Mathematics subjective question scoring method and system based on expression linked list tree matching degree

Abstract

The present invention relates to a scoring method for subjective mathematics questions based on the matching degree of expression linked list trees, comprising: obtaining the answer results of subjective mathematics questions; performing word segmentation processing on the answer results; separating the various answer steps of the answer results; calculating the similarity between the expression in the answer steps and the expression of the standard answer as the first review feature; determining the relationship between the steps of the answer steps, calculating the similarity between the answer steps and the relationship between the steps and the steps and the relationship between the steps of the standard answer as the second review feature; and calculating the score of the answer result according to the first review feature and the second review feature. The present invention also discloses a scoring system for subjective mathematics questions. The present invention improves the objectivity and rationality of the calculation results of the scoring of subjective mathematics questions, replaces manual labor, saves time and labor; the scoring system of the present invention can be used for batch marking of subjective mathematics questions, greatly shortens the marking and scoring time of subjective mathematics questions, and avoids unreasonable scoring caused by human subjectivity.

Description

Technical Field

[0001] The invention belongs to the field of natural language processing, and in particular relates to a method and system for scoring subjective mathematics questions based on the matching degree of an expression linked list tree. Background Art

[0002] In the process of education and teaching, examination and assessment are important links in the process of education and teaching, which are conducive to evaluating the teaching effect of teachers and the learning effect of learners. In the traditional teaching process, examinations are usually in written form, and the main types include objective questions and subjective questions. Objective questions are usually multiple-choice and judgment questions, and their answers are clear and unique. The existing automatic scoring methods can be very accurate; while subjective questions are mostly short answers and essays, and manual scoring is still the main method at this stage. Teachers, as the main body of marking papers, have been responsible for a large amount of repeated marking and statistics for a long time. The automatic marking system for subjective questions using computer technology has the characteristics of fast marking speed, high accuracy, and no fatigue. It can not only replace teachers to complete large-scale and large-volume test marking tasks and reduce teachers' workload, but also can give scoring results instantly, reduce scoring errors caused by subjectivity, and ensure the fairness and justice of scoring results, so as to truly and objectively reflect students' learning outcomes and teachers' teaching achievements. Summary of the invention

[0003] The technical problem of the present invention is that the prior art lacks a system for automatically reviewing and scoring the answers to subjective math questions containing formulas.

[0004] The purpose of the present invention is to address the above problems and provide a method for scoring subjective mathematics questions based on the matching degree of expression linked list trees. The method uses a neural network model to identify step demarcation points in the answer results of subjective mathematics questions, separates each answer step according to the step demarcation points, represents the expression in the answer result steps as a linked list tree, determines the similarity between the linked list tree of the answer result step expression and the linked list tree of the standard answer step expression and uses it as the first review feature, calculates the similarity between the relationship between the steps of the answer result and the relationship between the steps of the standard answer and uses it as the second review feature, and automatically calculates the score of the answer result according to the first review feature and the second review feature. The present invention also provides a corresponding scoring system for subjective mathematics questions.

[0005] The technical solution of the present invention is a method for scoring subjective mathematics questions based on the matching degree of expression linked list tree, comprising the following steps:

[0006] Step 1: Get the answer results of subjective mathematics questions;

[0007] Step 2: Perform word segmentation on the answer results;

[0008] Step 3: Determine the demarcation points of the answering steps and separate the answering steps of the answering results;

[0009] Step 4: Calculate the similarity between the expression in the answer step and the expression in the standard answer step as the first review feature;

[0010] Step 5: Calculate the structural similarity between the answer and the standard answer as the second review feature;

[0011] Step 6: Calculate the score of the answer result based on the first review feature and the second review feature.

[0012] In step 1, the obtaining of the answer results of the subjective mathematics questions includes obtaining the text version of the student answer results and the image format or scanned version of the student answer results from the answer system; using image recognition technology to convert the student answer results in the image format into the text version of the student answer results.

[0013] In step 2, the answer results are segmented according to the Chinese character data corpus commonly found in math answers.

