A cognitive state evaluation method and system for mathematics teaching

Abstract

The application relates to the technical field of artificial intelligence. By providing a cognitive state evaluation method and system for mathematics teaching, the method comprises the following steps: based on a causal diagram and collected multi-modal behavior characteristics of students, joint causal parameter learning is performed to obtain a behavior-cognition inference function and an intervention-behavior prediction function; based on the real-time collected multi-modal behavior characteristics of a target student, the behavior-cognition inference function and the intervention-behavior prediction function, counterfactual reasoning is performed to generate a cognitive state transition probability distribution; and based on the cognitive state transition probability distribution and a causal path in the causal diagram, controllable explanation generation is performed to obtain a natural language explanation report, so that the technical effects of improving dynamic behavior characteristic analysis precision, enhancing mathematics subject logic adaptability, strengthening multi-modal causal reasoning capability and optimizing teaching guidance explanation value are achieved.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and in particular to a method and system for assessing cognitive state in mathematics teaching. Background Technology

[0002] With the deep integration of artificial intelligence and education, intelligent assessment technology for mathematics teaching is gradually becoming a key means to improve teaching quality. Mathematical cognitive status assessment aims to quantify students' depth of understanding of mathematical concepts, problem-solving abilities, and thinking patterns, thereby providing scientific and reliable data support for personalized teaching.

[0003] In traditional cognitive assessment technology systems, relevant technical solutions mostly adopt standardized test models, using test scores or multiple-choice question answers as the basis for assessing cognitive levels. However, this model has core flaws, such as ignoring the dynamic behavioral characteristics of the problem-solving process and failing to effectively distinguish between correct guesses and true answers. When conducting knowledge mastery status diagnosis, traditional technical solutions rely on a general cognitive diagnostic framework, combined with item response theory or deterministic input noise gate model for diagnostic processing. However, because they do not incorporate the knowledge graph structure unique to mathematics, their assessment results are fundamentally disconnected from the internal logic of mathematics.

[0004] Furthermore, traditional cognitive assessment techniques often neglect the modeling of complex causal mechanisms between multimodal behavior and cognition, as well as the effective correlation between assessment explanations and cognitive causal paths. Whether using behavior-cognition linear regression models to predict students' cognitive states based on behavioral data such as answer duration and click frequency, or using black-box generative explanatory report technology to generate assessment descriptions based on long short-term memory networks or transformer models, both have significant core technical defects. The former is difficult to achieve counterfactual reasoning and cannot effectively predict changes in cognitive states under different teaching intervention strategies; the latter's assessment explanations are not related to cognitive causal paths, and therefore lack practical teaching guidance value. Summary of the Invention

[0005] Therefore, it is necessary to provide a cognitive state assessment method and system for mathematics teaching to address the above-mentioned technical problems, so as to improve the accuracy of dynamic behavioral feature analysis, enhance the logical adaptability of mathematics, strengthen multimodal causal reasoning ability, and optimize the technical effect of teaching guidance and interpretation.

[0006] Firstly, this application provides a method for assessing cognitive states in mathematics teaching, the method comprising:

[0007] Based on a pre-designed mathematical subject knowledge graph, a pre-designed multimodal teaching intervention library, and a pre-designed cognitive dimension framework, a four-layer directed causal graph is constructed to obtain the causal graph.

[0008] Based on the causal graph and the collected multimodal behavioral characteristics of students, joint causal parameter learning is performed to obtain the behavior-cognition inference function and the intervention-behavior prediction function;

[0009] Based on the real-time collection of multimodal behavioral characteristics, behavior-cognition inference functions, and intervention-behavior prediction functions of target students, counterfactual reasoning is performed to generate a cognitive state transition probability distribution.

[0010] Based on the probability distribution of cognitive state transitions and the causal paths in the causal graph, a controllable interpretation is generated to obtain a natural language interpretation report.

[0011] In one embodiment, based on the real-time collected multimodal behavioral features, behavior-cognition inference function, and intervention-behavior prediction function of the target student, counterfactual reasoning is performed to generate a cognitive state transition probability distribution, including:

[0012] Based on the multimodal behavioral features collected in real time from the target students, the mathematical cognitive state is inferred abductively through the behavior-cognition inference function to obtain the posterior distribution of the current cognitive state.

[0013] The system receives hypothetical intervention instructions from teachers, assigns mathematical teaching intervention values ​​to the teaching intervention nodes in the cause-effect graph, and generates a modified cause-effect graph.

[0014] Based on the posterior distribution of the current cognitive state, the modified causal graph, and the intervention-behavior prediction function, a mathematical cognitive state transition simulation is performed to generate a cognitive state transition probability distribution.

[0015] In one embodiment, based on the multimodal behavioral features collected in real time by the target student, abductive inference of mathematical cognitive state is performed through a behavior-cognition inference function to obtain the posterior distribution of the current cognitive state, including:

[0016] The multimodal behavioral features collected in real time from the target students are analyzed to interpret their mathematical problem-solving behaviors, generating a sequence of mathematical learning behaviors. The expression for this sequence is as follows:

[0017]

[0018] in, Represents a sequence of mathematical learning behaviors. Let represent the multimodal behavior feature vector at time step ii. This represents a mask matrix representing a mathematical problem-solving pattern. Represents the context tensor of a mathematical problem. Represents the time series transformation weight matrix. Represents a non-linear activation function. It represents the Hadamah accumulation. This represents tensor addition. Represents the sequence normalization function. Represents the gradient operator. This indicates the number of time steps in the problem-solving process. Indicates the time step index;

[0019] Based on mathematical learning behavior sequences, the mathematical cognitive dimension state is inferred through the behavior-cognition inference function to generate an initial cognitive state distribution.

[0020] Based on the mathematical cognitive logic consistency rule, mathematical cognitive conflict resolution is performed on the initial cognitive state distribution to generate the posterior distribution of the current cognitive state.

[0021] In one embodiment, based on the posterior distribution of the current cognitive state, the modified causal graph, and the intervention-behavior prediction function, a mathematical cognitive state transition simulation is performed to generate a cognitive state transition probability distribution, including:

[0022] Based on the mathematical cognitive dimension association path of the modified causal graph, mathematical cognitive state propagation is performed on the posterior distribution of the current cognitive state to generate the propagated mathematical cognitive state. The expression of the propagated mathematical cognitive state is:

[0023]

[0024] in, This indicates the state of mathematical cognition after propagation. This represents the posterior distribution of the current cognitive state. This represents the adjacency tensor of the modified causal graph. This represents a mathematical cognitive logic constraint function. Represents the propagation weight matrix. This represents the bias vector. This represents the Sigmoid activation function. This represents the tensor product operation. It represents the Hadamah accumulation. This represents the tensor vectorization operation;

[0025] Based on the intervention-behavior prediction function, mathematical learning behavior is predicted based on the post-propagation mathematical cognitive state, and a predicted behavior feature distribution is generated.

[0026] Based on the predicted behavioral feature distribution and the modified causal graph, mathematical cognitive state correction is performed to generate the corrected cognitive state distribution.

[0027] By integrating the distributions of mathematical cognitive states after propagation and those after correction, the mathematical cognitive state transition probabilities are fused to generate a cognitive state transition probability distribution. The expression for the cognitive state transition probability distribution is as follows:

[0028]

[0029] in, This represents the probability distribution of cognitive state transitions. This indicates the state of mathematical cognition after propagation. This represents the corrected distribution of cognitive states. This represents the probability normalization operator. This represents the function for calculating information entropy. This represents the normalized matrix of mathematical cognitive dimensions. This represents element-wise division. Represents the propagation state weight coefficient. This represents the corrected state weight coefficient.

[0030] In one embodiment, based on the causal graph and the collected multimodal behavioral characteristics of students, joint causal parameter learning is performed to obtain a behavior-cognition inference function and an intervention-behavior prediction function, including:

[0031] Based on the topological constraints of the multimodal behavior layer of the causal graph, mathematical problem-solving behavior is embedded into the collected multimodal behavior features to generate a spatiotemporal fusion behavior representation vector.

[0032] Based on the cognitive state layer structure of behavioral representation vectors and causal graphs, variational inference of mathematical cognitive dimensions is performed to obtain the posterior distribution of potential cognitive states.

[0033] Based on the posterior distribution of latent cognitive states and a pre-set cross-student math intervention experiment dataset, we model the response to math teaching interventions to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

[0034] In one embodiment, based on the posterior distribution of latent cognitive states and a pre-defined cross-student mathematics intervention experiment dataset, mathematics teaching intervention response modeling is performed to obtain a behavior-cognition inference function and an intervention-behavior prediction function, including:

[0035] Based on the intervention-behavior mapping relationship in the pre-defined cross-student mathematics intervention experimental dataset, features of mathematics teaching intervention are extracted to generate a mathematics intervention feature vector. The expression of the mathematics intervention feature vector is as follows:

[0036]

[0037] in, Represents the feature vector of mathematical intervention. Represents the feature activation function. This represents the feature extraction weight matrix. This indicates the tensor vectorization operation. Represents the tensor of the intervention experiment dataset. It represents the Hadamah accumulation. This represents the intervention-behavior mapping matrix. This represents the feature extraction bias vector. This represents the element-wise division operator. Represents the normalized matrix of mathematical intervention;

[0038] By integrating mathematical intervention feature vectors with the posterior distribution of potential cognitive states, mathematical cognition-intervention response modeling is performed to generate a set of intervention response functions;

[0039] Based on the causal consistency constraint of mathematics teaching, the function structure of the intervention response function group is optimized to obtain the behavior-cognitive inference function and the intervention-behavior prediction function.

