An online education information teaching optimization system based on a big data cloud platform

Abstract

This invention discloses an online education information-based teaching optimization system based on a big data cloud platform, relating to the fields of online education and big data analysis technology. The teacher analysis module collects teaching data and calculates the teaching difficulty value for each data segment, generating a teaching difficulty distribution sequence. The student analysis module collects feedback data and facial expression data, performs fusion analysis to obtain a comprehension index, and correlates it with the teaching difficulty value to obtain a learning fit index. The data collection module comprehensively analyzes the teaching difficulty distribution sequence and the learning fit index, establishes a coupling relationship model, and outputs teaching optimization decision parameters. The big data cloud platform calculates the actual teaching control quantity based on the control decision vector and adoption coefficient, dynamically regulating teaching difficulty, teaching pace, and resource allocation. By establishing an information cognition phase difference driving model and a coupling relationship model, the system achieves prediction and dynamic optimization of teaching effectiveness.

Description

Technical Field

[0001] This invention relates to the fields of online education and big data analysis technology, specifically to an online education information-based teaching optimization system based on a big data cloud platform. Background Technology

[0002] With the rapid development of internet technology, online education has become an important form of information-based teaching. However, existing online education systems still have shortcomings in practical applications. Traditional online teaching platforms typically use a fixed pace and uniform difficulty level for resource delivery, failing to dynamically adjust teaching content and pace based on students' real-time comprehension. This leads to some students experiencing cognitive overload due to excessively high difficulty or losing motivation due to excessively low difficulty. Existing systems lack the ability to finely model the dynamic relationship between teachers' teaching process and students' cognitive responses, making it difficult to quantitatively assess the fit between teaching difficulty and students' comprehension abilities from multiple dimensions such as teaching pace, frequency of knowledge point switching, and blackboard operation behavior. Furthermore, relying on a single answer accuracy rate or post-class assessment results for teaching feedback ignores real-time data rich in cognitive state information, such as students' facial expressions, interactive behaviors, and response times generated during the learning process, failing to achieve closed-loop dynamic optimization of the teaching process.

[0003] Therefore, there is an urgent need for an information-based teaching optimization system that can integrate teachers' teaching data and students' multimodal feedback data, and achieve adaptive adjustment of teaching difficulty based on a big data cloud platform. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing online education systems lack a dynamic matching mechanism between teaching difficulty and students' cognitive state, and cannot achieve real-time optimization of the teaching process. Therefore, this invention proposes an online education information-based teaching optimization system based on a big data cloud platform.

[0005] The objective of this invention can be achieved through the following technical solution: an online education information-based teaching optimization system based on a big data cloud platform, comprising: a big data cloud platform, a teacher analysis module, a student analysis module, and a data collection module;

[0006] The teacher analysis module collects teachers' teaching data in real time and performs structured decomposition processing on the teaching data, dividing it into several teaching data segments; it analyzes each teaching data segment and calculates the corresponding teaching difficulty value based on the teaching difficulty model; it then performs statistical sorting processing based on the teaching difficulty values ​​corresponding to each teaching data segment to obtain a teaching difficulty distribution sequence.

[0007] The student analysis module collects feedback data and facial expression data of each student in real time; it performs fusion analysis based on the feedback data and facial expression data to obtain the comprehension index corresponding to each student; and it performs correlation and fusion analysis with the teaching difficulty value of the corresponding teaching data segment to obtain the learning fit index.

[0008] The data collection module acquires the teaching difficulty distribution sequence and the corresponding learning fit index, and performs comprehensive analysis and processing on the two to establish a coupling relationship model between the teaching side and the learning side, thereby obtaining teaching optimization decision parameters. The teaching optimization decision parameters include teaching optimization index, adoption coefficient, and control decision vector.

[0009] The big data cloud platform receives the control decision vector, calculates it in conjunction with the adoption coefficient to obtain the actual teaching control quantity, and executes the corresponding teaching adjustment operation based on the teaching control quantity.

[0010] As a preferred embodiment of the present invention, the specific process of analyzing each teaching data segment in the teacher analysis module is as follows:

[0011] Any teaching data segment is represented as a time interval from the start time to the end time. An information cognition phase difference driven model is established, setting a teaching information input phase function, which is obtained by performing an arctangent transformation on the ratio of the cumulative teaching information quantity function to the information release rate per unit time. A student cognitive response phase function is set, which is obtained by performing an arctangent transformation on the ratio of the cumulative cognitive absorption quantity function to the cognitive absorption rate per unit time. The absolute value of the difference between the information input phase and the student cognitive response phase is calculated as the phase mismatch function. Then, a teaching difficulty evolution equation is established, where the historical phase mismatch accumulation is obtained by integrating the phase mismatch function from the start time of the data segment to the current time. The teaching difficulty evolution equation is then integrated from the start time of the data segment to the end time to obtain the overall teaching difficulty value of the teaching data segment.