[0014] In step 3, the step demarcation point of the answering step is determined, the word segmentation point obtained by the word segmentation processing in step 2 is used as a candidate separation point, and the step separation model is used to determine whether the candidate separation point is a step demarcation point.

[0015] Preferably, the step separation model adopts a support vector machine (SVM) classification model.

[0016] Step 4 includes the following sub-steps:

[0017] Step 4.1: Represent the expressions in the answering steps and the standard answer step expressions as a to-be-evaluated linked list tree and a reference linked list tree respectively; Step 4.2: Calculate the similarity between the to-be-evaluated linked list tree and the reference linked list tree to obtain the first type of formula similarity;

[0018] Step 4.3: Determine whether the similarity of the first type of formula is equal to 1. If the similarity of the first type of formula is equal to 1, set the calculation result of the similarity between the expression in the answering step and the expression in the standard answer step to 1, and end step 4; otherwise, execute step 4.4;

[0019] Step 4.4: Calculate the similarity between the linked list tree of the answer step expression sub-formula and the linked list tree of the standard answer step expression sub-formula to obtain the second type of formula similarity;

[0020] Step 4.5: Compare the similarity between the first type of formula and the second type of formula, and take the larger value of the two as the calculation result of the similarity between the expression in the answering step and the standard answer expression.

[0021] In step 4.2, the structural similarity between the to-be-evaluated linked list tree and the reference linked list tree is calculated, and the to-be-evaluated linked list tree and the reference linked list tree are respectively traversed hierarchically to obtain an array P of the hierarchical traversal sequence of the to-be-evaluated linked list tree = {P 1 ,P 2 ,P 3 ,…,P n} and the array B of the level traversal sequence of the benchmark linked list tree = {B 1 ,B 2 ,B 3 ,…,B m}, the similarity between the linked list tree to be evaluated and the benchmark linked list tree is calculated based on the similarity between array P and array B, where P i , i=1,2,3,…,n represents the i-th element of the array P, i.e. the i-th traversal node of the hierarchical traversal sequence of the linked list tree to be evaluated, B j ,j=1,2,3,…,m represents the jth element of array B, i.e. the jth traversal node of the hierarchical traversal sequence of the benchmark linked list tree, n and m represent the number of nodes of the linked list tree to be evaluated and the benchmark linked list tree respectively;

[0022] The calculation formula for the similarity between the linked list tree to be evaluated and the benchmark linked list tree is as follows

[0023]

[0024] Where F sim1 It represents the first-class formula similarity between the linked list tree to be evaluated and the benchmark linked list tree, common(P,B) represents the similarity calculation function of array P and array B, and min(n,m) represents the smaller value of variables n and m.

[0025] In step 4.4, the calculation of the substructure similarity between the linked list tree to be evaluated and the reference linked list tree specifically includes:

[0026] 1) Obtain the atomic node set of the linked list tree to be evaluated and the atomic node set of the reference linked list tree;

[0027] 2) Compare and determine the number of matching atomic nodes in the atomic node sets of the linked list tree to be evaluated and the reference linked list tree;

[0028] 3) Calculate the semantic similarity between the atomic nodes that match the linked list tree to be evaluated and the reference linked list tree;

[0029] 4) Obtain the edge set of the linked list tree to be tested and the edge set of the reference linked list tree;

[0030] 5) Calculate the number of matches between the edge set of the linked list tree to be tested and the edge set of the reference linked list tree;

[0031] 6) Calculate the similarity. The similarity calculation formula is as follows

[0032]

[0033] where F sim2 Indicates the similarity of the second type of formula between the linked list tree to be evaluated and the benchmark linked list tree, N base Represents the total number of atomic nodes in the atomic node set of the base linked list tree, N match Indicates the number of atomic node matches between the linked list tree to be evaluated and the reference linked list tree, E match represents the number of matching edges between the linked list tree to be evaluated and the reference linked list tree, E base represents the total number of edges in the base linked list tree, σ i Indicates the semantic similarity between the i-th matching atomic nodes in the linked list tree to be evaluated and the reference linked list tree.

