CN109886851B

CN109886851B - Method and device for correcting mathematic questions

Info

Publication number: CN109886851B
Application number: CN201910134291.6A
Authority: CN
Inventors: 丁克玉; 周锋; 薛定龙; 彭朝阳; 邓彬彬
Original assignee: iFlytek Co Ltd
Current assignee: iFlytek Co Ltd
Priority date: 2019-02-22
Filing date: 2019-02-22
Publication date: 2023-04-07
Anticipated expiration: 2039-02-22
Also published as: CN109886851A

Abstract

A method and a device for correcting mathematic questions, wherein the method comprises the following steps: constructing a reasoning path of the mathematical problem according to a preset problem solving rule and the mathematical problem; the reasoning path represents a reasoning process from the mathematical topic to a correct answer; and gradually correcting the answer content by utilizing the reasoning path. The invention abandons the existing mode of only comparing the same or the same, not only can judge the correctness of the problem solving step, but also can provide effective and specific correction content for each step of the problem solving content based on an inference path, namely the thinking of the correct problem solving process.

Description

Method and device for correcting mathematic questions

Technical Field

The invention relates to the field of intelligent education, in particular to a method and a device for correcting a math question.

Background

At present, the mathematics questions mainly depend on manual correction, for example, a teacher can gradually judge the problems of students and analyze the reasons of the problems when the students answer so as to form a targeted teaching scheme. However, different students can give various solutions to the same subject, and the correction of each step in the solution requires rigorous calculation and analysis, so that a great deal of correction work can bring heavy manual burden.

With the application of artificial intelligence in the field of education, a technology for automatically judging the correctness of a problem by a computer is developed at present, for example, for a mathematical calculation problem, after the content of the problem is identified step by step, an interface of third-party mathematical calculation software such as mathematics, matlab, maple and the like is called to obtain the simplest result of the mathematical expression, and the result of the problem is compared with a standard answer to judge whether the step of the problem is correct or wrong.

However, the above-mentioned techniques have a limited application range, and only correct and wrong answer steps can be output, and the reason for the correct and wrong answer cannot be provided, for example, it cannot be determined which mathematical knowledge points are wrongly used by the answerer, so the prior art is not strictly correct. The correction can be judged, and an explanation aiming at the problem solving idea can be provided, so that a targeted personalized learning scheme can be formulated effectively according to the knowledge point mastering condition.

Disclosure of Invention

The invention aims to provide a method and a device for correcting mathematic questions, which realize automatic gradual correction in a strict sense by constructing an inference path.

The technical scheme adopted by the invention is as follows:

a method for correcting a mathematical problem comprises the following steps:

constructing an inference path of the mathematical question according to a preset solving rule and the mathematical question; the reasoning path represents a reasoning process from the mathematical topic to a correct answer;

and gradually correcting the answer content by utilizing the reasoning path.

Optionally, the problem solving rule includes:

and according to the operation priority level, carrying out stepwise simplification on the mathematical expression in the mathematical topic until a final answer is obtained.

Optionally, the stepwise simplification comprises:

obtaining an original analytic structure of the mathematical expression;

performing corresponding operation on one sub-expression node capable of independently operating in the original analysis structure to obtain a simplification result;

updating the expression before the simplification by using the simplification result to obtain the simplified expression after the simplification;

and analyzing the simplified expression to obtain a simplified analysis structure, and sequentially carrying out simplified operation in the above mode.

Optionally, the method further comprises, after each reduction:

recording a mathematical rule used in the simplification;

recording simplification nodes in the simplification analysis structure, wherein the simplification nodes are the current simplification result;

and recording the mapping relation between each node in the simplification analysis structure and each node in the analysis structure before the simplification.

Optionally, the step-by-step modifying the answer content by using the inference path includes:

matching each step of the answer content with each inference node in the inference path in sequence; the reasoning node comprises a result of each reasoning in each reasoning path;

if so, determining that the current problem solving step is correct;

and if not, determining that the current problem solving step is wrong, and taking the error reason of the current problem solving step as correction content.

Optionally, the method further comprises:

acquiring a shortest inference path from the inference paths;

and using the reasoning process of the shortest reasoning path as the correcting content.

Optionally, the step of taking the error reason of the current problem solving step as the correction content includes:

searching a target reasoning node with highest correlation with the current problem solving step in the reasoning path, and determining an error position in the target reasoning node;

acquiring a target inference path reaching the target inference node;

judging whether each inference process is related to the error position from back to front on the target inference path based on the target inference node;

and if so, determining the mathematical knowledge points applied by the reasoning process as the error reasons.

Optionally, the searching for the target inference node with the highest correlation with the current problem solving step in the inference path includes:

calculating a first similarity score of a current reasoning node in the reasoning path relative to the current problem solving step;

calculating a second similarity score of the current problem solving step relative to the current inference node;

fusing the first similarity score and the second similarity score to obtain a correlation score between the current problem solving step and the current reasoning node;

and traversing all the inference nodes according to the mode, and selecting the inference node with the highest relevance score as the target inference node.

A mathematical problem correcting device comprising:

the reasoning path construction module is used for constructing a reasoning path of the mathematical question according to a preset problem solving rule and the mathematical question; the reasoning path represents a reasoning process from the mathematical topic to a correct answer;

and the correcting module is used for gradually correcting the answer content by utilizing the reasoning path.

Optionally, the correcting module specifically includes:

the error positioning unit is used for searching a target reasoning node with highest correlation with the current problem solving step in the reasoning path aiming at the error problem solving step and determining an error position in the target reasoning node;

a relevant path determining unit, configured to acquire a target inference path reaching the target inference node;

the reverse reasoning unit is used for judging whether each reasoning process is related to the error position from back to front on the basis of the target reasoning node on the target reasoning path;

and the correction content determining unit is used for determining the mathematical knowledge point applied by the reasoning process as the error reason when the reasoning process is related to the error position.

