Method and system for mathematics teaching through implicit condition finding

Abstract

The present invention relates to a method which can be performed by an online system, and provides a method for mathematics teaching through implicit condition finding, the method comprising the steps of: constructing a DBMS which manages an implicit condition corresponding to a condition which is indirectly suggested or needs to be inferred by a learner himself / herself, in addition to a suggested condition which is directly suggested in a mathematical question; teaching the learner the implicit condition by using a concept description material written on the basis of the DBMS; and teaching the learner to find the implicit condition by using a problem solution material written on the basis of the DBMS. According to the present invention, a learner can solve a problem by inferring an implicit condition by himself / herself.

Description

Hidden Conditions Math Teaching Method and System

[0001] The present invention relates to a method and system for teaching mathematics by finding hidden conditions, and more particularly, to a method and system for teaching mathematics by finding hidden conditions on one's own and solving problems based on artificial intelligence and online.

[0002] Mathematics is a fundamental discipline of human culture, yet it can also be a challenging subject for learners. Due to the systematic nature of mathematics, problem analysis and solution processes inevitably become more complex as students progress through the grade levels. Therefore, it's crucial to structure these processes in a clear and logical pattern.

[0003] Korean Patent Publication No. 10-2496227 clearly presents a problem-solving method in a mathematics learning system and method using artificial intelligence and online convergence. However, it is lacking in showing the logical process of inferring hidden conditions during the problem-solving process, and thus has limitations in enabling students to analyze and solve mathematical problems on their own.

[0004] Accordingly, the present invention is disclosed to patternize hidden conditions that are indirectly presented in addition to the presented conditions directly presented in a mathematical problem or that the learner must directly infer, to have the learner learn the patterned hidden conditions in advance, to enable the learner to infer hidden conditions that can be directly inferred from the conditions presented in the problem or inferred during the problem-solving process by integrating artificial intelligence and online learning, and to derive the best learning results by solving the solution to the mathematical problem using the inferred hidden conditions.

[0005] The task that the present invention seeks to solve is not a simple conversation between artificial intelligence and a learner, that is, the artificial intelligence does not answer the questions asked by the learner, but rather, for the ultimate purpose of improving the ability to solve mathematical problems, provides an artificial intelligence-based hidden condition finding mathematics teaching method and system that enables the learner to figure out what the problem is trying to find, figure out what the given conditions are in the problem, set up an equation or proportion that can be set up using the given conditions, and enable the learner to infer the hidden conditions necessary for problem solving through a question-and-answer session with the learner during the problem solving process.

[0006] The problem that the present invention seeks to solve is to provide a training system that finds hidden conditions that enable learners to naturally derive hidden conditions in their heads in response to questions from artificial intelligence, that is, conditions hidden in the presented conditions or hidden conditions that can be inferred during the solution process, and to provide a mathematics teaching method and system that enables learners to achieve the best learning results by solving the most difficult and highest difficulty problems in mathematics through a process in which an artificial intelligence chatbot asks questions and a learner trained in an online learning system answers.

[0007] The problems to be solved by the present invention are not limited to the problems mentioned above, and other problems not mentioned will be clearly understood by those skilled in the art from the description below.

[0008] In order to achieve the above purpose, according to one embodiment of the technical idea of ​​the present invention, a method for teaching mathematics for finding hidden conditions is disclosed, which comprises the steps of: constructing a database management system (DBMS) that manages hidden conditions corresponding to conditions that are indirectly presented or that must be directly inferred by a learner in addition to the presented conditions directly presented in a mathematical problem; teaching hidden conditions to a learner using concept explanation materials created based on the DBMS; and teaching hidden condition finding to a learner using problem explanation materials created based on the DBMS, as a method that can be executed by an online system.

[0009] In addition, the method for teaching mathematics by finding hidden conditions may be configured such that the step of constructing a DBMS further includes the steps of collecting mathematical problems including hidden conditions; classifying the hidden conditions into at least one type according to the characteristics of the hidden conditions; and storing the hidden conditions in the DBMS according to the type-specific classification.

[0010] In addition, the method for teaching mathematics by finding hidden conditions may be configured such that the step of classifying hidden conditions into at least one type includes a step of classifying hidden conditions into a first type in which the hidden conditions are inferred from the form of a word or sentence presented in a mathematical problem into the form of a mathematical expression or formula; a second type in which the hidden conditions are inferred from the geometric properties of a shape or a definition related to a shape; a third type in which the hidden conditions are inferred from the relationship between mathematically defined terms; a fourth type in which the hidden conditions can be inferred into a complex form by systematicity; a fifth type in which the hidden conditions are inferred from the characteristics of numbers and functions defined in arithmetic or algebra; and a sixth type in which the hidden conditions are inferred through the graphs of functions and equations.

[0011] In addition, the method for teaching mathematics by finding hidden conditions may be configured such that the step of constructing a DBMS further includes a step of generating inference clues that induce learners to infer hidden conditions; and a step of linking and storing mathematical problems, hidden conditions extracted from mathematical problems, and inference clues corresponding to hidden conditions.

[0012] In addition, the method for teaching mathematics by finding hidden conditions may be configured such that the step of teaching hidden conditions includes a step of teaching hidden conditions classified by type in the concept learning step of mathematics; and a step of imprinting hidden conditions by type using a hidden condition map composed of keywords expressing the characteristics of hidden conditions as a visualization tool.

[0013] In addition, the hidden condition finding mathematics teaching method may be configured such that the step of teaching the hidden condition further includes a step of testing whether the learner has mastered the hidden condition; and a step of reviewing the learner's deficiencies revealed in the test.

[0014] In addition, the method for teaching mathematics on finding hidden conditions may be configured such that the step of teaching finding hidden conditions includes a step of reminding the learner of what is required in the practice problem through conversation during the step of solving the practice problem in the mathematics curriculum; and a step of reminding the learner of the presented conditions given in the practice problem through conversation.

[0015] In addition, the method for teaching mathematics on finding hidden conditions may be configured so that, when the step of teaching finding hidden conditions is such that the learner infers the hidden conditions included in the practice problem, the step of having the learner write an interpretation note describing the process of inferring the hidden conditions may be further included.

