Double triangle diagram learning support system, method, and program

Abstract

To support learning for creating a double triangle diagram.SOLUTION: A double triangle diagram learning support system 100 for supporting a learner in learning to create a double triangle diagram on a UI screen, the double triangle diagram including two abundances, two relational amounts that are reciprocals of each other and represent a relationship between the abundances, and a multiplier / divider that holds between the two abundances and any one of the relational amounts, the double triangle diagram learning support system 100 including a task presentation unit 42 that presents, on a UI screen 50, a double triangle frame in which two triangles are symmetrically arranged, the two triangles schematically representing a relationship between a movable component and a triplet, the movable component and the triplet respectively representing four amounts of the two abundances and the two relational amounts included in a correct double triangle diagram 32, and a component operation determination unit 62 that determines, on the UI screen 50, that the movable component has been arranged at a position at which the movable component can be arranged in the double triangle frame or has been removed from the position; And an evaluation part 46 for evaluating correctness / incorrectness of the double triangular diagram created by operating the movable component by the learner.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a system for supporting a learner's learning, and more particularly to a system, method, and program for supporting learning using a double triangular diagram. [Background technology]

[0002] Arithmetic word problems that can be solved with a single binary operation can be explained by the ternary proposition model. The ternary proposition model is composed of three quantities: two existential quantities that represent the existence of a certain quantity, and one relational quantity that relates these existential quantities; the existential quantities are independent of the operation, and the relational quantity is a quantity that determines the operation. The inventors of the present invention have previously developed a problem-making learning support system that uses the ternary proposition model as a domain model for arithmetic word problems and allows learners to create arithmetic word problems (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2015-138253 Summary of the Invention [Problem to be solved by the invention]

[0004] If multiplication or division exists in an arithmetic situation, then the relationship between two multiplications and four divisions necessarily exists, encompassing equal division, inclusive division, and multiplication and division using operands smaller than 1. Until now, attempts have been made to teach mathematical relationships between three quantities through tasks that require students to create arithmetic word problems based on the three-quantity proposition model. However, by directly learning the three-quantity proposition model itself, it is expected that students will be able to comprehensively learn multiplication and division in the same arithmetic situation. Therefore, the objective of this invention is to support learning to create double triangular diagrams based on the three-quantity proposition model. [Means for solving the problem]

[0005] According to one aspect of the present invention, there is provided a system for supporting a learner's learning to create a double triangular diagram on a UI screen, which is composed of two quantities, two related quantities that are reciprocals of each other and represent the relationship between these quantities, and a multiplication or division that holds between the two quantities and any one of the related quantities. The double triangular diagram learning support system and corresponding method and program are provided, and include: a task presentation unit that presents on the UI screen a double triangular frame in which movable parts representing the two quantities and the four quantities and multiplication or division of the two related quantities contained in the correct double triangular diagram are arranged symmetrically, and two triangles that illustrate the relationship between the three quantities; a part operation determination unit that determines on the UI screen whether the movable parts have been placed in a position in the double triangular frame where the movable parts can be placed, or whether the movable parts have been removed from the position; and an evaluation unit that evaluates the accuracy of the double triangular diagram created by the learner by operating the movable parts. [Effects of the Invention]

[0006] According to the present invention, it is possible to support a learner in learning to create a double triangular diagram. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 is a schematic diagram of a double triangular diagram according to some examples. [Figure 2] 1 is a block diagram of a double triangular diagram learning support system according to an embodiment of the present invention; [Figure 3] 1 is a flowchart of a double triangular diagram learning support method according to an embodiment of the present invention. [Figure 4] FIG. 10 is a diagram showing an example of a screen presentation for a learning task of creating a double triangular diagram. [Figure 5A] FIG. 10 shows an example of a screen presentation for a double triangular diagram creation task including dummy abundance. [Figure 5B] FIG. 10 is a diagram showing an example of a screen presentation for a double triangular diagram creation task including a dummy relation quantity. [Figure 6A] FIG. 10 shows an example of a screen presentation for a double triangular diagram creation task in which the quantity of abundance is unknown. [Figure 6B]This figure shows an example of a screen presentation for a double triangular diagram creation task in which the quantity of the related quantity is unknown. [Figure 7A] This figure shows an example of a screen presentation for the double triangular diagram creation task in which all abundance information is omitted. [Figure 7B] This figure shows an example of a screen presentation for the task of creating a double triangular diagram in which all information on related quantities is omitted. DETAILED DESCRIPTION OF THE INVENTION