Optionally, the error locating unit specifically includes:

the first similarity score calculation component is used for calculating a first similarity score of a current reasoning node in the reasoning path relative to the current problem solving step;

a second similarity score calculating component for calculating a second similarity score of the current solving step with respect to the current reasoning node;

a relevance score calculating component for fusing the first similarity score and the second similarity score to obtain a relevance score between the current problem solving step and the current reasoning node;

and the target inference node determining component is used for selecting the inference node with the highest relevance score as the target inference node after traversing all the inference nodes.

A math problem correcting device comprising:

a memory for storing a computer program;

and the processor is used for realizing the mathematic subject correcting method when executing the computer program.

A readable storage medium, on which a computer program is stored, which, when executed, implements the above mathematical problem correcting method.

A computer program product, when running on a terminal device, causes the terminal device to execute the above mathematical problem correction method.

The invention abandons the existing mode of only comparing the same or the same, but constructs the reasoning path of the mathematical question according to the preset question solving rule and the mathematical question, and gradually modifies the answering content of the responder by utilizing the reasoning path. Therefore, the correctness of the problem solving step can be judged, and effective and specific correction content can be provided for each step of the problem solving content based on the reasoning path, namely the thought of the correct problem solving process.

Drawings

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described with reference to the accompanying drawings, in which:

FIG. 1 is a flow chart of an embodiment of a method for correcting a mathematical problem provided by the present invention;

FIG. 2 is a schematic diagram of an embodiment of a knowledgebase graph provided by the present invention;

FIG. 3 is a flow chart of an embodiment of an expression parsing method provided by the present invention;

FIG. 4 is a diagram illustrating an embodiment of an expression parse tree provided by the present invention;

FIG. 5 is a flow chart of an embodiment of a step-by-step reduction method provided by the present invention;

FIG. 6 is a schematic diagram of an embodiment of an inference path provided by the present invention;

FIG. 7 is a flow chart of an embodiment of a step-by-step modification method provided by the present invention;

FIG. 8 is a flow chart of an embodiment of determining wholesale content provided by the present invention;

FIG. 9a is a flow chart of an embodiment of calculating a relevance score provided by the present invention;

FIG. 9b is a diagram illustrating a first embodiment of setting weights for a parse tree according to the present invention;

FIG. 9c is a diagram illustrating an embodiment of setting weights for a parse tree according to the present invention;

FIG. 10 is a flow chart of an embodiment of a reverse reasoning analysis method provided by the present invention;

FIG. 11 is a schematic diagram of an embodiment of an inference path for thrust reversal provided by the present invention;

FIG. 12 is a schematic diagram of an embodiment of a mathematical problem batching device provided by the present invention.

Description of reference numerals:

1 inference path construction module 2 correction module

Detailed Description

Reference will now be made in detail to the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the drawings are illustrative only and should not be construed as limiting the invention.

The invention provides an embodiment of a method for correcting a mathematical problem, which can comprise the following steps as shown in figure 1:

s1, constructing an inference path of a mathematical problem according to a preset problem solving rule and the mathematical problem;

and S2, gradually modifying the answer content by using the reasoning path.

The reasoning path represents a reasoning process from a mathematical topic to a correct answer, that is, the subdivision steps of a correct solution idea are connected in series to obtain one or more complete solution contexts. Specifically, the reasoning path may be derived from a preset problem solving rule algorithm, that is, a mathematical problem is given, and the complete problem solving reasoning process can be obtained through the algorithm, so that different problem solving rules may obtain different reasoning paths, for example, the setting of the problem solving rule may be based on a mathematical axiom theorem, a large amount of problem solving statistical data, or an expert system; for example, in a scenario where an application object is a junior high school mathematics calculation problem correction, the set problem solving rule may be to gradually reduce the mathematical expression in the mathematical problem according to the operation priority involved in junior high school mathematics axiom theorem and the like until the final answer is obtained. The following is a detailed description based on this example, where two points are indicated:

first, the expression mode of the inference path: taking the first school mathematical calculation title "4/2+3 + 5" as an example, a preferred representation method of multiple problem solving paths as shown in fig. 2 is obtained by using a preset problem solving rule, wherein each mathematical expression uses a LaTeX format, "\\ times" represents "+" i.e. a multiplication symbol, "\ div" represents "/" i.e. a division symbol, and "\\ frac {1} {2} represents a score 1/2; it can be seen that one of the features of the inference path is to have a definite directional relationship, so that this relationship can be represented by a directed graph, where nodes in the directed graph represent expressions in the complete inference process, and directed edges represent the inference process, where arrow tails point to the pre-inference piece and arrow heads point to the post-inference piece, so that a plurality of inference paths represented by the directed graph are interleaved to form the knowledge inference graph shown in fig. 2; in fig. 2, the leftmost inference node of any inference path represents the topic expression to be processed, the rightmost inference node represents the most expression node (i.e., the final calculation result of the topic), and the middle inference nodes represent the non-most expression nodes generated in the inference process (i.e., the middle results when the topic is solved by the path), it is needless to say that the head and tail inference nodes are not limited to be the leftmost or the rightmost, and can be correspondingly displayed and adjusted as required.

Secondly, the pertinence of the inference path: the inference path proposed by this embodiment is an algorithmic inference for a mathematical problem, and then the inference path for the problem (or the above-mentioned knowledge inference graph represented by a directed graph) can be stored in a database in an actual operation; when the same theme is corrected next time, the generated reasoning path can be directly read from the database without repeated construction. Therefore, in a large-scale examination correction scene, the operation amount can be greatly reduced, the correction time can be shortened, and the correction efficiency can be improved.

The invention abandons the existing mode of only comparing the same or the same, but constructs the reasoning path of the mathematical question according to the preset question solving rule and the mathematical question, and gradually modifies the answering content of the responder by utilizing the reasoning path. Therefore, the correctness of the problem solving step can be judged, and effective and specific correction content can be provided for each step of the problem solving content based on the reasoning path, namely the thought of the correct problem solving process. Based on the invention, the application scene of the automatic correction technology can be expanded in a large range, the manual correction pressure can be greatly reduced, the correction efficiency is improved, and the following multiple extension effects can be realized:

1) The method is convenient for counting and analyzing the mastering conditions of the answerers on the knowledge points, provides a basic basis for personalized teaching, and can be used for carrying out reinforced training on the knowledge points and the like if the error rate of the knowledge points in a certain inference step is high.

