A problem-solving collaboration system and method

Abstract

A problem-solving collaboration system and method, including: a semantic structured annotation module, which labels each information segment with a type and assigns a role; a dynamic deduction whiteboard module, which provides an interactive visual canvas for displaying the initial form of a standardized mathematical model, receiving user-set tentative solutions, and providing real-time feedback on objective function values and constraint satisfaction states; a conflict diagnosis and heuristic guidance module, which identifies key variables and their impact coefficients that cause resource overruns when user-set tentative solutions violate any constraint conditions, and provides visual prompts for preferred adjustment directions and approximate correction magnitudes; and a conclusion extraction interaction unit, which generates visual charts based on solution distribution datasets and pushes guided questions. This system not only improves students' ability to solve complex application problems, but also effectively promotes the development of their high-order cognitive abilities such as logical reasoning, critical thinking, and model-based thinking, making it highly practical and technically advanced for teaching.

Description

Technical Field

[0001] This invention relates to the field of educational technology, and more specifically, to a collaborative problem-solving system and method. Background Technology

[0002] Currently, in educational tablets, learning machines, and other smart learning devices, the problem-solving function generally relies on a technical approach of "image recognition + Large Language Model (LLM) explanation." This model acquires the problem image through computer vision (CV) and then uses a large language model to generate solution steps and answer explanations. Essentially, it is a passive problem-solving mechanism oriented towards answer output. Although this method has certain advantages in terms of the breadth of knowledge coverage, it reveals significant limitations in actual teaching scenarios: students can often understand the explanation but still struggle to independently complete problem analysis and modeling, especially when faced with application problems with complex textual descriptions. They cannot accurately extract key elements or understand the relationships between variables, resulting in a lack of a starting point for solving the problem. Furthermore, existing systems lack support for students' thought processes, neither recording their exploration trajectory nor providing conflict attribution and adjustment suggestions, making it difficult to cultivate their structured thinking and problem diagnosis abilities. Summary of the Invention

[0003] To address the aforementioned technical problems in related technologies, this invention proposes a collaborative problem-solving system, the system comprising:

[0004] The semantic structured annotation module is configured to receive input question text and input key information fragments, and to perform type marking and role assignment on each information fragment, wherein the type includes at least one of entity variables, resource constraints, objective function coefficients, and consumption relationships;

[0005] The knowledge graph construction engine, connected to the semantic structured annotation module, is used to construct a directed graph G=(V,E) with attributes based on the user's annotation results. The vertex set V represents the entities and parameters in the question, and the edge set E represents the mathematical or logical relationship between entities, carrying weights, units and semantic labels.

[0006] The model identification and initialization module determines the mathematical model category of the current problem based on the topological structure and edge relationship features of the knowledge graph G. The category includes at least one of linear programming, system of equations, geometric optimization, and probabilistic decision-making, and generates the corresponding standardized mathematical expression and initial parameter space accordingly.

[0007] The dynamic derivation whiteboard module provides an interactive visual canvas for displaying the initial form of the standardized mathematical model. It allows users to set exploratory solutions by dragging sliders, inputting values, or drawing paths, and provides real-time feedback on the objective function value and constraint satisfaction status.

[0008] The conflict diagnosis and heuristic guidance module identifies the key variables that cause resource overruns and their impact coefficients when the user's tentative solution violates any constraint. It calculates the adjustment suggestion Δ = (current consumption - resource limit) / maximum impact coefficient and provides the user with priority adjustment directions and approximate correction ranges in a visual prompt.

[0009] The exploration path tree recorder is used to record all solution combinations (x1, x2, ..., xn) that the user tries during the solution process, and organizes these nodes into an exploration path tree with timestamps and result labels, which is presented as a point cloud or branch structure in a two-dimensional or multi-dimensional coordinate system.

[0010] The sensitivity analysis engine, after obtaining the optimal or feasible solution, initiates a lightweight Monte Carlo simulation. It applies a random perturbation conforming to a preset distribution to at least one parameter in the model, performs N repeated iterations to generate a solution distribution dataset, and outputs the high-frequency range of each decision variable and the fluctuation range of the objective function;

[0011] The conclusion is extracted from the interactive unit, which generates visual charts based on the solution distribution dataset and pushes guiding questions.