[0016] In addition, the method for teaching mathematics to find hidden conditions may be configured so that the step of teaching to find hidden conditions further includes a step of providing the learner with an inference clue that enables the learner to infer the hidden conditions included in the practice problem when the learner fails to infer the hidden conditions included in the practice problem.

[0017] In addition, the hidden condition finding mathematics teaching method may be configured such that the step of providing inference clues to the learner includes a step of determining the learner's level based on the learner's learning history; and a step of providing inference clues at a level of difficulty according to the learner's knowledge level.

[0018] Additionally, the hidden condition finding mathematics teaching method is characterized by providing inference clues in the form of questions or suggestions through conversation with the learner.

[0019] In order to achieve the above object, according to one embodiment of the technical idea of ​​the present invention, a hidden condition finding mathematics teaching system is disclosed, which is configured to include a database management system (DBMS) for managing hidden conditions corresponding to conditions not directly presented in a mathematical problem in addition to the presented conditions presented in the mathematical problem in an online system for solving mathematical problems; a storage for storing concept explanation materials and problem explanation materials created based on the DBMS; a memory for storing an explanation program for teaching hidden conditions to a learner using audiovisual concept explanation materials and a problem explanation program for teaching finding hidden conditions to a learner using problem explanation materials; and a processor for executing a command included in the explanation program for teaching hidden conditions and a command included in the problem explanation program for teaching finding hidden conditions.

[0020] In addition, the hidden condition finding math teaching system can be configured to control the processor and DBMS to manage inference clues that induce inference of hidden conditions from learners, and to store mathematical problems, hidden conditions extracted from mathematical problems, and inference clues corresponding to hidden conditions by linking them to each other.

[0021] In addition, the hidden condition finding math teaching system may be configured such that, when the learner fails to infer the hidden condition included in a math problem, the memory stores a problem solving program that provides the learner with an inference clue that can induce the learner to infer the hidden condition, and the processor may be configured to execute a command included in the problem solving program that provides the inference clue to the learner.

[0022] According to one embodiment of the present invention, a program for finding and training patterns and hidden conditions in solving mathematical problems using artificial intelligence and online convergence comprises a very special mathematical content configuration for patterning the process of solving mathematical problems required for executing the present invention.

[0023] Usually, the structure of mathematical content (textbook) is composed of concept explanation, basic problem, application problem, and flow of problem with highest difficulty, but the structure of the new mathematical content of the present invention has the same order of concept explanation and basic problem according to the problem structure, but has the order of problem structure organized according to the number and type of the presented conditions given in advance in the problem and the hidden conditions that are not given in advance or are given indirectly even if given in advance. More specifically, it consists of problems that only include the presented condition, problems from which the hidden condition must be inferred, and problems that include the presented condition and from which the hidden condition must be inferred, and it provides methods for composing mathematical problems with hidden conditions (the first hidden condition that can be inferred immediately before solving the problem and the second hidden condition that can be inferred during the problem-solving process), cases where hidden conditions are inferred from the presented condition, hidden conditions related to definitions or concepts, hidden conditions that can be inferred when two or more concepts are combined, hidden conditions related to mathematical definitions and terms, hidden conditions related to the systematicity of mathematics, hidden conditions related to indirect expressions, hidden conditions related to graphs, and hidden conditions that can be inferred during the problem-solving process.

[0024] Meanwhile, in the present invention, the AI ​​differentiates itself from other AIs by categorizing the learner's conversation process into a mathematical reasoning process. Specifically, the AI ​​and the learner engage in a conversation that maintains the following pattern.

[0025] First, the AI ​​helps the learner identify what the problem is trying to achieve. Second, it asks the learner to identify the stated and hidden conditions within the problem. Third, it helps the learner formulate the equation. Fourth, it identifies whether the difficulty in solving the problem is due to the hidden conditions and asks the learner to identify the hidden conditions and solve the problem. This process provides the AI ​​and the learner with these routines.

[0026] Additionally, we provide a system that trains learners to find hidden conditions in problems using artificial intelligence and online, enabling them to solve complete problems.

[0027] Specific details of other embodiments are included in the “Specific Details for Carrying Out the Invention” and the attached “Drawings.”

[0028] The advantages and / or features of the present invention and the methods for achieving them will become clear with reference to the various embodiments described in detail below together with the accompanying drawings.

[0029] However, the present invention is not limited to the configuration of each embodiment disclosed below, but may be implemented in various different forms, and each embodiment disclosed in this specification is provided only to ensure that the disclosure of the present invention is complete and to fully inform a person having ordinary skill in the art to which the present invention pertains of the scope of the present invention, and it should be understood that the present invention is defined only by the scope of each claim of the claims.

[0030] According to the present invention, the process of a learner logically tracing the problem-solving process with artificial intelligence is a process in which a routine is given on how to solve a problem, so that when a problem to be solved is given, a clear direction is given, and through the solving process, the effect of developing not only mathematical problems but also logical thinking can be derived.

[0031] In addition, training to find hidden conditions in problems has been known for a long time, but there has been no mathematical content that specifically mentions what is hidden and how it is hidden in the problem. However, the hidden condition training system can be predicted to be effective in helping numerous learners overcome frustration and solve the most difficult problems.

[0032] The effects that can be obtained by the hidden condition finding mathematics teaching method and the hidden condition finding mathematics teaching system according to the technical idea of ​​the present invention are not limited to the effects mentioned above, and other effects not mentioned can be clearly understood by a person having ordinary skill in the technical field to which the present invention belongs from the description below.

[0033] Figure 1 is a network relationship diagram of a hidden condition finding mathematics teaching system according to one embodiment of the present invention.

[0034] Figure 2 is a block diagram of a hidden condition finding mathematics teaching system according to one embodiment of the present invention.

[0035] Figure 3 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0036] Figure 4 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0037] Figure 5 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0038] Figure 6 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0039] Figure 7 is an example problem that includes a hidden condition of type 1.

[0040] Figure 8 is an example problem that includes a hidden condition of the second type.