2) The answerer can make clear the merits of all reasoning ideas in the question solving process by correcting the results, find the answer mode of the question or a better answer mode in time, realize autonomous high-efficiency learning and improve the capability of solving the mathematic questions.

In addition, it can be understood by those skilled in the art that the present invention inevitably includes a process of acquiring the mathematical questions and answer contents, for example, a text format entered manually may be received, an image format may be received first, and then the text format is processed by an image recognition technology, or a real-time handwriting recognition technology, a voice recognition technology, and the like may be directly adopted. Moreover, before the batch modification method provided by the invention is implemented, the received text can be preprocessed, for example, in order to facilitate extracting useful information in the text, operations such as word segmentation, part of speech tagging, reference resolution and the like can be performed according to the existing syntactic and semantic analysis technology, and then the useful information is translated by a template to be simplified into a first-order predicate form; the first-order predicate form is composed of an individual word and a predicate, wherein the individual word is an event or an object which can exist independently, and the predicate is a word for describing the property of the individual word and instantly describing a certain relation between the event and the object; applied to the present invention, for example, mathematical topic "calculation: 4/2+3*5.", answer content" =2+3 +5 "" calculation "", "=" is predicate, information extraction can be expressed as "computer (4/2 +3 + 5)", "Equal (2 +3 + 5)", and after the preprocessing, an expression form with uniform format and convenience for computer processing can be obtained, and meanwhile, useful information cannot be lost. When the first-order predicate is read, the first-order predicate is represented in the memory in the form of an instantiated object of a class, such as "computer (4/2 +3 + 5)", which needs to calculate an expression, and then an object of an expression class can be created in the memory to describe the expression class, so that different types of mathematical titles are modified in actual operation, and classes of the created objects can be different, which is not limited in the present invention.

Based on the above mentioned example of the mathematical calculation questions, the invention provides a 'early stage' basic processing method for setting the solution rules and constructing the reasoning path, i.e. analyzing the mathematical questions and/or the answering contents. The traditional expression analysis mode (such as inverse wave blue) is designed for quickly calculating results, simplifies excessive information and is not suitable for the strict correction of mathematical questions. Therefore, the invention designs an expression analysis method, which is beneficial to improving the effect and efficiency of mathematical correction, and as shown in fig. 3, the analysis scheme includes the following procedures:

s10, determining the expression type of the original expression according to the operation priority level;

s11, dividing the original expression into expression units by using operators related to the expression types as dividing points;

s12, extracting the sub-expressions from the expression unit and determining the types of the sub-expressions;

s13, dividing the sub-expressions into expression subunits by using operators related to the sub-expression types as dividing points;

and S14, resolving the original expression into the most simplified expression in the same way.

In the actual operation of the process, the type of the expression can be judged by using the regular expression, and then the expression is divided into one or more units by taking an operator related to the type of the expression as a division point, wherein each unit comprises a sub-expression; and then returning to the previous step, continuously judging the type of the sub-expression in the unit and carrying out partition in the same way, and circularly processing in the way until the original expression is divided into independent digital units. It should be noted that the most simplified expression referred to in the present invention is only one of the naming manners, and may also be referred to as the base expression in combination with the defined expression class, and the present invention is not limited thereto.

Specifically, the expression type may include the following expression classes according to the junior middle school mathematical schema referred to by example:

zero: the number 0 indicates "no" or "empty".

Positive number: such numbers larger than 0 as 3, 2, etc. are called positive numbers.

Negative number: such numbers as-3, -2, etc. that have a negative sign "-" appended to the positive number are called negative numbers.

And (3) fraction: such a structure

True score: the structure is as fractional, but the denominator is larger than the numerator.

Adding and subtracting the expression: such as "\\9633; + \9633;" \\9633, such expressions connected by addition and subtraction symbols are called addition and subtraction expressions, "\9633, which may be numerical or higher priority expressions than addition and subtraction calculation, such as successive multiplication and division expressions, i.e. the types of expressions accompanied with operators are determined at a lower level according to the operation priority, such as expressions" 4/2+3 +5 "are addition and subtraction expressions.

Successive multiplication and division expressions: the expression connected by a plurality of multiplication symbols or division symbols is called continuous multiplication-division expression, "\9633", and the expression can be a number or an expression with higher calculation priority than multiplication-division, such as power exponent expression, root expression and absolute value expression; similarly, according to the operation priority level, the expression type with the operator is determined at a lower level, such as the expressions "4/2", "3 x 5

It is a sequential multiplication and division expression.

Power exponent expression: such as "\9633 ^□ "the expression of the structure is a power exponent expression, the exponent may be any expression, and the base may be a number, a root expression, an absolute value expression, a bracket expression, for example," 2 ³ ”、“|2+3| ³ ”、

It is a power exponent expression.

The root expression: such as

Expression (2)Is a radical expression, the number of radices can be any expression, and the number of the radices is a positive number.

Absolute value expression: such as "\9633 |", the expression of the structure is an absolute value expression, "\9633 |" may be any expression.

