Teaching resource allocation method based on educational software platform data

Abstract

This invention relates to the field of intelligent allocation of teaching resources. Specifically, it relates to a method for allocating teaching resources based on data from an educational software platform, applicable to after-school tutoring for linear equations. This invention collects student answer data and resource interaction data in real time through the platform, analyzes error correction trajectories and hesitation durations, identifies error chains and chain effects in preceding steps, infers student preferences for paused, step-by-step interactive formats through interactive behavior decomposition and interruption frequency analysis, determines the transitional needs for basic variations by combining the click ratio and abandonment rate of variation questions, and allocates resources accordingly. Priority is given to pushing resources for consolidating preceding steps, transforming continuous animations into step-by-step paused courseware, and adjusting the ratio of variation questions with and without parentheses according to a gradient. This achieves precise adaptation of resource presentation order, interaction format, and push ratio, improving students' efficiency in self-correction.

Description

Technical Field

[0001] This invention relates to the field of intelligent allocation of teaching resources, and more specifically, to a method for allocating teaching resources based on data from an educational software platform. Background Technology

[0002] Intelligent allocation of teaching resources is an important technology, specifically applied to the after-school tutoring of seventh-grade linear equations. The core is to achieve precise matching of resource presentation order, interaction form and push ratio by analyzing the coupling characteristics of answer data and resource interaction data, so as to meet the core needs of accurate error tracing and efficient student self-correction.

[0003] Current resource allocation methods based on educational software platform data in this scenario fail to analyze the dual coupling characteristics of error chains in preceding steps and resource interaction preferences in the answer data. They only analyze the data of each step in isolation, failing to identify the chain reaction of subsequent steps caused by errors in preceding steps. This easily leads to misjudging weak points, resulting in a misalignment between resource allocation and the root cause of errors. Furthermore, they fail to capture students' potential preferences for resource interaction formats. Even when students briefly close continuous animations, they still repeatedly push similar unsuitable resources without adjusting the interaction format to meet the need for pausing to think. At the same time, they fail to adjust the push ratio based on students' click preferences for variation questions without parentheses, still pushing variation questions with and without parentheses in a fixed ratio, ignoring students' need for transitioning from basic variation questions. These coupled problems result in low accuracy of resource allocation, insufficient accuracy of error tracing chains, and excessively long time for students to self-correct, failing to meet the core need for efficient self-correction in after-school homework tutoring. To solve this technical problem, we provide a teaching resource allocation method based on educational software platform data. Summary of the Invention

[0004] The purpose of this invention is to provide a method for allocating teaching resources based on data from an educational software platform, in order to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, one of the objectives of this invention is to provide a method for allocating teaching resources based on data from an educational software platform, comprising the following steps:

[0006] S1. Collect students' answer data and resource interaction data in their homework on linear equations in one variable in real time through the educational software platform. The answer data includes the answer time and error correction trajectory of each solution step. The resource interaction data includes the dwell time after clicking on a resource, the closing time, and the number of repeated clicks. The resources include animated demonstrations of removing parentheses, interactive courseware on transposing logic, and similar variant problems.

[0007] S2. By analyzing the number of modifications in the error correction trajectory and the hesitation time in the answering time, we can identify whether the error in the preceding step leads to the error in the subsequent step. When it is detected that the number of modifications in the preceding step exceeds the preset number of modifications and the hesitation time exceeds the preset hesitation time, and is accompanied by skipping the answer in the subsequent step, it is determined that the error chain of the preceding step exists. At the same time, by analyzing the difference between the dwell time after clicking the resource and the full resource duration and the closing time occurring when the resource is not completed, we can infer the resource interaction preference. When the dwell time is less than the preset dwell time and the closing time occurs in the middle of the resource playback, it is determined that the student prefers to pause the step-by-step interaction form rather than continuous animation. Finally, by analyzing the click ratio of similar variant questions, we can determine the student's preference for basic variant transition.

[0008] S3. For error chains in the preceding steps, the order of resource presentation is to prioritize pushing the consolidation resources of the preceding steps and then push the resources of the subsequent steps.

[0009] For the pauseable step-by-step interactive format, the continuous animation has been adjusted to a step-by-step explanation courseware where each pause requires a click to continue. At the same time, for the basic variation transition, the ratio of variation questions with and without parentheses has been adjusted.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0011] This invention analyzes answer data using a step-dependency analysis model, identifies error chains and cascading effects in preceding steps, locates the root cause of errors, and prioritizes pushing resources from preceding steps to reinforce them, thus solving the problem of misalignment between resources and the root cause of errors. The accuracy of error tracing chains meets the standard. By deconstructing interactive behavior patterns and analyzing interruption frequencies, it captures students' interactive preferences for continuous animations and inserts an interactive control layer into keyframes of the animation, changing the format to require clicking to continue after each pause, adapting to the need for pausing and thinking. Based on the click preferences of variant questions, a gradient push algorithm is used to adjust the push ratio, gradually transitioning from basic questions without parentheses to questions with parentheses, aligning with students' acceptance levels. This achieves precise adaptation of resource presentation order, interactive form, and push ratio, significantly reducing the resource allocation misalignment rate, shortening the time students spend on self-correction, and meeting the core need for efficient self-correction in after-school tutoring of linear equations. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating the overall workflow of the present invention. Detailed Implementation

[0013] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] Please see Figure 1 As shown, this embodiment provides a method for allocating teaching resources based on data from an educational software platform, including the following steps:

[0015] S1. Collect students' answer data and resource interaction data in their homework on linear equations in one variable in real time through the educational software platform. The answer data includes the answer time and error correction trajectory of each solution step. The resource interaction data includes the dwell time after clicking on the resource, the closing time, and the number of repeated clicks. The resources include animated demonstrations of the steps to remove parentheses, interactive courseware on the logic of transposing terms, and similar variant problems.

[0016] S2. By analyzing the number of modifications in the error correction trajectory and the hesitation time in the answering time, we can identify whether the error in the preceding step leads to the error in the subsequent step. When it is detected that the number of modifications in the preceding step exceeds the preset number of modifications and the hesitation time exceeds the preset hesitation time, and is accompanied by skipping the answer in the subsequent step, it is determined that the error chain of the preceding step exists. At the same time, by analyzing the difference between the dwell time after clicking the resource and the full resource duration and the closing time occurring when the resource is not completed, we can infer the resource interaction preference. When the dwell time is less than the preset dwell time and the closing time occurs in the middle of the resource playback, it is determined that the student prefers to pause the step-by-step interaction form rather than continuous animation. Finally, by analyzing the click ratio of similar variant questions, we can determine the student's preference for basic variant transition.

[0017] S3. For error chains in the preceding steps, the order of resource presentation is to prioritize pushing the consolidation resources of the preceding steps and then push the resources of the subsequent steps.

[0018] For the pauseable step-by-step interactive format, the continuous animation has been adjusted to a step-by-step explanation courseware where each pause requires a click to continue. At the same time, for the basic variation transition, the ratio of variation questions with and without parentheses has been adjusted.

[0019] The collection of error-modified trajectories specifically includes:

[0020] By embedding an event listener module in each step input box of the problem-solving interface, the system records the student's incorrect expression before each modification, the modified expression after modification, and the corresponding timestamp in real time. Multiple modifications to the same problem-solving step are then chained together in chronological order to form an error trajectory sequence. When the system detects that the student has clicked the submit button, it automatically compares the error trajectory sequence with the final answer of the current step to generate an error modification trajectory that includes the evolution path of the incorrect expression.

[0021] Step dependency analysis models are used to identify the cascading effects of errors in preceding steps leading to errors in subsequent steps, specifically including:

[0022] The algorithm analyzes the modifications made in the preceding steps of the error correction trajectory, identifies key error types, and verifies the logical correlation between the final error expression of the preceding step and the initial input expression of the subsequent step. When the verification finds that the initial input expression of the subsequent step inherits the characteristics of the final error expression of the preceding step and the subsequent step skips the answer, it is determined that there is a chain effect. This process realizes the cross-step transmission verification of error characteristics through the expression syntax tree comparison algorithm.

[0023] The step dependency analysis model further introduces the calculation of error impact weights, specifically including:

[0024] Based on the error type in the preceding steps, different weight values ​​are assigned to the blocking strength of the solution path in the subsequent steps. When it is detected that the number of modifications in the preceding steps exceeds the preset number of modifications and the hesitation time exceeds the preset hesitation time, the chain effect judgment criteria are adjusted in combination with whether the error impact weight value reaches the chain trigger threshold. Among them, the chain judgment is automatically triggered by completely blocking errors, while the chain judgment is triggered by the number of modifications in the subsequent steps reaching more than 2.

[0025] The preset number of modifications and preset hesitation time settings adopt an adaptive threshold generation mechanism, specifically including:

[0026] Personalized thresholds are generated by multiplying the average number of modifications and the average hesitation time in students' historical answer data by a dynamic adjustment coefficient. When it is detected that the number of modifications in the preceding steps exceeds the personalized threshold and the hesitation time exceeds the personalized threshold, and the subsequent steps involve skipping the answer, the error chain of the preceding steps is automatically activated to determine the existence of the error chain. Skipping the answer specifically refers to the behavior of jumping to the next question before the dwell time in the subsequent steps reaches the minimum solution time of that step.

[0027] Inferring resource interaction preferences is achieved through interaction behavior pattern decomposition techniques, specifically including:

[0028] The proportion of dwell time after a resource click to the total resource duration is captured. Combined with the location of the resource node where the closing action occurs, a two-dimensional analysis matrix of duration nodes is constructed. When the proportion of dwell time after a resource click to the total resource duration is lower than a preset proportion and the closing node is located before the explanation of the core knowledge points of the resource, it is determined that the student has given up learning due to difficulty in understanding. When the closing node is located after the explanation of the core knowledge points but the proportion of dwell time is still lower than the preset proportion, it is determined that the student has given up learning due to the incompatibility of the interaction format.