[0040] In one embodiment, a controllable interpretation is generated based on the probability distribution of cognitive state transitions and the causal paths in the causal graph to obtain a natural language interpretation report, including:

[0041] Based on the key mathematical cognitive dimension transition probabilities in the cognitive state transition probability distribution, the dominant causal chain is extracted to generate a mathematical cognitive evolution path. The expression of the mathematical cognitive evolution path is as follows:

[0042]

[0043] in, Representing the evolutionary path of mathematical cognition, This represents the set of all possible paths in a causal graph. Represents a node The probability of cognitive state transition, Represents the topological matrix of mathematical cognitive dimensions. Represents the topological consistency distance function. Represents the path smoothing coefficient. Represents an exponential function. This represents a single candidate cognitive evolution path. Indicates path length. Indicates the path node index. Representing a path The Middle One node;

[0044] Based on the teacher's input of the specified explanation focus instruction, the teaching-related segments of the mathematical cognition evolution path are selected to generate the target teaching influence path;

[0045] Based on the transfer probability of key mathematical cognitive dimensions, a quantitative description of the mathematical intervention effect is generated, resulting in a natural language effect statement. The expression of the natural language effect statement is as follows:

[0046]

[0047] in, This represents a statement of natural language effects. Indicates the first The difference in the transition probability of each cognitive dimension express, This represents the attention vector used by the teacher to interpret focus instructions. Represents the dimension weight coefficient. Represents a natural language generation model. This indicates a feature concatenation operation. This represents the total number of mathematical cognitive dimensions. Indicates the cognitive dimension index;

[0048] By integrating the impact path of target-oriented teaching, natural language effect statements, and a pre-set mathematical teaching terminology database, teaching decision interpretation is synthesized to generate a natural language interpretation report.

[0049] Secondly, this application also provides a cognitive state assessment system for mathematics teaching, the system comprising:

[0050] The causal graph construction module is used to construct a four-layer directed causal graph based on a preset mathematical subject knowledge graph, a preset multimodal teaching intervention library, and a preset cognitive dimension framework, thereby obtaining the causal graph.

[0051] The joint causal learning module is used to learn joint causal parameters based on the causal graph and the collected multimodal behavioral characteristics of students, so as to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

[0052] The counterfactual reasoning module is used to perform counterfactual reasoning based on the real-time collected multimodal behavioral characteristics, behavior-cognition inference function, and intervention-behavior prediction function of the target students, and generate a cognitive state transition probability distribution.

[0053] The controllable explanation generation module is used to generate controllable explanations based on the probability distribution of cognitive state transitions and causal paths in the causal graph, and obtain a natural language explanation report.

[0054] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of any of the methods in the first aspect of this application.

[0055] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of any of the methods in the first aspect of this application.

[0056] This application provides a method and system for assessing cognitive states in mathematics teaching. The method includes: constructing a four-layer directed causal graph based on a pre-defined mathematical knowledge graph, a multimodal teaching intervention library, and a cognitive dimension framework. This ensures that the assessment structure deeply aligns with the inherent logic of mathematics, thereby enhancing the logical adaptability of mathematics. By combining the causal graph with collected student multimodal behavioral characteristics for joint causal parameter learning, the correlation between behavior and cognition, and between intervention and behavior, is captured, helping to improve the accuracy of dynamic behavioral characteristic analysis.

[0057] By leveraging real-time collected multimodal behavioral characteristics of target students and combining learned behavior-cognition inference functions and intervention-behavior prediction functions for counterfactual reasoning, a cognitive state transition probability distribution is generated. This effectively deepens the mining of causal relationships between multimodal data and cognitive states, enhancing multimodal causal reasoning capabilities. Controllable interpretations are generated based on the cognitive state transition probability distribution and causal paths in the causal graph, ensuring that natural language interpretation reports are closely linked to the core logic of cognitive evolution and better meet the decision-making needs in teaching practice, thereby optimizing the interpretive value of teaching guidance. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of a cognitive state assessment method for mathematics teaching, as shown in one embodiment of the present invention.

[0060] Figure 2 A flowchart is generated to perform counterfactual reasoning on the multimodal behavioral features, behavior-cognition inference function and intervention-behavior prediction function of the target student in one embodiment of the present invention, and to generate a probability distribution of cognitive state transition.

[0061] Figure 3 This is a structural diagram of a cognitive state assessment system for mathematics teaching, as shown in one embodiment of the present invention. Detailed Implementation

[0062] To make the above-mentioned objects, features, and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0063] First, the application scenarios of the embodiments of this application will be described. In the embodiments of this application, a cognitive state assessment method and system for mathematics teaching are provided, applicable to scenarios such as cognitive state assessment in primary and secondary school mathematics classroom teaching, cognitive diagnosis of after-school mathematics homework, dynamic monitoring of cognitive levels in personalized mathematics tutoring, and cognitive state analysis for in-school mathematics academic quality assessment.

[0064] In illustrative purposes, the cognitive state assessment method and system for mathematics teaching provided in this application embodiment can also be applied to applications such as tracking the learning cognitive state of online mathematics teaching platforms, identifying cognitive shortcomings in mathematics competition training, assessing the development of mathematical cognition in special education, and diagnosing the cognitive mastery of mathematics-related courses in vocational education. These are merely illustrative examples and do not limit the specific application scenarios.

[0065] like Figure 1 As shown, this application provides a method for assessing cognitive state in mathematics teaching, the method comprising:

[0066] S101: Based on the pre-set mathematical subject knowledge graph, the pre-set multimodal teaching intervention library, and the pre-set cognitive dimension framework, a four-layer directed causal graph is constructed to obtain the causal graph.

[0067] For example, based on a pre-set mathematical subject knowledge graph, a pre-set multimodal teaching intervention library, and a pre-set cognitive dimension framework, the conceptual association logic and hierarchical relationship of knowledge points in the mathematical subject knowledge graph are extracted, the intervention types and action paths in the multimodal teaching intervention library are refined, and the assessment dimensions and cognitive evolution standards in the cognitive dimension framework are used as the core basis for constructing a four-layer directed causal graph.

[0068] The hierarchical scope of the four-layer directed causal graph is clarified, the basis of inter-layer connections is determined based on knowledge logic, the transmission direction is clarified by combining the intervention path, the state transition relationship is determined by referring to the laws of cognitive evolution, the directed causal relationships and mechanisms of action of elements within and across each layer are sorted out, and the four-layer structure and causal relationships are integrated to form a closed-loop system, thus obtaining the causal graph.

[0069] S102: Based on the causal graph and the collected multimodal behavioral characteristics of students, joint causal parameter learning is performed to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

[0070] For example, based on the causal graph and the collected multimodal behavioral characteristics of students, the core information of the multimodal behavioral characteristics is screened and time-sequentially aligned. Combining the hierarchical structure of the causal graph and the causal relationship constraints, the correlation dimensions between behavior and cognition, and between intervention and behavior are clarified.

[0071] By integrating behavioral characteristics with causal graph structure information, this study explores the mapping patterns between behavior and cognition, as well as the mechanisms by which interventions affect behavior. Calibration parameters are iteratively optimized to align with causal transmission logic and actual learning data. The optimized parameters are then formalized into functional forms, yielding behavior-cognition inference functions and intervention-behavior prediction functions.

[0072] S103: Based on the multimodal behavioral characteristics, behavior-cognition inference function and intervention-behavior prediction function collected in real time by the target students, counterfactual reasoning is performed to generate a cognitive state transition probability distribution.

[0073] For example, based on real-time collected multimodal behavioral characteristics, behavior-cognition inference functions, and intervention-behavior prediction functions of target students, key information from real-time multimodal behavioral characteristics is selected, and the posterior distribution of the current cognitive state is obtained through causal inference using the behavior-cognition inference function. A clear hypothetical teaching intervention instruction is established, and behavioral changes under intervention are simulated using the intervention-behavior prediction function. Cognitive evolution trends are deduced using causal logic, cognitive conflicts are calibrated with reference to mathematical cognitive logic constraints, the probability of cognitive dimension shifts is quantified, and the integrated analysis results generate a probability distribution of cognitive state shifts.

[0074] S104: Based on the probability distribution of cognitive state transitions and the causal paths in the causal graph, controllable interpretation is generated to obtain a natural language interpretation report.

[0075] For example, based on the probability distribution of cognitive state transitions and causal paths in the causal graph, the transition trends of key cognitive dimensions are extracted, and the core causal chains that dominate cognitive evolution are identified. Combined with the explanation needs of teaching scenarios, controllable explanatory focus is clarified, and the logic of cognitive state changes is sorted out by linking the transition trends with the core causal chains. The quantitative characteristics of cognitive dimension transitions are transformed into descriptive language suitable for mathematics teaching, and the results of logical sorting and standardized description are integrated to obtain a natural language interpretation report.

[0076] One embodiment of this application provides a cognitive state assessment method for mathematics teaching, comprising: constructing a four-layer directed causal graph based on a pre-set mathematical subject knowledge graph, a multimodal teaching intervention library, and a cognitive dimension framework, so that the assessment structure deeply fits the inherent logic of the mathematical subject, thereby enhancing the logical adaptability of the mathematical subject. By performing joint causal parameter learning between the causal graph and collected student multimodal behavioral characteristics, the association patterns between behavior and cognition, and between intervention and behavior are captured, helping to improve the accuracy of dynamic behavioral feature analysis.

[0077] By leveraging real-time collected multimodal behavioral characteristics of target students and combining learned behavior-cognition inference functions and intervention-behavior prediction functions for counterfactual reasoning, a cognitive state transition probability distribution is generated. This effectively deepens the mining of causal relationships between multimodal data and cognitive states, enhancing multimodal causal reasoning capabilities. Controllable interpretations are generated based on the cognitive state transition probability distribution and causal paths in the causal graph, ensuring that natural language interpretation reports are closely linked to the core logic of cognitive evolution and better meet the decision-making needs in teaching practice, thereby optimizing the interpretive value of teaching guidance.

[0078] like Figure 2 As shown, based on the real-time collected multimodal behavioral characteristics, behavior-cognition inference function, and intervention-behavior prediction function of the target students, counterfactual reasoning is performed to generate a cognitive state transition probability distribution, including:

[0079] S201: Based on the multimodal behavioral features collected in real time by the target students, the mathematical cognitive state is inferred abductively through the behavior-cognition inference function to obtain the posterior distribution of the current cognitive state.

[0080] For example, based on the real-time collection of multimodal behavioral characteristics of target students, and referring to the core knowledge point association requirements defined by the mathematical subject knowledge graph and the logical standards corresponding to the standardized mathematical problem-solving process, behavioral information directly related to the core steps of mathematical problem-solving is filtered. Error records, duplicate submissions of invalid data, and redundant information unrelated to problem-solving are eliminated to ensure the relevance of the behavioral data. The data is sorted step-by-step according to the chronological order of mathematical problem-solving, aligning the timelines of different modal behavioral information to form an ordered sequence of behavioral data. Key information items in each behavioral record are checked one by one to identify missing core data, abnormal formatting, or logical contradictions. Supplements or corrections are made according to the conventional behavioral patterns of mathematical problem-solving to ensure data integrity and validity.