The foregoing is merely exemplary and the invention is not so limited; however, it should be noted that, after the type of the expression is determined, the original expression may be divided into expression units by using an operator related to the type as a division point, for example: for addition and subtraction expression "\\9633; + \9633; - \9633;", i.e. division is performed according to addition and subtraction symbols to obtain addition and subtraction expression units "\9633;", "+ \9633;", "- \9633;", here the invention proposes a preferable division method, as shown above, the addition and subtraction symbols are all stored in the divided next unit, the symbol of the first unit is empty, for example, the expression "4/2+3 + 5" can be divided into two expression units "4/2"; "+3 + 5"; for the continuous multiplication and division expression units '\9633;' 9633; '/\9633;', i.e., division according to the multiplication and division number, the continuous multiplication and division expression units '\9633;', '9633;', 'and'/'9633;', are obtained, and similarly, the multiplication and division symbol is stored in the divided latter unit, the symbol of the first unit is null, and for example, the expression '4/2' can be divided into two expression units '4', '2'. Extracting the sub-expressions from the expression unit according to the above flow, for example, extracting "3 × 5" from "+3 × 5" as the sub-expressions to continue the subsequent division, which is summarized by the example shown in fig. 4: the type of the mathematical expression "4/2+3 + 5" is an addition and subtraction expression, so that two addition and subtraction expression units "4/2", "+3 + 5" can be separated, the addition and subtraction expression unit "4/2" can extract the sub expression "4/2", and the addition and subtraction expression unit "+3 + 5" can extract the sub expression "3 + 5"; the type of the sub expression "4/2" is a continuous multiplication and division expression, so that two expression subunits "4", "/2" can be separated, and the type of the sub expression "3 × 5" is a continuous multiplication and division expression, so that two expression subunits "3", "5" can be separated (it is required to know that the last sub expression is used as a parent expression); then, the expression subunits "4", "/2", "3", ". 5" can separate out the positive integers "4", "2", "3" and "5", so far, the expression analysis is completed, and the most probable expression represented by the positive integer is obtained.

Of course, in practical operation, various parsing structures may be adopted, and fig. 4 illustrates a tree structure, which may be referred to as a parsing tree of expressions, and identifies node types at each level in the parsing tree, where: "A" represents an addition-subtraction expression; "AU" represents an addition-subtraction expression unit; "C" represents a sequential multiplication-division expression; "CU" denotes a sequential multiply-divide expression unit; "PI" represents a positive integer. It should be noted that each identifier in fig. 4 is self-defined, and other identifier formats may be adopted for different expression types or different analysis structures, which is not limited in the present invention.

The node codes in the parse tree are described only by way of example in fig. 4: in the first embodiment, for each node in the parse tree, node names on paths from the root node to the current node are connected and then appropriately modified to obtain a unique code, because the sibling node class names of "AU" and "CU" are the same and cannot be distinguished, the modification mode is that "AU and CU do not use node names and are distinguished by using subscript indexes of tree branches, the subscript indexes are numbered from left to right and from 0, for example, the code of the root node" a:4/2 3 +5 "in the expression parse tree in fig. 4 is" a ", the code of the right addition and subtraction expression unit" AU: +3 +5 "is" A1 "(the index starts from 0 on the left), the code of the sub expression node" C:3 +5 "is" A1C1", the code of the expression sub unit node" CU: "5" is "A1C1", and the code of the most simple expression node "PI:5" is "A1C1 PI; in the second embodiment, the coding may also completely use index of subscripts of tree branches, for example, the coding of the Root node "a:4/2+3 + 5" in the expression tree in fig. 4 may be "R" (initial of Root), the coding of the expression unit "AU: +3 + 5" is "R1" (index starts from left side with 0), the coding of the sub-expression node "C:3 + 5" is "R10", the coding of the expression sub-unit node "CU:" 5 "is" R101", and the coding of the most similar expression node" PI:5 "is" R1011". In practice, the two encoding methods or other encoding methods are not limited to be adopted, and for the convenience of description, the first encoding method is taken as an example in the following.

Based on the above analytic description of the mathematical expressions, the solving rule "stepwise simplify the mathematical expressions in the mathematical topics according to the operation priority until the final answer" in the foregoing example can be further set by using the following specific stepwise simplification method, as shown in fig. 5, where the step of simplification may include:

s100, obtaining an original analytic structure of a mathematical expression;

s101, performing corresponding operation on a sub-expression node capable of independently operating in an original analysis structure to obtain a simplification result;

step S102, updating the expression before the simplification by using the simplification result to obtain the simplified expression after the simplification;

and step S103, analyzing the simplification expression to obtain a simplification analysis structure, and sequentially carrying out simplification operation in the above mode.

In actual operation, the rule may be set by first collecting mathematical knowledge points such as mathematical axiom, theorem, algorithm, etc., and then, according to the analysis structure (e.g., analysis tree) of the mathematical expression, sequentially simplifying the nodes therein one by one to obtain corresponding simplified expressions and corresponding analysis structures, and so on, until a final result is obtained, wherein whether the independent operation is determined according to the characteristics of the nodes in the analysis structure, for example, the "AU" and "CU" nodes are not the nodes capable of independent operation, because they are only the divided units (operators reserved as the division points), but not the expressions capable of direct operation. FIG. 6 shows the reasoning path of "A:4/2+3 + 5" constructed by applying the solving problem rule: the sub-expression node C:4/2 which can be independently operated is extracted after the analysis of A:4/2+3 +5, and the reduction operation is carried out by utilizing a division rule, and the result is PI: 2; then updating PI:2 back to the original mathematical expression to obtain a simplified expression A:2+3 +5, and obtaining the (1) th section in the inference path in the process; in this way, the simplification expression "a:2+3 + 5" is further reduced step by step, and the (2) th segment and the (3) th segment in the inference path are obtained.

In order to facilitate the subsequent gradual correction by using the inference path, the relevant parameters of each simplification can be recorded when the inference path is constructed, for example, after each simplification:

1) Recording a mathematical rule used in the simplification;

2) Recording simplification nodes in the simplification analysis structure, wherein the simplification nodes are the current simplification result;

3) And recording the mapping relation between each node in the simplification analysis structure and each node in the analysis structure before the simplification.

As illustrated in fig. 6, when a division rule is used in the (1) th segment (i.e., the first operation process) of the inference path, the "knowledge point: division rule "; in the analytic structure of the simplified expression "a:2+3 + 5", the simplified node where the operation occurs is "PI:2", and the simplified node may be recorded as "operation table: a0 PI' indicating that the simplified node obtained by actual operation in the reasoning process is A0PI; as can be seen from the combination of the nodes in the two parsing structures before and after the segment (1), the latter node "PI:2" (code "A0 PI") is obtained by the former node "C:4/2" (code "A0C") according to the division rule, and the other nodes before and after the simplification have no operation, such as node "C:3 × 5", which is previously coded as "A1C", and is still "A1C" after the simplification, and thus can be recorded as "mapping table: a0PI ← A0C, A1C ← A1C, \8230; (other node encodings remain unchanged as well, not listed here). Again in the same manner, corresponding reduction parameters may be recorded for each reduction operation (in the example, paragraph (2) and paragraph (3)).