[0029] The determination of whether a step-by-step interaction can be paused relies further on the analysis of interaction interruption frequency, specifically including:

[0030] The system counts the number of times students repeatedly click on the same resource and the duration of each click. When it detects that the duration of a single click is less than the preset duration, the click is closed midway through the playback, and the interval between repeated clicks is less than the preset interval, it is determined that the student is experiencing an interactive dilemma where they have tried to understand the content multiple times but are hindered by the continuous playback format. At this point, an interaction format conversion instruction is automatically triggered, breaking down the continuous animation into segmented knowledge point modules and inserting a forced pause control point after each module.

[0031] The determination of the transition from basic to variation problems is verified using the variation problem difficulty attenuation coefficient, specifically including:

[0032] Based on the click order data of similar variation questions, the abandonment rate after the first click of the variation question containing parentheses is calculated, that is, the proportion of people who close the page before completing the question. When the number of clicks on the variation question without parentheses reaches 3 times the number of clicks on the variation question with parentheses and the abandonment rate of the variation question with parentheses exceeds the preset abandonment rate, it is determined that students have a need for basic variation transition. At the same time, by comparing the correct answer rate of variation questions, the interference of click volume differences caused by the difficulty of the questions is eliminated.

[0033] The order in which reinforcement resources for the preceding steps are pushed is tied to the deep analysis results of the error chain of the preceding steps. If an error chain of the preceding steps is found to exist, the starting step of the error chain is first located, and the special reinforcement resources in the resource library that precisely match the error type of the starting step are retrieved. Only when the answer data after the error correction of the starting step is detected to meet the expected standard is the permission to push resources for subsequent steps unlocked. If a chain error occurs again in subsequent steps, the process returns to the starting step for secondary reinforcement.

[0034] An interactive control layer is inserted into the keyframe nodes of the original continuous animation. The single-step animation is decomposed into three stages: the initial state display frame, the transformation rule explanation frame, and the transformation process demonstration frame. After each frame ends, the continue button is activated. The proportion of variation questions pushed is adjusted based on the basic variation transition preference judgment result. Variation questions without parentheses are extracted from the variation question resource pool as the first round of push. After their accuracy reaches the standard, variation questions with parentheses are mixed in proportionally to form a gradient training group. All variation questions with parentheses are accompanied by a micro-tutoring prompt module for the preceding steps.

[0035] It needs further explanation that, in the process of collecting students' answers to linear equations homework on the educational software platform, the error correction trajectory is the core basis for identifying the chain reaction of errors in preceding steps. It can completely reconstruct the evolution of students' thinking process when solving problems, accurately locate the root cause of errors and the direction of correction. Therefore, a refined collection and comparison mechanism is needed to ensure the integrity and accuracy of the trajectory data. The specific implementation method is as follows:

[0036] First, an event listening module is embedded in the input box of each step in the problem-solving interface. This module is a lightweight program embedded in the underlying code of the input box. It requires no additional operation from the student and can automatically capture content change events in the input box. When the student enters an expression, deletes content, or modifies characters in the input box, the module will immediately trigger the recording logic. The core data recorded includes three parts: First, the incorrect expression before modification, that is, the complete content in the input box before the student's modification operation. Here, the incorrect expression refers to the formula that does not conform to the preset correct problem-solving logic or mathematical rules of the step. Even if the student's subsequent modification is still not correct, the intermediate state must be fully recorded. Second, the modified expression, that is, the content in the input box after the student completes the modification. This content may be a partially corrected intermediate result or the final submitted answer. Third, the corresponding timestamp, that is, the precise time when the modification operation occurred. It is synchronized and calibrated by the platform system clock to ensure that the time accuracy reaches the millisecond level, providing data support for subsequent analysis of the duration of the modification.

[0037] After completing the real-time recording of multiple modifications in a single step, the system automatically concatenates all modification records for the same problem-solving step in chronological order of timestamps, forming an error trajectory sequence for that step. This sequence is structured array data, with each array element corresponding to a modification operation. It stores three core fields: the incorrect expression before modification, the expression after modification, and the timestamp. It also includes a step identifier and a unique student ID to avoid data confusion across steps and across students. For example, if a student makes two modifications in the parentheses removal step, first mistakenly writing 2(x+3)=5 as 2x+3=5, then correcting it to 2x+6=5, and then adjusting it to 2x-6=5, the error trajectory sequence will record the complete data of these two modifications in chronological order, clearly showing the direction of each adjustment.

[0038] When a student clicks the submit button on the problem-solving interface, the system initiates a comparison process between the error trajectory sequence and the final answer of the current step. This step is crucial for generating a complete error correction trajectory, requiring multi-dimensional comparison to reconstruct the error evolution path. First, the final answer of the current step is identified. This answer is a standard result pre-entered by the subject teacher and grammatically validated, based on the platform's problem-solving logic for linear equations. It includes not only the final mathematical expression but also the core problem-solving rules for that step, ensuring that the comparison not only determines the correctness of the result but also identifies the error type. The comparison process begins with sequence traversal. The system first extracts the last record from the error trajectory sequence, obtaining the student's submitted final expression—the final modified version—and compares it initially with the platform's preset correct answer. If the two are completely identical, it means the student has passed the test. After multiple modifications, the error is finally corrected. The system adds a status marker indicating that the error has been corrected to the end of the error trajectory sequence, and records the total time taken from the first error to the final correctness, as well as the difference between the timestamp of the last record and the timestamp of the first record. If the final expression does not match the correct answer, a node-by-node comparison is required. Starting from the first record in the sequence, the modified expression of each node is compared with the correct answer and the original incorrect expression of the previous node. On the one hand, the differences between the current modified expression and the correct answer are identified through string comparison combined with mathematical expression syntax analysis, and the error type of the node is marked according to the platform's preset error classification library. On the other hand, the modified expression of the current node is compared with the original expression of the previous node to determine the direction of the error correction operation and record the effectiveness of the modification.

[0039] After node-by-node comparison, the system integrates all information to generate an error modification trajectory containing the evolution path of the incorrect expression. This trajectory is stored in the form of a visualized data stream. Each node is accompanied by a timestamp, the content of the incorrect expression, the error type, the direction of modification, the degree of difference from the correct answer, and the modification time. At the end of the trajectory, the total number of modifications, the distribution of error types, and the final error status are summarized. The entire data collection and comparison process is executed automatically in the background, with the time controlled within 1 second, so as not to affect the student's answering experience. The generated error modification trajectory is associated with the student's answer data and step identifiers and stored in the platform database. This provides traceable and high-precision core data support for subsequent step dependency analysis models to identify error chain effects and accurately allocate teaching resources.

[0040] After collecting and structuring the error correction trajectory, it is necessary to further explore the transitivity of errors through a step dependency analysis model. The steps for solving linear equations in one variable have strict logical dependencies. If only the surface errors in subsequent steps are corrected while ignoring the root causes of errors in preceding steps, students will repeatedly fall into the same pitfalls. Therefore, it is necessary to accurately identify whether errors in preceding steps trigger a chain reaction in subsequent steps. The specific implementation method is as follows:

[0041] First, we need to clarify the definition criteria for the preceding steps. In the standardized problem-solving process of a linear equation in one variable, the steps follow a causal logical chain, usually progressing in the order of removing parentheses → transposing terms → merging like terms → reducing the coefficient to 1. The preceding step of a certain step refers to the step that is located before it in the logical chain and whose solution process must be based on the result of that step. For example, the preceding step of the transposing step is the parenthesis removal step, and it is necessary to determine which terms need to be transposed based on the algebra after removing the parentheses. The preceding step of the merging like terms step is the transposing step, which requires first transposing like terms to bring them together on the same side of the equal sign. The parenthesis removal step has no prior dependency and is the starting step of the process. If a student leaves an uncorrected error in a certain preceding step, the initial input of the subsequent steps will inevitably be directly affected by the result of that error. This is the logical premise for determining the chain effect.

[0042] Next, the system analyzes the modifications in the error correction trajectory of the preceding steps to locate the key error types. The system first extracts the complete error trajectory sequence of the preceding steps, then traces back in reverse chronological order by timestamp, from the final submission record to the first error record. It focuses on filtering the error points with the highest modification frequency and persistent, uncorrected errors. For example, in the trajectory sequence of the bracket removal step, if the student's four modifications all revolve around the expansion result of 2(x-4), initially mistakenly writing 2x-4, then correcting it to 2x+4, and then correcting it to 2x-8 (correct) before mistakenly reverting to 2x-4, then the bracket removal coefficient... Omitting the sign of the constant term (in this case, omitting the negative sign results in 4 remaining unchanged and -8 remaining) is a high-frequency error. Combining this with the core problem-solving rules for linear equations in one variable, the errors are categorized into critical error types. These errors are different from typos and will directly block the correct solution path in subsequent steps. Specifically, they can be divided into errors such as omitting the sign of the parenthesis removal, omitting the multiplication of the coefficient when removing parentheses, and omitting the sign when transposing terms. Each critical error type corresponds to the platform's preset error feature library. By comparing the modified content with the feature library tags, the system automatically marks the critical error type of the preceding steps, providing a clear target for subsequent tracking of error propagation.

[0043] After identifying the key error types, the final error expression of the preceding steps is extracted. This expression refers to the final content in the input box when the student clicks the submit button after completing all the modification operations in the preceding steps. Regardless of whether it conforms to the correct answer, it represents the final result of solving the problem in the preceding steps and is also the only basis for the student to carry out subsequent steps. For example, in the step of removing parentheses, the student finally submits 2x-4=10 after multiple modifications (the correct answer should be 2x-8=10). This 2x-4=10 is the final error expression of the preceding steps. Subsequent transposition steps must be based entirely on this expression. If the error of -4 in this expression is not corrected, the initial input of subsequent steps will inevitably carry this error mark.