[0081] The modified multimodal behavioral features collected in real time from the target students are input into the behavior-cognition inference function. According to the preset mathematical cognition dimension classification criteria, the behavioral performance data of each dimension are analyzed one by one. The degree of state matching within dimensions and the degree of correlation between dimensions are calculated. Referring to cognitive logic rules such as the definition boundaries of mathematical concepts, the logical closure of formula derivation, and the sequential correlation of problem-solving steps, potential cognitive contradictions are identified. The scope of influence and priority ranking of the identified cognitive contradictions are defined, and their rationality is verified in conjunction with the general laws of mathematics learning. Based on the verification results, the cognitive state inference parameters are adjusted, and the behavioral feature analysis and cognitive state matching are repeated to complete multiple rounds of abductive inference, obtaining the posterior distribution of the current cognitive state.

[0082] Among them, the real-time collected multimodal behavioral characteristics of the target students include operational behavior data, thinking time data, answer step record data, and interactive feedback data during the mathematical problem-solving process; the behavior-cognition inference function is a function that describes the mapping relationship between multimodal behavioral characteristics and mathematical cognitive state; the current cognitive state posterior distribution is a probability distribution that quantifies the current mastery of each mathematical cognitive dimension of the target students after comprehensive behavioral analysis and cognitive logic verification.

[0083] S202: Receive the hypothetical intervention instructions input by the teacher, assign mathematical teaching intervention values ​​to the teaching intervention nodes in the cause-effect graph, and generate a modified cause-effect graph.

[0084] For example, upon receiving hypothetical intervention instructions input by teachers, the system extracts core elements from the instructions according to a pre-defined intervention instruction parsing framework, including the clearly defined intervention type, pre-defined intervention goals, specified intervention scope, and limited intervention conditions. By comparing these elements with the feasibility standards for mathematics teaching interventions, the system verifies the completeness of each core element, checks the logical consistency between elements, and supplements any missing necessary information based on the general requirements of common mathematics teaching intervention scenarios.

[0085] Based on the hierarchical division rules and node function classification standards of the causal graph, the teaching intervention nodes responsible for carrying teaching intervention information and playing an intervention role in the causal graph are located. Combining the core intervention elements obtained from the analysis, node assignment rules are formulated, clarifying the data type, value range, assignment priority corresponding to different intervention types, and the adaptation requirements between assignment and related nodes.

[0086] Assign values ​​to each teaching intervention node in the causal graph according to the assignment rules, and simultaneously analyze the causal transmission relationship between the node and its upstream and downstream related nodes. Adjust the influence weights between related nodes based on the assignment results, update the hierarchical relationship logic and node interaction mechanism of the causal graph as a whole, and generate a modified causal graph.

[0087] In this context, the intervention instruction is assumed to be a virtual teaching intervention plan instruction proposed by the teacher based on teaching needs; the teaching intervention node in the causal graph is the core node in the causal graph used to carry teaching intervention information and reflect the intervention effect; and the modified causal graph is the causal graph after the teaching intervention node is assigned a value and the association logic is updated.

[0088] S203: Based on the posterior distribution of the current cognitive state, the modified causal graph, and the intervention-behavior prediction function, perform mathematical cognitive state transition simulation to generate a cognitive state transition probability distribution.

[0089] For example, based on the posterior distribution of the current cognitive state, the transmission order of the cognitive dimension association paths in the modified causal graph is clarified, and the influence weight values ​​corresponding to each path are extracted. Following the evolutionary law of mathematical cognition from basic to advanced and from single to comprehensive, the current mathematical cognitive state is gradually propagated, and the potential direction and degree of change of each cognitive dimension under the hypothetical intervention are deduced dimensionally. The trend deduction results of each dimension are input into the intervention-behavior prediction function, and according to different modal categories of mathematical learning behavior, the mathematical learning behavior characteristics data such as the operational behavior patterns, thinking time intervals, answering step logic, and interactive feedback forms that the target students may produce under the intervention scenario are predicted one by one.

[0090] Based on the causal constraint rules of the modified cause-effect graph, the consistency between the predicted behavioral characteristics and the corresponding cognitive dimension change trends is compared one by one. For inconsistencies, the analysis determines whether the error stems from intervention transmission bias or trend extrapolation error, and trend corrections are made in conjunction with the actual scenarios of mathematics teaching. Based on the corrected cognitive state change trends and predicted behavioral characteristic data, a state transition assessment model for each mathematical cognitive dimension is established. The probability of each cognitive dimension transitioning from the current state to different target states is calculated, and the transition probability value corresponding to each dimension is quantified.

[0091] By adopting a weighted fusion method based on the importance of cognitive dimensions, the consistency verification results are integrated with the transition probability values ​​of each dimension, and the simulation and deduction of mathematical cognitive state transition are completed in stages, and a complete cognitive state transition probability distribution is formed.

[0092] Among them, the cognitive dimension association path in the modified causal graph is the path that connects different mathematical cognitive dimension nodes and reflects the cognitive influence relationship in the modified causal graph; the intervention-behavior prediction function is a function that describes the correspondence between teaching intervention and mathematical learning behavior characteristics; and the cognitive state transition probability distribution is the distribution data that quantifies the probability of changes in the state of each mathematical cognitive dimension of the target student under different teaching interventions.

[0093] In one embodiment, based on the multimodal behavioral features collected in real time by the target student, abductive inference of mathematical cognitive state is performed through a behavior-cognition inference function to obtain the posterior distribution of the current cognitive state, including:

[0094] (1) Analyze the mathematical problem-solving behavior of the multimodal behavioral features collected in real time from the target students to generate a mathematical learning behavior sequence. The expression of the mathematical learning behavior sequence is:

[0095]

[0096] in, Represents a sequence of mathematical learning behaviors. Let represent the multimodal behavior feature vector at time step ii. This represents a mask matrix representing mathematical problem-solving patterns. Represents the context tensor of a mathematical problem. Represents the time series transformation weight matrix. Represents a non-linear activation function. It represents the Hadamah accumulation. This represents tensor addition. Represents the sequence normalization function. Represents the gradient operator, This indicates the number of time steps in the problem-solving process. Indicates the time step index.

[0097] For example, real-time multimodal behavioral features of the target student are acquired. Following the natural temporal progression of the mathematical problem-solving process, the overall behavioral features are broken down into multimodal behavioral feature vectors corresponding to different time steps, ensuring a one-to-one correspondence between the behavioral features at each time step and the current problem-solving stage. A mathematical problem-solving pattern mask matrix is ​​introduced, and the multimodal behavioral feature vectors at each time step are processed with the mathematical problem-solving pattern mask matrix to retain behavioral information that conforms to mathematical problem-solving norms while filtering out redundant behavioral data irrelevant to problem-solving. A nonlinear activation function is then used to perform a nonlinear transformation on the filtered behavioral information, strengthening the key information related to mathematical cognition within the behavioral features.

[0098] This process involves obtaining a context tensor for the mathematical problem, performing gradient operations on it to extract context features highly relevant to the current problem-solving stage, and then introducing a time-series transformation weight matrix. The extracted context features are then processed against this matrix to adapt the context features to the current time step dimension, ensuring a match between the context information and the behavioral features at the corresponding time step. The processed behavioral information at each time step is then integrated with the adapted context features using tensor addition to form a preliminary behavior-context integration sequence. Finally, this preliminary sequence is input into a sequence standardization function to normalize the numerical range and distribution of the sequence, eliminating interference from differences in data across different time steps, and generating a mathematical learning behavior sequence.

[0099] Among them, the multimodal behavioral features collected in real time by the target students include operational behavior data, thinking time data, answer step record data, and interactive feedback data during the mathematical problem-solving process; the mathematical problem-solving pattern mask matrix is ​​a matrix used to filter behavioral information that conforms to the mathematical problem-solving norms; the nonlinear activation function is a function used to strengthen cognitive-related information in the behavioral features; and the mathematical problem context tensor is a tensor that carries the background information of the current mathematical problem.

[0100] The gradient operator is an operator that extracts the core features of the context of a mathematical problem; the time series transformation weight matrix is ​​a matrix that adapts to the time dimension of context features; tensor addition is an operation that integrates behavioral information with context features; the sequence normalization function is a function that regularizes and integrates the distribution of sequence data; and the mathematical learning behavior sequence is an ordered set of behaviors organized according to the problem-solving time steps.

[0101] (2) Based on the mathematical learning behavior sequence, the mathematical cognitive dimension state is inferred through the behavior-cognition inference function to generate the initial cognitive state distribution.

[0102] For example, a sequence of mathematical learning behaviors is obtained, and the complete sequence of mathematical learning behaviors is input into a behavior-cognition inference function. The function calls a pre-defined mapping relationship library of multimodal behavioral features and mathematical cognition dimensions to establish an association mapping between each behavioral item in the behavior sequence and the corresponding mathematical cognition dimension.

[0103] For each mathematical cognitive dimension, behavioral items associated with each behavioral sequence are extracted. Based on the behavioral performance quantification criteria set in the behavior-cognition inference function, the cognitive dimension performance level corresponding to each behavioral item is quantified and assigned a value. The quantified values ​​of all behavioral items under the same mathematical cognitive dimension are summarized, and the overall performance value of that dimension is calculated. Following the complete classification system of mathematical cognitive dimensions, the overall performance values ​​of all mathematical cognitive dimensions are organized to form the quantified result set corresponding to each dimension, thus generating the initial cognitive state distribution.

[0104] Among them, the behavior-cognition inference function is a function that describes the mapping relationship between the sequence of mathematical learning behaviors and the state of mathematical cognitive dimensions; the mathematical cognitive dimension is a classification dimension used to evaluate the state of mathematical cognition; and the initial cognitive state distribution is a set of quantitative results of the performance of each mathematical cognitive dimension.

[0105] (3) Based on the mathematical cognitive logic consistency rule, the initial cognitive state distribution is subjected to mathematical cognitive conflict resolution to generate the current cognitive state posterior distribution.