In summary, those skilled in the art can know that all possible inference paths can be covered by using the collected mathematical knowledge points and problem solving habit data in a certain application scenario; then, the constructed reasoning path can be used to modify the actual answer content of the responder, and the invention provides a gradually modifying idea, as shown in fig. 7, which may include the following steps:

s20, matching each step of the answer content with each inference node in an inference path in sequence;

if the answer is matched, executing the step S21 and determining that the current problem solving step is correct;

if not, step S22 is executed to determine that the current problem solving step is wrong, and the error reason of the current problem solving step is used as the correction content.

The modification content is the opinion given after the modification in strict sense, which may include the conclusion about whether the step is correct or not, and for the error step, may provide the specific contents of the display of the error reason, the error analysis, the correct reasoning reference, etc.; of course, the correct steps may be modified, and although usually, a step does not need to be modified, considering that the invention aims to improve the learning ability of the respondents, the modification content may be analyzed or the best reasoning idea may be shown according to the reason why the solution is correct by the reasoning path.

As mentioned above, the answer content may be received and the segmentation processing of the answer step may be performed by using the prior art, so that the answer content represents the answer reasoning process of the answerer. When correcting, specifically, each step of answering is matched with each inference node in the inference path, since the embodiment focuses on the answer process, the first inference node in the inference path, namely the original node corresponding to the mathematical topic, may not be in the matching range, but does not exclude matching with the original node in other embodiments, for example, the topic is copied again by the habit of the answering person, so the written topic stem can be matched with the first node of the inference path and correction content such as "this step is the topic stem condition" is output when correcting; however, in this embodiment, it is emphasized that the inference nodes participating in matching mainly represent the result of each inference in each inference path, which, of course, includes the intermediate result and the final result of the inference link.

Specifically, the reasoning node in the reasoning path represents the simplified expression obtained after each simplification, so in this embodiment, the matched object is the expression in the problem solving step and the simplified expression in the reasoning path, and if a consistent simplified expression is found in a certain reasoning path, the current problem solving step of the responder can be determined to be correct; conversely, if no consistent simplified expression is found in any of the inference paths, it may be determined that the responder's current solving step is incorrect. Two points are indicated here: firstly, only judging the steps are correct at this time, but not belonging to the 'correction' emphasized by the invention, the invention is characterized in that because the reasoning path is adopted as the correction basis, when the current solving step is determined to be wrong, the reason of reasoning error can be output, and the specific process is explained in the following; secondly, because the correction is performed step by step according to the inference path, a person skilled in the art can understand that in the sequential step-by-step judgment process, as long as an error step occurs, the correction of the subsequent solution step is not needed in some application scenarios, because the inference process is carried out at one pulse, the subsequent error necessarily comes from the previous inference deviation, but the invention is not limited in other scenarios, and all the solution steps can be corrected regardless of whether a certain step is correct or not. In addition, whether a step is judged to be correct or incorrect or not can be further considered, the shortest reasoning path can be obtained from the reasoning paths, and the reasoning process of the shortest reasoning path is used as correction content. Namely as mentioned earlier: if a certain problem solving step is determined to be correct, the shortest path (or the shortest and complete reasoning path for outputting the problem) reaching the reasoning node matched with the problem solving step can be selected from the reasoning path to be used as the correction content output of the correct step, so that the best solution reference is provided for the answerer, and the answerer can conveniently master a better problem solving idea; if a certain problem solving step is determined to be wrong, not only the error reasons mentioned above can be output, but also the shortest path to the reasoning node with the highest correlation with the current error step (or the shortest and complete reasoning path of the problem) can be given as the correction content supplement, so that the answering person can know the correct and optimal problem solving idea.

Two questions are raised here, how to determine the cause of the error for the error solving step and how to determine the inference node with the highest relevance to the error step. The invention takes the mathematical calculation problem as an example, and provides a specific processing mode: the inference node with the smallest difference with the error step can be found in the inference path, the error position is analyzed through the analytic structure of the expression, a mathematical knowledge point influencing the error position is searched in the inference process that the previous inference node reaches the similar inference node, and the correction content aiming at the error step is obtained based on the mathematical knowledge point. As described in detail below with reference to fig. 8, the process of determining the correction content includes:

s200, searching a target reasoning node with highest correlation with the current problem solving step in a reasoning path, and determining an error position in the target reasoning node;

step S210, obtaining a target inference path reaching a target inference node;

step S220, on the target reasoning path, based on the target reasoning node, judging whether each reasoning process is related to the error position from back to front;

step S230, if the two are determined to be related, determining that the mathematical knowledge point applied by the inference process is an error reason.

For the target inference node mentioned in step S200, which is searched for and has the highest correlation with the current problem solving step, the measurement may be performed from multiple angles, such as calculating the euclidean distance or the cosine distance between the problem solving step and the inference node, or outputting the probability value of the correlation between the two through a pre-established model, or comparing the edit distance from the expression corresponding to the current problem solving step to the expression corresponding to the inference node, and the like, hereinafter, a measurement method for calculating a correlation score based on an analytic structure is provided, as shown in fig. 9a, the method includes:

step S201, calculating a first similarity score of a current reasoning node in a reasoning path relative to a current problem solving step;

s202, calculating a second similarity score of the current problem solving step relative to the current reasoning node;

s203, fusing the first similarity score and the second similarity score to obtain a correlation score between the current problem solving step and the reasoning node;

and S204, traversing all the inference nodes according to the mode, and selecting the inference node with the highest relevance score as a target inference node.