[0041] Figure 9 is another example problem that includes a hidden condition of the second type.

[0042] Figure 10 is another example problem that includes a hidden condition of the second type.

[0043] Figure 11 is an example problem that includes a hidden condition of the third type.

[0044] Figure 12 is an example problem that includes a hidden condition of type 5.

[0045] Figure 13 is an example problem including a hidden condition of the sixth type. Figure 14 is a flowchart of a mathematics teaching method for finding hidden conditions according to an embodiment of the present invention.

[0046] Figure 15 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0047] Figure 16 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0048] Figure 17 is an example of an interpretation note according to one embodiment of the present invention.

[0049] Figure 18 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0050] Figure 19 is an example diagram of a hidden condition map according to one embodiment of the present invention.

[0051] Before describing the present invention in detail, it should be understood that the terms or words used in this specification should not be interpreted as being unconditionally limited to their usual or dictionary meanings, and that the inventor of the present invention may appropriately define and use the concepts of various terms in order to explain his or her invention in the best possible manner, and further, that these terms or words should be interpreted as meanings and concepts that are consistent with the technical idea of ​​the present invention.

[0052] That is, it should be noted that the terms used in this specification are only used to describe preferred embodiments of the present invention, and are not intended to specifically limit the contents of the present invention, and that these terms are defined in consideration of various possibilities of the present invention.

[0053] Additionally, it should be noted that in this specification, singular expressions may include plural expressions unless the context clearly indicates a different meaning, and similarly, even if expressed in plural, may include a singular meaning.

[0054] Throughout this specification, whenever a component is described as "including" another component, it may mean that the component may further include any other component, rather than excluding any other component, unless specifically stated otherwise.

[0055] Furthermore, when a component is described as being "inside or connected to" another component, it should be understood that the component may be installed in direct connection with or in contact with the other component, may be installed spaced apart from the other component by a certain distance, and if installed spaced apart from the other component by a certain distance, there may be a third component or means for fixing or connecting the component to the other component, and the description of this third component or means may be omitted.

[0056] On the other hand, if a component is described as being "directly connected" or "directly connected" to another component, it should be understood that no third component or means exists.

[0057] Likewise, other expressions that describe the relationship between components, such as "between" and "directly between", or "adjacent to" and "directly adjacent to", should be interpreted as having the same meaning.

[0058] Additionally, it should be noted that the terms “one side,” “the other side,” “one side,” “the other side,” “first,” “second,” etc. in this specification, if used, are used to clearly distinguish one component from another component, and that the meaning of the component is not limited by such terms.

[0059] In addition, terms related to position, such as “upper,” “lower,” “left,” and “right,” etc., in this specification, if used, should be understood to indicate relative positions of the corresponding components in the corresponding drawings, and unless absolute positions are specified for these positions, these position-related terms should not be understood to refer to absolute positions.

[0060] In addition, in this specification, when specifying the drawing numbers for each component of each drawing, the same component has the same drawing number even if the component is shown in a different drawing, that is, the same reference number indicates the same component throughout the specification.

[0061] In the drawings attached to this specification, the size, position, connection relationship, etc. of each component constituting the present invention may be described with some exaggeration, reduction, or omission in order to sufficiently clearly convey the idea of ​​the present invention or for convenience of explanation, and therefore the proportions or scales may not be strict.

[0062] In addition, in the following description of the present invention, a detailed description of a configuration that is judged to unnecessarily obscure the gist of the present invention, for example, a known technology including a prior art, may be omitted.

[0063] Hereinafter, embodiments of the present invention will be described in detail with reference to the relevant drawings.

[0064] Figure 1 is a network relationship diagram of a hidden condition finding mathematics teaching system according to one embodiment of the present invention.

[0065] Referring to Fig. 1, the hidden condition finding math learning system (100) can be connected to a learner's terminal (200) through a network (500). That is, the hidden condition finding math learning system (100) can provide a hidden condition finding math learning service to the learner's terminal (220) online.

[0066] The hidden condition finding mathematics teaching system (100) can provide a teaching service of hidden conditions classified by type in the concept learning stage of mathematics education, and a teaching service of finding hidden conditions by type in the problem solving process of mathematics education to learners through a learner terminal (200).

[0067] Hidden conditions refer to conditions that are presented indirectly in addition to the conditions directly presented in a math problem (121), or conditions that the learner, i.e., the problem solver, must directly infer. Finding hidden conditions refers to the process of finding these hidden conditions, in which the learner derives the hidden conditions through their own efforts or by using inference clues that can lead to inference of the hidden conditions. Artificial intelligence and online teaching methods can be utilized in the process of preparing information or data regarding hidden conditions and inference clues in advance, and in the process of providing information and data regarding hidden conditions and inference clues to the learner.

[0068] Information or data consisting of hidden conditions will be referred to as hidden condition DB (111), and information or data consisting of inference clues will be referred to as inference clue DB (112). Materials provided to learners in the concept learning stage will be referred to as concept explanation materials (122), and materials provided to learners in the problem solving process will be referred to as problem solving materials (123). In addition, a program that teaches learners hidden conditions based on concept explanation materials (122) will be referred to as concept explanation program (131), and a program that teaches learners how to find hidden conditions based on problem solving materials (123) will be referred to as problem solving program (132).

[0069] The hidden condition finding math teaching system (100) may be composed of one device as depicted in Fig. 1, or may be composed of multiple devices for each service provided or each function included in the service.

[0070] The learner terminal (200) may be configured to include a desktop-type wired terminal (210) and a tablet or smartphone-type wireless terminal (229). The learner may access the hidden condition finding math teaching system (100) online using a teaching-only program, also known as an application, or a web browser installed on the learner terminal (200) and receive the hidden condition teaching service and the hidden condition finding teaching service provided by the hidden condition finding math teaching system (100).

[0071] The network (500) may be any suitable communication network, including wired and wireless networks, such as serial communications, local area networks (LANs), wide area networks (WANs), the Internet, intranets, and extranets, and mobile networks, such as cellular, 3G, LTE, WiFi networks, ad hoc networks, and combinations thereof.