[0106] For example, a mathematical cognitive logic consistency rule is introduced. By comparing the quantitative results of each mathematical cognitive dimension in the initial cognitive state distribution, the logical relationships between different mathematical cognitive dimensions are analyzed, and combinations of dimensions with logical contradictions are identified. For the identified contradictory dimension combinations, the rationality of the quantitative results of the contradictory dimensions is verified based on the dependency relationships and logical priorities of each dimension in the mathematical cognitive logic consistency rule. Based on the verification conclusion, the quantitative values ​​of the contradictory dimensions are adjusted so that the adjusted results conform to the logical progression of mathematical cognition from basic to advanced.

[0107] The quantitative results of all mathematical cognitive dimensions are re-verified to ensure that there are no logical contradictions between the results of each dimension, forming the final quantitative probability set of the mastery of each mathematical cognitive dimension, that is, generating the posterior distribution of the current cognitive state.

[0108] Among them, the mathematical cognitive logic consistency rule is a rule that regulates the logical connections between various mathematical cognitive dimensions; the current cognitive state posterior distribution is a probability distribution that quantifies the current mastery of each mathematical cognitive dimension by the target student after cognitive conflict resolution.

[0109] In one embodiment, based on the posterior distribution of the current cognitive state, the modified causal graph, and the intervention-behavior prediction function, a mathematical cognitive state transition simulation is performed to generate a cognitive state transition probability distribution, including:

[0110] (1) Based on the mathematical cognitive dimension association path of the modified causal graph, the mathematical cognitive state is propagated to the posterior distribution of the current cognitive state to generate the propagated mathematical cognitive state. The expression of the propagated mathematical cognitive state is:

[0111]

[0112] in, This indicates the state of mathematical cognition after dissemination. This represents the posterior distribution of the current cognitive state. This represents the adjacency tensor of the modified causal graph. This represents a mathematical cognitive logic constraint function. Represents the propagation weight matrix. This represents the bias vector. This represents the Sigmoid activation function. This represents the tensor product operation. It represents the Hadamah accumulation. This indicates the tensor vectorization operation.

[0113] For example, the mathematical cognitive dimension association paths of the modified causal graph are obtained, the starting and target positions of each mathematical cognitive dimension node in the path are located, and the transmission direction and association strength between nodes of different dimensions are clarified. The adjacency tensor of the modified causal graph is obtained, and the adjacency tensor is converted into a vector form that matches the posterior distribution dimension of the current cognitive state through tensor vectorization operations, thus eliminating the problem of dimension incompatibility.

[0114] The mathematical cognitive logic constraint function is invoked, taking the posterior distribution of the current cognitive state as input. The partial derivative of this distribution with respect to the mathematical cognitive logic constraint function is calculated to obtain the adjustment direction reflecting the logical adaptability of the cognitive dimension. The transformed adjacency tensor and the partial derivative result are then multiplied by tensor to integrate the associated path information and the logical adjustment direction.

[0115] The product result is then processed with the propagation weight matrix. Based on the numerical distribution of the propagation weight matrix, the influence of different association paths is adjusted. A bias vector is superimposed to correct the numerical baseline of the result, making it more closely match the quantification range of the cognitive state. A sigmoid activation function is used to perform a non-linear transformation on the result, constraining it within a reasonable numerical range. The transformed result is then processed with the posterior distribution of the current cognitive state, combined with the basic values ​​of the original cognitive state, to obtain the quantification results of each mathematical cognitive dimension after path propagation. These results are then summarized to generate the propagated mathematical cognitive state.

[0116] Among them, the mathematical cognitive dimension association path of the modified causal graph is the path that connects nodes of different mathematical cognitive dimensions and reflects the cognitive influence relationship in the modified causal graph; the posterior distribution of the current cognitive state is the probability distribution that quantifies the current mastery of each mathematical cognitive dimension of the target student; and the adjacency tensor of the modified causal graph is the tensor that represents the node association relationship in the modified causal graph.

[0117] The mathematical cognitive logic constraint function is a function that regulates the logical association of mathematical cognitive dimensions; the propagation weight matrix is ​​a matrix that adjusts the degree of cognitive state propagation; the bias vector is a vector that assists in the calculation of cognitive state propagation; the sigmoid activation function is a function that performs nonlinear transformation; and the propagated mathematical cognitive state is the cognitive state result after propagation through the cognitive dimension association path.

[0118] (2) Based on the intervention-behavior prediction function, predict the mathematical learning behavior of the mathematical cognitive state after dissemination and generate the predicted behavior feature distribution.

[0119] For example, the post-propagation mathematical cognitive state is obtained, and the quantitative values ​​corresponding to each mathematical cognitive dimension are broken down to clarify the cognitive performance level of each dimension. The quantitative values ​​of all dimensions are then fully input into the intervention-behavior prediction function, which calls a pre-set mapping relationship library between cognitive states and mathematical learning behaviors. This library covers the behavioral characteristic types and performance patterns corresponding to different cognitive states. For the quantitative value of each mathematical cognitive dimension, the corresponding mathematical learning behavior characteristic type is matched in the mapping relationship library. For example, the formula application dimension corresponds to the formula calling behavior in the problem-solving steps, and the concept understanding dimension corresponds to the expression logic behavior in the question-answering process.

[0120] For each matched behavioral feature, its specific manifestation and degree (such as the range of thinking time and the level of detail in the steps) are predicted by combining the quantitative values ​​of the cognitive dimension, ensuring that the prediction results are consistent with the performance level of the cognitive dimension. The prediction results of behavioral features corresponding to all mathematical cognitive dimensions are summarized and categorized according to behavioral modalities such as operational behavior, thinking time, answering steps, and interactive feedback to form a structured distribution of predicted behavioral features.

[0121] Among them, the intervention-behavior prediction function is a function that characterizes the mapping relationship between teaching intervention and mathematical learning behavior characteristics; the post-propagation mathematical cognitive state is the cognitive state result after propagation through the cognitive dimension association path; and the predicted behavior characteristic distribution is a set of predicted results of mathematical learning behavior characteristics under the intervention scenario.

[0122] (3) Based on the predicted behavioral feature distribution and the modified causal graph, the mathematical cognitive state is corrected to generate the corrected cognitive state distribution.

[0123] For example, the predicted behavioral feature distribution is obtained, and the feature information corresponding to different behavioral modalities is broken down to clarify the specific manifestation and degree of each behavioral feature. The association constraint rules between the behavioral layer and the cognitive layer in the modified causal graph are obtained; these rules define the cognitive state performance standards corresponding to different mathematical learning behavioral features. By comparing each behavioral feature in the predicted behavioral feature distribution with the corresponding mathematical cognitive dimension in the propagated mathematical cognitive state, the logical matching between the two is analyzed, and cognitive dimensions whose behavioral feature performance and cognitive dimension values ​​are inconsistent are identified.

[0124] Based on the cognitive association logic of the modified causal graph, the direction of numerical adjustment for inconsistent cognitive dimensions is determined. Combined with the performance level of behavioral characteristics, the quantitative values ​​of the corresponding cognitive dimensions are adjusted to ensure that the adjusted values ​​align with the performance of the behavioral characteristics. A secondary check is performed on the values ​​of all mathematical cognitive dimensions to ensure that the values ​​of each dimension and the corresponding predicted behavioral characteristics comply with the association constraint rules. The adjusted quantitative values ​​of all cognitive dimensions are then compiled to generate the corrected cognitive state distribution.

[0125] Among them, the predicted behavioral feature distribution is the set of predicted results of mathematical learning behavioral features under the intervention scenario; the modified causal graph is the causal graph after the teaching intervention node is assigned and the association logic is updated; and the corrected cognitive state distribution is the cognitive state distribution result after behavioral feature matching adjustment.

[0126] (4) Integrate the mathematical cognitive state distribution after propagation and the distribution after correction, perform mathematical cognitive state transition probability fusion, and generate a cognitive state transition probability distribution. The expression for the cognitive state transition probability distribution is:

[0127]

[0128] in, This represents the probability distribution of cognitive state transitions. This indicates the state of mathematical cognition after dissemination. This represents the corrected distribution of cognitive states. This represents the probability normalization operator. This represents the function for calculating information entropy. This represents the normalized matrix of mathematical cognitive dimensions. This represents element-wise division. Represents the propagation state weight coefficient. This represents the corrected state weight coefficient.

[0129] For example, the system obtains the post-propagation mathematical cognitive state, performs logarithmic calculations on the quantified values ​​of each mathematical cognitive dimension to amplify the differences between values ​​of different dimensions and enhance the distinguishability of the values. A propagation state weight coefficient is then added to the calculation results, adjusting the influence of each dimension's result according to the importance of the post-propagation cognitive state in the teaching scenario. Simultaneously, the system obtains the corrected cognitive state distribution, calls the information entropy calculation function to calculate the information entropy of this distribution, reflecting the degree of uncertainty in the corrected cognitive state distribution. A corrected state weight coefficient is then added to the information entropy result, adjusting its influence according to the reliability of the corrected cognitive state distribution.

[0130] The results from the two processing steps above are then integrated dimension-by-dimensionally. The two results for each cognitive dimension are summed to obtain a preliminary integrated result. This preliminary integrated result is then input into a probability normalization operator to normalize the result, ensuring that the value of each cognitive dimension is between 0 and 1, meeting the numerical requirements of the probability distribution. The normalization matrix for the mathematical cognitive dimensions is obtained, and the normalized result is divided element-by-element by this matrix to smooth out the numerical differences between different cognitive dimensions, ensuring that the probability distributions of each dimension are horizontally comparable. Finally, the processed values ​​for all cognitive dimensions are summarized to generate a cognitive state transition probability distribution.

[0131] Among them, the post-propagation mathematical cognitive state is the result of cognitive state propagation through the cognitive dimension association path; the corrected cognitive state distribution is the result of cognitive state distribution adjusted by behavioral feature matching; the propagation state weight coefficient is the coefficient that adjusts the degree of influence of the post-propagation cognitive state; the information entropy calculation function is the function that calculates the uncertainty of the cognitive state distribution; the corrected state weight coefficient is the coefficient that adjusts the degree of influence of the corrected cognitive state distribution; the probability normalization operator is the operator that makes the result conform to the probability distribution requirements; the mathematical cognitive dimension normalization matrix is ​​the matrix that normalizes the numerical range of the cognitive dimension; and the cognitive state transition probability distribution is the distribution data that quantifies the probability of changes in the state of each mathematical cognitive dimension of the target student under different teaching interventions.