[0012] Specifically, the semantic structured annotation module guides users to select key information segments sentence by sentence on the graphical interface. It adopts a step-by-step guidance strategy and prompts users to map natural language segments into structured semantic tuples through pop-up dialog boxes, drop-down menus, or icon drag-and-drop methods.

[0013] Specifically, the model recognition and initialization module includes a built-in model classifier whose training samples are derived from the labeled "question text -> correct model type" pairing data in the historical question bank. The output of the model classifier is used to automatically fill the formal template of the standard mathematical model.

[0014] Specifically, the dynamic simulation whiteboard module is also used to respond to user modifications to a decision variable, instantly calculate the total amount of related resource consumption and compare it with the upper limit of the constraint, and intuitively display the resource usage ratio and remaining capacity through color coding, progress bars or animation effects.

[0015] Specifically, the conflict diagnosis and heuristic guidance module is also configured to sort the constraints according to the resource scarcity index Ri = (actual demand / availability) when multiple constraints are violated at the same time, prioritize the most stressful constraints, and recommend an adjustment list for user reference based on the technical coefficient of the variable in the constraint.

[0016] Specifically, the exploration path tree recorder further supports path clustering analysis, grouping similar attempts into the same branch and identifying failure reason categories on the interface with different colors or shapes.

[0017] Specifically, in the Monte Carlo simulation used by the sensitivity analysis engine, the parameter perturbation range is preset by the teacher or automatically derived by the system according to the subject standards. Each simulation calls the built-in fast solver to recalculate the optimal solution, and the final statistical results are displayed on the dynamic whiteboard in the form of box plots, heat maps or confidence ellipses.

[0018] Specifically, the system runs in a local edge computing environment, and all modules are adapted to low-latency touch interaction, supporting stylus input, gesture zooming, and multi-point operation.

[0019] Specifically, the system also includes a teaching log database to store the complete trajectory of each collaborative process, including user-annotated sequences, attempt records, guidance response logs, and final conclusions.

[0020] Secondly, another embodiment of the present invention discloses a problem-solving method applied to the above-mentioned collaborative problem-solving system, which includes the following steps:

[0021] S1 receives the question text and initiates an interactive semantic annotation process to guide the user to complete the role classification of key information;

[0022] S2, construct a knowledge graph G based on the annotation results, and extract entities, relations and numerical parameters;

[0023] S3, Based on the knowledge graph, determine the mathematical type of the question and automatically generate a standard model expression and variable domain;

[0024] S4. Display the initial model of the standardized mathematical model on the dynamic whiteboard, accept user's tentative solution input, and verify constraint satisfaction in real time;

[0025] S5. If there are constraint conflicts, identify the main dependent variable and propose quantitative adjustment suggestions;

[0026] S6 records all attempted solutions to form an exploration path tree, and graphically displays the feasible region;

[0027] S7. After approaching the optimal solution, initiate Monte Carlo sensitivity analysis to simulate the solution distribution under parameter fluctuations.

[0028] S8 outputs visual reports and triggers reflective questioning.

[0029] This invention's collaborative problem-solving system, firstly, employs an interactive semantic structured annotation mechanism to guide students in actively participating in information extraction and role definition, significantly enhancing their depth of understanding of the problem. Secondly, it combines natural language understanding and knowledge graph technology to achieve automatic mapping from natural language to formal mathematical models, lowering the modeling threshold. Thirdly, it introduces a heuristic conflict diagnosis algorithm and a dynamic deduction whiteboard, enabling the system to accurately locate the root cause of errors and provide quantitative adjustment suggestions when students make mistakes, truly playing the guiding role of a "thinking partner." Finally, through exploring path tree records and Monte Carlo sensitivity analysis, it helps students build a holistic understanding of the solution space and the ability to reflect on strategies. Overall, this system not only improves students' ability to solve complex application problems but also effectively promotes the development of their higher-order cognitive abilities such as logical reasoning, critical thinking, and modeling thinking, demonstrating significant pedagogical practicality and technological advancement. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of a collaborative problem-solving system provided in an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of a collaborative problem-solving method provided in an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram of a collaborative problem-solving device provided in an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0035] Example 1