[0044] Correspondingly, the initial input expression for subsequent steps refers to the complete content that students first enter in the input box of the subsequent step after entering the problem-solving interface. It directly reflects the student's initial thinking in deriving the subsequent steps based on the previous final result. For example, the transposition step is a subsequent step after the parenthesis removal step. After entering the transposition interface, if the student directly enters 2x=10+4 without making any modifications, this expression is the initial input expression for the subsequent step. Its derivation logic completely depends on the previous incorrect final expression 2x-4=10 (moving -4 from the left side of the equals sign to the right side). If -4 in the previous expression is incorrect (it should be -8), +4 in the subsequent initial expression will also be incorrect, forming an error propagation. To verify whether the subsequent initial expression inherits the characteristics of the previous incorrect final expression, it is necessary to combine the relevance of the expression content with the student's answering behavior for a comprehensive judgment. First, analyze the relevance of the content. If the previous incorrect final expression has a missing negative sign in the parenthesis removal and... If the logic relies entirely on the result of a previous error, then the subsequent expression is determined to inherit the error characteristics of the previous one. If the subsequent initial expression uses correct data, there is no inheritance relationship. Next, it judges the behavior of skipping the answer. Skipping the answer specifically refers to the student's dwell time in the subsequent steps not reaching the preset minimum solution time for that step. This time is set based on the difficulty of the step and the student's average solution speed, and the core input of the step is not completed. For example, after entering the moving item step, the student only enters 2x= in the input box and clicks the next question, with a dwell time of only 4 seconds or no input content and jumps directly. This behavior usually indicates that the student cannot understand the solution logic of the subsequent steps due to a previous error and is forced to give up answering the question. If there is only an inheritance of error characteristics but no skipping the answer (the student completes the subsequent steps completely and may correct it in other ways), or only skipping the answer but no inheritance characteristics, it is not judged as a chain effect. Only when both conditions are met is a chain effect initially judged to exist.

[0045] The verification of the aforementioned inherited features requires precise cross-step verification through the expression syntax tree comparison algorithm. The expression syntax tree is a model that decomposes mathematical expressions into tree-like data structures according to operation priority and logical relationship. The root node of the tree is the highest priority operator, and the child nodes are the elements participating in the operation. Each node carries the node type, node value, and parent node relationship, reflecting the upper-level operation that the node depends on. It can clearly trace the source and operation logic of each element. In specific implementation, the syntax trees of the previous final incorrect expression and the subsequent initial input expression are constructed separately. Taking the previous incorrect expression 2x-4=10 as an example, the root node of the syntax tree is = (highest priority), the left child node of the root node is - (second priority operation), the left child node of - is 2x (the product node formed by the coefficient 2 and the variable x), the right child node is constant 4 (marked as an incorrect constant node, because it should be 8 if correct), and the right child node of the root node is constant 10 (correct node).

[0046] For the subsequent initial expression 2x = 10 + 4, the root node of the syntax tree is also =, the left child node is 2x (completely consistent with the structure of the 2x node in the previous syntax tree), and the right child node is + (operator). The left child node of + is 10, and the right child node is the constant 4 (marked as a node to be verified). Then, the system performs a hierarchical comparison of the syntax tree nodes. The system first locates the erroneous node in the previous syntax tree, namely the erroneous constant 4, and extracts its core features: node value 4, node type constant, parent node operation relationship (minuend to the right of -), and associated variable (2x). Then, it traverses all nodes in the subsequent syntax tree to find a node to be verified that matches the features of the erroneous node. The matching criteria include: the node value is completely consistent (both are 4), the node type is the same (both are constant), and the parent node operation relationship of this node in the subsequent syntax tree depends on the parent node result of the previous erroneous node. In the subsequent syntax tree, 4 is the addend to the right of +, which comes from the 4 to the right of - in the previous syntax tree. That is, the student moves -4 in the previous syntax tree to... The right side then becomes +4, indicating a direct dependency in the operation relationship. If a matching node is found, the irreplaceability of that node can be further verified. For example, if the 4 in the subsequent syntax tree is replaced with the correct value 8, the subsequent expression will become 2x=10+8, which is fundamentally different from the original subsequent initial expression 2x=10+4. This shows that the construction of the subsequent expression completely depends on the erroneous node, meaning that the error feature has been propagated across steps. If the syntax tree comparison results show that the key node of the subsequent initial expression has a matching and dependency relationship with the preceding erroneous node, and combined with the judgment of skipping the answer behavior, it can be finally confirmed that the error in the preceding step has triggered a chain reaction in the subsequent steps. For example, the omission of the negative sign when removing parentheses in the preceding step leads to the erroneous constant 4. The subsequent term-shifting initial expression inherits this 4 and is skipped because it cannot be calculated correctly. The syntax tree algorithm accurately verifies this error propagation process, providing a technical basis for the subsequent platform's strategy of prioritizing the allocation of preceding reinforcement resources, avoiding resource pushes that only target subsequent surface errors while ignoring the root cause.

[0047] After initially verifying the cross-step propagation of error characteristics using the expression syntax tree comparison algorithm, to avoid overly absolute judgments of cascading effects due to differences in error types, the step dependency analysis model needs to further introduce error impact weight calculations. By quantifying the degree of interference of preceding errors on subsequent steps and dynamically adjusting the cascading effect judgment criteria in conjunction with student answer behavior data, the judgment results can better reflect the actual logic of solving linear equations in one variable. The specific implementation method is as follows:

[0048] First, let's define the error impact weight value. It's a quantified numerical value assigned based on the type of error in the preceding steps and its blocking effect on the solution path of subsequent steps. The value ranges from 0 to 10, with higher values ​​indicating stronger blocking. Blocking strength refers to the degree to which an error prevents subsequent steps from proceeding logically. If an error deprives subsequent steps of the correct solution basis, the blocking strength is high; if the error only affects the final result but doesn't hinder the progress of steps, the blocking strength is low. For accurate assignment, the platform needs to pre-build an error type and weight mapping table. This table is based on the logical dependencies of the solution steps for a linear equation in one variable, classifying and assigning values ​​according to the degree of impact of errors on subsequent steps. One type is the completely blocking error, which directly destroys the solution foundation of subsequent steps, resulting in no correct data to rely on. This type has the highest blocking strength and a weight value set at 8-10, specifically including:

[0049] Common errors include: omissions in multiplying all terms when removing parentheses (e.g., writing 3(2x-5) as 6x-5, omitting the constant term -5); completely reversing signs when removing parentheses (e.g., writing -(x-4) as -x-4, failing to correctly pass the negative sign); and omitting key terms when transposing terms (e.g., when transposing 2x+3=5x-1, only 2x is moved, not -1, leading to a failure to group like terms). For example, a student might mistakenly write 2(3x-4)=7 as 6x-4=7 (omitting the coefficient 2 of the constant term -4; the correct value should be 6x-8=7). This error will cause the initial input expression in subsequent transposing steps (e.g., 6x=7+4) to be entirely based on the incorrect -4, inevitably leading to incorrect results when merging like terms and setting the coefficient to 1. Furthermore, students cannot correct the omissions in the preceding multiplications through subsequent steps. Therefore, this type of error is classified as a complete blocking error, with a weight of 10. Another type is the partial blocking error, which only causes deviations in the results of subsequent steps but does not hinder the progress of the steps themselves (students can still follow the process of moving terms → merging like terms). This type of error has a moderate blocking strength, with a weight of 3-7. Specifically, it includes: omissions of individual symbols when removing parentheses, such as in 4(x-2)+3(y+1), where only the negative sign is missed for -2, while +1 is correct; errors in the sign of a single term when moving terms (e.g., x+5=3x-2 moved to x-3x=-2+5, where +5's sign remains unchanged after moving but other terms are correct); and errors in calculating coefficients when merging like terms (e.g., 3...). (e.g., x + 2x is calculated as 6x instead of 5x). For example, in the rearrangement step, a student mistakenly writes 2x - 6 = 5x + 3 as 2x - 5x = 3 + 6 (the sign of -6 is not changed after rearrangement; the correct answer should be 2x - 5x = 3 + 6, but the actual result is correct by chance; another example is 2x - 6 = 5x + 3 mistakenly written as 2x - 5x = 3 - 6). This error will lead to an incorrect result in the subsequent merging of like terms (-3x = -3 becomes -3x = -9), but the student can still complete the steps of merging like terms and reducing the coefficient to 1 normally. Only the final answer is wrong. Therefore, this type of error is classified as partially blocking, with a weight of 5. The preset number of modifications and preset hesitation time continue the adaptive threshold generation mechanism, that is, based on the student's historical number of answers. Personalized thresholds are generated by multiplying the average number of modifications and the average hesitation time by a dynamic adjustment coefficient (usually 1.2-1.5, which can be lowered to 1.1 for students with learning difficulties). For example, if a student has made an average of 2 modifications to the parenthesis removal step and an average hesitation time of 15 seconds, and the dynamic adjustment coefficient is 1.3, then the preset number of modifications for this student is 2 × 1.3 ≈ 3 times, and the preset hesitation time is 15 × 1.3 ≈ 20 seconds. These two thresholds are used to determine whether the student is in a predicament of repeatedly correcting errors in the preceding steps but failing. If the number of modifications exceeds the threshold and the hesitation time exceeds the threshold, it means that the student has realized that there is an error in the preceding steps but cannot correct it. At this time, the probability of the error being passed on to subsequent steps increases significantly.