[0072] The network (500) may include a connection of network elements such as hubs, bridges, routers, switches, and gateways. The network (500) may include one or more connected networks, such as a multi-network environment, including a public network such as the Internet and a private network such as a secure corporate private network. Access to the network (500) may be provided via one or more wired or wireless access networks.

[0073] Figure 2 is a block diagram of a hidden condition finding mathematics teaching system according to one embodiment of the present invention.

[0074] Referring to FIG. 2, a hidden condition finding mathematics teaching system (100) according to an embodiment of the present invention is an online system connected through a network (500), and may be configured to include a database management system (DBMS) (110), storage (120), memory (130), and processor (140).

[0075] The DBMS (110) has the function of managing hidden conditions and inference clues. Hidden conditions can be stored and managed within the DBMS (110) in the form of a hidden condition DB (111), and inference clues can be stored and managed within the DBMS (110) in the form of an inference clue DB (112).

[0076] Storage (120) has a function of storing concept explanation data (122) and problem explanation data (123) created based on DBMS (110). Concept explanation data (122) and problem explanation data (123) may include audiovisual data such as video and voice.

[0077] The memory (130) has a function of storing a concept explanation program (131) and a problem solving program (132). The concept explanation program (131) is a program that teaches learners about hidden conditions using audiovisual concept explanation materials (122). The problem solving program (132) is a program that teaches learners how to find hidden conditions using problem solving materials (123). The concept explanation program (131) and the problem solving program (132) may include programs that can converse with learners through text and language, such as artificial intelligence agents and chatbots (150).

[0078] The processor (140) has a function of executing a command included in the concept explanation program (131) and teaching hidden conditions and a command included in the problem solving program (132) and teaching finding hidden conditions.

[0079] The processor (140) can control the DBMS (110) to manage inference clues that induce inference of hidden conditions from learners, and to store the mathematical problem (121), the hidden conditions extracted from the mathematical problem (121), and the inference clues corresponding to the hidden conditions by linking them to each other. Accordingly, when explaining the mathematical problem (121) for each unit of the mathematics curriculum through the problem-solving program (132), the hidden conditions extracted from the mathematical problem (121) and the inference clues corresponding to the hidden conditions can be referenced together.

[0080] That is, the memory (130) can store a problem-solving program (132) that provides the learner with an inference clue that can induce the learner to infer the hidden condition in the mathematical problem (121) when the learner fails to infer the hidden condition. In addition, the processor (140) can execute a command included in the problem-solving program (132) that provides the learner with an inference clue.

[0081] A hidden condition finding mathematics teaching system (100) that can be implemented using a computer can be configured to include a power supply and a communication device as other components.

[0082] Figure 3 is a block diagram of a chatbot according to one embodiment of the present invention.

[0083] Referring to Figure 3, a block diagram of a chatbot (150) included in a problem-solving program (132) is depicted. The chatbot (150) has the function of teaching hidden conditions to learners through conversation during the problem-solving process. The chatbot (150) may be configured to include a user interface (151) that accepts user input, and a chatbot engine (152) that recognizes the learner's voice or text and synthesizes sentences necessary for the conversation.

[0084] The chatbot engine (152) may be configured to include a natural language understanding (NLU) (153) that understands the learner's intention and context information through the learner's voice and text, a response generator (154) that outputs an answer to the learner, a conversation manager (155) that manages a conversation with the learner, an action execution unit (156) that executes an action on the collected information, and an information collector (157) that collects information necessary for the conversation. The information collector (157) may collect information necessary for composing a voice or text to be output to the learner from web sources on the Internet and from a mathematical problem (121), concept explanation data (122), problem solution data (123), hidden condition DB (111), and inference clue DB (112) according to an embodiment of the present invention.

[0085] Figure 4 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0086] Referring to FIG. 4, a hidden condition finding mathematics teaching method (S100) according to an embodiment of the present invention can be configured to include building a DBMS (S100), teaching a hidden condition to a learner (S120), and teaching a hidden condition finding to a learner (S130).

[0087] The hidden condition finding mathematics teaching method (S100) according to one embodiment of the present invention can be executed online by the hidden condition finding mathematics teaching system (100).

[0088] The hidden condition finding math teaching system (100) can build a database management system (DBMS) (110) that manages hidden conditions corresponding to conditions not directly presented in the math problem (121) in addition to the presented conditions in the math problem (121) in solving math problems.

[0089] The hidden condition finding math teaching system (100) can teach hidden conditions to learners using concept explanation materials (122) created based on DBMS (110).

[0090] The hidden condition finding math teaching system (100) can teach learners how to find hidden conditions using problem-solving materials (123) created based on DBMS (110).

[0091] Figure 5 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0092] Referring to FIG. 5, the hidden condition finding math teaching system (100) collects math problems (121) containing hidden conditions in the construction of a DBMS (110), classifies the hidden conditions into at least one type according to the characteristics of the hidden conditions, and stores hidden condition classification information according to the classification in the DBMS (110).

[0093] Figure 6 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0094] Referring to Figure 6, the hidden condition finding math teaching system (100) can classify hidden conditions into at least one type, for example, Type 1 to Type 6. Types 1 to 6 will be described with example problems.

[0095] Referring again to Figure 6, the first type is a type in which the hidden condition is inferred from the form of a word or sentence presented in a mathematical problem (121) into the form of a mathematical expression or formula.

[0096] Figure 7 is an example problem that includes a hidden condition of type 1.

[0097] Referring to Figure 7, the condition presented in Example Problem 1 is that the intersection of the linear equations lies on the y-axis. The condition presented in Example Problem 2 is that one line intersects another line perpendicularly at a single point.

[0098] In Example Problem 1, the condition that the intersection point is on the y-axis is expressed as a sentence, but it contains a hidden condition that the point (o, t) satisfies both equations of the two lines. And in Example Problem 2, the condition that the two lines meet perpendicularly is expressed as a sentence, but it contains a hidden condition that the slopes of the two lines (y+2) = a(x-1) + b are the slopes a of the lines. The slope of the straight line is the product of -1 / 2, i.e. It contains a hidden condition called . Example problem 2 also contains the same hidden condition as the first problem.