[0034] In step 3), the semantic similarity between the atomic nodes matching each other in the linked list tree to be evaluated and the reference linked list tree is calculated, and the types of the atomic nodes are divided into numbers, variables and operators. The calculation rules of the semantic similarity include:

[0035] a) If the atomic node of the to-be-evaluated linked list tree is of a different type from the atomic node of the matching reference linked list tree, the semantic similarity of the atomic node of the to-be-evaluated linked list tree is 0;

[0036] b) If the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both numbers and the two are equal, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 1; if the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both numbers and the two are not equal, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 0;

[0037] c) If the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both variables and the two are the same, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 1; if the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both variables and the two are different, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 0;

[0038] d) If the atomic nodes of the linked list tree to be evaluated and the atomic nodes of the matching reference linked list tree are both operators and the two are the same or similar, then the semantic similarity of the atomic nodes of the linked list tree to be evaluated is 1; if the atomic nodes of the linked list tree to be evaluated and the atomic nodes of the matching reference linked list tree are both variables and the two are neither the same nor similar, then the semantic similarity of the atomic nodes of the linked list tree to be evaluated is 0.

[0039] In step 4.4, the similarity between the linked list tree of the calculation answer step expression sub-formula and the linked list tree of the standard answer step expression sub-formula is calculated using formula (2) to obtain the second type of formula similarity.

[0040] Preferably, the second review feature includes whether the number of steps in the answer result and the structural relationship of the answer steps are consistent with the number of steps and the structural relationship of the steps in the standard answer respectively.

[0041] Step 5 uses a step relationship analysis model to determine the relationship between the steps of answering questions. The step relationship analysis model includes an input layer, a hidden layer, a classification layer and an output layer. The input of the input layer is the answering step vector, the hidden layer is multi-layered, and the output of the hidden layer is the step feature vector. The input of the classification layer is the step feature vector and the statistical features of the answering step vector, and the output of the output layer is the judgment result of the relationship between steps.

[0042] The system of the above-mentioned mathematics subjective question scoring method includes the following modules:

[0043] Answer result acquisition module: obtain the answer results of subjective math questions;

[0044] Answering step separation module: identifies and determines the step demarcation points from the obtained answering results, separates the answering results into multiple answering steps according to the step demarcation points, and obtains the answering step vector;

[0045] Expression similarity calculation module: calculates the expression similarity between the steps of the question to be reviewed and the steps of the standard answer as the first review feature;

[0046] Answer structure similarity calculation module: calculates the structural similarity between the answer to be evaluated and the standard answer as the second review feature; review module: calculates the score of the answer result based on the first review feature and the second review feature.

[0047] The expression similarity calculation module includes the following units:

[0048] Processing unit: representing the mathematical formula to be evaluated and the benchmark mathematical formula as a linked list tree to be evaluated and a linked list tree to be benchmark respectively;

[0049] Calculation unit: Calculate the similarity of the first type of formula and the similarity of the second type of formula to obtain the first review feature;

[0050] Comparison unit: determines whether the similarity of the first type of formula is less than 1, and compares the similarity of the first type of formula with the similarity of the second type of formula.

[0051] Compared with the prior art, the beneficial effects of the present invention include:

[0052] 1) The scoring method of the present invention calculates the similarity between the linked list tree of the step expression of the answer result and the linked list tree of the step expression of the standard answer as the first review feature, and calculates the similarity between the relationship between the steps of the answer result and the relationship between the steps of the standard answer as the second review feature. The score of the answer result is calculated based on the first review feature and the second review feature, which improves the objectivity and rationality of the score calculation result, and is easy to execute by computer, replacing manual work, saving time and labor;