[0132] In one embodiment, based on the causal graph and the collected multimodal behavioral characteristics of students, joint causal parameter learning is performed to obtain a behavior-cognition inference function and an intervention-behavior prediction function, including:

[0133] (1) Based on the topological constraints of the multimodal behavior layer of the causal graph, the collected multimodal behavior features are embedded with mathematical problem-solving behavior to generate spatiotemporal fusion behavior representation vectors.

[0134] For example, the topological constraints of the multimodal behavior layer in the causal graph are obtained, clarifying the node association methods and dimension adaptation rules of the multimodal behavior features in the causal graph. The collected multimodal behavior features are acquired, and the data of each modality is split according to the time sequence of mathematical problem-solving, filtering out the behavior information directly related to mathematical problem-solving.

[0135] Based on the topological constraints of the multimodal behavior layer, dimensional alignment processing is performed on the behavioral information of different modalities to eliminate dimensional differences between modalities. Through behavior embedding methods, the temporal-dimensional behavioral sequences are fused with the spatial-dimensional modal features to enhance the spatiotemporal correlation attributes in the behavioral information.

[0136] The fused behavioral information is feature-normalized, redundant behavioral features are filtered out, core features closely related to mathematical cognition are retained, and a spatiotemporal fusion behavioral representation vector is generated.

[0137] Among them, the topological constraints of the multimodal behavior layer in the causal graph are the association rules and dimensional requirements of the nodes in the multimodal behavior layer of the causal graph; the collected multimodal behavior features are math learning-related behavior data obtained from students; math problem-solving behavior embedding is a processing method that integrates spatiotemporal behavior features; the spatiotemporal fusion behavior representation vector is the vector form result after integrating spatiotemporal behavior features.

[0138] (2) Based on the cognitive state layer structure of behavioral representation vector and causal graph, perform variational inference of mathematical cognitive dimension to obtain the posterior distribution of potential cognitive state.

[0139] For example, the spatiotemporal fusion behavior representation vector is obtained, and its included behavioral feature dimensions and numerical distribution are clarified. The cognitive state layer structure of the causal graph is obtained, and the division criteria and correlation logic of each mathematical cognitive dimension in the cognitive state layer are determined.

[0140] The behavioral representation vector is input into the variational inference process of mathematical cognitive dimensions. Based on the mapping relationship between behavior and cognition in the cognitive state layer structure, the mathematical cognitive dimensions corresponding to the behavioral features are matched one by one. The latent state probability of each mathematical cognitive dimension is quantified using variational inference methods, and the degree of correlation between dimensions is analyzed. The rationality of the inferred probabilities of each cognitive dimension is verified, and probability values ​​that are inconsistent with the logic of the cognitive state layer structure are corrected. The verified probabilities of each dimension are summarized to generate the posterior distribution of the latent cognitive states.

[0141] Among them, the behavior representation vector is the vector form result after integrating the spatiotemporal features of behavior; the cognitive state layer structure of the causal graph is the division and association rules of the cognitive dimension in the causal graph; the variational inference of the mathematical cognitive dimension is the method of inferring the latent state of the cognitive dimension; and the posterior distribution of the latent cognitive state is the probability distribution result of quantifying the latent state of the mathematical cognitive dimension.

[0142] (3) Based on the posterior distribution of potential cognitive states and the pre-set cross-student mathematical intervention experimental dataset, mathematical teaching intervention response modeling is carried out to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

[0143] For example, the posterior distribution of potential cognitive states is obtained to clarify the probability distribution characteristics of each mathematical cognitive dimension. A pre-defined cross-student mathematical intervention experimental dataset is obtained, and information on the teaching intervention type, corresponding changes in students' behavioral characteristics, and changes in cognitive states are extracted from the dataset.

[0144] This study correlates and matches the posterior distribution of latent cognitive states with intervention information in the dataset to analyze the response patterns of cognitive states and behavioral characteristics under different teaching interventions. Through modeling methods, a mapping relationship between behavioral characteristics and cognitive states is constructed, forming the core logic of the behavior-cognitive inference function. Simultaneously, a response relationship between teaching interventions and behavioral characteristics is constructed, forming the core logic of the intervention-behavior prediction function. The validity of the logic of both functions is verified, and the mapping parameters are adjusted to improve matching accuracy, resulting in the behavior-cognitive inference function and the intervention-behavior prediction function.

[0145] Among them, the posterior distribution of latent cognitive states is the probability distribution result of the latent states of mathematical cognitive dimensions; the pre-set cross-student mathematical intervention experiment dataset is a dataset containing information on multi-student intervention experiments; mathematical teaching intervention response modeling is the process of constructing the relationship between intervention, behavior, and cognition; the behavior-cognition inference function is a function that describes the mapping relationship between behavior and cognition; and the intervention-behavior prediction function is a function that describes the mapping relationship between intervention and behavior.

[0146] In one embodiment, based on the posterior distribution of latent cognitive states and a pre-defined cross-student mathematics intervention experiment dataset, mathematics teaching intervention response modeling is performed to obtain a behavior-cognition inference function and an intervention-behavior prediction function, including:

[0147] (1) Based on the intervention-behavior mapping relationship in the pre-set cross-student mathematics intervention experimental dataset, mathematics teaching intervention features are extracted to generate a mathematics intervention feature vector. The expression of the mathematics intervention feature vector is:

[0148]

[0149] in, Represents the feature vector of mathematical intervention. Represents the feature activation function. This represents the feature extraction weight matrix. This indicates the tensor vectorization operation. Represents the tensor of the intervention experiment dataset. It represents the Hadamah accumulation. This represents the intervention-behavior mapping matrix. This represents the feature extraction bias vector. This represents the element-wise division operator. This represents the normalized matrix of mathematical intervention.

[0150] For example, a pre-defined cross-student mathematics intervention experiment dataset is obtained. Records of changes in student behavioral characteristics corresponding to different teaching intervention types are analyzed, and the correlation between intervention types and behavioral characteristics is extracted to form an intervention-behavior mapping relationship. The intervention experiment dataset is organized according to dimensions such as intervention type, implementation period, and behavioral changes, and converted into an intervention experiment dataset tensor, retaining the core correlation information in the dataset. Through tensor vectorization, the intervention experiment dataset tensor is converted into a one-dimensional vector form, eliminating the dimensional differences of multi-dimensional tensors and making it suitable for the subsequent feature extraction operation requirements. The intervention-behavior mapping relationship matrix is ​​called, and the converted intervention experiment dataset tensor vector is operated on with the intervention-behavior mapping relationship matrix to filter out information fragments with strong correlations between intervention types and behavioral characteristics, and filter out redundant data with weak correlations.

[0151] The filtered information is processed with the feature extraction weight matrix. Based on the numerical allocation of the weight matrix, the influence of key intervention features is strengthened while the interference of secondary features is weakened. A feature extraction bias vector is superimposed to correct the numerical benchmark of the calculation result, making the result more closely match the quantization range of the intervention features. A non-linear transformation is applied to the calculation result using a feature activation function to constrain the result within a reasonable numerical range and avoid excessive fluctuations in feature values. The transformed result is then divided element-wise with the mathematical intervention normalization matrix to normalize the numerical differences between different intervention features, ensuring that all features are on a uniform quantization scale. All processed intervention feature information is summarized to generate a mathematical intervention feature vector.

[0152] Among them, the pre-set cross-student mathematics intervention experiment dataset is a dataset containing multiple student intervention types and behavioral change records; the intervention-behavior mapping relationship is the corresponding association between intervention types and behavioral characteristics; mathematics teaching intervention feature extraction is the process of extracting the core features of intervention; the intervention experiment dataset tensor is the tensor form of the intervention experiment dataset; tensor vectorization operation is the operation of converting tensors into one-dimensional vectors.

[0153] The intervention-behavior mapping matrix is ​​a matrix that represents the relationship between intervention and behavior; the feature extraction weight matrix is ​​a matrix that adjusts the weights of intervention features; the feature extraction bias vector is a vector that corrects the feature value benchmark; the feature activation function is a function that constrains the range of feature values; the mathematical intervention normalization matrix is ​​a matrix that normalizes the intervention feature values; and the mathematical intervention feature vector is the vector form of the core intervention features.

[0154] (2) Integrate mathematical intervention feature vectors and potential cognitive state posterior distributions to perform mathematical cognition-intervention response modeling and generate intervention response function sets.

[0155] For example, a mathematical intervention feature vector is obtained, clarifying its intervention feature dimensions and numerical distribution. The posterior distribution of the latent cognitive state is obtained, and the probability distribution features of each mathematical cognitive dimension are extracted. The mathematical intervention feature vector and the posterior distribution of the latent cognitive state are dimensionally aligned, and the intervention features and cognitive state features are integrated using a feature fusion method to clarify the correlation strength between them. Based on the integrated features, a mathematical cognition-intervention response model is constructed to analyze the changing patterns of cognitive states under different intervention features, as well as the behavioral feature response patterns corresponding to changes in cognitive states.

[0156] The relationships between cognition and intervention, and behavior and intervention in the model are transformed into functional forms to form a preliminary set of intervention response functions, which cover the response logic of cognitive state to intervention and the response logic of behavioral characteristics to intervention.

[0157] Among them, the mathematical intervention feature vector is the vector form of the extracted core intervention features; the posterior distribution of the latent cognitive state is the probability distribution of the latent state of the mathematical cognitive dimension; mathematical cognition-intervention response modeling is the process of constructing the relationship between cognition and intervention; and the intervention response function set is a set of functions that include the logic of cognition and behavior on intervention response.

[0158] (3) Based on the causal consistency constraint of mathematics teaching, the function structure of the intervention response function group is optimized to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

[0159] For example, causal consistency constraints in mathematics teaching are obtained to clarify the causal logical order and association rules among cognition, behavior, and intervention in the mathematics teaching process. The intervention-response function set is compared with the causal consistency constraints in mathematics teaching to analyze whether the logic of each function in the function set conforms to the causal order, and to identify logically conflicting function structures.