[0012] As a preferred embodiment of the present invention, the specific process of statistically sorting based on the teaching difficulty value corresponding to each teaching data segment includes:

[0013] A difficulty potential field evolution model is established. For each teaching data segment, its difficulty potential function value and difficulty potential gradient function are calculated. A difficulty stability constraint function is set. A comprehensive difficulty ranking driving function is established. Finally, based on the value of the comprehensive difficulty ranking driving function from large to small, all teaching data segments are reconstructed to obtain the teaching difficulty distribution sequence.

[0014] As a preferred embodiment of the present invention, the specific process of fusing and analyzing feedback data and facial expression data is as follows:

[0015] The system collects feedback and facial expression data sequences for each student in real time within the same time interval. The feedback data sequence is obtained by weighting and summing the answer results, the reciprocal of the response time, the intensity of the interactive behavior, and the frequency of operation at each sampling moment using a dimensionless coefficient. The facial expression data sequence is obtained by weighting and summing the amplitude of facial expression changes, the degree of gaze deviation, and the concentration index at each sampling moment using a feature mapping coefficient. A time-diffusion mapping model is established to map the discrete feedback and facial expression data sequences into continuous functions of feedback behavior and cognition, respectively. A behavioral response phase function and a cognitive performance phase function are defined, and the absolute value of the difference between the behavioral response phase and the cognitive performance phase is calculated as the behavioral-cognitive phase mismatch function. A comprehension state function is established. Finally, the comprehension state function is integrated from the start to the end of the data segment to obtain the student's overall comprehension index of the current teaching content.

[0016] As a preferred embodiment of the present invention, the specific process of correlating and analyzing the understanding indicators with the teaching difficulty values ​​of the corresponding teaching data segments is as follows:

[0017] A learning evolution curvature difficulty-driven curvature matching model is established, mapping the student's comprehension index on a certain teaching data segment to a comprehension curvature function; mapping the teaching difficulty value of the corresponding teaching data segment to a difficulty-driven curvature function; calculating the absolute value of the difference between the comprehension curvature and the difficulty-driven curvature as the learning difficulty curvature deviation function; establishing a learning fit evolution function; and performing an integral operation on the learning fit evolution function from the start time to the end time of the teaching data segment to obtain the student's learning fit index on that teaching data segment.

[0018] As a preferred embodiment of the present invention, the specific process of comprehensively analyzing and processing the teaching difficulty distribution sequence and learning fit index is as follows:

[0019] The discrete sequence of teaching difficulty distribution is mapped to a continuous distribution function of teaching difficulty; the discrete sequence of learning fit indexes is mapped to a continuous response function of learning fit; a teaching-learning coupling functional is defined; the extreme values ​​of this coupling functional are taken to obtain the coupling constraint equation; a variational mismatch strength function is defined based on the coupling constraint equation; the teaching-learning coupling strength function is established by setting the evolution process driven by the functional; the teaching-learning coupling strength function is integrated from the zero point to the endpoint of the structural coordinates to obtain the teaching optimization index; the average value of the variational mismatch strength function on the structural coordinates is negatively exponentially taken to obtain the adoption coefficient; a control decision vector is generated; finally, the teaching optimization decision parameters containing the teaching optimization index, the adoption coefficient, and the control decision vector are output.

[0020] As a preferred embodiment of the present invention, the specific process of calculating and executing teaching adjustment operations based on the received control decision vector and adoption coefficient in the big data cloud platform includes:

[0021] The control decision vector is mapped into a vector form containing three components; each component is continuously modulated using the adoption coefficient, and the correlation mapping between the control intensity and the judgment result is established; a memory kernel function with time decay characteristics is set to obtain the actual teaching control quantity with time delay superposition effect; the actual teaching control quantity is nonlinearly compressed and mapped to obtain the final execution control quantity; and a teaching control vector containing three final execution control components is established; the teaching control vector is used as a driving quantity in the teaching execution process, and mapped to the teaching difficulty function, teaching rhythm function, and teaching resource allocation function respectively; the entire process of the control decision vector being modulated by the adoption coefficient, superimposed by time delay memory, and then continuously executed is completed.

[0022] In a preferred embodiment of the present invention, the process of mapping to the teaching difficulty function, the teaching pace function, and the teaching resource allocation function is as follows:

[0023] The mapping process of the teaching difficulty function is as follows: the teaching difficulty at the current moment is equal to the teaching difficulty at the initial moment multiplied by the negative value of the exponential function of the integral of the control component from the initial moment to the current moment. When the control component is positive, the teaching difficulty decreases monotonically with time, which triggers the calling of low-complexity teaching content and the insertion of auxiliary explanations.