[0053] 2) When the scoring method of the present invention determines that the first type of formula similarity is not equal to 1, that is, the expression of the answer result step is not completely equal to the expression of the standard answer step, the second type of formula similarity, that is, the similarity of the sub-formula of the answer result step expression and the sub-formula of the standard answer step expression is calculated, and the first type of formula similarity and the second type of formula similarity are compared, and the larger value of the two is taken as the calculation result of the similarity between the expression in the answer step and the standard answer expression, which further improves the objectivity and rationality of the calculation result of the scoring of the subjective mathematics question;

[0054] 3) The scoring method of the present invention represents the expression in the answer result step as a linked list tree, determines whether the edges and atomic nodes of the linked list tree match the edges and atomic nodes of the standard answer step expression linked list tree respectively, and calculates the semantic similarity of the matched atomic nodes, and then calculates the similarity between the expression in the answer result step and the standard answer step expression, which is convenient for computer execution, and on the premise of ensuring the rationality of the similarity calculation result, improves the calculation efficiency of the similarity between the mathematical subjective question expression and the standard answer expression;

[0055] 4) The scoring system of the present invention realizes automatic review and scoring of answers to subjective mathematics questions, replacing manual marking, and can be used for batch marking of subjective mathematics questions, greatly shortening the marking and scoring time of subjective mathematics questions, and avoiding unreasonable scoring caused by human subjectivity in marking and scoring, making the marking and scoring results more fair and just. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0057] Figure 1 The figure is a flow chart of a method for scoring subjective mathematics questions according to an embodiment of the present invention.

[0058] Figure 2 FIG. 4 is a schematic diagram of a flow chart of calculating a first review feature according to an embodiment of the present invention.

[0059] Figure 3a A schematic diagram of a linked list tree of expressions of steps of questions to be evaluated in an embodiment of the present invention.

[0060] Figure 3bA schematic diagram of a linked list tree of standard answer expressions according to an embodiment of the present invention.

[0061] Figure 4 Schematic diagram of a step relationship analysis model according to an embodiment of the present invention.

[0062] Figure 5 The figure is a schematic diagram of the module structure of the mathematics subjective question scoring system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] like Figure 1 and Figure 2 As shown, a mathematical subjective question scoring method based on the matching degree of an expression linked list tree includes the following steps: Step 1: obtaining an image of the answer result of the mathematical subjective question, identifying mathematical entities and texts in the answer result image, and obtaining the answer result;

[0064] Step 2: Segment the answer results, and identify the keywords indicating the structural relationship of the answer, namely structural keywords or mathematical reasoning symbols and step-related words from the segmented results; for the mathematical answer text mixed with keywords and mathematical formulas, since Chinese characters are quite different from the numbers and letters that constitute the mathematical formulas, a mathematical template matching method is adopted in the embodiment to match the answer keywords in the standard answer to obtain Chinese character keywords, and make corresponding annotations on them.

[0065] The embodiment uses an encoder-decoder model to recognize mathematical formulas, and uses an LSTM network as a decoder. The LSTM network can effectively capture long-term dependencies and promote back-propagation gradients. The LSTM network of the embodiment is an LSTM of the prior art. Step 3: Use the word segmentation point obtained by the word segmentation process in step 2 as a candidate separation point, and use the step separation model to determine whether the candidate separation point is a step demarcation point. After determining the step demarcation point of the answering step, separate the various answering steps of the answering result; the step separation model uses an SVM classification model, and the input is the candidate answer step separation point obtained by word segmentation in step 2. According to the existing standard answer, the SVM classification model and label are constructed and trained to predict whether the word segmentation point is a step demarcation point.

[0066] The SVM classification model of the embodiment is the SVM classification model of the prior art.

[0067] Step 4: Calculate the similarity between the expression in the answer step and the expression in the standard answer step;

[0068] Step 4.1: Represent the expressions in the answering steps and the standard answer step expressions as a to-be-evaluated linked list tree and a reference linked list tree respectively; Step 4.2: Calculate the similarity between the to-be-evaluated linked list tree and the reference linked list tree to obtain the first type of formula similarity.