[0099] In cases where sentences, not equations, are given, as in Example Problems 1 and 2, if the sentences are expressed as equations, the given sentences can be converted into hidden conditions. In Example Problem 1, 'what the intersection of two lines expressed as linear equations means' and 'what the point on the y-axis means' can be used as inference clues. In Example Problem 2, 'what the intersection of two lines expressed as linear equations means' and 'what the point on the y-axis means' can be used as inference clues, and 'the mathematical meaning of the product of the slopes of two lines' can be additionally used as an inference clue.

[0100] Referring back to Figure 6, the second type is one in which the hidden conditions are inferred from the geometric properties of the shape or from definitions related to the shape.

[0101] Figure 8 is an example problem that includes a hidden condition of the second type.

[0102] Referring to Figure 8, Example Problem 3 presents the angles of one vertex of two triangles out of three triangles within the entire triangle, and another presented condition is that the center O of the triangle is the circumcenter.

[0103] To solve Example Problem 3, you must know the definition and properties of the circumcenter, and then infer the hidden condition based on this.

[0104] The circumcenter is the center of the circumcircle of a triangle. The perpendicular bisectors of the triangle's three sides intersect at a single point, the circumcenter, the center of the circumcircle. The property of the circumcenter is that the distances from the circumcenter to each of the three vertices are all equal.

[0105] The concepts that serve as foundational knowledge for problem solving must be understood and memorized. In Example Problem 3, the property of the circumcenter—that is, the distances from the circumcenter to all three vertices are equal—can be used to infer the hidden condition that all three triangles within the triangle are isosceles.

[0106] If the three triangles are isosceles triangles, the size of the base angles of each triangle is the same, so the sum of the base angles of the three triangles is 180 degrees, which can act as another hidden condition.

[0107] In Example Problem 3, the fact that the three triangles are isosceles must ultimately be deduced. To find this hidden condition, a thorough understanding of the properties derived from the definition of circumcenter is a prerequisite.

[0108] The condition that the center of a triangle is the circumcenter becomes the presented condition, and based on the presented condition, the property of the circumcenter that 'the distances from the circumcenter to the three vertices are equal' must be evoked, and further, the hidden condition that the three triangles, which are the conditions for the solution, are isosceles triangles and the base angles of the isosceles triangles are equal must be inferred.

[0109] In example problem 3, 'the three triangles are isosceles triangles', therefore 'the base angles of the three triangles are equal' can be used as a hidden condition.

[0110] The first task in finding the hidden condition is to find the clue condition and the term circumcenter given by it.

[0111] Second, when a circumcenter is given, we must recall all the things associated with the definition. In this case, we must recall the property of the circumcenter. That is, we must derive that the distances to all three vertices are equal.

[0112] Here, depending on the learner's ability, some students may be able to immediately think that the three triangles are isosceles triangles and thus have equal base angles, but there are cases where this is not the case. So, if we organize the level of recognition at each stage according to the learner's ability,

[0113] There may be cases where the property of the circumcenter is associated with the circumcenter and the property of the circumcenter is recognized as a direct condition, cases where only the fact that the distances to the three vertices are equal is recognized from the property of the circumcenter and the three triangles are not associated with isosceles triangles, and cases where the three triangles are associated with isosceles triangles but the fact that the base angles are equal is not associated.

[0114] In Example Problem 3, the clue condition is the definition of circumcenter, and the solution condition is clearly the property of circumcenter.

[0115] However, if we look more closely, the stages of recognition are divided according to the learner's ability, and there are more stages leading to the solution conditions.

[0116] If the learner's ability is very lacking, only the properties of the circumcenter are recognized in the definition of the circumcenter.

[0117] Recognize that three triangles are isosceles triangles from the properties of the circumcenter

[0118] Since the three triangles are isosceles triangles, many steps must be taken to recognize that the base angles are equal.

[0119] An interactive intelligent agent (artificial intelligence) included in a hidden condition finding mathematics teaching system (100) according to one embodiment of the present invention not only enables learners who are unable to reason to reason step by step by providing them with reasoning clues consisting of questions and answers, but also enables learners who are capable of reasoning to reason by reducing the number of reasoning steps through multiple stages of reasoning.

[0120] That is, when a learner is in a dilemma because he or she cannot infer the hidden condition from the condition presented during the problem-solving process, the hidden condition finding math teaching system (100) has a function that enables the learner to infer the hidden condition by leading a conversation with the learner through artificial intelligence and presenting an appropriate level of inference clues that enable the learner to derive the hidden condition according to the learner's level of knowledge, rather than directly and spoon-feedingly informing the learner of the hidden condition, thereby enabling the learner to infer the hidden condition on his or her own. This is because directly and spoon-feedingly informing the learner of the hidden condition does not help at all in improving the learner's inference ability in training to infer the hidden condition.

[0121] Figure 9 is another example problem that includes a hidden condition of the second type.

[0122] Referring to 9, Example Problem 2-2 requires a+b. That is, it is the sum of a and b included in the area of ​​triangle PHQ. And the given conditions are that the size of the central angle of sector OAB is 90° (Condition #1), ∠QOA is 30° (Condition #2), ∠QHA is 90° (Condition #3), and the area of ​​PHQ = (Condition #4)

[0123] To find the area of ​​triangle PHQ based on condition #4, we need to find the length of the base and height of triangle PHQ, and before that, we need to determine the base whose height we can find. Here, to infer the hidden condition, we need to 'construct the straight line PA', and based on the properties of the circle drawn in the semicircle, the hidden condition ∠OPA can be inferred to be 90°.

[0124] The lengths of lines OP and PQ are obtained through trigonometric ratios, and when line PQ is used as the base, the height becomes line PA. Likewise, the length of line PA can also be obtained through trigonometric ratios.