[0036] refer to Figure 1 This embodiment discloses a collaborative problem-solving system, which is deployed on a student tablet or learning machine. The system includes:

[0037] The semantic structured annotation module is configured to receive input question text and key information fragments input by the user, and to perform type marking and role assignment on each information fragment, wherein the type includes at least one of entity variables, resource constraints, objective function coefficients, and consumption relationships;

[0038] Specifically, the semantic structured annotation module in this embodiment guides users to select key information fragments sentence by sentence on the graphical interface. It adopts a step-by-step guidance strategy and prompts users to map natural language fragments into structured semantic tuples, such as (subject-relationship-object-value), through pop-up dialog boxes, drop-down menus, or icon drag-and-drop methods. The module also updates the node and edge attributes of the knowledge graph G in the background.

[0039] Subject and object correspond to the "vertex set V" in a knowledge graph. "Subject" and "object" refer to specific mathematical objects or parameter instances identified in a natural language segment. In a problem-solving context, they can be specific items, resources, variable names, or other objects involved in mathematical operations. For example, in a production planning problem, "product A" can be the subject, and "raw material B" can be the object.

[0040] A relation corresponds to the "edge set E" in a knowledge graph. It refers to the logical link or operational rule connecting subjects and objects. It describes how subjects and objects interact, such as logical or mathematical connections like "consume," "equal to," "less than," and "belong to."

[0041] "Numerical value" is a specific quantitative description of the above relationship, usually carrying information such as weight and unit, and is used to improve the attributes of the knowledge graph edges.

[0042] This tuple (subject, relation, object, value) is used to transform natural language questions into a knowledge graph structure that the system can process. Here, "subject" and "object" correspond to the "entities" defined earlier, and "relation" corresponds to the "mathematical or logical relationships" between entities. Through this mapping, unstructured question text can be transformed into a directed graph with attributes, thereby supporting subsequent model recognition and solving.

[0043] Role assignment in this embodiment refers to semantic-level classification labeling, which determines whether a text fragment belongs to a mathematical model as an "entity variable," "resource constraint," or something similar. It identifies and labels the "role" a piece of text plays in the problem-solving model (e.g., does the text represent a "variable," a "constraint," or a "coefficient"), thereby achieving a structured mapping from natural language to a formal mathematical model. It is a fundamental step in constructing knowledge graphs and generating standardized mathematical expressions.

[0044] The assignment of values ​​to characters is explained in the example of this embodiment.

[0045] The knowledge graph construction engine, connected to the semantic structured annotation module, is used to construct a directed graph G=(V,E) with attributes based on the user's annotation results. The vertex set V represents the entities and parameters in the question, and the edge set E represents the mathematical or logical relationship between entities, carrying weights, units and semantic labels.

[0046] The model identification and initialization module determines the mathematical model category of the current problem based on the topological structure and edge relationship features of the knowledge graph G. The category includes at least one of linear programming, system of equations, geometric optimization, and probabilistic decision-making, and generates the corresponding standardized mathematical expression and initial parameter space accordingly.

[0047] Specifically, this embodiment can use a combination of rule matching and machine learning to determine the mathematical model category of the current problem. In one implementation, the model identification and initialization module has a built-in model classifier. The training samples of the model classifier come from the labeled "problem text -> correct model type" pairing data in the historical problem database. The output of the classifier is used to automatically fill the formal template of the standard mathematical model, including but not limited to maximizing c. T x is a linear programming prototype that satisfies Ax≤b and x≥0.

[0048] The dynamic derivation whiteboard module provides an interactive visual canvas to display the initial form of the standardized mathematical model and allows users to set exploratory solutions by dragging sliders, inputting values, or drawing paths, providing real-time feedback on the objective function value and constraint satisfaction status.