[0160] Conflicting function structures are adjusted to correct the input-output relationships, aligning them with the causal logic of mathematics teaching. Simultaneously, the mapping parameters of the functions are optimized to improve their accuracy in characterizing the relationship between cognition, behavior, and intervention. From the optimized intervention response function set, functions characterizing the mapping relationship between behavioral characteristics and cognitive states are extracted and identified as behavior-cognition inference functions. Functions characterizing the mapping relationship between teaching intervention and behavioral characteristics are also extracted and identified as intervention-behavior prediction functions, resulting in behavior-cognition inference functions and intervention-behavior prediction functions.

[0161] Among them, the causal consistency constraint in mathematics teaching is the causal logic rule of cognition, behavior, and intervention in mathematics teaching; the intervention response function set is a set of functions that include the logic of cognition and behavior in response to intervention; function structure optimization is the process of adjusting function logic and parameters; behavior-cognition inference function is a function that describes the mapping relationship between behavioral characteristics and cognitive state; intervention-behavior prediction function is a function that describes the mapping relationship between teaching intervention and behavioral characteristics.

[0162] In one embodiment, a controllable interpretation is generated based on the probability distribution of cognitive state transitions and the causal paths in the causal graph to obtain a natural language interpretation report, including:

[0163] (1) Based on the key mathematical cognitive dimension transition probabilities in the cognitive state transition probability distribution, the dominant causal chain is extracted to generate a mathematical cognitive evolution path. The expression of the mathematical cognitive evolution path is:

[0164]

[0165] in, Representing the evolutionary path of mathematical cognition, This represents the set of all possible paths in a causal graph. Represents a node The probability of cognitive state transition, Represents the topological matrix of mathematical cognitive dimensions. Represents the topological consistency distance function. Represents the path smoothing coefficient. Represents an exponential function. This represents a single candidate cognitive evolution path. Indicates path length. Indicates the path node index. Representing a path The Middle Each node.

[0166] For example, the probability distribution of cognitive state transitions is obtained, the transition probabilities of key mathematical cognitive dimensions with significant numerical changes are identified, and the quantitative characteristics of the transition probabilities of each dimension are clarified. The set of all possible paths in the causal graph is obtained, and the sequence of nodes contained in each path and the connections between nodes are analyzed.

[0167] The mathematical cognitive dimension topology matrix is ​​invoked, and the degree of matching between each path and the topology matrix is ​​calculated using a topological consistency distance function, quantifying the path's topological fit. Combining the cognitive state transition probability of nodes with the path's topological fit, a path smoothing coefficient is introduced to adjust the influence weights of both, and an exponential function is used to strengthen the priority of high-fit paths. From all possible paths in the causal graph, the single candidate cognitive evolution path with the optimal comprehensive transition probability and topological fit is selected, and the node sequence and length of this path are determined, generating the mathematical cognitive evolution path.

[0168] Among them, the cognitive state transition probability distribution is the distribution data that quantifies the possibility of changes in the state of mathematical cognitive dimensions; the key mathematical cognitive dimension transition probability is the dimension transition probability with significant numerical changes in the distribution; the dominant causal chain extraction is the process of screening the optimal cognitive path; the set of all possible paths in the causal graph is the set of paths formed by connecting nodes in the causal graph; the mathematical cognitive dimension topology matrix is ​​a matrix that represents the topological relationship of cognitive dimensions; the topological consistency distance function is a function that calculates the degree of matching between the path and the topology matrix; the path smoothing coefficient is a coefficient that adjusts the path fit weight; and the mathematical cognitive evolution path is the optimal cognitive dimension change path.

[0169] (2) Based on the teacher's input of the specified explanation focus instruction, the teaching-related segments of the mathematical cognition evolution path are screened to generate the target teaching influence path.

[0170] For example, the process involves obtaining the teacher's input instruction specifying the focus of explanation, and parsing the explicit teaching focus dimensions and explanation scope within the instruction. A mathematical cognitive evolution path is then obtained, and the sequence of nodes within the path is broken down to identify the corresponding mathematical cognitive dimension and teaching step for each node. Based on the focus dimension of the specified explanation instruction, node segments directly related to that dimension in the mathematical cognitive evolution path are selected, preserving the node connections and transition logic within each segment, while filtering out path nodes unrelated to the focus of explanation. The selected node segments undergo path integrity verification, and necessary related nodes are added to ensure logical coherence, generating a target teaching influence path.

[0171] Among them, the teacher-input instruction specifying the focus of explanation is the teacher's instruction to clarify the dimension of teaching focus; the mathematical cognitive evolution path is the optimal path of cognitive dimension change; the screening of teaching-related segments is the process of extracting the focus-related parts in the path; and the goal-oriented teaching influence path is the cognitive path segment associated with the focus of explanation.

[0172] (3) Based on the transfer probability of key mathematical cognitive dimensions, a quantitative description of the mathematical intervention effect is generated, resulting in a natural language effect statement. The expression of the natural language effect statement is:

[0173]

[0174] in, This represents a statement of natural language effects. Indicates the first The difference in the transition probability of each cognitive dimension express, This represents the attention vector used by the teacher to interpret focus instructions. Represents the dimension weight coefficient. This represents a natural language generation model. This indicates a feature concatenation operation. This represents the total number of mathematical cognitive dimensions. This represents the cognitive dimension index.

[0175] For example, the transition probabilities of key mathematical cognitive dimensions are obtained, the difference in transition probabilities for each cognitive dimension is calculated, and the magnitude of change in dimension states is determined. The attention vector of the teacher interpreting the focus instruction is obtained, and the weight allocation corresponding to the instruction's focus dimension is determined.

[0176] By introducing dimensional weight coefficients and combining them with the attention vector of the teacher's interpretation of focus instructions, the influence of the transition probability difference across cognitive dimensions is adjusted. The processed transition probability difference is then concatenated with the corresponding teaching terminology features to integrate quantitative data with teaching expression elements. The integrated result is input into a natural language generation model. Based on the expression habits of mathematics teaching, the model transforms the quantitative data into natural language descriptions that conform to the teaching scenario, resulting in a natural language effect statement.

[0177] Among them, the key mathematical cognitive dimension transition probability is the dimension transition probability with significant numerical changes in the distribution; the transition probability difference is the magnitude of change in the cognitive dimension state; the attention vector of the teacher's interpretation of the focus instruction is the weight vector of the instruction focus dimension; the dimension weight coefficient is the coefficient that adjusts the degree of influence of the dimension; the feature splicing operation is the operation of integrating quantitative data with teaching elements; the natural language generation model is the model for generating teaching descriptions; and the natural language effect statement is the natural language description of the intervention effect.

[0178] (4) Integrate the target teaching influence path, natural language effect statement and pre-set mathematical teaching terminology database to synthesize teaching decision interpretation and generate natural language interpretation report.

[0179] For example, the system obtains the target teaching influence path and extracts the node logic and cognitive transfer relationships of the path. It also obtains natural language effect statements to clarify the description of the intervention effect. Finally, it retrieves a pre-defined mathematics teaching terminology database and calls upon standardized teaching terms from the database that match the explanation content.

[0180] The logical relationships of the impact paths of target-oriented teaching are transformed into a description of the teaching process, which is then integrated with the quantitative descriptions of the effects in natural language. Standardized terms from a pre-designed mathematics teaching terminology database are incorporated, replacing colloquial expressions to meet the requirements of the teaching document. The integrated content is then logically organized, and necessary explanations of teaching connections are added to improve the report's readability, resulting in a natural language explanation report.

[0181] Among them, the target-oriented teaching influence path is a cognitive path segment associated with the explanatory focus; the natural language effect statement is a natural language description of the intervention effect; the pre-set mathematics teaching terminology database is a set of terms that standardize teaching expressions; the teaching decision explanation synthesis is the process of integrating content to generate a report; and the natural language explanation report is a teaching explanation document that includes the path and the effect.

[0182] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0183] In one embodiment, such as Figure 3 As shown, this application also provides a cognitive state assessment system 300 for mathematics teaching, the system 300 including:

[0184] The causal graph construction module 301 is used to construct a four-layer directed causal graph based on a preset mathematical subject knowledge graph, a preset multimodal teaching intervention library, and a preset cognitive dimension framework, thereby obtaining the causal graph.

[0185] The joint causal learning module 302 is used to learn joint causal parameters based on the causal graph and the collected multimodal behavioral characteristics of students, so as to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

[0186] The counterfactual reasoning module 303 is used to perform counterfactual reasoning based on the multimodal behavioral characteristics, behavior-cognition inference function and intervention-behavior prediction function collected in real time by the target student, and generate a cognitive state transition probability distribution.

[0187] The controllable explanation generation module 304 is used to generate a controllable explanation based on the probability distribution of cognitive state transitions and the causal path in the causal graph, and obtain a natural language explanation report.

[0188] Specifically, the cause-effect graph construction module 301 retrieves a pre-defined mathematical subject knowledge graph and analyzes the classification system of mathematical knowledge points and the logical dependencies between them. It also retrieves a pre-defined multimodal teaching intervention library to analyze the implementation forms of various teaching interventions and the corresponding knowledge content categories. Finally, it retrieves a pre-defined cognitive dimension framework to clarify the dimensional division standards and hierarchical structure of mathematical cognitive abilities.

[0189] Based on the four-layer architecture definition of knowledge layer, intervention layer, behavior layer and cognition layer, the knowledge points of the mathematics subject knowledge graph are mapped to knowledge layer nodes, the intervention types of the multimodal teaching intervention library are mapped to intervention layer nodes, the typical behaviors of students in the process of learning mathematics are mapped to behavior layer nodes, and the dimensions of the preset cognitive dimension framework are mapped to cognition layer nodes.

[0190] Following the logical transmission order from the knowledge layer to the intervention layer to the behavior layer to the cognition layer, directed connections are established between nodes: knowledge layer nodes are associated with the appropriate intervention layer nodes, intervention layer nodes are associated with the corresponding behavior layer nodes, and behavior layer nodes are associated with the corresponding cognition layer nodes. At the same time, logical connection edges between nodes in the same layer are added to complete the construction of a four-layer directed causal graph, thus obtaining the causal graph.