[0069] Perform hierarchical traversal on the linked list tree to be evaluated and the reference linked list tree respectively, and obtain the array P of the hierarchical traversal sequence of the linked list tree to be evaluated = {P 1 ,P 2 ,P 3 ,…,P n} and the array B of the level traversal sequence of the benchmark linked list tree = {B 1 ,B 2 ,B 3 ,…,B m}, use the longest common subsequence algorithm to calculate the similarity between the linked list tree to be evaluated and the benchmark linked list tree, where P i , i=1,2,3,…,n represents the i-th element of the array P, i.e. the i-th traversal node of the hierarchical traversal sequence of the linked list tree to be evaluated, B j ,j=1,2,3,…,m represents the jth element of array B, i.e. the jth traversal node of the hierarchical traversal sequence of the benchmark linked list tree, n and m represent the number of nodes of the linked list tree to be evaluated and the benchmark linked list tree respectively;

[0070] The calculation formula for the similarity between the linked list tree to be evaluated and the benchmark linked list tree is as follows

[0071]

[0072] Where F sim1 It represents the first-class formula similarity between the linked list tree to be evaluated and the benchmark linked list tree, common(P,B) represents the similarity calculation function of array P and array B, and min(n,m) represents the smaller value of variables n and m.

[0073] Step 4.3: Calculate the substructure similarity between the linked list tree to be evaluated and the benchmark linked list tree to obtain the second type of formula similarity. The calculation process is as follows:

[0074] 1) Obtain the atomic node set of the linked list tree to be evaluated and the atomic node set of the reference linked list tree;

[0075] 2) Compare and determine the number of matching atomic nodes in the atomic node sets of the linked list tree to be evaluated and the reference linked list tree;

[0076] 3) Calculate the semantic similarity between the atomic nodes that match the linked list tree to be evaluated and the reference linked list tree. The types of atomic nodes are divided into numbers, variables, and operators. The calculation rules of semantic similarity include:

[0077] (a) If the atomic node of the to-be-evaluated linked list tree is of a different type from the atomic node of the matching reference linked list tree, the semantic similarity of the atomic node of the to-be-evaluated linked list tree is 0;

[0078] (b) If the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both numbers and the two are equal, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 1; if the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both numbers and the two are not equal, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 0;

[0079] (c) If the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both variables and the two are the same, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 1; if the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both variables and the two are different, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 0;

[0080] (d) If the atomic nodes of the linked list tree to be evaluated and the atomic nodes of the matched reference linked list tree are both operators and the two are the same or similar, then the semantic similarity of the atomic nodes of the linked list tree to be evaluated is 1; if the atomic nodes of the linked list tree to be evaluated and the atomic nodes of the matched reference linked list tree are both variables and the two are neither the same nor similar, then the semantic similarity of the atomic nodes of the linked list tree to be evaluated is 0;

[0081] 4) Obtain the edge set of the linked list tree to be tested and the edge set of the reference linked list tree;

[0082] 5) Calculate the number of matches between the edge set of the linked list tree to be tested and the edge set of the reference linked list tree;

[0083] 6) Calculate the similarity. The similarity calculation formula is as follows

[0084]

[0085] where F sim2 Indicates the similarity of the second type of formula between the linked list tree to be evaluated and the benchmark linked list tree, N base Represents the total number of atomic nodes in the atomic node set of the base linked list tree, N match Indicates the number of atomic node matches between the linked list tree to be evaluated and the reference linked list tree, E match represents the number of matching edges between the linked list tree to be evaluated and the reference linked list tree, E base represents the total number of edges in the base linked list tree, σ i Indicates the semantic similarity between the i-th matching atomic nodes in the linked list tree to be evaluated and the reference linked list tree.