[0050] When the number of modifications to the preceding steps exceeds the preset number of modifications and the hesitation time exceeds the preset hesitation time, the model will initiate a weight and threshold linkage judgment process. First, it retrieves the weight value of the current preceding error from the error type and weight mapping table. At the same time, it reads the platform's preset chain triggering threshold. This threshold is based on a large amount of teaching data statistics and is set to 6 by default, meaning that the error needs to reach a moderate to high blocking strength to trigger a chain effect. If the weight value of the preceding error is greater than or equal to the chain triggering threshold, i.e., a complete blocking error with a weight of 8-10, then automatic chain judgment is triggered directly. There is no need to further verify the behavior of subsequent steps; it can be determined that the preceding error will trigger subsequent... The model considers the chain reaction effect of steps. For example, if a student modifies the parenthesis removal step 4 times (exceeding the preset 3 times), hesitates for 25 seconds (exceeding the preset 20 seconds), and the error type is a missing coefficient multiplication of a constant term symbol (weight 10 ≥ 6), the model directly marks the existence of a chain reaction effect. Subsequent resource allocation will prioritize pushing parenthesis removal-specific reinforcement resources. If the weight value of the preceding error is less than the chain trigger threshold, i.e., a partial blocking error (weight 3-7), then the modification count of subsequent steps needs to be added for further verification. The model will extract the error modification trajectory of subsequent steps, count the number of modifications made by the student in that step, only count valid modifications, exclude typos and delete re-entry, and if the number of modifications in subsequent steps is large... If the number of modifications in subsequent steps is less than 2, it indicates that the student also gets stuck in the dilemma of repeatedly correcting errors in subsequent steps, indirectly proving that the previous error has been passed on to the subsequent steps and triggered a chain reaction. At this time, the conditional chain reaction judgment is triggered. If the number of modifications in subsequent steps is less than 2, it means that the student may have independently corrected the impact of the previous error in subsequent steps, and it is not judged as a chain reaction. For example, if the student modified the previous item-moving step 3 times (exceeding the preset 2 times), hesitated for 18 seconds (exceeding the preset 15 seconds), and the error type was a single item moving without changing the sign (weight 5 less than 6), and the subsequent step of merging like items was modified 2 times (greater than or equal to 2 times), then the model judges that there is a chain reaction. If the subsequent step of merging like items only corrects the previous error, then the model judges that there is a chain reaction. If a single correction is made, it is determined that there is no chain effect. The entire error impact weight calculation and judgment process, through the logic of error type quantification → behavioral data verification → weight threshold linkage, achieves refined chain effect judgment. This avoids students making repeated mistakes due to judgment delays in completely blocking errors, and also prevents partially blocking errors from being misjudged as chain effects. It ensures that the subsequent allocation of teaching resources can accurately locate the root cause of the error. For example, completely blocking errors will be given priority to push specific error correction resources for the preceding steps, while partially blocking errors will be pushed a combination of preceding consolidation and subsequent correction resources based on the modification of subsequent steps. This makes resource allocation more in line with students' actual problem-solving difficulties and improves error correction efficiency.

[0051] After introducing error impact weight calculation into the step dependency analysis model, to avoid overlooking individual student answering habits due to the use of a uniform fixed threshold, which could lead to missed or incorrect judgments in the error chain determination for different students, the preset modification number and preset hesitation time settings need to adopt an adaptive threshold generation mechanism. This mechanism uses students' own historical answer data as the core basis and dynamically adjusts the threshold in combination with their learning level to ensure that the judgment criteria for students with different learning situations are consistent with their actual answering behavior. At the same time, it is necessary to activate the error chain determination of the preceding steps through multi-condition linkage. The specific implementation method is as follows:

[0052] First, let's clarify the core logic of the adaptive threshold generation mechanism. It's a dynamic adjustment strategy that departs from a one-size-fits-all fixed standard and generates personalized judgment benchmarks based on individual student historical data. The core is to adapt the threshold to the student, rather than the student adapting to the threshold. Its generation process relies on the platform's student learning profile database and data analysis module. Specifically, the platform first retrieves the student's relevant answer records from the database over the past 30 days using the student's unique ID and question type tag (linear equations in one variable). From these records, two core indicators are extracted: first, the average number of modifications, which is the total number of modifications made for each step of every problem in all linear equations, divided by the product of the total number of problems and the number of steps, to obtain the average number of modifications per step; second, the average hesitation time, which specifically refers to the interval exceeding one second after a student enters content in a certain step without immediately submitting or modifying it. The platform synchronously records the duration of each hesitation through the input box's event listener module and timer, and then divides the sum of the hesitation times for all steps by the number of hesitations to obtain the average... To ensure the threshold better aligns with students' learning levels, a dynamic adjustment coefficient is introduced to measure the average hesitation time. This coefficient is a correction value set based on students' historical answer accuracy and learning progress, aiming to avoid biases in threshold settings for students of different levels. For high-achieving students with a historical answer accuracy of over 80% and whose learning progress is ahead of the teaching plan, the coefficient is set to 1.5; for average students with an accuracy of 60%-80% and whose progress is in line with the teaching plan, the coefficient is set to 1.2; and for struggling students with an accuracy of less than 60% and whose progress is lagging behind, the coefficient is set to 1.0. The dynamic adjustment coefficient is updated monthly based on the latest answer data to ensure it always adapts to the student's current learning status. Based on the above indicators and coefficients, personalized thresholds are generated. The average number of modifications is multiplied by the dynamic adjustment coefficient, and the result is rounded up to the nearest integer to avoid the difficulty of calculating decimal thresholds. The average hesitation time is multiplied by the dynamic adjustment coefficient, and the result is rounded to the nearest integer in seconds. After the personalized thresholds are generated, they are stored in the threshold configuration table of the student's learning file and synchronized in real time to the step dependency analysis model as a benchmark for subsequent judgments.

[0053] After setting the personalized threshold, the model monitors the answering behavior of the preceding steps and the jumping behavior of the subsequent steps in real time. When three conditions are met simultaneously, the system automatically activates the determination of the existence of an error chain in the preceding steps. The first condition is that the number of modifications to the preceding steps exceeds the personalized threshold. The model uses the event listener module of the input box to count the number of all modification operations for this step from when the student enters the answering interface to when they click the submit button. For example, if the personalized modification threshold for the student's preceding step of removing parentheses is 2, and the step is counted as being modified 3 times, then this condition is met. The second condition is that the preceding steps are still... If the hesitation time exceeds the personalized threshold, the model records the total hesitation time for that step using a timer, thus satisfying this condition. The third condition is that subsequent steps involve skipping the answer. To address this, a minimum solution time must be defined. This time is a baseline time set by the platform based on the knowledge complexity of each step in a linear equation and the average problem-solving speed of students in the same grade. For example, the minimum solution time for removing parentheses is 15 seconds, for transposing terms it's 10 seconds, and for combining like terms it's 8 seconds. If a student is struggling academically, their minimum solution time can be reduced by 20% to ensure it matches their actual problem-solving speed. Skipping a question specifically refers to a situation where, after a student moves to a subsequent step, the timer starts counting down. If, before the minimum time for solving the question has been reached, the student actively clicks the "Next Question" or "Submit All Questions" button on the interface, and the input box for that step is not filled with a complete solution expression, excluding accidental jumps caused by network lag, the skipping behavior is determined by detecting whether there is continuous input in the input box before the jump. For example, if a student enters the "Move Item" step and the timer only stays for 7 seconds (below the minimum of 10 seconds), and the student only enters "2x=" in the input box before clicking "Next Question," then it is considered skipping a question. When all three conditions are met, the model's background judgment program will immediately trigger a flag indicating the existence of an error chain in the preceding steps. This flag is structured data containing the student ID, question ID, preceding step identifier, and error type, which will be automatically written to the error chain log of the student's answer record. At the same time, a trigger signal is sent to the resource allocation module. After receiving the signal, the resource allocation module will prioritize retrieving reinforcement resources that match the error type of the preceding steps, rather than directly pushing resources for subsequent steps, ensuring that the student is helped to correct the error from the root and preventing the error chain from being further propagated. The entire judgment process takes less than 1 second, requires no manual intervention, and generates a judgment log for teachers to review later, clearly presenting the specific basis for the activation of the error chain, allowing teachers to accurately grasp the difficulties students face in answering questions.

[0054] After identifying and determining the error chain in the preceding steps, the educational software platform needs to further analyze the interaction behavior of students with the teaching resources for linear equations in one variable in order to accurately infer their resource interaction preferences. This is the core basis for subsequently adjusting continuous animations into step-by-step explanation courseware and optimizing the proportion of variation questions pushed. This inference process needs to be achieved through interaction behavior pattern decomposition technology. The core is to decompose complex interaction behaviors into two quantifiable dimensions: the percentage of dwell time and the position of the closing node. Then, through two-dimensional matrix correlation analysis, the root cause of students giving up learning can be located. The specific implementation method is as follows:

[0055] First, let's clarify the core logic of the interactive behavior pattern decomposition technology. It's a technique that breaks down the interaction process between students and resources into key behavioral indicators and uncovers potential preferences through multi-dimensional correlation analysis. It doesn't require active student feedback; analysis is achieved solely through behavioral data automatically collected by the platform's backend. Here, we focus on two core indicators: First, the ratio of the dwell time after clicking a resource to the total resource duration. Dwell time refers to the duration from when a student clicks the play button to when they click the close button or navigate to another page. The total resource duration is the total time from start to finish. The ratio reflects the student's level of engagement with the resource. Second, the resource node where the close action occurs. In this context, a resource node refers to a continuous segmentation of resource content according to teaching logic. When creating resources, the platform pre-labels each node with a time range and content type. For resources related to linear equations, these are typically divided into introductory demonstration nodes, core knowledge point explanation nodes, example demonstration nodes, and summary review nodes. When a close action occurs, the system matches the corresponding node based on the current playback time to determine the close node position. Next, a two-dimensional analysis matrix of duration nodes is constructed. This matrix is ​​a tool that correlates the indicators of the above two dimensions to form a visual analysis table. Through data analysis of the matrix cells, it is possible to quickly distinguish between two types of reasons for abandonment: difficulty in understanding and incompatibility of the interaction format. The specific process of matrix construction is as follows:

[0056] The matrix is ​​defined with horizontal and vertical axes. The horizontal axis represents the location of the resource node where the closing action occurs, arranged sequentially as follows: import / demo node, core knowledge point explanation node, example demonstration node, and summary / review node. Each node is labeled with its corresponding time interval. The vertical axis represents the percentage of time spent on the resource relative to its total duration, divided into three intervals based on the percentage: low percentage (0-30%), medium percentage (30%-60%), and high percentage (60%-100%). Each interval corresponds to a different level of student engagement. Interaction data is collected and preprocessed. The platform uses a timer in the resource playback module to record each student's time spent on the resource in real time, calculates the percentage based on the total duration of the resource, and utilizes the built-in node marking module within the resource. Time-triggered code is embedded during resource creation. When playback reaches the start time of a node, it is automatically marked, and the node position when the closing action occurs is recorded. The collected data is cleaned, outliers are removed, and matrix data is populated. The pre-processed interaction data of each student is mapped to the corresponding cell in the matrix. For example, if student A clicks the bracket removal animation (full duration 60 seconds), stays for 15 seconds, and then closes, with a proportion value of 25% (low proportion range), and playback reaches 10 seconds when closing (import demo node), this data entry is counted in both the import demo node and the low proportion range cell. Simultaneously, the number of data entries (records of multiple interactions by the same student with the same resource need to be counted separately) and the student ID are recorded in each cell, forming a complete two-dimensional analysis matrix of duration nodes. The data distribution within the matrix directly reflects the concentrated trend of students abandoning learning. Based on the constructed two-dimensional analysis matrix, two types of reasons for abandonment are determined. The first is the determination of abandonment due to difficulty in understanding, which requires meeting two core conditions: First, the proportion of time spent on the resource is lower than a preset proportion. The preset proportion is a critical value set based on the average proportion of time spent on similar resources by students of the same grade (based on teaching data statistics, the preset proportion for resources on linear equations in one variable is usually set at 30%, and a value lower than this indicates that students have not fully engaged in learning). Second, the closing node is located before the explanation of the core knowledge point, that is, the closing action occurs before the start time of the introduction demonstration node (the core knowledge point explanation node), because the core knowledge point explanation node is the core content of the resource. If a student closes the resource before entering a specific node due to insufficient time spent, it's usually because they didn't understand the content in the introduction demonstration, making it impossible to continue with the subsequent core explanations. To ensure accurate judgment, further verification is needed. The system will retrieve the student's interaction details at the introduction demonstration node, such as whether they repeatedly dragged the progress bar to rewind (attempting to understand the content again) or clicked the question mark button within the resource (actively marking content they didn't understand). If these behaviors exist and the above two core conditions are met, it's further confirmed that difficulty in understanding led to abandoning learning. For example, if student B clicks on the item-moving logic interactive courseware (complete duration 90 seconds, core knowledge point explanation node starts at 27 seconds), stays for 20 seconds, and then closes it, the proportion is approximately 22% (less than 30%).When closing, the playback stopped at 25 seconds (within the import demo node), and the interaction log showed that the student dragged the progress bar three times to return to the beginning of the import demo. No question mark was clicked, but the dwell time was short. At this point, it's judged as abandoning learning due to difficulty in understanding. The second judgment is abandoning learning due to the interaction format being unsuitable. This also requires meeting two core conditions: first, the dwell time as a percentage of the total resource time is still lower than the preset percentage (30%); second, the closing node is located after the core knowledge point explanation, meaning the closing action occurs after the core knowledge point explanation node ends, possibly in the example demonstration node or summary review node. Because the content of the core knowledge point explanation node is already complete, if the student has difficulty understanding, they will usually close the resource before or during the core knowledge point explanation. If they still close it after entering subsequent nodes due to short dwell time, it's more likely that the resource's interaction format doesn't meet their learning habits. The auxiliary verification stage needs to focus on analyzing repeated interaction behavior. The system will count the number of times the student repeatedly clicks on the same resource and the location of each closing node. If the student clicks on the same resource multiple times, closing it each time after the core knowledge point explanation, and the dwell time is shorter than expected, then the system will be considered successful. If all examples are below the preset proportion, and there are instances of rapid clicking on the progress bar and frequent clicking of the pause button, it can be confirmed that the interaction format is incompatible. For example, student C repeatedly clicked on the continuous animation to remove parentheses (full duration 60 seconds, core knowledge point explanation ends at 36 seconds), first pausing for 18 seconds (proportion 30%, closes at 40 seconds, example demonstration node), and second pausing for 15 seconds (proportion 25%, closes at 38 seconds, example demonstration node). The interaction log shows that he frequently clicked the screen to try to pause each time it played (but the continuous animation has no pause function), and did not revert to the import demonstration node. In this case, it is determined that he gave up learning due to incompatible interaction format. By combining the two-dimensional analysis matrix of duration nodes with the two types of judgment logic, the interaction behavior pattern decomposition technology can accurately infer students' resource interaction preferences. If the difficulty in understanding judgment data is concentrated, the import demonstration content of the resources needs to be optimized. If the incompatible interaction format judgment data is concentrated, the resource interaction format needs to be adjusted, providing a clear optimization direction for the subsequent resource allocation of the platform, ensuring that the pushed resources can both match the students' knowledge weaknesses and fit their interaction habits.

[0057] After initially determining, through interactive behavior pattern analysis, that some students had given up learning due to unsuitable interaction methods, to avoid confusing occasional accidental closing of resources with continuous playback obstacles, it is necessary to further refine the determination of pauseable, step-by-step interaction methods by relying on interaction interruption frequency analysis. This analysis, by statistically analyzing students' repeated click behavior and interval characteristics on the same resource, accurately captures their predicament of repeatedly trying but being limited by the interaction method, thereby triggering an interaction method switch to ensure that resource interaction aligns with students' actual learning habits. The specific implementation method is as follows:

[0058] First, we clarify the core indicators and definitions of the interaction interruption frequency analysis. It focuses on two types of data: First, the number of times a student repeatedly clicks on the same resource. This refers to the total number of times a student actively clicks on the same teaching resource within a 10-minute period (a short interaction period preset by the platform to avoid interference from irrelevant repeated clicks over longer periods). This excludes clicks caused by automatic system recommendations or accidental touches. Each click must be accompanied by resource playback, meaning the resource starts playing after the click, not just the resource cover being opened but not playing. Second, the interval between each click. This refers to the difference between the timestamp of closing the resource after the previous click and the timestamp of starting playback after the next click. For example, if a student closes the resource for the first time at 15:30:20 and starts playing it again at 15:30:20... The interval between 30:25, or 5 seconds, reflects the time interval between two attempts by a student to understand the resource. A shorter interval indicates a student's eagerness to resolve previously uncomprehended content, and a higher likelihood of being hindered by the interaction format. After collecting this indicator, three key conditions need to be considered to determine if a student is experiencing interaction difficulties. The first condition is that the single dwell time is less than the preset dwell time. The preset dwell time is a critical value set based on the duration of the core knowledge point explanation nodes in the resource. For continuous animations related to linear equations, the preset dwell time is set to 50% of the core node duration, i.e., 15 seconds. If the student's dwell time after clicking on the resource (the duration from the start of playback to closing) is less than 15 seconds, it indicates that they were forced to leave before fully understanding the core knowledge point explanation. The first condition is that the app was closed because the continuous playback could not be paused, causing the user to miss key content. The second condition is that the closure occurred midway through the resource playback. "Midway through playback" specifically means that the closure action occurred within the core knowledge point explanation or example demonstration node of the resource, excluding the initial exploration closure of the import demonstration node and the closure of the summary review node after the content has been mastered. For example, in a 60-second animation, if the closure occurs between 12-48 seconds (the core and example node range), it indicates that the student was interrupted due to an interactive problem while learning the core content, rather than being uninterested in the imported content. The third condition is that the interval between repeated clicks is shorter than the preset interval. The preset interval is set at 30 seconds based on the attention span characteristics of students in short-term learning. If the interval between two clicks on the same resource is less than 30 seconds, it indicates that the student missed the previous click. After closing the app, the student didn't shift their attention but immediately tried to understand it again, further confirming that it was limited by the continuous playback format. When all three conditions are met, the judgment logic will refine and verify in three steps to ensure no misjudgment, eliminate interference from the inherent difficulty of the resource content, and retrieve the student's interaction data with similar basic resources. If the student's dwell time on basic resources is normal (exceeding the preset dwell time) and there are few repeated clicks, and the above three conditions are only met for continuous animations with complex steps, it indicates that the problem lies in the interaction format rather than content comprehension. Verify the operational details before closing the app by checking the logs of the resource playback module to see if the student quickly dragged the progress bar or clicked on the blank area of ​​the screen to try to pause (continuous playback has no pause button, and the student mistakenly believed that it could be clicked to pause).If an obstacle exists, it is further confirmed to be an obstacle in the interaction format. The threshold for the number of times the statistical conditions are met is reached; the above three conditions must be met consecutively at least twice to avoid triggering the judgment with a single, accidental action. Finally, based on the combined results of the three verification steps, it is determined that the student has experienced an interaction dilemma where multiple attempts to understand are hindered by the continuous playback format. Once the judgment is confirmed, the system automatically triggers an interaction format conversion instruction. This instruction is generated by the platform's resource adaptation module, carrying the unique ID of the target resource and conversion parameters, and is synchronized to the resource rendering engine. The specific implementation process of the conversion is divided into two steps. The first step is to break down the continuous animation into segmented knowledge point modules. The breakdown is based on the teaching logic nodes of the resource, following the order of introduction demonstration → core rule explanation → single-step example demonstration → immediate mini-exercise. For example, a 60-second continuous animation of removing parentheses is broken down into four modules: Module 1 is the introduction demonstration (0-12 seconds, using an item-sorting scene to introduce removing parentheses), Module 2 is the core rule explanation (12-27 seconds, explaining the distributive property and sign rule of multiplication), and Module 3 is the single-step example demonstration (27-45 seconds). The first module (45-60 seconds) demonstrates the process of removing parentheses from 2(x-3) step by step. Module 4 is a short, immediate exercise demonstrating 3(2x+1) and allowing students to predict the result. Each module's duration is controlled to 10-15 seconds (suitable for students' short-term attention span). The decomposed modules retain the original animation's visual style and content logic, only the playback units are separated. The second step is to insert a forced pause control point after each module. This forced pause control point is an interactive component embedded at the end of the module; when the module reaches the last second, the animation automatically stops. Simultaneously, a button displaying "Continue Learning" pops up in the center of the screen. This button cannot be skipped and requires active student click. Below the button are two auxiliary options: "Review This Module" and "Mark Questions." Clicking "Continue Learning" takes the student to the next module, "Review This Module" replays the current module, and "Mark Questions" records questions and synchronizes them to the teacher's end. Furthermore, the pause control point automatically saves the current learning progress. If a student closes the resource and clicks again, they can resume playback from the last paused module without restarting. After the conversion, the system will push a notification to the student indicating that the interaction format has been optimized. The converted segmented resource replaces the original continuous animation. Students can pause learning by module upon clicking again. The conversion effect will be verified through interaction data. If the student's single pause time exceeds the preset pause time and the number of repeated clicks decreases by more than 50%, the conversion is considered effective, and the segmented interaction format will be retained by default. If the effect is unsatisfactory, the module splitting granularity will be further optimized or an immediate prompt after pausing will be added to ensure that the resource interaction always adapts to student needs.