[0049] The dynamic simulation whiteboard module integrates a real-time calculator, which can respond to user modifications to a decision variable, instantly calculate the total amount of relevant resources consumed and compare it with the upper limit of constraints, and intuitively display the resource usage ratio and remaining capacity through color coding, progress bars or animation effects.

[0050] The conflict diagnosis and heuristic guidance module activates the constraint propagation algorithm to analyze the conflict source when the user's tentative solution violates any constraint condition. It identifies the key variables that cause resource overruns and their impact coefficients, calculates the adjustment suggestion amount Δ = (current consumption - resource limit) / maximum impact coefficient, and provides the user with priority adjustment directions and approximate correction ranges in a visual prompt.

[0051] The constraint propagation algorithm in this embodiment is existing technology and will not be described in detail here.

[0052] The conflict diagnosis and heuristic guidance module is also configured to, when multiple constraints are violated simultaneously, sort them according to the resource scarcity index Ri = (actual demand / availability), prioritize the most pressing constraints, and, in conjunction with the technical coefficient of the variable in that constraint, recommend an adjustment list for the user's reference.

[0053] The exploration path tree recorder is used to record all solution combinations (x1, x2, ..., xn) that the user tries during the solution process, and organizes these nodes into an exploration path tree with timestamps and result labels, which is presented as a point cloud or branch structure in a two-dimensional or multi-dimensional coordinate system.

[0054] The exploration path tree recorder further supports path clustering analysis, grouping similar attempts into the same branch, and using different colors or shapes on the interface to indicate the categories of failure reasons, including "Material A exceeds limits", "Material B is insufficient", "Non-integer solution", etc., to help users identify invalid search patterns.

[0055] The sensitivity analysis engine, after obtaining the optimal or feasible solution, starts a lightweight Monte Carlo simulation, applies a random perturbation that conforms to a preset distribution to at least one parameter in the model, performs N repeated solutions to generate a solution distribution dataset, and outputs the high-frequency range of each decision variable and the fluctuation range of the objective function.

[0056] In the Monte Carlo simulation used by the sensitivity analysis engine, the parameter perturbation range is preset by the teacher or automatically derived by the system according to the subject standards. Each simulation calls the built-in fast solver to recalculate the optimal solution, and the final statistical results are displayed on the dynamic whiteboard in the form of box plots, heat maps or confidence ellipses.

[0057] The conclusion is extracted from the interactive unit, which generates visual charts based on the solution distribution dataset and pushes guiding questions.

[0058] This implementation, by pushing guided questions, can encourage users to independently summarize the robustness, parameter sensitivity, or boundary condition characteristics of a solution, thereby completing higher-order thinking skills training.

[0059] Specifically, the content of the guiding questions in this embodiment can be directly embedded on the "Dynamic Deduction Whiteboard" interface and displayed adjacent to the box plots, heat maps and other visual charts generated by the sensitivity analysis, ensuring that users receive guidance information while performing visual analysis.

[0060] Furthermore, the push notification method may include pop-up dialog boxes, drop-down menu prompts, or icon-related prompts to accommodate different levels of question depth.

[0061] After a question is pushed to the system, users can answer it or interact with the chart by using a stylus, gesture zooming, multi-point operation, or touch click, so as to express their understanding of the robustness of the solution or the sensitivity of the parameters.

[0062] After the "Sensitivity Analysis Engine" obtains the optimal or feasible solution, it initiates a lightweight Monte Carlo simulation, applies random perturbations to the model parameters, and performs N repeated solutions, generating a "solution distribution dataset" and corresponding visualizations (including box plots, heatmaps, or confidence ellipses). Only then is the conclusion extraction interaction unit activated and a question pushed out. The question is generated based on the solution distribution dataset and aims to utilize the high-frequency ranges of each decision variable and the fluctuation range of the objective function.

[0063] This example guides the questioning through the following directions:

[0064] Summary of robustness of the solution: Guide users to observe the degree of dispersion of the solution distribution and evaluate the stability of the solution under parameter fluctuations.