[0024] The mapping process of the teaching rhythm function is as follows: the teaching rhythm at the current moment is equal to the teaching rhythm at the beginning moment plus the difference between the teaching rhythm at the beginning moment and the preset rhythm benchmark value multiplied by the negative value of the exponential function of the integral value of the control component from the beginning moment to the current moment, so that the teaching rhythm converges and adjusts around the benchmark value. The larger the control component, the faster the convergence speed, and the smooth control of the rhythm is performed, corresponding to the slowing down and stabilizing control of the rhythm of the teaching process.

[0025] The mapping process of the teaching resource allocation function is as follows: the teaching resource allocation amount at the current moment is equal to the upper limit of resource allocation minus the difference between the upper limit of resource allocation and the resource allocation amount at the beginning moment, multiplied by the negative value of the exponential function of the integral of the control component from the beginning moment to the current moment. By exponentially compressing the remaining resource space, the resource allocation gradually increases with the control quantity and tends to the upper limit, avoiding sudden loading of resources, which corresponds to the dynamic supplementation and push of cloud teaching resources.

[0026] Compared with the prior art, the beneficial effects of the present invention are:

[0027] 1. This invention collects and breaks down teachers' teaching data into segments during the teaching process, along with students' feedback and facial expression data, to establish a teaching difficulty distribution sequence and a learning fit index. If the curvature deviation between the teaching difficulty and the student's understanding in a certain teaching data segment exceeds a threshold, a control decision vector is generated and the actual teaching control quantity is calculated based on the adoption coefficient. The difficulty, pace, and resource allocation of subsequent teaching content are adjusted accordingly, ensuring that the teaching supply actively adapts to the student's cognitive rhythm. After implementation, the phase mismatch between teaching difficulty and student understanding decreases, and the learning fit index improves. During the teaching execution phase, the teaching pace smoothly converges around a baseline value, reducing student cognitive load and increasing interactive activity. In the long-term learning process, because teaching resources are dynamically replenished as needed and the trend of difficulty changes maintains geometric consistency with the curvature of student understanding, the overall student understanding index improves, and knowledge absorption efficiency is enhanced. By actively controlling the coupling relationship between teaching and learning, the invention achieves prediction and dynamic optimization of teaching effectiveness. We construct an information cognition phase difference-driven model and a teaching and learning coupling model to feedforward regulate the dynamic mismatch between teachers' teaching pace and students' cognitive response, thereby solving the problem of low learning efficiency caused by the mismatch between teaching difficulty and students' comprehension ability in online education. Attached Figure Description

[0028] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0029] Figure 1 This is a schematic diagram of the principle of the present invention. Detailed Implementation

[0030] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0031] It should be understood that the terms “comprising” and “including” used in this disclosure and claims indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0032] It should also be understood that the terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to limit the disclosure. As used in this disclosure and claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this disclosure and claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations.

[0033] Please see Figure 1 As shown, an online education information-based teaching optimization system based on a big data cloud platform includes: a big data cloud platform, a teacher analysis module, a student analysis module, and a data collection module;

[0034] The teacher analysis module collects teachers' teaching data in real time and performs structured decomposition processing, dividing the data into several teaching data segments. These segments include teaching speed, explanation duration, frequency of knowledge point switching, and blackboard / PowerPoint operation behaviors. Each teaching data segment is then analyzed individually, and the corresponding teaching difficulty value is calculated based on a teaching difficulty model.

[0035] Furthermore, based on the teaching difficulty values ​​corresponding to each teaching data segment, statistical and sorting processing is performed to obtain a teaching difficulty distribution sequence, which is used to characterize the trend of difficulty changes and the distribution of key difficulties in the current teaching process.

[0036] The student analysis module collects feedback and facial expression data from each student in real time. Feedback data includes answer results, response time, interactive behavior, and operation frequency, while facial expression data includes changes in facial expressions, gaze direction, and focus characteristics. Based on the fusion analysis of feedback and facial expression data, a comprehension index corresponding to each student is obtained.

[0037] Furthermore, the comprehension index is correlated and integrated with the teaching difficulty value of the corresponding teaching data segment to obtain the learning fit index, which represents the degree of matching between the student's current comprehension ability and the teaching difficulty.

[0038] The data collection module acquires the teaching difficulty distribution sequence and the corresponding learning fit index, and performs comprehensive analysis and processing on the two to establish a coupling relationship model between the teaching side and the learning side, thereby obtaining teaching optimization decision parameters. The teaching optimization decision parameters include teaching optimization index, adoption coefficient, and control decision vector.