Taking the mathematical calculation problem mentioned above as an example, the method is essentially an edit distance algorithm with a structure, that is, the similarity between the expression corresponding to the current step and any simplified expression in the inference path is calculated, and when actual comparison is performed, an inference node participating in the comparison in the inference path is the current inference node. In practical operation, the algorithm can be performed by assigning a weight score to an analytic node of an expression, and a preferred scheme is provided here: firstly, the error problem solving step is analyzed to obtain a tree structure (abbreviated as tree 1), and each node of the tree 1 is given a different weight, for example, the weight of the root node is 1, the weight of the child node is the weight of the parent node divided by the number of branches, so as to obtain the basic score of the tree 1, where it is noted that: based on the analysis method explained above, after the expression calculation topic is decomposed to form an analysis structure in the form of a multi-branch tree, generally speaking, if the analyzed sub-expression structure is an expression structure (non-optimal expression) which can still continue independent operation, the analyzed sub-expression structure belongs to a non-leaf node and is closer to a root node, and if the analyzed sub-expression structure is in the simplest form, for example, if the analyzed sub-expression structure is a positive/negative integer, the analyzed sub-expression structure belongs to a leaf node and is farther from the root node; moreover, the expression which can be continuously operated is structured information, and the structures of the two similar expressions are the same as the skeleton of the expression, so that the weight is set to be higher; in this way, if it is determined that the relevance score of the current solving step (non-final answer, for example, an intermediate expression which may refer to the content of the solving problem) and the current reasoning node is higher in the stepwise modification process, the more similar the structures of the two expressions are explained. In addition, when the two correlation score representations are identical, the two correlation score representations are matched, so that the method for calculating the correlation score used herein can also be used for the process of judging whether the problem solving step is correct or incorrect in the early stage. In the foregoing, a breadth-first traversal is used to determine the same node and different nodes of the parse tree (abbreviated as tree 2) and tree 1 of each inference node in the inference path (where the same node is, for example, an expression calculation problem, when the tree 1 and the tree 2 perform node comparison, if the node is a number, the requirement number is the same, and if the node is a non-optimal expression, the requirement structure is the same, where the structure refers to a specific structure of a certain expression class mentioned in the foregoing, and if the addition and subtraction expressions are connected by addition and subtraction symbols, and if the addition and subtraction expressions do not satisfy the above requirements, the different nodes are different), the same node obtains a weight score corresponding to the tree 1 node, and the different nodes do not obtain a score, thereby calculating a relative score of the tree 2 of any current inference node, and finally obtains a normalized score, i.e., a first similarity score, of the tree 2 with respect to the tree 1 from the "relative score/basic score";

exchanging the tree 1 and the tree 2, and obtaining the normalized score of the tree 1 to the tree 2, namely the second similarity score, according to the same weighting mode, namely the tree 2 provides the basic score and the tree 1 provides the relative score.

The manner of obtaining the first and second similarity scores is merely exemplary, and the invention is not limited to obtaining the first and second similarity scores in other manners; similarly, the fusion means of the two scores may also have various implementations, such as summing or averaging the two similar scores.

For the convenience of understanding the above correlation determination method, referring to fig. 9b and fig. 9c and being exemplified with reference to fig. 2 and fig. 6, it is assumed that for the mathematical title "4/2+3 + 5", the answer content is:

4/2+3*5

＝2+8

＝10

since the problem solving step "2+8" is not matched to a consistent inference node in the inference path (fig. 2), it is determined that the step is wrong, and the error expression "2+8" is analyzed, and meanwhile, a corresponding weight score is given to the tree 1 of "2+8" (fig. 9 b); the inference nodes adopt a traversal mode, so that in this example, the node "2+3 + 5" represents any inference node, and "2+3 + 5" is analyzed, and meanwhile, the corresponding weight score is given to the tree 2 of "2+3 + 5" (fig. 9 c).

It can be seen that the basic score of tree 1 is 1+1/2 =3, and each node in tree 2 can obtain the relative score of tree 1 node "a:2+8" (same structure), "AU:2", "PI:2", "AU: +8" (same structure) is 1+1/2 =5/2, so the first similar score is (5/2)/3 =5/6;

moreover, the basic score of tree 2 is 4, and the relative scores of nodes "A:2+3 + 5", "AU:2", "PI:2", "AU: +3 + 5" in tree 1 can be obtained by each node in tree 1 as 1+1/2 =5/2, so the second similar score is (5/2)/4 =5/8;

then, the average value of the two values can be calculated, and the correlation score between the error step "2+8" and the inference node "2+3 + 5" is (5/6 + 5/8)/2 =35/48.

In this way, traversing the inference node in this example, it can be known that the relevance score of the error step "2+8" and the inference node "2+15" is 40/48, which is the inference node with the highest score, and accordingly, the inference node "2+15" can be selected as the target inference node, that is, the basis for the subsequent correction analysis.

Continuing with the example of FIG. 8, after the target inference node is determined, the location of the error that actually occurred may be determined. It should be noted that the present invention determines the error position from the target inference node, but as can be seen from the above, the target inference node is from the inference path, and the inference path characterizes the correct solving process, so that the "error position" referred to herein essentially means: the correct form of the error step is determined in the target inference node. In the previous example, the error position of the error step "2+8" is determined to be "15" in the target inference node "2+15", i.e., "15" is written as "8" in response, and there is an error. In addition, the meaning of the "error position" in the present invention is understood by combining the aforementioned parsing structure and encoding method, the node where the error step is different from the correct form is the called error position, and the encoding of the error position is the encoding in the parsing tree of the correct form. Example (c): the error of "2+8" is encoded in "PI:8", the correct version of "PI:15" is "A1PI", which is called the encoding of the error location.

Next, a target inference path to the target inference node is obtained, where the target inference path may include all paths to the target inference node, but in a simpler application of mathematical topics, it is preferable to perform the inverse analysis described in steps S220 and S230 starting from the shortest path. Regarding the reverse reasoning analysis (reverse reasoning analysis), it is essential to track backward step by step which reasoning in the correct solution idea leads to the occurrence of the "wrong location", and reiterate that the "wrong location" is the correct form of error, and the mathematical operation method applied in the reasoning process leading to the occurrence of the "wrong location" can be regarded as a knowledge point which is not mastered by the responder, so that the error cause which can be used as the specific correction content can be determined.