[0065] Parameter sensitivity analysis: prompts users to identify which parameter perturbations have the greatest impact on the objective function.

[0066] Boundary condition characteristic identification: guide users to think about the relationship between the feasible region boundary and the optimal solution.

[0067] The entire system in this embodiment runs in a local edge computing environment. All modules are adapted to low-latency touch interaction and support stylus input, gesture zooming and multi-point operation, ensuring that students can independently complete the entire process from problem analysis and modeling to exploration and solution without a network connection.

[0068] The system in this embodiment also includes a teaching log database, which stores the complete trajectory of each collaborative process, including user-annotated sequences, attempt records, guidance response logs, and final conclusions, which can be used for subsequent personalized review recommendations or teacher-side learning analysis.

[0069] This collaborative problem-solving system, as described in this embodiment, firstly employs an interactive semantic structured annotation mechanism to guide students in actively participating in information extraction and role definition, significantly enhancing their depth of understanding of the problem. Secondly, it combines natural language understanding and knowledge graph technology to achieve automatic mapping from natural language to formal mathematical models, lowering the modeling threshold. Thirdly, it introduces a heuristic conflict diagnosis algorithm and a dynamic deduction whiteboard, enabling the system to accurately locate the root cause of errors and provide quantitative adjustment suggestions when students make mistakes, truly playing the guiding role of a "thinking partner." Finally, through exploring path tree records and Monte Carlo sensitivity analysis, it helps students build a holistic understanding of the solution space and the ability to reflect on strategies. Overall, this system not only improves students' ability to solve complex application problems but also effectively promotes the development of their higher-order cognitive abilities such as logical reasoning, critical thinking, and modeling thinking, demonstrating significant pedagogical practicality and technological advancement.

[0070] This embodiment uses the example of a junior high school student solving a linear programming application problem on a learning and practice machine to illustrate the actual operation process of the intelligent problem-solving collaboration system in this embodiment.

[0071] The problem is as follows: A factory produces two products, A and B. Producing one unit of product A requires 4 kg of material A and 1 kg of material B; producing one unit of product B requires 1 kg of material A and 3 kg of material B. There are 40 kg of material A and 30 kg of material B available. The profit per unit of product A is 5 yuan, and the profit per unit of product B is 4 yuan. How should production be arranged to maximize total profit?

[0072] After students enter the question list into the computer for practice by handwriting or voice input, the system starts the collaborative problem-solving process, guiding students step by step through the entire process from understanding the question to solving it.

[0073] Step 1: Interactive Semantic Structured Annotation

[0074] The system prompts students to identify and circle key information segments sentence by sentence. When a student circles "two products, A and B", the system displays a type option, guiding them to select "entity / variable". Subsequently, the student circles "4 kg of material A and 1 kg of material B", and the system further asks, "What relationship does this describe?" and provides several options. The student selects "consumption relationship" and specifies that the relationship relates "product A" to "material A" and "material B".

[0075] Similarly, students annotate the material consumption, total existing materials, and product profit information for product B. Based on these annotations, the system constructs an attributed knowledge graph in real time, which includes the following:

[0076] Entity nodes: Product A, Product B, Material A, Material B;

[0077] Consumption relationship edge: Product A consumes 4 kg of material A and 1 kg of material B; Product B consumes 1 kg of material A and 3 kg of material B.

[0078] Resource constraints: The maximum weight of material A is 40 kg, and the maximum weight of material B is 30 kg;

[0079] Objective function coefficients: Product A's unit profit is 5 yuan, and Product B's unit profit is 4 yuan.

[0080] The system automatically introduces decision variables x_A and x_B, representing the production quantities of products A and B respectively, and initially forms the objective function expression: maximize Z = 5x_A + 4x_B.

[0081] Specifically, role assignment refers to assigning Product A, Product B, Material A, and Material B as entity nodes for use in the construction of the knowledge graph.

[0082] Similarly, consumption relationship encoding, resource constraints, objective function coefficients, etc., are all role assignments. They are used for knowledge graph construction.