[0039] The teaching optimization index is calculated based on the teaching difficulty distribution sequence and the learning fit index to characterize the degree of deviation between the current teaching difficulty and the students' comprehension status.

[0040] Subsequently, the teaching optimization indicators are input into the preset judgment model and compared with the set threshold to generate the corresponding adoption coefficient. When the teaching optimization indicators are less than the preset threshold, the adoption coefficient approaches zero to suppress teaching adjustments. When the teaching optimization indicators are greater than or equal to the preset threshold, the adoption coefficient increases with the degree of deviation to enhance the adjustment intensity. On this basis, the control decision vector is generated by combining the teaching difficulty distribution sequence and the learning fit index to determine the adjustment direction and magnitude of teaching difficulty, teaching pace, and teaching resource recommendations.

[0041] The generated control decision vector is transmitted to the big data cloud platform for the collection, integration, and control management of teaching materials. The big data cloud platform calculates the actual teaching control quantity based on the received control decision vector and the adoption coefficient, and performs corresponding teaching adjustment operations based on the teaching control quantity. These operations include dynamically filtering and calling materials in the teaching resource library, adaptively adjusting the difficulty of teaching content, and controlling the teaching pace in real time.

[0042] The specific process of analyzing each teaching data segment is as follows:

[0043] The i-th teaching data segment is represented as the time interval [t0, t1], where i represents the teaching data segment number and t represents the continuous time variable. Based on this, an information cognition phase difference driven model is established to describe the phase shift relationship between information supply and student cognitive response during the teaching process.

[0044] Set the phase function θ for inputting teaching information i in (t), which is used to characterize the rhythmic state of the teacher's information output at time t, is specifically defined as: ,in, This function represents the cumulative amount of teaching information. This indicates the rate at which information is released per unit time. Used to map the information growth rate to a phase angle, and used to characterize the nonlinear state of changes in teaching rhythm;

[0045] Furthermore, a student cognitive response phase function is set. This characterizes the learner's rhythmic state of absorbing instructional information, and is defined as follows: , where C i (t) represents the cumulative cognitive absorption function. This represents the rate of cognitive absorption per unit time, and this structure is used to characterize the dynamic changes in learners' comprehension rhythm.

[0046] Based on this, the teaching difficulty is set from the information phase cognitive phase mismatch, and a phase mismatch function is established: Δθ i (t)=∣θ iin (t)-θ i out (t)∣where, Δθ i (t) represents the degree of phase shift between information input and cognitive output at time t, which describes the intensity of the misalignment of teaching rhythm;

[0047] Furthermore, a phase accumulation enhancement mechanism is established to describe the amplification effect of long-term misalignment on teaching difficulty, and an evolution equation for teaching difficulty is constructed. , where D i (t) represents the instantaneous teaching difficulty function, the exponential term represents the enhancing effect of historical phase mismatch accumulation on the current difficulty, and τ is the integral dummy variable;

[0048] Finally, integrating the above difficulty evolution equation over the time interval [t0, t1] yields the overall teaching difficulty value for the i-th teaching data segment: , where D i This represents the cumulative teaching difficulty value of the teaching data segment. By establishing a dynamic mismatch process between the information phase and the cognitive phase, the model transforms the teaching difficulty from a traditional static statistic into a dynamic evolution driven by rhythm mismatch.

[0049] The statistical and sorting process based on the teaching difficulty values ​​corresponding to each teaching data segment specifically includes:

[0050] The teaching difficulty value corresponding to the i-th teaching data segment is Di, where i = 1, 2, ..., N, and N represents the total number of teaching data segments. Here, a difficulty potential field evolution model is established to map discrete teaching difficulty values ​​to continuous difficulty potential functions, describing the structural distribution characteristics of teaching difficulty in the overall teaching process.

[0051] Define a difficulty potential function Φ(i) to characterize the difficulty influence of the i-th teaching data segment in the overall sequence, as follows: Among them, D j Let |ij| represent the teaching difficulty value of the j-th teaching data segment, and |ij| represent the index distance between data segments, j∈{1, 2, ..., N}. p is the distance attenuation index, used to control the degree of attenuation of the influence of distant data segments on the current segment; for example, the distance attenuation index p is a constant between 1 and 3; preferably, p is 2.

[0052] Furthermore, the difficulty gradient function is calculated as follows: G(i) = Φ(i+1) - Φ(i), where G(i) represents the difficulty trend of the i-th teaching data segment. The value of i in G(i) ranges from N-1 to avoid i=1 exceeding the total number of teaching data segments N. When G(i) > 0, it indicates that the difficulty is increasing; when G(i) < 0, it indicates that the difficulty is decreasing.