[0059] After accurately identifying students' interactive difficulties with continuously played resources through interaction interruption frequency analysis and completing the form transformation, for the variation problems in the homework of linear equations in one variable (including and without parentheses), it is necessary to further verify whether students have a need for transitioning from basic to advanced variations by verifying the variation problem difficulty attenuation coefficient. This verification analyzes students' click preferences and answering behaviors for variation problems of different difficulty levels, avoiding directly pushing complex variation problems that may cause students to give up due to difficulty, while eliminating interference from the difficulty of the problems themselves, ensuring that resource allocation is appropriate to students' current problem-solving abilities. The specific implementation method is as follows:

[0060] First, we need to clarify the core concepts and data foundation. Similar variation questions refer to a set of questions that revolve around the same core knowledge point of linear equations in one variable, differing only in complexity. Specifically, this refers to basic variation questions without parentheses and advanced variation questions with parentheses. Both types of questions maintain consistency in question description and answer interface design, only differing in step complexity. This ensures that students' clicks are only influenced by their difficulty tolerance. The core data source for verifying the variation question difficulty decay coefficient is the platform's answer behavior log. This log records in real-time information such as the student's click timestamp for each variation question, whether the question was completed, the answering time, and the accuracy rate. This provides a basis for subsequent calculations of abandonment rate and click volume ratio. The first step is to analyze similar variation questions... This calculation uses the click sequence data to determine the abandonment rate after the first click on a variation question containing brackets. The first click refers to the student's first active click on a variation question containing brackets during the current learning session, excluding accidental clicks from system-generated pop-ups and invalid clicks that do not lead to the answer interface. The abandonment rate is the percentage of students who close the page before completing the question. The calculation involves first filtering all first click records for variation questions containing brackets, then counting the number of abandoned records (records where students clicked to enter the answer interface but did not click the submit button, and closed the interface before reaching the minimum solution time for that question). Finally, the abandonment rate is obtained by dividing the number of abandoned records by the total number of first click records for variation questions containing brackets. The value ranges from 0-100%. The specific calculation process is as follows:

[0061] First, records of instantaneous clicks to close (with a dwell time of less than 2 seconds, judged as accidental clicks) are excluded. Second, records of closing due to network lag are eliminated (by detecting whether there was continuous input before closing; if input was interrupted and there was no active closing action, it was judged as lag). Third, multiple first clicks by the same student on the same question containing brackets are merged to ensure data authenticity. For example, if a student clicks on 5 variation questions containing brackets for the first time within 1 hour, 3 of them are closed without submitting answers (the dwell time is all less than the minimum solution time), 1 is an accidental click (closed within 2 seconds), and 1 is completed. If there are 4 valid initial clicks and 3 abandoned clicks, the abandonment rate is 75%. The second step, implementing the core judgment of the basic variation transition needs, requires the simultaneous fulfillment of two key conditions. The first condition is that the click volume of variation questions without parentheses reaches 3 times the click volume of variation questions with parentheses. Here, click volume refers to the total number of times students actively click on the two types of variation questions within the same learning period (excluding invalid clicks). The 3-fold ratio is based on the cognitive pattern of learning linear equations in one variable. If students can easily handle basic variation questions, they will naturally try advanced questions, and the click volume ratio usually increases. If the click-through rate is close to 1:1, but the difference is more than three times (e.g., 15 clicks for questions without parentheses, only 5 clicks for questions with parentheses), it indicates that students are deliberately avoiding complex variation questions and prefer to consolidate their skills with basic questions. When compiling statistics, attention should be paid to the priority of the click order. If students always complete all questions without parentheses first and only occasionally click on questions with parentheses, even if the total click-through rate difference is not more than three times, it should still be included in the observation. If the difference is more than three times and the click order always prioritizes basic questions, then this condition is valid. The second condition is that the abandonment rate for variation questions with parentheses exceeds the preset abandonment rate, which is based on the same grade and knowledge level. The threshold for the average abandonment rate of students in the knowledge-sharing section is set by retrieving the average abandonment rate of students in the same grade over the past month when doing similar questions with parentheses (e.g., 25%), and then increasing it by 10% as the personalized preset abandonment rate (i.e., 35%). This takes into account both the average level of the group and leaves room for individual differences. If the student's abandonment rate for questions with parentheses (e.g., the calculated 75%) exceeds this preset value, it indicates that they frequently give up when faced with questions with parentheses, further confirming the need to transition from basic variations. When both conditions are met, a three-step refined judgment logic is required to ensure no misjudgment:

[0062] To verify the consistency of click preferences, the aforementioned click volume ratio and abandonment rate must be met in two consecutive learning sessions to avoid accidental data caused by poor performance in a single assignment. Analyze problem-solving behavior before abandonment, and retrieve the answer interface logs of abandoned questions containing parentheses. If a student repeatedly deletes input expressions and stays for a period of time far exceeding the minimum solution time without submitting, it indicates that they did attempt to solve the problem but abandoned it due to insufficient ability, rather than simply being afraid of difficulty. Eliminate the interference of the question push order. If the platform pushes questions containing parentheses first and then those without, students may choose basic questions due to initial frustration. In this case, the push order should be adjusted to basic questions first and then advanced questions, and then observed. If there is no significant change in click preferences and abandonment rates, it can be confirmed that it is a need for transitioning to basic questions, rather than being caused by the push order. Finally, it is necessary to compare the accuracy rate of answering variant questions to eliminate the interference of click volume differences caused by excessively difficult questions. The core of eliminating interference is to distinguish between students' insufficient ability and the difficulty of the questions themselves. If a student's level is above the curriculum syllabus, firstly, the average accuracy rate of students in the same class or at the same level on the same batch of variation questions containing parentheses should be retrieved. If the group average accuracy rate exceeds 60%, it indicates that the difficulty of the questions meets the teaching requirements. However, if the student's accuracy rate on questions containing parentheses is below 30%, far below the group average, it means that the low click-through rate and high abandonment rate are due to the student's need for basic transition, rather than the questions being too difficult. Secondly, the student's accuracy rate on questions without parentheses should be compared with their accuracy rate on questions with parentheses. If the accuracy rate on questions without parentheses exceeds 70% (basic ability meets the standard), but the accuracy rate on questions with parentheses is below 30% (inadequate advanced ability), it further confirms that the student needs basic transition, rather than overall weak problem-solving ability. If the group average accuracy rate is below 30% (the questions are indeed too difficult), feedback should be given to the teaching and research team to adjust the difficulty of the questions before reassessing the student's transition needs. Once it is confirmed that the student has a need for basic variation transition, the system will automatically adjust the variation question push strategy.

[0063] The first round only pushes basic variation questions without parentheses. When students complete 5 questions with an accuracy rate of over 80% (basic ability consolidation meets the standard), advanced questions are mixed in at a ratio of 3 basic questions + 1 question with parentheses. When pushing questions with parentheses, a micro-tutoring prompt module for the preceding steps is added, such as a pop-up on the right side of the answer interface reminding students to remove the parentheses first and to remember to use the distributive property of multiplication. Clicking on the prompt will show a micro-animation of removing parentheses, helping students gradually adapt to complex variation questions. Through this verification and transition strategy based on the difficulty decay coefficient, we can avoid students feeling frustrated when facing complex questions directly, and ensure that resource allocation is always synchronized with the improvement of students' abilities, achieving a smooth transition from basic to advanced.

[0064] After determining the existence of an error chain in the preceding steps through a step dependency analysis model, simply pushing general resources for the preceding steps may not accurately target the root cause of the error, leading to the continuous propagation of the error chain. Therefore, it is necessary to bind the order of pushing reinforcement resources with the results of in-depth analysis of the error chain in the preceding steps. By mining the starting position of the error chain and the propagation path of the error type, targeted pushing can be achieved. Subsequent resources are unlocked by verifying the correction effect, ensuring that students correct errors from the root cause. The specific implementation method is as follows:

[0065] First, it's crucial to understand the core content of the deep analysis results of the preceding step error chain. It's not merely about confirming the existence of an error chain; rather, it involves using the platform's error chain analysis engine to deeply mine error modification trajectories and syntax tree comparison data. This results in a structured report containing the starting step location, core error type, error propagation hierarchy, and affected step range. The error propagation hierarchy refers to the number of subsequent steps affected by a preceding error, and the affected step range refers to the specific steps impacted by the error chain. This information provides precise guidance for subsequent push order and resource type selection, preventing indiscriminate resource pushes. For confirmed preceding step error chains, the primary task is to locate the starting step, the root of the error chain from which all subsequent errors originate. Locating this root requires cross-validation using two types of data: first, chronological backtracking of the error modification trajectory, deriving from the initial input expression of subsequent steps to find the earliest uncorrected error that propagated to subsequent steps. The first step is to verify the error in the parenthesis removal step. For example, if the initial expression of a subsequent rearrangement step inherits the erroneous constant term from the parenthesis removal step, and the error trajectory sequence of the parenthesis removal step shows that the constant term was not corrected from the first input to the final submission, and it occurred before the answer time of the rearrangement step, then the parenthesis removal step is initially determined to be the starting step. The second step is to verify the hierarchical dependency of the expression syntax tree. Construct a complete syntax tree chain from the preceding step to the subsequent steps, and analyze the source of the error nodes in the syntax tree of each step. If the error nodes in the syntax tree of the subsequent steps can all be traced back to the error node of a certain step, then that step is the starting step. For example, in solving a linear equation in one variable, the erroneous constant node (-4, the correct one should be -8) in the parenthesis removal step syntax tree evolves into an erroneous addend node (+4) in the rearrangement syntax tree, and evolves into an erroneous coefficient node (-3x=11, the correct one should be -3x=15) in the merging like terms syntax tree. Then it can be clearly determined that the starting step is the parenthesis removal step, and the location result will be synchronized to the resource push decision module.After locating the initial step, it is necessary to search the resource library for specialized reinforcement resources that precisely match the error type of the initial step. Specialized reinforcement resources refer to refined resources targeting a specific error type or a specific step, as opposed to general resources covering all steps. The resource library uses a two-dimensional tag system for classification and storage based on steps and error types. The first-level tag is the problem-solving step (e.g., removing parentheses, moving terms, merging like terms), and the second-level tag is the specific error type (e.g., removing parentheses, omitting multiplication of negative signs, removing parentheses, omitting multiplication of coefficients or constant terms, moving terms, single-step error type). Each resource includes three parts: error characteristic description, correction method demonstration, and targeted practice (e.g., removing parentheses, omitting multiplication of negative signs). The resource library includes a special section containing an animated demonstration of passing a negative sign and three practice questions involving removing parentheses with only a negative sign. During retrieval, the resource recommendation decision module reads the starting step label (e.g., removing parentheses) and core error type label (e.g., omitting a negative sign) from the error chain deep analysis results. It performs precise matching in the resource library, first filtering the set of resources with the primary label "removing parentheses," then filtering resources from the set with the secondary label "omitting a negative sign" and whose error feature description matches the current error (e.g., the resource description "2(x-3) expands with an omitting negative sign, resulting in 3 remaining unchanged -6," which perfectly matches the student's error). Finally, it selects one core demonstration resource (e.g., animated courseware). A reinforcement resource package consisting of three targeted practice questions is pushed to students in the order of demonstration resources first, followed by practice resources. This avoids students completing the questions without mastering the correction methods. After the reinforcement resources are pushed, students must verify that their corrected answers meet the expected standards before unlocking access to subsequent resource pushes. The expected standards are multi-dimensional indicators based on students' personalized thresholds and error correction goals, including three core conditions: first, the accuracy rate of targeted practice questions is greater than or equal to 80%; second, after completing the three practice questions in the reinforcement resource package, students must answer at least two questions correctly (one is allowed due to a pen error, but the core condition must be met). Error types need to be corrected, such as previously omitting the negative sign; now only 1 out of 3 questions has illegible handwriting on the sign, which is considered acceptable. Second, the number of modifications to the practice steps should be less than or equal to 50% of the personalized modification threshold. If the student's personalized modification threshold for the preceding steps is 3 times, the number of modifications during practice should be less than or equal to 1 time, indicating that they have mastered the correction method and do not need repeated adjustments. Third, the hesitation time for the practice steps should be less than or equal to 80% of the personalized hesitation threshold. If the personalized hesitation threshold is 15 seconds, the total hesitation time during practice should be less than or equal to 12 seconds, indicating that their problem-solving approach is clear and there is no obvious confusion. The specific implementation process of the verification is divided into three steps:

[0066] The system collects practice answer data in real time. As students complete targeted practice questions, the input box's event listener module synchronously records the answering process (number of modifications, hesitation time, final answer) and compares it with the correct answers in the resource package. A practice answer report is generated, and multi-dimensional indicators are used for evaluation. The resource push decision module reads the practice answer report. If all three expected standard conditions are met simultaneously, the initial step error correction is deemed successful. If any condition is not met, the reason for failure is analyzed: if it's due to a misunderstanding of the practice questions, a short video explaining the question is pushed for re-practice; if it's due to uncorrected core error types, more basic specialized resources are pushed until the standard is met. After success, the module sends an unlock signal to the resource push channel for subsequent steps, allowing the push of resources for subsequent steps such as moving or merging similar items. However, this must be done on the right side of the answer interface for subsequent resources. Adding key hints for the preceding steps reinforces students' awareness of errors in the initial steps. If a chain of errors occurs in subsequent steps, it is necessary to return to the initial steps for secondary reinforcement. Two conditions must be met to determine if a chain of errors occurs in subsequent steps: First, the error type in the subsequent step is related to the core error type in the initial step. For example, if the initial error is a missed multiplication of a negative sign during parenthesis removal, and the subsequent transposition error is a misjudgment of the transposition sign due to an incorrect constant term, both originate from a sign error in the initial step. Second, the error node in the syntax tree of the subsequent step can still be traced back to the error node in the initial step, and the error sign node in the transposition syntax tree can be traced back to the node where a missed multiplication of a negative sign occurred in the parenthesis removal syntax tree. This avoids misjudging newly occurring independent errors in subsequent steps, such as omitting a term during transposition unrelated to parenthesis removal, as chain errors. The specific implementation process for secondary reinforcement is as follows:

[0067] First, the resource push decision module automatically locks the push permission for subsequent steps' resources and pauses the current exercise. Second, it retrieves the secondary reinforcement resource package from the initial step. This resource package is more basic and interactive than the initial resource; for example, the initial package is an animated demonstration, while the secondary package is a step-by-step drag-and-drop interactive courseware for removing parentheses. Students need to manually drag coefficients and symbols to remove parentheses, and the exercises are less difficult (e.g., 3(x-2)-4 in the initial package and 2(x-3) in the secondary package). Finally, it sets a stricter achievement standard for the secondary reinforcement than the initial package. After achieving the standard, students need to complete an additional consecutive exercise from the initial step to the subsequent steps to ensure that the error chain is completely broken before unlocking the subsequent step resources again to prevent repeated errors.

[0068] After analyzing the frequency of interactive interruptions and determining that students have difficulty with continuous playback, and clarifying the transition needs from basic to complex problems, it is necessary to simultaneously modify the interactive features of continuous animation resources related to linear equations in one variable, and adjust the proportion of variation questions pushed. The animation modification aims to solve the problems of not being able to pause and easily missing key information, while the gradual push of variation questions helps students smoothly transition from basic to complex questions. Both work together to adapt to students' interactive habits and learning abilities. The specific implementation method is as follows:

[0069] The first step is to modify the existing continuous animation for interactive functionality. The core of this modification is to insert an interactive control layer at keyframe nodes. Keyframe nodes are crucial frames in the animation that carry core mathematical information, such as the initial equation frame for 2(x-3)=7 in the bracket removal animation, the intermediate frames for calculating 2×x and 2×(-3), and the final unfolding frame for 2x-6=7. These nodes are key to students' understanding of the logical steps. The interval between two adjacent keyframe nodes is typically 3-5 seconds, aligning with students' short attention spans. The interactive control layer is a lightweight interactive component embedded between keyframe nodes. It does not disrupt the original animation's visual style or content continuity, and only uses a semi-transparent interactive interface to implement pause, prompt, and continue control functions. Its core code is integrated into the animation player's interactive interface. In the interoperable plugin, the animation is automatically bound to keyframe nodes during loading, without requiring modification of the original animation source file. During modification, the single-step animation is broken down into three stages: initial state display frame, explanation of transformation rules, frame transformation process demonstration frame, and so on. Each stage corresponds to a keyframe node. The first stage, the initial state display frame, clearly presents the original mathematical expression and scene background of the current step. Taking the bracket removal animation as an example, this frame displays the complete equation 2(x-3)=7, with a small icon on the right side indicating that the brackets need to be removed. Simultaneously, a semi-transparent text prompt appears at the bottom of the animation indicating the initial state: the distributive property of multiplication has not been applied, and the expression within the brackets needs to be expanded. This frame stays for 3 seconds by default, and the duration can be adjusted through the interactive control layer, allowing students to fully see the starting point of the current step and avoid subsequent comprehension gaps. The second stage... The first frame, explaining the transformation rules, focuses on the mathematical rules of the current step, continuing the example of removing parentheses. The left side of this frame clearly states the distributive property of multiplication: a(bc) = ab - ac, where the coefficient before the parentheses must be multiplied by each term inside the parentheses. A mini-demonstration animation plays simultaneously on the right side, with keywords highlighted in different colors. This frame lasts for 5 seconds and includes an optional button at the bottom for clicking to view more examples, catering to students with different comprehension levels. The third-stage transformation process demonstration frame shows the specific transformations of the mathematical expression step by step. Again using the example of removing parentheses, this frame first shows the intermediate state of 2(x-3) split into 2×x + 2×(-3) (the split is marked with a green dashed box). After 2 seconds, it then shows the calculation process 2×x = ​​2x2×(-3) = -6. The process (the calculation result is highlighted in blue) ultimately presents the complete unfolding of 2x-6=7. The entire process is seamless, ensuring students clearly see the origin of each transformation. This frame pauses for 4 seconds, and students can slow down the playback speed by 50% using the slow-motion button in the interactive control layer. After each stage frame finishes playing, the interactive control layer automatically activates the continue button. This button features a striking blue rounded corner design and is located slightly below the center of the screen to avoid obscuring the core animation content. A subtle visual cue accompanies the button's pop-up to prevent students from ignoring it. Students must actively click the continue button to proceed to the next stage frame; otherwise, the animation remains paused. Below the button, two auxiliary options are displayed: "Review this frame" and "Mark for questions." Clicking "Review this frame" will replay the current stage frame.To facilitate students' repeated viewing of key content, clicking on a question mark will pop up a text input box where students can enter questions such as "Why is 2×(-3) -6?". The system will automatically associate and store these questions with the current animation node and student ID, synchronizing them to the teacher's student question management module for targeted tutoring. While completing the animation interaction modification, the system adjusts the proportion of variation questions pushed based on the basic variation transition preference judgment results. These results, derived from click-through rate and abandonment rate analysis, indicate that students need to gradually transition from variation questions without parentheses to those with parentheses. This result is stored in the student's learning file as a preference tag. After reading this tag, the resource push module automatically calls the gradient push algorithm to generate push notifications. The delivery strategy begins with an initial round of pushes: Basic variation problems (excluding parentheses) are extracted from the variation problem resource pool. This pool is a database of linear equation variation problems categorized by knowledge point, difficulty, and whether or not they contain parentheses. Variation problems without parentheses are marked as difficulty level 1. Each problem involves simple expressions requiring only transposition and combining like terms, and each comes with a complete solution explanation. The initial push consists of 5 problems, pushed in the order of single-transposition problems first, followed by problems involving combining like terms, to avoid pushing multi-step basic problems at the beginning. For each problem a student completes, the system calculates the accuracy rate in real time: 1 point for a correct answer and 0 points for an incorrect answer. The current accuracy rate is displayed at the bottom of the answer interface to help students understand their level of mastery. This is before the initial push. Once the student achieves a certain accuracy rate on the parenthesis-free variation questions, a gradient mixing process is initiated. The accuracy standard is based on the student's historical basic question accuracy rate, typically 80% (i.e., at least 4 out of 5 questions answered correctly). If the student does not meet the standard (e.g., only 2 questions answered correctly), 3 more parenthesis-free questions of difficulty level 1 are automatically added (e.g., 4x-7=9, 10-3x=1) until the accuracy rate is reached. This prevents students from encountering complex questions before their basic skills are solidified. After meeting the standard, a system pop-up message indicates that the student has mastered the basic variation questions well and will soon begin practicing parenthesis-containing variation questions. Simultaneously, the resource push module extracts parenthesis-containing variation questions of difficulty level 2 from the resource pool and mixes them in at an initial ratio of 3 parenthesis-free questions and 1 parenthesis-containing question, forming the first gradient training group. As the student's accuracy rate on parenthesis-containing questions improves... The system gradually adjusts the proportions of questions, from two questions without parentheses to one with parentheses, then another without parentheses, and finally another with parentheses, eventually transitioning to all questions with parentheses. This entire adjustment process is automated, requiring no manual intervention. Before each adjustment, a difficulty adjustment prompt is sent to the student to reduce their anxiety. All parenthesis-containing variations are accompanied by a micro-tutoring module for the preceding steps. This module is a small floating window embedded on the right side of the answer interface, displaying key hints for the preceding steps related to the current parenthesis-containing question. Through this animation interaction modification and the gradual push of variation questions, the system not only solves the problem of students missing information due to the inability to pause continuous animations, but also helps students gradually build confidence from basic variation questions and smoothly transition to complex parenthesis-containing variation questions.This achieves the dual goals of interactive adaptation and skill advancement, laying the foundation for further improvement in the ability to solve comprehensive problems involving linear equations in one variable.