[0086] Step 4.3: Determine whether the similarity of the first type of formula is equal to 1. If the similarity of the first type of formula is equal to 1, set the calculation result of the similarity between the expression in the answering step and the expression in the standard answer step to 1, and end step 4; otherwise, execute step 4.4;

[0087] Step 4.4: Use formula (2) to calculate the similarity between the linked list tree of the answer step expression sub-formula and the linked list tree of the standard answer step expression sub-formula, and obtain the second type of formula similarity;

[0088] Step 4.5: Compare the similarity between the first type of formula and the second type of formula, and take the larger value of the two as the calculation result of the similarity between the expression in the answering step and the standard answer expression.

[0089] Step 5: Calculate the structural similarity between the answer result and the standard answer as the second review feature. The second review feature includes whether the number of steps in the answer result and the structural relationship of the answer steps are consistent with the number of steps and the structural relationship of the steps in the standard answer respectively, and use the step relationship analysis model to obtain the step relationship of the answer steps;

[0090] like Figure 4 As shown in the figure, the step relationship analysis model includes an input layer, a hidden layer, a classification layer, and an output layer connected in sequence; the input of the input layer is the answer step vector x 1 ,x 2 ,x 3 ,..,x n ; The hidden layer is multi-layer, and the output of the hidden layer is the step feature vector; the input of the classification layer is the step feature vector and the statistical features of the answer step vector, and the output of the output layer is the step relationship judgment result y 1 ,y 2 The statistical features of the answer step vector include the number of steps and the structural keywords, mathematical reasoning symbols, and step-related words identified in step 2. Step-related words include "because" and "so".

[0091] Step 6: Calculate the score of the answer based on the first review feature and the second review feature

[0092] In the embodiment, the expression for obtaining two copies of student answers is:

[0093]

[0094]

[0095] The Latex format of the expression of the student answering steps is

[0096] (\sinB\cosC+\sin C\cosB)\sinB=-\sqrt 3\sin B\cosA (5)

[0097] (\sinB\cosC+\sin C\cosB)\sinB=-\sqrt 3\sin B\sinA (6)

[0098] The corresponding standard answer expression is

[0099]

[0100] The Latex format of the standard answer expression is

[0101] (b\cosC+c\cosB)\sinB=-\sqrt 3 b\cosA (8)

[0102] In the embodiment, the Latex format expression of the answering steps, that is, formula (3), is expressed as a linked list tree to be evaluated, such as Figure 3a As shown; the standard answer expression in Latex format, that is, formula (8), is expressed as a benchmark linked list tree, as Figure 3b As shown. Starting from the root node of the linked list tree to be evaluated, follow the pre-order traversal principle of the tree, that is, "traverse the parent node first, then traverse the left subtree node, and then traverse the right subtree node" to complete the traversal of the linked list tree to be evaluated, and obtain the atomic node set of the linked list tree to be evaluated. The atomic nodes in the atomic node set are numbered in the order of traversal. Similarly, traverse the benchmark linked list tree to obtain the atomic node set of the benchmark linked list tree with a sequential relationship. Compare the atomic nodes in the atomic node set of the linked list tree to be evaluated with the atomic nodes in the atomic node set of the benchmark linked list tree in turn to determine whether they match one by one. If the traversal path of the atomic nodes of the linked list tree to be evaluated is the same as the traversal path of the atomic nodes of the benchmark linked list tree, it is determined to be a match and the similarity of the matched atomic nodes is further calculated; similarly, determine whether the edges of the linked list tree to be evaluated match the edges of the benchmark linked list tree one by one.

[0103] like Figure 3b As shown in the figure, the longest common subsequence number of nodes between the linked list tree to be evaluated and the reference linked list tree is 9, and the minimum number of total nodes of the tree is 18. According to formula (1), the similarity between the linked list tree to be evaluated and the reference linked list tree is 0.5, that is, the first type of formula similarity is 0.5. The total number of atomic nodes N of the reference linked list tree base = 17, the total number of edges of the base linked list tree E base = 16. The number of atomic node matches N between the linked list tree to be evaluated and the reference linked list tree obtained through comparison and judgment match = 14, the number of edge matches E match =16. The similarity result of the second type of formula calculated by formula (2) is 0.515. By comparison, it is found that the similarity of the first review feature is 0.515.