[0053] Next, a difficulty stability constraint function is set to suppress local abnormal fluctuations, which is defined as: , where S(i) represents the stability coefficient of the i-th teaching data segment, which measures the consistency between the difficulty of the data segment and the overall distribution;

[0054] Subsequently, a comprehensive difficulty ranking driving function is established: Where R(i) represents the sorting driving value of the i-th teaching data segment, The second-order change represents the trend of difficulty change and is used to characterize the characteristics of sudden changes in difficulty.

[0055] Finally, all teaching data segments are reconstructed according to the size of the sorting driving value R(i). The corresponding teaching data segments are arranged from largest to smallest according to the sorting driving value R(i) to obtain the teaching difficulty distribution sequence {D(1), D(2), ..., D(N)}. Through the above joint modeling process based on difficulty potential field, gradient evolution and stability constraints, the teaching difficulty distribution is structurally reconstructed.

[0056] The process of fusing and analyzing feedback data and facial expression data is as follows:

[0057] Real-time collection of feedback and facial expression data of the m-th student within the time interval [t0, t1]; where the discretely collected feedback data sequence is represented as f. m (k), the expression data sequence is represented as e m (k), where k = 1, 2, ..., K, represents the k-th sampling time, t k This represents the corresponding sampling time, and K represents the total number of samples.

[0058] Here, to endow discrete data with continuous evolution characteristics, a time-diffusion mapping model is established to map discrete data into continuous-time functions:

[0059] Feedback data continuous function: , of which F m (t) represents a continuous function of the student's feedback behavior at time t, and σ represents a time diffusion parameter used to control the influence range of discrete sampling points on the neighborhood time. For example, the value of the time diffusion parameter σ is positively correlated with the sampling interval, typically ranging from 0.5 to 2.0. Preferably, when the sampling frequency is 1 time / second, σ is 1. m (k) Established from multi-source feedback data: , where a m (k) represents the answer result, τ m (k) represents the response time, b m (k) represents the intensity of the interaction behavior, c m(k) represents the operation frequency, and α1, α2, α3 and α4 are dimensionless coefficients used to map different types of behavior to a unified feedback quantity; for example, the dimensionless coefficients satisfy the normalization constraint α1+α2+α3+α4=1, and the specific values ​​of each coefficient are preset according to the importance of the behavior data; preferably, α1=0.4, α2=0.2, α3=0.2 and α4=0.2 are taken.

[0060] Furthermore, establish a continuous function for facial expression data: , of which E m (t) represents a continuous function of student's facial expression cognition at time t; e m (k) Calculation based on facial features: , where p m (k) represents the range of facial expression changes, q m (k) represents the degree of line-of-sight deviation, r m (k) represents the focus index, and β1, β2 and β3 are feature mapping coefficients; for example, the feature mapping coefficients satisfy the normalization constraint β1+β2+β3=1, and each coefficient is assigned a weight according to the significance of the facial features; preferably, β1=0.5, β2=0.3 and β3=0.2 are taken.

[0061] In obtaining the continuous function F m (t) and E m After (t), the behavioral feedback rhythm state and the cognitive performance rhythm state are obtained through the response-cognitive performance phase coupling model, and the behavioral response phase function is defined: And the cognitive performance phase function: ,in, Indicates the state of behavioral feedback rhythm. It indicates the rhythmic state of cognitive performance.

[0062] Further establish the behavioral-cognitive phase mismatch function: Δθ m (t)=∣ - |, where Δθ m (t) represents the degree of rhythmic shift between behavior and cognition.

[0063] Based on this, we establish the understanding of the state function: , among which, U m (t) represents the student's instantaneous comprehension state at time t, and the exponents represent the current mismatch inhibition and the historical cumulative inhibition effect, respectively.

[0064] Finally, by integrating the comprehension state function over the time interval [t0, t1], we obtain the comprehension index for the m-th student: , among which, I mThis represents the student's overall level of understanding of the current teaching content; through the complete process described above, from discrete data construction, continuous mapping, phase coupling to the evolution of understanding, a dynamic model of the student's understanding state is formed.

[0065] The process of correlating and integrating comprehension indicators with the teaching difficulty values ​​of corresponding teaching data segments specifically involves:

[0066] Let I be the comprehension index of the m-th student on the i-th instructional data segment. m，i Here, a curvature matching model driven by the difficulty of knowledge evolution curvature is established. This model describes the geometric consistency between the changing trends of student comprehension and the changing trends of teaching difficulty. Specifically, comprehension indicators and teaching difficulty values ​​are mapped to curvature spaces, and the comprehension curvature function is defined. And the difficulty-driven curvature function: Where τ represents the evolution time parameter within the teaching data segment, dI m，i To represent the rate of change of the indicator, d 2 I m，i To represent the acceleration of change, dD i and d 2 D i These represent the first and second rates of change of teaching difficulty, respectively;

[0067] Furthermore, a learning difficulty curvature deviation function is established: Δκ m，i =∣ - ∣, where Δκ m，i This indicates the degree of geometric curvature difference between the trend of change in students' understanding and the trend of change in teaching difficulty.