In conjunction with the example of the mathematical calculation problem, the present invention provides a specific embodiment of the back-stepping analysis, which is further described in conjunction with fig. 10 and 11, and may include:

step S221, using the target inference node as the last inference node on the target inference path, and judging whether the operation position where the operation occurs is related to the error position in the inference process from the penultimate inference node to the target inference node;

step S222, if the error position is not related, mapping the error position to a penultimate reasoning node to obtain a corresponding new error position;

step S223, judging whether the operation position where the operation occurs is related to a new error position in the reasoning process from the third to last reasoning node to the second to last reasoning node;

step S224, according to the mode, judging whether the inference node before the target inference node is related to the error position in the target inference path.

The core of the idea is to search the inference path from the previous step to the correct form (as the inference path from inference node "2+3 + 5" to target inference node "2+15" in section (2) shown in fig. 11), which results in the correct form of inference process due to the occurrence of actual operation, and it should be pointed out that "correlation" in "correlation with the error position" and "correlation" in "correlation with the new error position" refers to: since each segment of the inference path constructed in the foregoing manner has been subjected to inference operation, but the operation position where the operation is performed from the previous inference node to the target inference node is not necessarily related to the error position, a determination needs to be made as to whether the error position is determined to be "related", which means that the error position is generated due to a change of the previous node after inference. For example, "15" is calculated from "3 x 5", then "15" is the operation position, and the operation position is related to the error position "15", so that the mathematical knowledge point applied by the inference process can be determined as the error reason; as another example, referring to FIG. 2, the operation position is "2" from inference node "4/2+15" to target inference node "2+15" in another path, which is independent of error position "15"; for the situation, the '15' in the target inference node '2 + 15' can be mapped to the previous inference node '4/2 + 15' to obtain a new error position (also '15') in the inference node, and then whether the position of the operation from the inference node '4/2 +3 + 5' to the inference node '4/2 + 15' is related to the new error position is judged according to the same way, so that the error reason is determined.

Taking the mathematical calculation problem as an example, and combining the analytic structure, the coding method and the recorded reasoning parameters mentioned in the foregoing embodiments, the above-mentioned back-stepping method will be further specifically explained:

in actual operation, the codes of the error positions and the codes in the operation table of the record can be compared in the analytic structure of the inference node (one of the codes starts with the other code, which indicates that the two are related, otherwise, the two are unrelated), and if the two are related, the knowledge points in the step inference parameters, namely the reason for the step error, can be output; if not, mapping the error position to the previous analysis tree through the mapping table of the record to obtain a new error position, and continuously judging whether the error position is related or not in this way.

In terms of the above-mentioned answering contents

4/2+3*5

＝2+8

＝10

As can be known from FIG. 11, the error position is encoded as "A1PI" (the leaf node "PI:15" is encoded on the parse tree of "2+ 15"), and the table of operations in section (2) of the inference path: a1PI, therefore, determining that the step of reasoning is related to the error position, and inquiring the knowledge point of the step of reasoning: the multiplication rule determines that the error reason of the problem solving step is the application error of the multiplication rule, that is, the correction content of the error step is the application error of the multiplication rule

However, it should be added that the above-mentioned is only an example of simple mathematical calculation questions, and for complex mathematical questions, the reason that may cause errors is related to the multi-step reasoning process, so that all related reasoning processes can be further judged upwards through the mapping table, so as to improve the accuracy and integrity of the correction content. For example, the error position "PI:15" is simplified from "C:3 × 5", and the code of the mapped new error position "2+3 × 5" is "A1C"; based on this, the operation table of the inference in the (1) th segment is continuously inquired as "A0PI" (the node "PI:2" is coded on the parse tree of the expression "2+3 + 5"), but the operation position "A0PI" and the new error position "A1C" do not start with each other, that is, after the inference operation in the (1) th segment, the node "PI:2" which actually changes is not related to the error position "C:3 + 5", so the knowledge point "division rule" used in the inference in the (1) th segment is unrelated to the error point, so that the whole inference process of the error step is searched, and the final batch modification content is the multiplication application error. Of course, as mentioned above, the correcting process may also include a process of giving a correct and optimal solution to the problem according to the inference path.

In summary, the present invention abandons the existing way of comparing only the same or equal, but constructs the reasoning path of the mathematical question according to the preset question solving rule and the mathematical question, and then modifies the answer content of the responder step by using the reasoning path. Therefore, the correctness of the problem solving step can be judged, and effective and specific correction content can be provided for each step of the problem solving content based on the reasoning path, namely the thought of the correct problem solving process.

Corresponding to the foregoing embodiments and preferred solutions, the present invention further provides an embodiment of a mathematical problem modification apparatus, as shown in fig. 12, the apparatus may include:

the reasoning path constructing module 1 is used for constructing a reasoning path of the mathematical topic according to a preset solving rule and the mathematical topic; the reasoning path represents a reasoning process from the mathematical topic to a correct answer;

and the correcting module 2 is used for gradually correcting the answer content by utilizing the reasoning path.

Further, the inference path construction module specifically includes a problem solving rule unit:

and the problem solving rule unit is used for simplifying the mathematical expression in the mathematical problem step by step according to the operation priority level until a final answer is obtained.

Further, the problem solving rule unit specifically includes:

the analysis subunit is used for obtaining an original analysis structure of the mathematical expression;

the simplification subunit is used for carrying out corresponding operation on one sub-expression node capable of independently operating in the original analysis structure to obtain a simplification result;

a simplification expression obtaining subunit, configured to update the expression before the present simplification by using the simplification result, and obtain a simplification expression after the present simplification;

and the first circulation unit is used for analyzing the simplification expressions to obtain a simplification analysis structure and sequentially carrying out simplification operation in the above mode.

Further, the apparatus further comprises a reduction parameter recording module for, after each reduction:

recording a mathematical rule used in the simplification;

Further, the correcting module specifically includes:

the matching submodule is used for matching each step of the answer content with each reasoning node in the reasoning path in sequence; the reasoning node comprises a result of each reasoning in each reasoning path;

the correct step correcting submodule is used for determining that the current problem solving step is correct if the current problem solving step is matched with a certain inference node;

and the error step correcting submodule is used for determining that the current problem solving step is wrong if the current problem solving step is not matched with a certain reasoning node, and taking the error reason of the current problem solving step as correcting content.