[0104] The system of the above-mentioned mathematical subjective question scoring method is as follows Figure 5 As shown, it includes the following modules:

[0105] Answer result acquisition module: obtain the answer results of subjective math questions;

[0106] Answering step separation module: identifies and determines the step demarcation points from the obtained answering results, separates the answering results into multiple answering steps according to the step demarcation points, and obtains the answering step vector;

[0107] Expression similarity calculation module: calculates the expression similarity between the steps of the question to be reviewed and the steps of the standard answer as the first review feature;

[0108] Answer structure similarity calculation module: calculates the structural similarity between the answer to be evaluated and the standard answer as the second review feature; review module: calculates the score of the answer result based on the first review feature and the second review feature.

[0109] The expression similarity calculation module includes the following units:

[0110] Processing unit: representing the mathematical formula to be evaluated and the benchmark mathematical formula as a linked list tree to be evaluated and a linked list tree to be benchmark respectively;

[0111] Calculation unit: Calculate the similarity of the first type of formula and the similarity of the second type of formula to obtain the first review feature;

[0112] Comparison unit: determines whether the similarity of the first type of formula is less than 1, and compares the similarity of the first type of formula with the similarity of the second type of formula.

[0113] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A scoring method for subjective mathematics questions based on the matching degree of expression list tree, characterized in that: The following steps are involved: Step 1: Get the answer results of subjective mathematics questions; Step 2: Perform word segmentation on the answer results; For math answer texts that are mixed with keywords and math formulas, a math template matching method is used to match the answer keywords in the standard answer to obtain Chinese character keywords; an encoder-decoder model is used to recognize math formulas, and an LSTM network is used as a decoder; Step 3: Determine the demarcation points of the answering steps and separate the answering steps of the answering results; Step 4: Calculate the similarity between the expression in the answer step and the expression in the standard answer step as the first review feature; Step 5: Calculate the structural similarity between the answer and the standard answer as the second review feature; Step 6: Calculate the score of the answer result based on the first review feature, the second review feature and the scoring rule; In step 3, the step demarcation point of the answering step is determined, and the word segmentation point obtained by the word segmentation processing in step 2 is used as a candidate separation point, and a step separation model is used to determine whether the candidate separation point is a step demarcation point; the step separation model adopts an SVM classification model, and the input is the candidate answer step separation point obtained by word segmentation in step 2. According to the existing standard answer, an SVM classification model and a label are constructed and trained to predict whether the word segmentation point is a step demarcation point; Step 4 includes the following sub-steps: Step 4.1: Represent the expressions in the answering step and the standard answer step expressions as a to-be-evaluated linked list tree and a reference linked list tree respectively; Step 4.2: Calculate the similarity between the linked list tree to be evaluated and the benchmark linked list tree to obtain the first type of formula similarity; Step 4.3: Determine whether the similarity of the first type of formula is equal to 1. If the similarity of the first type of formula is equal to 1, then set the calculation result of the similarity between the expression in the answering step and the expression in the standard answer step to 1, and end step 4; Otherwise, proceed to step 4.4; Step 4.4: Calculate the similarity between the linked list tree of the answer step expression sub-formula and the linked list tree of the standard answer step expression sub-formula to obtain the second type of formula similarity; Step 4.5: Compare the similarity of the first type of formula and the similarity of the second type of formula, and take the larger value of the two as the calculation result of the similarity between the expression in the answering step and the standard answer expression; In step 4.2, the structural similarity between the linked list tree to be evaluated and the reference linked list tree is calculated, and the linked list tree to be evaluated and the reference linked list tree are respectively traversed hierarchically to obtain an array of hierarchical traversal sequences of the linked list tree to be evaluated. P ={ P 1, P 2, P 3,…, P n } and an array of level traversal sequences of the base linked list tree B ={ B 1, B 2, B 3, …, B m }, according to the array P and arrays B The similarity between the linked list tree to be evaluated and the benchmark linked list tree is calculated by the similarity calculation, where P i , i=1, 2, 3, …, n represents an array P The i-th element is the i-th traversal node of the hierarchical traversal sequence of the linked list tree to be evaluated. B j , j=1, 2, 3, …, m represents an array B The j-th element is the j-th traversal node of the level traversal sequence of the benchmark linked list tree. n , m Respectively represent the number of nodes in the linked list tree to be evaluated and the benchmark linked list tree; The calculation formula for the similarity between the linked list tree to be evaluated and the benchmark linked list tree is as follows: ； （1） In the formula Indicates the similarity of the first type of formula between the linked list tree to be evaluated and the benchmark linked list tree, Representing an array P and arrays B The similarity calculation function is: Indicates variable n , m The smaller value of The second review feature includes whether the number of steps in the answer and the structural relationship of the answer steps are consistent with the number of steps and the structural relationship of the steps in the standard answer respectively; Step 5 uses a step relationship analysis model to determine the relationship between the steps of the answering step. The step relationship analysis model includes an input layer, a hidden layer, a classification layer and an output layer. The input of the input layer is the answering step vector, the hidden layer is multi-layered, and the output of the hidden layer is the step feature vector. The input of the classification layer is the step feature vector and the statistical features of the answering step vector, and the output of the output layer is the judgment result of the relationship between the steps; the statistical features of the answering step vector include the number of steps and the structural keywords, mathematical reasoning symbols, and step-related words identified in step 2.

