized preliminary feature data; nonlinear transformation is introduced, and feature embedding is performed on the standardized preliminary feature data to obtain embedded feature data.

4. The mathematics teaching method based on big data according to claim 3 is characterized in that: The S1 specifically includes: The embedded feature data is subjected to multi-layer nonlinear fusion processing, and the weighted summation of the embedded feature data is performed using a multi-layer fusion structure to obtain the fused feature data.

5. The mathematics teaching method based on big data according to claim 4 is characterized in that: The S1 specifically includes: Genetic algorithms are introduced to perform feature selection and optimization on the fused feature data to obtain comprehensive feature data; based on the comprehensive feature data, learning status analysis is performed through a deep hierarchical neural network to obtain analysis results; based on the analysis results, personalized learning feedback is generated that includes students’ current learning status, degree of mastery, and areas that need improvement.

6. The mathematics teaching method based on big data according to claim 1 is characterized in that: The S2 specifically includes: In the process of implementing the intelligent recommendation algorithm, the cognitive state function and the emotional state function are defined, and the cognitive state adjustment coefficient and the emotional state adjustment coefficient are introduced to construct a learning cognitive model and an emotional dynamic analysis model to obtain the cognitive state and the emotional state.

7. The mathematics teaching method based on big data according to claim 6 is characterized in that: The S2 specifically includes: A nonlinear spatiotemporal weight adjustment mechanism is introduced to dynamically adjust the spatiotemporal weight of the learning content based on the cognitive state and the recommended time point of the learning content. The specific formula is as follows: ， in, It is the learning content exist The spatiotemporal weight of the moment; It is the learning content The initial importance coefficient of is the time decay factor; It is the learning content Recommended time point: is the influence coefficient of cognitive state on the spatiotemporal weight of learning content; is the total number of knowledge points; It is the nonlinear influence index of cognitive state on the spatiotemporal weight of learning content; is Students should always keep in mind the knowledge points cognitive state.

8. The mathematics teaching method based on big data according to claim 7 is characterized in that: The S2 specifically includes: Based on the spatiotemporal weight of the learning content, combined with cognitive state and emotional state, dynamic analysis is performed to generate the recommended priority of the learning content. The formula is as follows: ， in, It is the learning content exist Recommendation priority at the moment; is the influence coefficient of emotional state on recommendation priority; It's a student emotional state at the moment; is the influence coefficient of learning progress on recommendation priority; It's a student Always check the knowledge points learning progress; is the nonlinear adjustment coefficient used to control the impact of learning progress; is the influence coefficient of cognitive status on recommendation priority; It's a student The cognitive state at the moment.

9. The mathematics teaching method based on big data according to claim 8 is characterized in that: The S2 specifically includes: The recommended priorities of learning contents are arranged from large to small, and personalized learning plans are pushed to students based on the recommended priorities of learning contents. Those with high recommendation priorities are studied first to achieve mathematics teaching.

10. A mathematics teaching system based on big data, applied to the mathematics teaching method based on big data as claimed in claim 1, characterized in that: Includes the following parts: Data collection module, intelligent processing and feature optimization module, learning status analysis and feedback module, personalized learning module, intelligent recommendation module; The data acquisition module is responsible for collecting students' learning behavior data and obtaining raw data containing learning behavior data; the raw data is transmitted to the intelligent processing and feature optimization module; The intelligent processing and feature optimization module pre-processes the original data to obtain pre-processed data; Through the adaptive multi-layer nonlinear feature fusion and optimization algorithm, the pre-processed data is extracted and optimized to obtain comprehensive feature data; the comprehensive feature data is transmitted to the learning state analysis and feedback module; The learning status analysis and feedback module analyzes the learning status based on comprehensive feature data, obtains analysis results, and generates personalized learning feedback; transmitting personalized learning feedback to the personalized learning module; Personalized learning module, which automatically adjusts learning paths and content based on personalized learning feedback; Transferring learning paths and learning contents to the intelligent recommendation module; The intelligent recommendation module pushes personalized learning plans to students based on learning paths and learning content through intelligent recommendation algorithms to improve learning efficiency.

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