[0125] In Example Problem 2-2, the hidden conditions that can be inferred are, in order, ∠OPA formed by the straight line PA is 90°, the length of the base of the triangle PHQ = PQ, and the height of the triangle PHQ = PA. And, in order to infer each hidden condition, 'a triangle inscribed in a semicircle', 'characteristics of the vertex angles of a triangle inscribed in a semicircle', 'finding the length of the straight line PQ using trigonometric ratios', and 'which line segment to set as the base and which line segment to set as the height in triangle PHQ' can correspond to inference clues. Even if the learner cannot directly infer the hidden condition, the learner can infer the hidden condition based on the inference clues through a question-and-answer session with the hidden condition finding math learning system (100). And, depending on the learner's knowledge level, the hidden conditions and inference clues can be provided to the learner in various expression methods. For example, in order to guide a learner to construct a straight line PA, the hidden condition finding math teaching system (100) may suggest to the learner 'to use basic triangles with angles of 30 degrees, 60 degrees, and 90 degrees.' In addition, the hidden condition finding math teaching system (100) may suggest to the learner 'to think about why the length of the straight line OA is 2.'

[0126] Figure 10 is another example problem that includes a hidden condition of the second type.

[0127] Referring to Fig. 10, the required value in Example Problem 2-3 is 9k. That is, since it is not simply k but 9k, the hidden condition finding math teaching system (100) can advise the learner that the required value is not simply k but 9k, and that the area of ​​triangle EGF can be expressed as a fraction with a denominator of 9. In addition, the presented conditions are trapezoid ABCD which is AD / BC, the intersection of two diagonals = E, the intersection of two line segments AC and BF = G, AD = 4, and EF = 3.

[0128] In cases where hidden conditions are not expressed in formulas, such as in Example Problem 2-3, the hidden conditions and the inference clues needed to infer the hidden conditions can be treated indiscriminately.

[0129] That is, in Example Problem 2-3, considering that the ratio k of the area of ​​trapezoid ABCD and the area of ​​triangle EGF is presented as a hidden condition or inference clue, 'assuming the area of ​​triangle EGF to be any a, and expressing the area of ​​trapezoid ABCD in terms of a' can be discussed. In addition, 'what does it mean that the lengths of the straight lines AD = 4 and EF = 3', 'how can the ratio of the areas of triangles be expressed when the ratio of the lengths is given', and 'information about the wear ratio of triangles' can be discussed as hidden conditions and inference clues.

[0130] Referring back to Figure 6, the third type is a type inferred from the association between definitions and conditions within a concept.

[0131] Figure 11 is an example problem that includes a hidden condition of the third type.

[0132] Referring to Figure 11, Example Problem 4 uses the formulas for the median and mean to determine a, b, and c, and then calculate the variance. While the variance is the correct answer, calculating the variance requires first calculating the variance, which can then be calculated using the mean. In other words, the following relationship must be derived.

[0133]

[0134] Therefore, in the example problem above, the deviation can be seen as a hidden condition for problem solving. Median, mean, deviation, and variance are taught within the same unit, and these terms are deeply interrelated, so they can be used as hidden conditions that provide clues to problem solving. Examples of inferential clues include "what must be calculated before calculating variance," "the formula for variance," "factors included in variance," and "what is the basis for calculating deviation?"

[0135] Referring back to Figure 6, the fourth type is a type inferred from a basic concept that can be expressed in a complex manner by systematicity of hidden conditions.

[0136] Terms related to slope appear frequently in elementary, middle, and high school mathematics courses. Therefore, if the slope is a given condition, then by systematicity, the slope of the triangle is , is related to orthogonal equations, the condition of coincidence of tangent lines, and the average rate of change of differentiation. Therefore, if the slope is the given condition, the triangle , orthogonal equations, tangent line coincidence conditions, and the average rate of change of differentiation can be utilized as hidden conditions. In this way, when a single mathematical term contains complex concepts due to systematicity and is called by several other terms, these other terms can be utilized as hidden conditions.

[0137] Referring back to Figure 6, the fifth type is a type in which hidden conditions are inferred from the characteristics of numbers and functions defined in arithmetic or algebra.

[0138] Figure 12 is an example problem that includes a hidden condition of type 5.

[0139] Referring to Figure 12, Example Problem 4-1 (1) asks about the coefficients of a quadratic equation. The given conditions are a quadratic equation and one root. The root of the given condition is an irrational root. In this case, the 'conjugate root' of the quadratic equation with an irrational root can be used as a hidden condition. In this case, can be used for other purposes.

[0140] Similarly, Example Problem 4-1 (2) asks about the coefficients of a quadratic equation. The given condition is a quadratic equation and a single root. The root of the given condition is a complex root. In this case, the "conjugate root" of the quadratic equation with a complex root can be used as the hidden condition. In this case, 1+i can be used as the other root.

[0141] In Example Problem 4-1, the formula for the sum and difference of roots can be additionally used. Therefore, in two example problems, the formulas for conjugate roots and the sum and difference of roots of quadratic equations can be utilized as hidden conditions. In this case, inference clues such as "the relationship between the coefficients of the sum and product of the roots of a quadratic equation" and "the condition that irrational and imaginary numbers do not appear in the coefficients of a quadratic equation" can be mentioned. The term "conjugate root" may be unfamiliar to learners with low knowledge levels, so it can be used selectively depending on the level of knowledge.

[0142] Referring back to Figure 6, the sixth type is one in which hidden conditions are inferred through the graph of the function.

[0143] Figure 13 is an example problem that includes a hidden condition of type 6.

[0144] Referring to Figure 13, the graph of a linear function intersecting the graphs of two exponential functions is displayed. The equation for the linear function, which is a straight line, two equations for the exponential function, and an additional equation for the length of the straight line can constitute the presented conditions. In order to solve the example problem, the coordinates of P and Q must be determined, and the determined coordinates must be substituted into the function equation to ultimately obtain the value of k. Specifically, if the coordinates of P are determined as (a, b), the coordinates of Q can be determined as (a+1, b+2) by the hidden condition, the Pythagorean theorem. That is, in this example problem, the coordinates of P (a, b), the Pythagorean theorem, and the coordinates of Q (a+1, b+2) can each correspond to the hidden conditions.