[0070] This invention collects student answer data and resource interaction data in real time through a platform, analyzes error correction trajectories and hesitation durations, identifies error chains and chain effects in preceding steps, infers student preferences for paused, step-by-step interaction formats through interactive behavior breakdown and interruption frequency analysis, determines basic variation transition needs by combining the click ratio and abandonment rate of variation questions, allocates resources accordingly, prioritizes pushing resources to consolidate preceding steps, transforms continuous animations into step-by-step pause courseware, and adjusts the push ratio of variation questions with and without parentheses according to gradients, achieving precise adaptation of resource presentation order, interaction format, and push ratio, thereby improving students' efficiency in self-correction.

[0071] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for allocating teaching resources based on data from an educational software platform, characterized by: Includes the following steps: S1. Collect students' answer data and resource interaction data in their homework on linear equations in one variable in real time through the educational software platform. The answer data includes the answer time and error correction trajectory of each solution step. The resource interaction data includes the dwell time after clicking on a resource, the closing time, and the number of repeated clicks. The resources include animated demonstrations of removing parentheses, interactive courseware on transposing logic, and similar variant problems. S2. By analyzing the number of modifications in the error correction trajectory and the hesitation time in the answer duration, the chain effect of errors in previous steps leading to errors in subsequent steps is identified. When the number of modifications in a previous step exceeds the preset number of modifications and the hesitation time exceeds the preset hesitation time, accompanied by skipping the answer in subsequent steps, it is determined that an error chain of previous steps exists. At the same time, by analyzing the difference between the dwell time after clicking on a resource and the total duration of the resource, and the timing of closing the window when the resource is not completed, resource interaction preferences are inferred. When the dwell time is less than the preset dwell time and the closing time occurs in the middle of the resource playback, it is determined that students prefer to pause the step-by-step interaction form rather than continuous animation. Finally, by analyzing the click ratio of similar variant questions, it is determined that students prefer the basic variant transition. Among these, the step dependency relationship analysis model is used to identify the chain effect of errors in previous steps leading to errors in subsequent steps, specifically including: The modification content of the preceding steps in the error modification trajectory is analyzed to identify key error types. The logical correlation between the final error expression of the preceding step and the initial input expression of the subsequent step is verified. When the verification finds that the initial input expression of the subsequent step inherits the characteristics of the final error expression of the preceding step and the subsequent step skips the answer, it is determined that there is a chain effect. This process realizes the cross-step transmission verification of error characteristics through the expression syntax tree comparison algorithm. S3. For error chains in the preceding steps, the order of resource presentation is to prioritize pushing the consolidation resources of the preceding steps and then push the resources of the subsequent steps. For the pauseable step-by-step interactive format, the continuous animation has been adjusted to a step-by-step explanation courseware where each step requires a click to continue. At the same time, for the basic variation transition, the ratio of variation questions with and without parentheses has been adjusted. The order in which reinforcement resources for the preceding steps are pushed is tied to the deep analysis results of the error chain of the preceding steps. If an error chain of the preceding steps is found to exist, the starting step of the error chain is first located, and the special reinforcement resources in the resource library that precisely match the error type of the starting step are retrieved. Only when the answer data after the error correction of the starting step is detected to meet the expected standard is the permission to push resources for subsequent steps unlocked. If a chain error occurs again in subsequent steps, the process returns to the starting step for secondary reinforcement.

2. The method for allocating teaching resources based on educational software platform data according to claim 1, characterized in that: The collection of error-modified trajectories specifically includes: By embedding an event listener module in each step input box of the problem-solving interface, the system records the student's incorrect expression before each modification, the modified expression after modification, and the corresponding timestamp in real time. Multiple modifications to the same problem-solving step are then chained together in chronological order to form an error trajectory sequence. When the system detects that the student has clicked the submit button, it automatically compares the error trajectory sequence with the final answer of the current step to generate an error modification trajectory that includes the evolution path of the incorrect expression.

3. The method for allocating teaching resources based on educational software platform data according to claim 1, characterized in that: The step dependency analysis model further introduces the calculation of error impact weights, specifically including: Based on the error type in the preceding steps, different weight values ​​are assigned to the blocking strength of the solution path in the subsequent steps. When it is detected that the number of modifications in the preceding steps exceeds the preset number of modifications and the hesitation time exceeds the preset hesitation time, the chain effect judgment criteria are adjusted in combination with whether the error impact weight value reaches the chain trigger threshold. Among them, the chain judgment is automatically triggered by completely blocking errors, while the chain judgment is triggered by the number of modifications in the subsequent steps reaching more than 2.

4. The method for allocating teaching resources based on educational software platform data according to claim 3, characterized in that: The preset number of modifications and preset hesitation time are set using an adaptive threshold generation mechanism, specifically including: Personalized thresholds are generated by multiplying the average number of modifications and the average hesitation time in students' historical answer data by a dynamic adjustment coefficient. When it is detected that the number of modifications in the preceding steps exceeds the personalized threshold and the hesitation time exceeds the personalized threshold, and the subsequent steps involve skipping the answer, the preceding step error chain is automatically activated to determine the existence of the error chain. The skipping the answer specifically refers to the behavior of jumping to the next question before the dwell time in the subsequent steps reaches the minimum solution time for that step.

5. The method for allocating teaching resources based on educational software platform data according to claim 1, characterized in that: Inferring resource interaction preferences is achieved through interaction behavior pattern decomposition techniques, specifically including: The proportion of dwell time after a resource click to the total resource duration is captured. Combined with the location of the resource node where the closing action occurs, a two-dimensional analysis matrix of duration nodes is constructed. When the proportion of dwell time after a resource click to the total resource duration is lower than a preset proportion and the closing node is located before the explanation of the core knowledge points of the resource, it is determined that the student has given up learning due to difficulty in understanding. When the closing node is located after the explanation of the core knowledge points but the proportion of dwell time is still lower than the preset proportion, it is determined that the student has given up learning due to the incompatibility of the interaction format.

6. The method for allocating teaching resources based on educational software platform data according to claim 5, characterized in that: The determination of whether a step-by-step interaction can be paused relies further on the analysis of interaction interruption frequency, specifically including: The system counts the number of times students repeatedly click on the same resource and the duration of each click. When it detects that the duration of a single click is less than the preset duration, the click is closed midway through the playback, and the interval between repeated clicks is less than the preset interval, it is determined that the student is experiencing an interactive dilemma where they have tried to understand the content multiple times but are hindered by the continuous playback format. At this point, an interaction format conversion instruction is automatically triggered, breaking down the continuous animation into segmented knowledge point modules and inserting a forced pause control point after each module.

7. The method for allocating teaching resources based on educational software platform data according to claim 1, characterized in that: The determination of the transition from basic to variation problems is verified using the variation problem difficulty attenuation coefficient, specifically including: Based on the click order data of similar variation questions, the abandonment rate after the first click of the variation question containing parentheses is calculated, that is, the proportion of people who close the page before completing the question. When the number of clicks on the variation question without parentheses reaches 3 times the number of clicks on the variation question with parentheses and the abandonment rate of the variation question with parentheses exceeds the preset abandonment rate, it is determined that students have a need for basic variation transition. At the same time, by comparing the correct answer rate of variation questions, the interference of click volume differences caused by the difficulty of the questions is eliminated.

8. The method for allocating teaching resources based on educational software platform data according to claim 7, characterized in that: An interactive control layer is inserted into the keyframe nodes of the original continuous animation. The single-step animation is decomposed into three stages: the initial state display frame, the transformation rule explanation frame, and the transformation process demonstration frame. After each frame ends, the continue button is activated. The proportion of variation questions pushed is adjusted based on the basic variation transition preference judgment result. Variation questions without parentheses are extracted from the variation question resource pool as the first round of push. After their accuracy reaches the standard, variation questions with parentheses are mixed in proportionally to form a gradient training group. Variation questions with parentheses are all accompanied by micro-tutoring prompts for the preceding steps.

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