[0083] Step 2: Model Recognition and Dynamic Whiteboard Initialization

[0084] The system analyzes the structural characteristics of the knowledge graph, determines that the problem belongs to the linear programming type, and automatically generates a standard mathematical model:

[0085] Maximize: 5x_A + 4x_B

[0086] Satisfy constraints:

[0087] 4x_A + x_B ≤ 40 (Material A)

[0088] x_A + 3x_B ≤ 30 (Material B)

[0089] x_A ≥ 0, x_B ≥ 0

[0090] The system opens a dynamic simulation whiteboard interface, displaying the above model and providing two adjustable sliders corresponding to the values ​​of x_A and x_B, respectively. The interface simultaneously displays the resource consumption and total profit value under the current scheme.

[0091] The system guides students to try an initial plan: "Suppose that 7 units of product A are produced, please observe the material usage." The student sets x_A to 7, and the system immediately calculates that the consumption of material A is 28 kg and the consumption of material B is 7 kg, both within the limits, and the result shows that it is feasible.

[0092] The student continued to try to increase the production of product B to 10 units. The system detected that the demand for material B had reached 37 kg, exceeding the 30 kg limit, triggering a conflict warning.

[0093] Step 3: Conflict Diagnosis and Heuristic Guidance

[0094] Instead of directly stating the cause of the error, the system activated the conflict diagnosis module. First, it determined that the constraint on material B was violated. Then, it analyzed the consumption intensity of each product on that resource and found that product B's unit consumption of 3 kg was significantly higher than product A's 1 kg.

[0095] The system calculates the recommended adjustment amount: Δ = (37 - 30) / 3 ≈ 2.3, and suggests that students reduce the production of product B by about 2 units.

[0096] The screen displays the message: "Product B consumes a large amount of material B, which may be the main factor causing resource shortages. It is recommended to prioritize adjusting its production."

[0097] The student reduced product B to 8 units as suggested, and after recalculation, found that all constraints were met, thus entering the feasible solution region.

[0098] Step 4: Explore Path Recording and Graphical Guidance

[0099] The system automatically records all the student's previous attempts, including (x_A=10,x_B=10), (x_A=8,x_B=10), (x_A=8,x_B=8), etc., and marks them as points in a two-dimensional coordinate system to form an exploration path map.

[0100] At the same time, the system draws two constraint lines: 4x_A + x_B = 40 and x_A + 3x_B = 30, and fills the feasible region enclosed by the two lines and the coordinate axes.

[0101] The students intuitively observed that most of their previous attempts fell outside the feasible region, while the successful solutions were close to the boundary. The system prompted: "The optimal solution usually appears near the vertex of the feasible region." Based on this, the students explored along the boundary and finally found the combination that maximized the profit: x_A=6, x_B=8, with a total profit of 62 yuan.

[0102] Step 5: Sensitivity Analysis and Conclusion Extraction

[0103] After obtaining the optimal solution, the system initiates a Monte Carlo simulation to analyze parameter fluctuations that the students had not yet considered. The supply of material A is set to vary uniformly and randomly between 35 and 45 kg, while the supply of material B varies between 28 and 32 kg. A total of 100 simulations are performed, with the optimal production plan being re-solved each time.

[0104] The results show that, in most cases, the optimal output of product A is concentrated between 5.8 and 6.3, and that of product B is concentrated between 7.9 and 8.2, with total profit remaining stable in the range of 61 to 63 yuan.

[0105] The system generates a bar chart to display the distribution of results and poses a guiding question to students: "If raw material prices fluctuate slightly every day, do you think this production plan is reliable?"

[0106] After observing the chart, the students replied: "Although the specific numbers may change, as long as A makes about 6 and B makes about 8, the profit difference is not significant, which shows that this plan is relatively stable."