[0068] Based on this, a curvature consistency decay process is set up to describe the inhibitory effect of curvature deviation on learning fitness, and a learning fitness evolution function is established: in, τ represents the instantaneous learning fit of the m-th student in the i-th teaching data segment, τ0 represents the initial evolution time of the data segment, and the exponential terms represent the current curvature matching degree and the cumulative effect of historical curvature deviation, respectively.

[0069] Finally, integrating the fitness evolution function over the interval [tau0, tau1] yields the learning fitness index: , where A m，i τ represents the learning fit index of the m-th student on the i-th teaching data segment; τ1 represents the termination evolution time of the i-th teaching data segment; through the above dynamic modeling process based on the matching relationship between the curvature of understanding and the curvature of difficulty, the geometric consistency between the trend of changes in student cognition and the trend of changes in teaching difficulty is characterized.

[0070] Obtain the teaching difficulty distribution sequence and the corresponding learning fit index, and perform comprehensive analysis and processing on the two, specifically as follows:

[0071] Let the sequence of teaching difficulty distribution be D = {D(1), D(2), ..., D(N)}, and the corresponding learning fit index be A. m ={A m，1 A m，2 A m，N}, where i = 1, 2, ..., N, m = 1, 2, ..., M, N represents the total number of teaching data segments, and M represents the total number of students;

[0072] Next, the discrete sequence is mapped to a continuous function: , Where: D(x) represents the continuous distribution function of teaching difficulty, A m (x) represents the learning adaptation continuous response function, and x represents the continuous coordinates of the instructional structure. and The smoothing diffusion parameter is used to control the kernel function width during the mapping process of the teaching difficulty sequence and learning fit sequence to a continuous function, and its value determines the intensity of mutual influence between adjacent data segments; for example, and The value of is a constant ranging from 0.5 to 2.0; preferably, = =1.

[0073] Next, we define the instruction-learning coupling functional: , where: J[A m [Indicates the overall mismatch energy] Due to differences in trends, For numerical deviation, μ1 represents the structural constraint parameter; for example, the structural constraint parameter μ1 is a constant between 0.1 and 1.0, used to adjust the weight ratio of the numerical deviation term in the total mismatch energy; preferably, μ1 = 0.5.

[0074] Furthermore, by taking the extreme values ​​of the functional, we obtain the coupling constraint equations: ,in: This indicates the acceleration of learning to adapt to changes. This indicates the acceleration of the change in difficulty.

[0075] Based on the acceleration of learning adaptation and the acceleration of difficulty change, the coupling bias function is defined as follows: Where: Δ V (x) represents the variational mismatch intensity.

[0076] Next, by setting the evolution process driven by the functional, the teaching-learning coupling strength function is obtained, specifically: Where: C(x) represents the teaching-learning coupling strength function, and s1 is an integral dummy variable used to characterize the variational mismatch strength Δ in the interval [0, x]. V The historical cumulative calculation process of (x).

[0077] Based on the obtained teaching-learning coupling strength function, teaching optimization indicators are extracted: ,in, To optimize teaching indicators; the adoption coefficient is calculated based on the obtained coupling deviation function: ,in, This is the adoption coefficient;

[0078] Based on the above process, the control decision vector U is generated: C(N) represents the terminal value of the teaching-learning coupling strength function C(x) at the structural coordinate boundary x=N, which is used to characterize the residual coupling strength between the teaching side and the learning side after all teaching content has been completed.

[0079] Finally, output the teaching optimization decision parameters. .

[0080] The process of calculating the control decision vector based on the received control decision vector and the adoption coefficient includes:

[0081] Received control decision vector After that, it is mapped to ;

[0082] Next, the control decision vector is continuously modulated using the adoption coefficient λ, so that each component is transformed into the initial control input. = ·u o , where o=1, 2, 3, to achieve the correlation mapping between the control intensity and the judgment result;

[0083] Here, a memory kernel function K(t−τ)=exp(−β(t−τ)) with time decay characteristics is set, and the initial control input is convolved with the historical control trajectory to obtain the actual teaching control quantity with historical influence: , where β represents the memory decay coefficient, which controls the degree of influence of historical information on current regulation; through the above time delay superposition process, the teaching control quantity has the characteristics of continuity and historical consistency;

[0084] Subsequently, the actual teaching control quantity is subjected to nonlinear compression mapping to obtain the final execution control quantity: ,in, For final execution control quantity;

[0085] Therefore, a teaching control vector is established. The control vector is then used as a driving force in the teaching execution process. During the teaching execution process, the control vector is mapped to the teaching difficulty function H(t), the teaching rhythm function V(t), and the teaching resource allocation function R(t), respectively.