[0191] Among them, the pre-set mathematical subject knowledge graph is a structured graph covering mathematical knowledge points and their relationships; the pre-set multimodal teaching intervention library is a resource library containing various forms of teaching intervention; the pre-set cognitive dimension framework is a system for defining the dimensions of mathematical cognitive ability; the four-layer directed causal graph is a directed relational graph containing four layers of nodes: knowledge, intervention, behavior, and cognition; and the causal graph is the completed four-layer directed causal graph.

[0192] The joint causal learning module 302 retrieves the causal graph and clarifies the topological constraints and association rules of each layer of nodes. It retrieves the collected multimodal behavioral features of students, filters out behavioral data related to mathematics learning, and performs data standardization. Based on the topological constraints of the multimodal behavioral layer of the causal graph, it performs behavioral embedding processing on the collected multimodal behavioral features of students, generating behavioral representation vectors that fuse spatiotemporal features. Combining the cognitive state layer structure of the causal graph, it performs variational inference of the mathematical cognitive dimension on the behavioral representation vectors to obtain the posterior distribution of the latent cognitive state.

[0193] A pre-defined cross-student mathematics intervention experiment dataset is retrieved, and the intervention-behavior mapping relationship in the dataset is extracted. This relationship is then matched with the posterior distribution of potential cognitive states to construct a mathematics teaching intervention response model. Through the model, the mapping rules between behavioral characteristics and cognitive states, and between teaching intervention and behavioral characteristics are learned, ultimately yielding the behavior-cognition inference function and the intervention-behavior prediction function.

[0194] Among them, the causal graph is a directed association graph containing four layers of nodes: knowledge, intervention, behavior, and cognition; the collected multimodal behavioral characteristics of students are behavioral data generated during students' mathematics learning process; joint causal parameter learning is the process of mapping the relationship between learning behavior and cognition, and intervention and behavior; the behavior-cognition inference function is a function that describes the mapping relationship between behavioral characteristics and cognitive state; and the intervention-behavior prediction function is a function that describes the mapping relationship between teaching intervention and behavioral characteristics.

[0195] The counterfactual reasoning module 303 retrieves real-time multimodal behavioral features of the target students, filters out core behavioral information, and completes temporal alignment and data validity verification. It retrieves the behavior-cognitive inference function and the intervention-behavior prediction function, clarifying the input and output specifications of these functions.

[0196] A causal analysis is performed on the real-time collected multimodal behavioral characteristics of target students using a behavior-cognition inference function to obtain the posterior distribution of the current cognitive state. The system receives hypothetical intervention instructions from teachers, assigns parameter values ​​to the teaching intervention nodes in the causal graph, and generates a modified causal graph. Based on the posterior distribution of the current cognitive state, the modified causal graph, and the intervention-behavior prediction function, the evolution trend of cognitive state under the hypothetical intervention is simulated. Inconsistencies in the trend are calibrated using the mathematical cognitive logic consistency rule, the state transition probability of each mathematical cognitive dimension is quantified, and a cognitive state transition probability distribution is generated.

[0197] Among them, the real-time collected multimodal behavioral characteristics of the target students are the mathematical learning behavior data generated by the target students in real time. The behavior-cognition inference function is a function that describes the mapping relationship between behavioral characteristics and cognitive states. The intervention-behavior prediction function is a function that describes the mapping relationship between teaching intervention and behavioral characteristics. Counterfactual reasoning is the reasoning process that simulates changes in cognitive states under hypothetical intervention. The cognitive state transition probability distribution is the distribution data that quantifies the probability of changes in the state of mathematical cognition.

[0198] The controllable explanation generation module 304 retrieves the cognitive state transition probability distribution and extracts the transition probabilities of key mathematical cognitive dimensions that show significant changes. It then retrieves the causal paths in the causal graph and analyzes the node sequences and logical connections within those paths. Based on the transition probabilities of key mathematical cognitive dimensions, it selects the dominant cognitive evolution path from the causal paths in the causal graph, generating a mathematical cognitive evolution path. Combining this with the teacher's input specifying the focus of explanation, it extracts segments from the path related to the focus of explanation, generating a target teaching influence path.

[0199] Based on the transfer probabilities of key mathematical cognitive dimensions, natural language descriptions of the effects of mathematical interventions are generated, resulting in natural language effect statements. By integrating the target teaching influence path, the natural language effect statements, and a pre-designed mathematical teaching terminology database, content integration and logical organization are completed, yielding a natural language interpretation report.

[0200] Among them, the probability distribution of cognitive state transition is the distribution data that quantifies the probability of changes in the state of mathematical cognition; the causal path in the causal graph is the directed association path of the nodes in the causal graph; the controllable explanation generation is the process of generating teaching-related explanation content; and the natural language explanation report is a teaching explanation document that includes cognitive paths and intervention effects.

[0201] Counterfactual reasoning module 303 is also used for:

[0202] Based on the multimodal behavioral features collected in real time from the target students, the mathematical cognitive state is inferred abductively through the behavior-cognition inference function to obtain the posterior distribution of the current cognitive state.

[0203] The system receives hypothetical intervention instructions from teachers, assigns mathematical teaching intervention values ​​to the teaching intervention nodes in the cause-effect graph, and generates a modified cause-effect graph.

[0204] Based on the posterior distribution of the current cognitive state, the modified causal graph, and the intervention-behavior prediction function, a mathematical cognitive state transition simulation is performed to generate a cognitive state transition probability distribution.

[0205] Counterfactual reasoning module 303 is also used for:

[0206] The multimodal behavioral features collected in real time from the target students are analyzed to interpret their mathematical problem-solving behaviors, generating a sequence of mathematical learning behaviors. The expression for this sequence is as follows:

[0207]

[0208] in, Represents a sequence of mathematical learning behaviors. Let represent the multimodal behavior feature vector at time step ii. This represents a mask matrix representing a mathematical problem-solving pattern. Represents the context tensor of a mathematical problem. Represents the time series transformation weight matrix. Represents a non-linear activation function. It represents the Hadamah accumulation. This represents tensor addition. Represents the sequence normalization function. Represents the gradient operator. This indicates the number of time steps in the problem-solving process. Indicates the time step index;

[0209] Based on mathematical learning behavior sequences, the mathematical cognitive dimension state is inferred through the behavior-cognition inference function to generate an initial cognitive state distribution.

[0210] Based on the mathematical cognitive logic consistency rule, mathematical cognitive conflict resolution is performed on the initial cognitive state distribution to generate the posterior distribution of the current cognitive state.

[0211] Counterfactual reasoning module 303 is also used for:

[0212] Based on the mathematical cognitive dimension association path of the modified causal graph, mathematical cognitive state propagation is performed on the posterior distribution of the current cognitive state to generate the propagated mathematical cognitive state. The expression of the propagated mathematical cognitive state is:

[0213]

[0214] in, This indicates the state of mathematical cognition after propagation. This represents the posterior distribution of the current cognitive state. This represents the adjacency tensor of the modified causal graph. This represents a mathematical cognitive logic constraint function. Represents the propagation weight matrix. This represents the bias vector. This represents the Sigmoid activation function. This represents the tensor product operation. It represents the Hadamah accumulation. This represents the tensor vectorization operation;

[0215] Based on the intervention-behavior prediction function, mathematical learning behavior is predicted based on the post-propagation mathematical cognitive state, and a predicted behavior feature distribution is generated.

[0216] Based on the predicted behavioral feature distribution and the modified causal graph, mathematical cognitive state correction is performed to generate the corrected cognitive state distribution.

[0217] By integrating the distributions of mathematical cognitive states after propagation and those after correction, the mathematical cognitive state transition probabilities are fused to generate a cognitive state transition probability distribution. The expression for the cognitive state transition probability distribution is as follows:

[0218]

[0219] in, This represents the probability distribution of cognitive state transitions. This indicates the state of mathematical cognition after propagation. This represents the corrected distribution of cognitive states. This represents the probability normalization operator. This represents the function for calculating information entropy. This represents the normalized matrix of mathematical cognitive dimensions. This represents element-wise division. Represents the propagation state weight coefficient. This represents the corrected state weight coefficient.

[0220] The Joint Causal Learning Module 302 is also used for:

[0221] Based on the topological constraints of the multimodal behavior layer of the causal graph, mathematical problem-solving behavior is embedded into the collected multimodal behavior features to generate a spatiotemporal fusion behavior representation vector.

[0222] Based on the cognitive state layer structure of behavioral representation vectors and causal graphs, variational inference of mathematical cognitive dimensions is performed to obtain the posterior distribution of potential cognitive states.

[0223] Based on the posterior distribution of latent cognitive states and a pre-set cross-student math intervention experiment dataset, we model the response to math teaching interventions to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

[0224] The Joint Causal Learning Module 302 is also used for:

[0225] Based on the intervention-behavior mapping relationship in the pre-defined cross-student mathematics intervention experimental dataset, features of mathematics teaching intervention are extracted to generate a mathematics intervention feature vector. The expression of the mathematics intervention feature vector is as follows:

[0226]

[0227] in, Represents the feature vector of mathematical intervention. Represents the feature activation function. This represents the feature extraction weight matrix. This indicates the tensor vectorization operation. Represents the tensor of the intervention experiment dataset. It represents the Hadamah accumulation. This represents the intervention-behavior mapping matrix. This represents the feature extraction bias vector. This represents the element-wise division operator. Represents the normalized matrix of mathematical intervention;

[0228] By integrating mathematical intervention feature vectors with the posterior distribution of potential cognitive states, mathematical cognition-intervention response modeling is performed to generate a set of intervention response functions;

[0229] Based on the causal consistency constraint of mathematics teaching, the function structure of the intervention response function group is optimized to obtain the behavior-cognitive inference function and the intervention-behavior prediction function.