Further, the correct step modifying sub-module is further configured to obtain a shortest inference path from the inference path; and taking the reasoning process of the shortest reasoning path as correcting content.

Further, the correcting module specifically includes:

a relevant path determining unit, configured to acquire a target inference path reaching the target inference node; the related path is an inference path containing a target inference node in the path;

Further, the error location unit specifically includes:

In view of the foregoing examples and their preferred embodiments, it will be understood by those skilled in the art that in practice, the present invention is applicable to various embodiments based on hardware carriers, which are schematically illustrated below:

(1) A mathematical problem correcting apparatus, which may include:

a memory for storing a computer program or the above-mentioned apparatus;

and the processor is used for realizing the mathematic subject correcting method when the computer program or the device is executed.

(2) A readable storage medium, on which a computer program or the above apparatus is stored, which when executed, implements the above mathematical problem modification method.

(3) A computer program product (which may include the above apparatus) when running on a terminal device, causes the terminal device to execute the above mathematical problem modification method.

From the above description of the embodiments, it is clear to those skilled in the art that all or part of the steps in the above implementation method can be implemented by software plus a necessary general hardware platform. Based on such an understanding, the above-described computer program products may include, but are not limited to, refer to APP; the readable storage medium can be ROM/RAM, magnetic disk or optical disk; the device may be a computer device (e.g., a mobile phone, a PC terminal, a cloud platform, a server cluster, or a network communication device such as a media gateway, etc.). Moreover, the hardware structure of the device may further specifically include: at least one processor, at least one communication interface, at least one memory, and at least one communication bus; the processor, the communication interface and the memory can complete mutual communication through the communication bus. The processor may be a central processing unit CPU, or an application specific Integrated Circuit ASIC (application specific Integrated Circuit), or one or more Integrated circuits configured to implement embodiments of the present invention, or the like; the memory may also be a high-speed RAM memory or a non-volatile memory (non-volatile) or the like, such as at least one disk memory.

Finally, although the working and technical principles of the above-described device embodiments and preferred solutions are described in the foregoing, it should be emphasized that the various component embodiments of the device may still be implemented in hardware, or as software modules running on one or more processors, or as a combination of them. The modules or units or components and the like in the device embodiments may be combined into one module or unit or component, or may be implemented by being divided into a plurality of sub-modules or sub-units or sub-components.

In addition, the embodiments in the present specification are all described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for system embodiments, since they are substantially similar to method embodiments, they are described in a relatively simple manner, and reference may be made to some descriptions of method embodiments for relevant points. The above-described system embodiments are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement without inventive effort.

The structure, features and effects of the present invention have been described in detail with reference to the embodiments shown in the drawings, but the above embodiments are only preferred embodiments of the present invention, and it should be understood that the technical features related to the above embodiments and the preferred modes thereof can be reasonably combined and configured into various equivalent schemes by those skilled in the art without departing from and changing the design idea and technical effects of the present invention; therefore, the invention is not limited to the embodiments shown in the drawings, and all the modifications and equivalent embodiments that can be made according to the idea of the invention are within the scope of the invention as long as they are not beyond the spirit of the description and the drawings.

Claims

1. A math problem correction method is characterized by comprising the following steps:

constructing an inference path of the mathematical question according to a preset solving rule and the mathematical question; the reasoning path represents a reasoning process from the mathematical subject to a correct answer;

gradually correcting the answer content by utilizing the reasoning path, comprising the following steps: finding the reasoning node with the minimum difference with the error step in the reasoning path, determining the error position, and determining the correction content by the mathematical knowledge point influencing the error position in the reasoning process reaching the reasoning node.

2. The method of claim 1, wherein the problem solving rule comprises:

3. The mathematical topic correction method of claim 2, wherein the stepwise reduction comprises:

obtaining an original analytic structure of the mathematical expression;

and analyzing the simplified expression to obtain a simplified analysis structure, and sequentially performing simplified operation in the above manner.

4. A method of mathematical topic correction according to claim 3, characterized in that the method further comprises after each reduction:

recording a mathematical rule used in the simplification;

5. The method for correcting math questions according to claim 1, wherein the step-by-step correcting the content of the questions by using the inference path comprises:

if so, determining that the current problem solving step is correct;

if not, determining that the current problem solving step is wrong, and taking the error reason of the current problem solving step as correction content.

6. The method of mathematical problem correction according to claim 5, further comprising:

acquiring a shortest inference path from the inference paths;

7. The method of claim 5, wherein the step of correcting the error cause of the current problem solving step comprises:

acquiring a target inference path reaching the target inference node;

8. The method of claim 7, wherein said finding a target inference node in said inference path that has the highest correlation with the current problem solving step comprises:

calculating a second similarity score of the current problem solving step relative to the current reasoning node;

9. A mathematical problem correcting device, comprising:

the reasoning path building module is used for building a reasoning path of the mathematical question according to a preset solving rule and the mathematical question; the reasoning path represents a reasoning process from the mathematical subject to a correct answer;

the correcting module is used for gradually correcting the answer content by utilizing the reasoning path, and comprises: finding the reasoning node with the minimum difference with the error step in the reasoning path, determining the error position, and determining the correction content by the mathematical knowledge point influencing the error position in the reasoning process reaching the reasoning node.

10. The mathematics topic correction device of claim 9, wherein the correction module specifically comprises:

a relevant path determining unit, configured to obtain a target inference path reaching the target inference node;

and the correction content determining unit is used for determining the mathematical knowledge points applied by the reasoning process as the error reasons when the reasoning process is related to the error positions.

11. The mathematical problem correcting device according to claim 10, wherein the error locating unit specifically comprises:

a second similarity score calculating component for calculating a second similarity score of the current solving problem step with respect to the current inference node;

12. A mathematical problem correcting apparatus, comprising:

a memory for storing a computer program;

a processor for implementing the method of correcting a mathematical problem according to any one of claims 1 to 8 when executing the computer program.

13. A readable storage medium, characterized in that the readable storage medium has stored thereon a computer program which, when executed, implements the mathematical problem modification method according to any one of claims 1 to 8.