[0086] For the teaching difficulty function H(t), establish a control component For the exponential evolutionary mapping of generators, the following relation is satisfied: Where H(t0) represents the initial teaching difficulty; t represents the current teaching execution time, and t0 represents the starting execution time corresponding to the teaching data segment. The teaching difficulty is continuously adjusted by accumulating the integral of the control variable over the time domain, and when... As the value increases, the integral term increases, causing H(t) to exhibit an exponential decay trend, which corresponds to a decrease in the complexity of the teaching content.

[0087] For the teaching rhythm function V(t), a relative deviation-driven mapping process is set up, with the process control component acting on the rhythm deviation, resulting in: Wherein, V0 is the preset rhythm baseline value; this mapping method enables the teaching rhythm to converge and adjust around the baseline value. The larger the control component, the faster the convergence speed, thus achieving smooth rhythm control.

[0088] For the teaching resource allocation function R(t), establish a controlled growth mapping so that the control component acts on the remaining resource space, and obtain: , where R max This indicates the upper limit of resource allocation; by exponentially compressing the remaining resource space, resource allocation gradually increases with the control amount and tends to the upper limit, thus avoiding sudden resource loading.

[0089] Through the above mapping process based on integral generators, each component of the control vector is transformed into a continuous function acting on teaching difficulty, teaching pace, and allocation of teaching resources. This enables the three types of teaching states to evolve collaboratively in the time domain and maintain a consistent adjustment trend with the control vector, thus realizing a functional mapping from control quantity to the teaching execution process.

[0090] Furthermore, when When the value is positive, the teaching difficulty function H(t) decreases monotonically with time, corresponding to the triggering of low-complexity teaching content and the insertion of auxiliary explanations; when... When the value is positive, the teaching rhythm function V(t) converges towards the baseline rhythm V0, thus slowing down and stabilizing the rhythm of the teaching process; when... When the value is positive, the teaching resource function R(t) increases towards the upper limit Rmax, dynamically supplementing and pushing cloud-based teaching resources; completing the entire process from the control decision vector through adoption coefficient modulation, time delay memory superposition to continuous execution control, realizing the dynamic allocation of teaching materials and the coordinated control of the teaching process.

[0091] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. An online education information-based teaching optimization system based on a big data cloud platform, comprising: The platform comprises a big data cloud platform, a teacher analysis module, a student analysis module, and a data collection module; its features include: The teacher analysis module collects teachers' teaching data in real time and performs structured decomposition processing on the teaching data, dividing it into several teaching data segments; it analyzes each teaching data segment and calculates the corresponding teaching difficulty value based on the teaching difficulty model; it then performs statistical sorting processing based on the teaching difficulty values ​​corresponding to each teaching data segment to obtain a teaching difficulty distribution sequence. The student analysis module collects feedback data and facial expression data of each student in real time; it performs fusion analysis based on the feedback data and facial expression data to obtain the comprehension index corresponding to each student; and it performs correlation and fusion analysis with the teaching difficulty value of the corresponding teaching data segment to obtain the learning fit index. The data collection module acquires the teaching difficulty distribution sequence and the corresponding learning fit index, and performs comprehensive analysis and processing on the two to establish a coupling relationship model between the teaching side and the learning side, thereby obtaining teaching optimization decision parameters. The teaching optimization decision parameters include teaching optimization index, adoption coefficient, and control decision vector. The big data cloud platform receives the control decision vector, calculates it in conjunction with the adoption coefficient to obtain the actual teaching control quantity, and executes the corresponding teaching adjustment operation based on the teaching control quantity.

2. The online education information-based teaching optimization system based on a big data cloud platform according to claim 1, characterized in that, The specific process of analyzing each teaching data segment in the teacher analysis module is as follows: Any teaching data segment is represented as a time interval from the start time to the end time; an information cognition phase difference driven model is established, and a teaching information input phase function is set, which is obtained by performing an arctangent transformation on the ratio of the cumulative teaching information quantity function to the information release rate per unit time; A student cognitive response phase function is set up, which is obtained by performing an arctangent transformation on the ratio of the cumulative cognitive absorption function to the cognitive absorption rate per unit time. The absolute value of the difference between the information input phase and the student cognitive response phase is calculated as the phase mismatch function. Then, an evolution equation for teaching difficulty is established, in which the historical phase mismatch accumulation is obtained by integrating the phase mismatch function from the start time of the data segment to the current time. The overall teaching difficulty value of the teaching data segment is obtained by integrating the teaching difficulty evolution equation from the start time of the data segment to the end time.