[0145] Figure 14 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0146] Referring to FIG. 14, the hidden condition finding math teaching system (100) can, when constructing a DBMS, generate inference clues to induce inference of hidden conditions from learners (S114) and store a math problem (121), a hidden condition extracted from the math problem (121), and inference clues corresponding to the hidden conditions by linking them to each other. That is, the math problem (121), the hidden condition DB (111) extracted from the math problem (121), and the inference clue DB (112) to be used for inferring the hidden condition can be stored by linking them to each other. Therefore, the hidden conditions and inference clues can be referenced and utilized in the problem solving process for the math problem (121).

[0147] Figure 15 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0148] Referring to Fig. 15, the hidden condition finding mathematics teaching system (100) teaches hidden conditions classified by type in the concept learning stage of mathematics when teaching hidden conditions (S121), and can imprint hidden conditions by type using a hidden condition map composed of keywords expressing the characteristics of hidden conditions as a visualization tool (S122).

[0149] Referring back to Figure 15, the hidden condition discovery math teaching system (100) tests whether the learner has mastered the hidden conditions while teaching them (S123) and can review any deficiencies the learner may have identified in the test (S124). Whether the learner has mastered the hidden conditions can be determined through a simple test, such as a parenthesis quiz. Furthermore, the hidden condition map described in Figure 18 can be utilized to address any deficiencies identified as a result of not mastering the hidden conditions.

[0150] Figure 16 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0151] Referring to Figure 16, the Hidden Conditions-Finding Mathematical Learning System (100) can, when explaining a math practice problem, remind learners of the requirements of the problem through dialogue (S131). As explained in the example problem, the final required answer to the problem can be transformed into a different form depending on the form of the solution obtained through problem solving. Therefore, it is necessary to cultivate in learners the habit of checking what the problem requires before beginning problem solving.

[0152] Additionally, the Hidden Condition Finding Mathematical Learning System (100) can remind learners of the given conditions in practice problems through dialogue (S132). The given conditions serve as clues for finding the hidden conditions. Alternatively, the hidden conditions can be inferred by simply modifying the given conditions expressed in words or sentences.

[0153] In addition, when teaching hidden condition finding, the math teaching system (100) can have the learner write an interpretation note expressing the inference process of the hidden condition when the learner infers the hidden condition included in the math problem (121). That is, even if the learner correctly infers the hidden condition, the math teaching system (100) can have the learner write an interpretation note expressing the inference process in order to check whether the inference process is correct.

[0154] Figure 17 is an example of an interpretation note according to one embodiment of the present invention.

[0155] Referring to Figure 17, an interpretation note written by a learner, such as a student, is depicted for Example Problem 2-2 depicted in Figure 9. If the student succeeds in inferring the hidden condition, he or she can express his or her reasoning process in the interpretation note.

[0156] Even if a student fails to infer the hidden condition in the first problem-solving, the student can describe the process of finding the hidden condition in the interpretation note based on the inference clues provided by the hidden condition finding math teaching system (100) according to the student's knowledge level during the problem-solving process. The interpretation note can be repeatedly written while adjusting the difficulty of the inference clues provided to the student. For example, if the student is unable to infer the hidden condition using the previously provided inference clues, the student is provided with an inference clue that is easier or more directly expressed than the existing inference clues, and the student can write an interpretation note based on the new inference clue.

[0157] In addition, the hidden condition finding mathematics teaching system (100) can, when teaching hidden condition finding, provide the learner with an inference clue that can induce the learner to infer the hidden condition if the learner fails to infer the hidden condition included in the mathematical problem (121). The inference clue corresponds to a hint that avoids directly informing the learner of the hidden condition if the learner fails to infer the hidden condition and allows the learner to infer the hidden condition on his / her own. In other words, the hidden condition can be expressed indirectly through the inference clue. The inference clue can be provided to the learner in the form of a question or a suggestion that requires a response.

[0158] Figure 18 is a flowchart of a hidden condition finding mathematics teaching method according to one embodiment of the present invention.

[0159] Referring to FIG. 18, the hidden condition finding math teaching system (100) can, when providing inference clues to learners, determine the learner's level based on the learner's learning history (S134) and provide inference clues at a level of difficulty corresponding to the learner's level (S135). In this case, the hidden condition finding math teaching system (100) can provide inference clues to learners in the form of questions or suggestions. Depending on the learner's knowledge level, inference clues may be useless, and the directness of inference clues may be too strong, reducing the learning effect. Therefore, inference clues can be provided to learners at an appropriate level of difficulty depending on the learner's knowledge level. As explained in the example problems, difficult terms included in inference clues can be changed into easier concepts depending on the learner's knowledge level and provided to the learner.

[0160] Figure 19 is an example diagram of a hidden condition map according to one embodiment of the present invention.

[0161] Referring to Figure 19, a hidden condition map, which serves as a review material for hidden conditions that can be used both in the concept explanation process and the problem-solving process, is depicted. The hidden condition map contains the keywords that constitute the hidden conditions, and each keyword is linked to another keyword based on their relevance. Furthermore, each keyword can be arranged in different sizes according to the tree structure. Although omitted due to space constraints, a brief explanation can also be included in addition to the keywords. Using a visualization tool such as the hidden condition map can effectively imprint the tree structure of the hidden conditions deeply in the learner's mind.

[0162] Referring to Figures 1 to 19, the entire content, i.e., mathematical problems (121), are collected, and the collected problems are stored by analyzable conditions. By condition, it can be said that the classification process is for concepts, terms, formulas, etc. that serve as given conditions when analyzing the problem. In addition, to infer hidden conditions, the infrastructure of the content can be built by classifying and storing by condition, such as terms and their changeable terms, systematic units and concepts, the relationship between definitions and properties, the relationship between concepts and definitions or properties, various types, and conditions that must be read from graphs or figures.

[0163] By analyzing this data, we are attempting to create new compositions of mathematical content.

[0164] When learning mathematics, most learning progresses by learning explanations of concepts and formulas, and solving basic problems, applied problems, and difficult problems. However, the present invention maximizes the completion of the problem-solving process by logically combining the given and hidden conditions in the problem. The mathematical content is structured to include learning explanations of concepts, formulas, etc., learning basic problems and types, and the order of problem composition can be provided according to the number of given and hidden conditions in the problem, and also according to the type of hidden conditions.