[0107] Example 2

[0108] This embodiment discloses a collaborative problem-solving method, which is applied to the collaborative problem-solving system described in Embodiment 1, and includes the following steps:

[0109] S1 receives the question text and initiates an interactive semantic annotation process to guide the user to complete the role classification of key information;

[0110] S2, construct a knowledge graph G based on the annotation results, and extract entities, relations and numerical parameters;

[0111] S3, Based on the knowledge graph, determine the mathematical type of the question and automatically generate a standard model expression and variable domain;

[0112] S4. Display the initial model of the standardized mathematical model on the dynamic whiteboard, accept user's tentative solution input, and verify constraint satisfaction in real time;

[0113] S5. If there are constraint conflicts, identify the main dependent variable and propose quantitative adjustment suggestions;

[0114] S6 records all attempted solutions to form an exploration path tree, and graphically displays the feasible region;

[0115] S7. After approaching the optimal solution, initiate Monte Carlo sensitivity analysis to simulate the solution distribution under parameter fluctuations.

[0116] S8 outputs visual reports and triggers reflective questioning.

[0117] Example 3

[0118] refer to Figure 3 , Figure 3 This is a schematic diagram of the structure of a collaborative problem-solving device according to this embodiment. The collaborative problem-solving device 20 of this embodiment includes a processor 21, a memory 22, and a computer program stored in the memory 22 and executable on the processor 21. When the processor 21 executes the computer program, it implements the steps in the above method embodiments. Alternatively, when the processor 21 executes the computer program, it implements the functions of each module / unit in the above device embodiments.

[0119] For example, the computer program can be divided into one or more modules / units, which are stored in the memory 22 and executed by the processor 21 to complete the present invention. The one or more modules / units can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in the problem-solving collaboration device 20. For example, the computer program can be divided into the modules shown in Embodiment 2. For the specific functions of each module, please refer to the working process of the device described in the above embodiments; further details will not be repeated here.

[0120] The problem-solving collaboration device 20 may include, but is not limited to, a processor 21 and a memory 22. Those skilled in the art will understand that the schematic diagram is merely an example of the problem-solving collaboration device 20 and does not constitute a limitation on the device. It may include more or fewer components than illustrated, or combine certain components, or use different components. For example, the problem-solving collaboration device 20 may also include input / output devices, network access devices, buses, etc.

[0121] The processor 21 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. The processor 21 is the control center of the problem-solving collaboration device 20, connecting all parts of the device through various interfaces and lines.

[0122] The memory 22 can be used to store the computer programs and / or modules. The processor 21 implements various functions of the problem-solving collaboration device 20 by running or executing the computer programs and / or modules stored in the memory 22 and calling the data stored in the memory 22. The memory 22 may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, phonebook, etc.). In addition, the memory 22 may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0123] If the modules / units integrated in the collaborative problem-solving device 20 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by the processor 21, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content contained in the computer-readable medium may be appropriately added to or subtracted from the content as required by the legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium may not include electrical carrier signals and telecommunication signals.

[0124] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components 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 embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0125] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A collaborative problem-solving system, characterized in that: The system includes: The semantic structured annotation module is configured to receive input question text and key information fragments input by the user, and to perform type marking and role assignment on each information fragment, wherein the type includes at least one of entity variables, resource constraints, objective function coefficients, and consumption relationships; The knowledge graph construction engine, connected to the semantic structured annotation module, is used to construct a directed graph G=(V,E) with attributes based on the user's annotation results. The vertex set V represents the entities and parameters in the question, and the edge set E represents the mathematical or logical relationship between entities, carrying weights, units and semantic labels. The model identification and initialization module determines the mathematical model category of the current problem based on the topological structure and edge relationship features of the knowledge graph G. The category includes at least one of linear programming, system of equations, geometric optimization, and probabilistic decision-making, and generates the corresponding standardized mathematical expression and initial parameter space accordingly. The dynamic derivation whiteboard module provides an interactive visual canvas for displaying the initial form of the standardized mathematical model. It allows users to set exploratory solutions by dragging sliders, inputting values, or drawing paths, and provides real-time feedback on the objective function value and constraint satisfaction status. The conflict diagnosis and heuristic guidance module identifies the key variables that cause resource overruns and their impact coefficients when the user's tentative solution violates any constraint. It calculates the adjustment suggestion Δ = (current consumption - resource limit) / maximum impact coefficient and provides the user with priority adjustment directions and approximate correction ranges in a visual prompt. The exploration path tree recorder is used to record all solution combinations (x1, x2, ..., xn) that the user tries during the solution process, and organizes these nodes into an exploration path tree with timestamps and result labels, which is presented as a point cloud or branch structure in a two-dimensional or multi-dimensional coordinate system. The sensitivity analysis engine, after obtaining the optimal or feasible solution, initiates a lightweight Monte Carlo simulation, applying a random perturbation conforming to a preset distribution to at least one parameter in the model, performing N repeated solutions to generate a solution distribution dataset, and outputting the high-frequency range of each decision variable and the fluctuation range of the objective function; and, The conclusion is extracted from the interactive unit, which generates visual charts based on the solution distribution dataset and pushes guiding questions.