3. The online education information-based teaching optimization system based on a big data cloud platform according to claim 1, characterized in that, The specific process of statistically sorting based on the teaching difficulty values ​​corresponding to each teaching data segment includes: A difficulty potential field evolution model is established. For each teaching data segment, its difficulty potential function value and difficulty potential gradient function are calculated. A difficulty stability constraint function is set. A comprehensive difficulty ranking driving function is established. Finally, based on the value of the comprehensive difficulty ranking driving function from large to small, all teaching data segments are reconstructed to obtain the teaching difficulty distribution sequence.

4. The online education information-based teaching optimization system based on a big data cloud platform according to claim 3, characterized in that, The specific process of fusing and analyzing feedback data and facial expression data is as follows: The system collects feedback and facial expression data sequences for each student in real time within the same time interval. The feedback data sequence is obtained by weighting and summing the answer results, the reciprocal of the response time, the intensity of the interactive behavior, and the frequency of operation at each sampling moment using a dimensionless coefficient. The facial expression data sequence is obtained by weighting and summing the amplitude of facial expression changes, the degree of gaze deviation, and the concentration index at each sampling moment using a feature mapping coefficient. A time-diffusion mapping model is established to map the discrete feedback and facial expression data sequences into continuous functions of feedback behavior and cognitive expression, respectively. A behavioral response phase function and a cognitive performance phase function are defined, and the absolute value of the difference between the behavioral response phase and the cognitive performance phase is calculated as the behavioral-cognitive phase mismatch function. A comprehension state function is established. Finally, the comprehension state function is integrated from the start to the end of the data segment to obtain the student's overall comprehension index of the current teaching content.

5. The online education information-based teaching optimization system based on a big data cloud platform according to claim 1, characterized in that, The specific process of correlating and integrating the understanding indicators with the teaching difficulty values ​​of the corresponding teaching data segments is as follows: Establish a learning evolution curvature difficulty-driven curvature matching model, which maps students' comprehension index on a certain teaching data segment to a comprehension curvature function; and maps the teaching difficulty value of the corresponding teaching data segment to a difficulty-driven curvature function. Calculate the absolute value of the difference between the understanding curvature and the difficulty-driven curvature, and use it as the learning difficulty curvature deviation function; establish the learning fit evolution function; perform an integral operation on the learning fit evolution function from the start time to the end time of the teaching data segment to obtain the student's learning fit index on the teaching data segment.

6. The online education information-based teaching optimization system based on a big data cloud platform according to claim 5, characterized in that, The specific process of comprehensively analyzing and processing the distribution sequence of teaching difficulty and learning fit index is as follows: The discrete sequence of teaching difficulty distribution is mapped to a continuous distribution function of teaching difficulty; the discrete sequence of learning fit index is mapped to a continuous response function of learning fit; a teaching-learning coupling functional is defined; the extreme values ​​of the coupling functional are taken to obtain the coupling constraint equation. Define a variational mismatch strength function based on the coupled constraint equation; By setting up a functional-driven evolution process, a teaching-learning coupling strength function is established; the teaching-learning coupling strength function is integrated from the zero point to the endpoint of the structural coordinates to obtain the teaching optimization index. The adoption coefficient is obtained by taking the negative exponent of the average value of the variational mismatch intensity function on the structural coordinates; Generate a control decision vector, and finally output the teaching optimization decision parameters, which include teaching optimization indicators, adoption coefficients, and control decision vectors.

7. The online education information-based teaching optimization system based on a big data cloud platform according to claim 6, characterized in that, The specific process of calculating and executing teaching adjustment operations based on the received control decision vector and adoption coefficient in the big data cloud platform includes: The control decision vector is mapped into a vector form containing three components; each component is continuously modulated using the adoption coefficient, and the correlation mapping between the control intensity and the judgment result is established; a memory kernel function with time decay characteristics is set to obtain the actual teaching control quantity with time delay superposition effect; the actual teaching control quantity is nonlinearly compressed and mapped to obtain the final execution control quantity; and a teaching control vector containing three final execution control components is established; the teaching control vector is used as a driving quantity in the teaching execution process, and mapped to the teaching difficulty function, teaching rhythm function, and teaching resource allocation function respectively; the entire process of the control decision vector being modulated by the adoption coefficient, superimposed by time delay memory, and then continuously executed is completed.

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