[0230] The controllable interpretation generation module 304 is also used for:

[0231] Based on the key mathematical cognitive dimension transition probabilities in the cognitive state transition probability distribution, the dominant causal chain is extracted to generate a mathematical cognitive evolution path. The expression of the mathematical cognitive evolution path is as follows:

[0232]

[0233] in, Representing the evolutionary path of mathematical cognition, This represents the set of all possible paths in a causal graph. Represents a node The probability of cognitive state transition, Represents the topological matrix of mathematical cognitive dimensions. Represents the topological consistency distance function. Represents the path smoothing coefficient. Represents an exponential function. This represents a single candidate cognitive evolution path. Indicates path length. Indicates the path node index. Representing a path The Middle One node;

[0234] Based on the teacher's input of the specified explanation focus instruction, the teaching-related segments of the mathematical cognition evolution path are selected to generate the target teaching influence path;

[0235] Based on the transfer probability of key mathematical cognitive dimensions, a quantitative description of the mathematical intervention effect is generated, resulting in a natural language effect statement. The expression of the natural language effect statement is as follows:

[0236]

[0237] in, This represents a statement of natural language effects. Indicates the first The difference in the transition probability of each cognitive dimension express, This represents the attention vector used by the teacher to interpret focus instructions. Represents the dimension weight coefficient. This represents a natural language generation model. This indicates a feature concatenation operation. This represents the total number of mathematical cognitive dimensions. Indicates the cognitive dimension index;

[0238] By integrating the impact path of target-oriented teaching, natural language effect statements, and a pre-set mathematical teaching terminology database, teaching decision interpretation is synthesized to generate a natural language interpretation report.

[0239] In one embodiment, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0240] In one embodiment, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-described method embodiments.

[0241] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0242] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. A method for assessing cognitive state in mathematics teaching, characterized in that, The method includes: Based on a pre-designed mathematical subject knowledge graph, a pre-designed multimodal teaching intervention library, and a pre-designed cognitive dimension framework, a four-layer directed causal graph is constructed to obtain the causal graph. Based on the causal graph and the collected multimodal behavioral characteristics of students, joint causal parameter learning is performed to obtain the behavior-cognition inference function and the intervention-behavior prediction function; Based on the real-time collected multimodal behavioral characteristics of the target students, the behavior-cognition inference function, and the intervention-behavior prediction function, counterfactual reasoning is performed to generate a cognitive state transition probability distribution. Based on the cognitive state transition probability distribution and the causal paths in the causal graph, a controllable interpretation is generated to obtain a natural language interpretation report.

2. The cognitive state assessment method for mathematics teaching according to claim 1, characterized in that, The method involves using real-time collected multimodal behavioral features of the target student, the behavior-cognition inference function, and the intervention-behavior prediction function to perform counterfactual reasoning and generate a cognitive state transition probability distribution, including: Based on the multimodal behavioral features collected in real time from the target students, the mathematical cognitive state is inferred abductively through the behavior-cognition inference function to obtain the posterior distribution of the current cognitive state. The system receives hypothetical intervention instructions input by teachers, assigns mathematical teaching intervention values ​​to the teaching intervention nodes in the causal graph, and generates a modified causal graph. Based on the current cognitive state posterior distribution, the modified causal graph, and the intervention-behavior prediction function, a mathematical cognitive state transition simulation is performed to generate the cognitive state transition probability distribution.

3. The cognitive state assessment method for mathematics teaching according to claim 2, characterized in that, The multimodal behavioral features collected in real time based on the target student are used to perform mathematical cognitive state abductive inference through the behavior-cognition inference function to obtain the posterior distribution of the current cognitive state, including: The multimodal behavioral features collected in real time from the target students are analyzed to analyze their mathematical problem-solving behaviors, generating a mathematical learning behavior sequence. The expression for the mathematical learning behavior sequence is as follows: in, Represents a sequence of mathematical learning behaviors. Let represent the multimodal behavior feature vector at time step ii. This represents a mask matrix representing a mathematical problem-solving pattern. Represents the context tensor of a mathematical problem. Represents the time series transformation weight matrix. Represents a non-linear activation function. It represents the Hadamah accumulation. This represents tensor addition. Represents the sequence normalization function. Represents the gradient operator, This indicates the number of time steps in the problem-solving process. Indicates the time step index; Based on the mathematical learning behavior sequence, the mathematical cognitive dimension state is inferred through the behavior-cognition inference function to generate an initial cognitive state distribution; Based on the mathematical cognitive logic consistency rule, the initial cognitive state distribution is subjected to mathematical cognitive conflict resolution to generate the posterior distribution of the current cognitive state.

4. The cognitive state assessment method for mathematics teaching according to claim 2, characterized in that, The step of performing mathematical cognitive state transition simulation based on the current cognitive state posterior distribution, the modified causal graph, and the intervention-behavior prediction function to generate the cognitive state transition probability distribution includes: Based on the mathematical cognitive dimension association path of the modified causal graph, mathematical cognitive state propagation is performed on the posterior distribution of the current cognitive state to generate a propagated mathematical cognitive state. The expression of the propagated mathematical cognitive state is: in, This indicates the state of mathematical cognition after propagation. This represents the posterior distribution of the current cognitive state. This represents the adjacency tensor of the modified causal graph. This represents a mathematical cognitive logic constraint function. Represents the propagation weight matrix. This represents the bias vector. This represents the Sigmoid activation function. This represents the tensor product operation. It represents the Hadamah accumulation. This represents the tensor vectorization operation; Based on the intervention-behavior prediction function, mathematical learning behavior is predicted for the post-propagation mathematical cognitive state, and a predicted behavior feature distribution is generated. Based on the predicted behavioral feature distribution and the modified causal graph, mathematical cognitive state correction is performed to generate a modified cognitive state distribution. Integrating the propagated mathematical cognitive state with the corrected cognitive state distribution, a mathematical cognitive state transition probability fusion is performed to generate the cognitive state transition probability distribution, the expression of which is: in, This represents the probability distribution of cognitive state transitions. This indicates the state of mathematical cognition after propagation. This represents the corrected distribution of cognitive states. This represents the probability normalization operator. This represents the function for calculating information entropy. This represents the normalized matrix of mathematical cognitive dimensions. This represents element-wise division. Represents the propagation state weight coefficient. This represents the corrected state weight coefficient.

5. The cognitive state assessment method for mathematics teaching according to claim 1, characterized in that, Based on the causal graph and the collected multimodal behavioral characteristics of students, joint causal parameter learning is performed to obtain a behavior-cognition inference function and an intervention-behavior prediction function, including: Based on the multimodal behavior layer topological constraints of the causal graph, mathematical problem-solving behavior is embedded into the collected multimodal behavior features to generate a spatiotemporal fusion behavior representation vector. Based on the cognitive state layer structure of the behavioral representation vector and the causal graph, variational inference of mathematical cognitive dimensions is performed to obtain the posterior distribution of the latent cognitive state. Based on the potential cognitive state posterior distribution and the pre-set cross-student mathematics intervention experiment dataset, mathematics teaching intervention response modeling is performed to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

6. The cognitive state assessment method for mathematics teaching according to claim 5, characterized in that, The method involves modeling the response to a math teaching intervention based on the posterior distribution of the potential cognitive states and a pre-defined cross-student math intervention experimental dataset, resulting in the behavior-cognition inference function and the intervention-behavior prediction function, including: Based on the intervention-behavior mapping relationship in the pre-defined cross-student mathematics intervention experimental dataset, mathematics teaching intervention features are extracted to generate a mathematics intervention feature vector. The expression of the mathematics intervention feature vector is as follows: in, Represents the feature vector of mathematical intervention. Represents the feature activation function. This represents the feature extraction weight matrix. This indicates the tensor vectorization operation. Represents the tensor of the intervention experiment dataset. It represents the Hadamah accumulation. This represents the intervention-behavior mapping matrix. This represents the feature extraction bias vector. This represents the element-wise division operator. Represents the normalized matrix of mathematical intervention; By integrating the mathematical intervention feature vector with the posterior distribution of the potential cognitive state, mathematical cognition-intervention response modeling is performed to generate a set of intervention response functions; Based on the causal consistency constraint of mathematics teaching, the function structure of the intervention response function group is optimized to obtain the behavior-cognition inference function and the intervention-behavior prediction function.

7. The cognitive state assessment method for mathematics teaching according to claim 1, characterized in that, The process of generating a controllable interpretation based on the cognitive state transition probability distribution and the causal path in the causal graph, resulting in a natural language interpretation report, includes: Based on the key mathematical cognitive dimension transition probabilities in the cognitive state transition probability distribution, a dominant causal chain is extracted to generate a mathematical cognitive evolution path. The expression of the mathematical cognitive evolution path is as follows: in, Representing the evolutionary path of mathematical cognition, This represents the set of all possible paths in a causal graph. Represents a node The probability of cognitive state transition, Represents the topological matrix of mathematical cognitive dimensions. Represents the topological consistency distance function. Represents the path smoothing coefficient. Represents an exponential function. This represents a single candidate cognitive evolution path. Indicates the path length. Indicates the path node index. Representing a path The Middle One node; Based on the teacher's input of a specified explanation focus instruction, the teaching-related segments of the mathematical cognitive evolution path are filtered to generate a target teaching influence path; Based on the transfer probability of the key mathematical cognitive dimensions, a quantitative description of the mathematical intervention effect is generated, resulting in a natural language effect statement. The expression of the natural language effect statement is as follows: in, This represents a statement of natural language effects. Indicates the first The difference in the transition probability of each cognitive dimension express, This represents the attention vector used by the teacher to interpret focus instructions. Represents the dimension weight coefficient. Represents a natural language generation model. This indicates a feature concatenation operation. This represents the total number of mathematical cognitive dimensions. Indicates the cognitive dimension index; By integrating the target teaching influence path, the natural language effect statement, and the preset mathematics teaching terminology database, a teaching decision interpretation synthesis is performed to generate the natural language interpretation report.

8. A cognitive state assessment system for mathematics teaching, characterized in that, The system includes: The causal graph construction module is used to construct a four-layer directed causal graph based on a preset mathematical subject knowledge graph, a preset multimodal teaching intervention library, and a preset cognitive dimension framework, thereby obtaining the causal graph. The joint causal learning module is used to learn joint causal parameters based on the causal graph and the collected multimodal behavioral characteristics of students, so as to obtain the behavior-cognition inference function and the intervention-behavior prediction function. The counterfactual reasoning module is used to perform counterfactual reasoning based on the multimodal behavioral characteristics of the target student collected in real time, the behavior-cognition inference function, and the intervention-behavior prediction function, and to generate a cognitive state transition probability distribution. The controllable interpretation generation module is used to generate a controllable interpretation based on the cognitive state transition probability distribution and the causal path in the causal graph, and obtain a natural language interpretation report.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the cognitive state assessment method for mathematics teaching as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the cognitive state assessment method for mathematics teaching as described in any one of claims 1 to 7.

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