2. The system according to claim 1, characterized in that: The semantic structured annotation module guides users to select key information segments sentence by sentence on the graphical interface. It adopts a step-by-step guidance strategy and prompts users to map natural language segments into structured semantic tuples through pop-up dialog boxes, drop-down menus or icon drag-and-drop methods.

3. The system according to claim 1, characterized in that: The model recognition and initialization module includes a built-in model classifier whose training samples are derived from the labeled "question text → correct model type" pairing data in the historical question bank. The output of the model classifier is used to automatically fill the formal template of the standard mathematical model.

4. The system according to claim 1, characterized in that: The dynamic simulation whiteboard module is also used to respond to user modifications to a decision variable, instantly calculate the total amount of related resource consumption and compare it with the upper limit of constraints, and intuitively display the resource usage ratio and remaining capacity through color coding, progress bars or animation effects.

5. The system according to claim 1, characterized in that: The conflict diagnosis and heuristic guidance module is also configured to sort multiple constraints according to the resource scarcity index Ri = (actual demand / availability) when multiple constraints are violated at the same time, prioritize the most critical constraints, and recommend adjustments to the priority list for user reference based on the technical coefficient of the variable in the constraint.

6. The system according to claim 1, characterized in that: The exploration path tree recorder further supports path clustering analysis, grouping similar attempts into the same branch and identifying failure reason categories on the interface with different colors or shapes.

7. The system according to claim 1, characterized in that: In the Monte Carlo simulation used by the sensitivity analysis engine, the parameter perturbation range is preset by the teacher or automatically derived by the system according to the subject standards. Each simulation calls the built-in fast solver to recalculate the optimal solution, and the final statistical results are displayed on the dynamic whiteboard in the form of box plots, heat maps or confidence ellipses.

8. The system according to claim 1, characterized in that: The system runs in a local edge computing environment, and all modules are adapted to low-latency touch interaction, supporting stylus input, gesture zooming, and multi-point operation.

9. The system according to claim 1, characterized in that: The system also includes a teaching log database to store the complete trajectory of each collaborative process, including user-annotated sequences, attempt logs, guidance response logs, and final conclusions.

10. A problem-solving method applied to a collaborative problem-solving system as described in any one of claims 1-9, comprising the following steps: S1 receives the question text and initiates an interactive semantic annotation process to guide the user to complete the role classification of key information; S2, construct a knowledge graph G based on the annotation results, and extract entities, relations and numerical parameters; S3, Based on the knowledge graph, determine the mathematical type of the question and automatically generate a standard model expression and variable domain; S4 displays the initial model of the standardized mathematical model in a dynamic whiteboard, accepts user's tentative solution input, and verifies constraint satisfaction in real time; S5. If there are constraint conflicts, identify the main dependent variable and propose quantitative adjustment suggestions; S6 records all attempted solutions to form an exploration path tree, and graphically displays the feasible region; S7. After approaching the optimal solution, initiate Monte Carlo sensitivity analysis to simulate the solution distribution under parameter fluctuations. S8 outputs visual reports and triggers reflective questions.

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