2. The method for scoring subjective mathematics questions according to claim 1, characterized in that: In step 4.4, the calculation process of the second type of formula similarity specifically includes: 1) Obtain the atomic node set of the linked list tree to be evaluated and the atomic node set of the benchmark linked list tree; 2) Compare and determine the number of matching atomic nodes in the atomic node sets of the linked list tree to be evaluated and the reference linked list tree; 3) Calculate the semantic similarity between the atomic nodes that match the linked list tree to be evaluated and the reference linked list tree; 4) Obtain the edge set of the linked list tree to be tested and the edge set of the benchmark linked list tree; 5) Calculate the number of matches between the edge set of the linked list tree to be tested and the edge set of the reference linked list tree; 6) Calculate the similarity. The similarity calculation formula is as follows: ；（2） in Indicates the similarity of the second type of formula between the linked list tree to be evaluated and the benchmark linked list tree, Represents the total number of atomic nodes in the atomic node set of the base linked list tree, Indicates the number of atomic node matches between the linked list tree to be evaluated and the reference linked list tree. Indicates the number of matching edges in the linked list tree to be evaluated and the reference linked list tree, represents the total number of edges in the base linked list tree, Indicates the first i The semantic similarity of the atomic nodes that match each other.

3. The method for scoring subjective mathematics questions according to claim 2, characterized in that: In step 3), the semantic similarity between the atomic nodes matching each other in the linked list tree to be evaluated and the reference linked list tree is calculated, and the types of atomic nodes are divided into numbers, variables and operators. The calculation rules of the semantic similarity include: a) If the atomic node of the linked list tree to be evaluated is of a different type from the atomic node of the matched reference linked list tree, the semantic similarity of the atomic node of the linked list tree to be evaluated is 0; b) If the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both numbers and the two are equal, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 1; if the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both numbers and the two are not equal, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 0; c) If the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both variables and the two are the same, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 1; if the atomic nodes of the to-be-evaluated linked list tree and the atomic nodes of the matching reference linked list tree are both variables and the two are different, then the semantic similarity of the atomic nodes of the to-be-evaluated linked list tree is 0; d) If the atomic nodes of the linked list tree to be evaluated and the atomic nodes of the matching reference linked list tree are both operators and the two are the same or similar, then the semantic similarity of the atomic nodes of the linked list tree to be evaluated is 1; if the atomic nodes of the linked list tree to be evaluated and the atomic nodes of the matching reference linked list tree are both variables and the two are neither the same nor similar, then the semantic similarity of the atomic nodes of the linked list tree to be evaluated is 0.

Images