[0165] If there is only one given condition in a problem, it can consist of either a given condition or a hidden condition.

[0166] In cases where there is only one given condition, most problems can be solved simply by knowing the concept or formula, and in cases where there is only one hidden condition, there are indirect expressions of terms in the problem, or things that allow you to infer the hidden condition from the given condition.

[0167] According to one embodiment of the present invention, the process of a learner logically tracing the problem-solving process with artificial intelligence is a process in which a routine is given on how to solve a problem, so that when a problem to be solved is given, a clear direction is given, and through the solving process, the effect of equipping the learner with not only mathematical problems but also logical thinking can be derived.

[0168] In addition, training to find hidden conditions in problems has been known for a long time, but there has been no mathematical content that specifically mentions what is hidden and how it is hidden in the problem. However, the hidden condition training system can be predicted to be effective in helping numerous learners overcome frustration and solve the most difficult problems.

[0169] Above, although some examples have been given and various preferred embodiments of the present invention have been described, the description of the various embodiments described in the “Specific Details for Carrying Out the Invention” section is merely exemplary, and those skilled in the art to which the present invention pertains will readily understand that they can carry out various modifications of the present invention or carry out equivalent implementations of the present invention based on the above description.

[0170] In addition, since the present invention can be implemented in various other forms, the present invention is not limited by the above description, and the above description is provided only to make the disclosure of the present invention complete and to fully inform a person having ordinary skill in the art to which the present invention belongs of the scope of the present invention, and it should be understood that the present invention is defined only by each claim of the claims.

[0171] The present invention can be used in the field of developing a mathematics teaching method and a mathematics teaching system.

Claims

1. A method that can be executed by an online system, A step of building a database management system (DBMS) that manages hidden conditions that are indirectly presented or that learners must directly infer in addition to the conditions directly presented in a mathematical problem; A step of teaching hidden conditions to learners using concept explanation materials created based on the above DBMS; and A method for teaching mathematics on finding hidden conditions, comprising a step of teaching the learner how to find hidden conditions using problem-solving materials created based on the above DBMS.

2. In claim 1, the step of constructing the DBMS comprises: A step of collecting mathematical problems containing the above hidden conditions; A step of classifying the hidden conditions into at least one type according to the characteristics of the hidden conditions; and A method for teaching mathematics by finding hidden conditions, further comprising a step of storing the above-mentioned hidden conditions in the DBMS according to type classification.

3. In claim 2, The step of classifying the above hidden conditions into at least one type is: Type 1, where the hidden condition is inferred from the form of a word or sentence presented in the above mathematical problem to the form of a mathematical expression or formula; A second type in which hidden conditions are inferred from geometric properties of figures or definitions related to figures; A third type in which hidden conditions are inferred from the relationships between mathematically defined terms; Type 4, where hidden conditions can be inferred in a complex form through systematicity; Type 5, in which hidden conditions are inferred from the characteristics of numbers and functions defined in arithmetic or algebra; and A method for teaching mathematics by finding hidden conditions, comprising a step of classifying the hidden conditions into the sixth type in which the hidden conditions are inferred through graphs of functions and equations.

4. In claim 2, the step of constructing the DBMS comprises: A step of generating an inference clue to induce inference of the hidden condition from the learner; and It is configured to further include a step of linking and storing the above mathematical problem, the hidden condition extracted from the above mathematical problem, and the inference clue corresponding to the hidden condition. Hidden Conditions Math Teaching Method.

5. In claim 2, the step of teaching the hidden condition comprises: A step of teaching the above hidden conditions classified by type in the concept learning stage of mathematics education; and It is configured to include a step of imprinting hidden conditions by type using a hidden condition map composed of keywords expressing the characteristics of the hidden conditions as a visualization tool. Hidden Conditions Math Teaching Method.

6. In claim 5, the step of teaching the hidden condition comprises: A step of testing whether the learner is familiar with the hidden conditions; and A method for teaching mathematics by finding hidden conditions, which further includes a step of reviewing the learner's deficiencies revealed in the above test.

7. In claim 2, the step of teaching the hidden condition search comprises: A step in which learners are reminded of what is required in the practice problem through conversation during the solving stage of the practice problem in mathematics; and A method of teaching mathematics by finding hidden conditions, comprising a step of having the learner recall the given conditions in the above-mentioned practice problem through conversation.

8. In claim 7, the step of teaching the hidden condition search comprises: A method for teaching mathematics by finding hidden conditions, further comprising a step of having the learner write an interpretation note describing the process of inferring the hidden condition when the learner infers the hidden condition included in the practice problem.

9. In claim 7, the step of teaching the hidden condition search comprises: A method for teaching mathematics by finding hidden conditions, further comprising a step of providing the learner with an inference clue that enables the learner to infer the hidden condition included in the practice problem, if the learner fails to infer the hidden condition included in the practice problem.

10. As an online system, In solving mathematical problems, a database management system (DBMS) that manages hidden conditions that are not directly presented in the mathematical problem in addition to the presented conditions in the mathematical problem; Storage for storing concept explanation materials and problem solving materials written based on the above DBMS; A memory storing an explanation program that teaches the learner about the hidden conditions using the above-mentioned audiovisual concept explanation materials, and a problem-solving program that teaches the learner how to find the hidden conditions using the above-mentioned problem-solving materials; and A hidden condition finding mathematics teaching system, comprising a processor configured to include a command included in the above description program and teaching the hidden condition, and a command included in the above problem solving program and teaching the hidden condition finding.

11. In claim 10, the processor, The DBMS is configured to manage inference clues that induce inference of the hidden condition from the learner, and to control the linking and storing of the mathematical problem, the hidden condition extracted from the mathematical problem, and the inference clues corresponding to the hidden condition. Hidden Condition Finding Math Learning System.

12. In claim 10, the memory, If the learner fails to infer the hidden condition included in the math problem, a problem-solving program is stored that provides the learner with an inference clue that can induce the learner to infer the hidden condition. The above processor, A hidden condition finding mathematics teaching system, which is included in the above problem solving program and is configured to execute a command that provides the above inference clue to the learner.

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