[0008] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings as appropriate. However, more detailed description than necessary may be omitted. For example, detailed description of well-known matters or redundant description of substantially identical configurations may be omitted. This is to avoid unnecessary redundancy in the following description and to facilitate understanding by those skilled in the art. Note that the inventors provide the accompanying drawings and the following description to enable those skilled in the art to fully understand the present invention, and are not intended to limit the subject matter described in the claims. Furthermore, the dimensions of each component depicted in the drawings, the detailed shapes of the details, and the like may differ from the actual ones. <Double Triangle>

[0009] When there is a quantity that represents a quantity for one concept and a quantity that represents a quantity for another concept, and there is a multiplication / division relationship between these two quantities, there are two related quantities between these two quantities that are inversely related to each other in terms of the mutual conversion of quantities. And between two quantities and one related quantity, there is one multiplication and two multiplications. The relationship between these four quantities can be visually represented using a double triangular diagram.

[0010] Figure 1 is a schematic diagram of several examples of double triangular diagrams. As shown, a double triangular diagram is constructed in a double triangular frame, where two triangles (obtuse isosceles triangles) are arranged symmetrically above and below each other. Two existential quantities are located at the two vertices of the base of each triangle, two relational quantities are located at the remaining vertices of each triangle, a division is located at the base of each triangle, and multiplication and division are located on the remaining two sides of each triangle. For convenience, existential quantities are represented by rectangular frames, relational quantities by rounded rectangular frames, and multiplication and division by circular frames. The side where division is located is represented by an arrow, with the base of the arrow representing the divisor and the tip of the arrow representing the dividend. Each of the two triangles in a double triangular diagram represents a three-quantity proposition model. In other words, a double triangular diagram is a combined representation of two three-quantity proposition models.

[0011] The double triangular diagram in Figure 1(a) represents two quantities, "4 plates" and "8 apples," and two related quantities, "2 apples per plate" and "1 / 2 plate per apple," as well as the multiplication and division that exist between these four quantities. The three-quantity proposition model represented by the upper triangle of the double triangular diagram includes equal division, such that dividing "8 apples" into "4 plates" results in "2 apples per plate," and inclusive division, such that dividing "8 apples" into "2 apples per plate" results in "4 plates." Furthermore, the three-quantity proposition model represented by the lower triangle includes multiplication and division with an operator smaller than 1, such as "1 / 2 plate per apple." In this way, the double triangular diagram comprehensively includes equal division, inclusive division, and multiplication and division with operators smaller than 1.

[0012] The double triangular diagram in Figure 1(b) contains two quantities: "four goals" and "eight shots." In this way, quantities are not limited to things with concrete shapes like plates or apples, but can also be abstract things like goals or shots, as long as they can be counted.

[0013] The double triangular diagrams in Figure 1(c) and (d) include related quantities such as "2 oranges per 1 apple" and "20g of juice per 1g of fruit juice." In this way, related quantities can also represent multiples or ratios.

[0014] Double triangular diagrams can be digitized for computer manipulation. For example, for each double triangular diagram, two quantities, two related quantities, and the relationship between those quantities can be tabulated.

[0015] <Embodiment> FIG. 2 is a schematic diagram of a double triangular diagram learning support system according to one embodiment of the present invention. The double triangular diagram learning support system 100 presents a double triangular frame and movable parts representing quantities, related quantities, and multiplication and division on a UI screen to support learners in creating double triangular diagrams on the UI screen. Specifically, the double triangular diagram learning support system 100 comprises a server 10 and a user terminal 20, which are capable of communicating with each other via a network 200 such as the Internet. The server 10 may be composed of one or more computers. The user terminal 20 may be a personal computer, tablet, smartphone, or the like.

[0016] The server 10 includes a storage 30 and a processor 40. The storage 30 is composed of an HDD, an SSD, a non-volatile memory, etc., and stores information necessary for learning using a double triangular diagram and for evaluating the results. As an example, the storage 30 stores a correct double triangular diagram 32 as well as various computer programs executed by the processor 40. The correct double triangular diagram 32 can be represented and managed using various tables, as described above. The processor 40 reads the computer programs stored in the storage 30 and operates as a task presenter 42, an evaluator 46, and a double triangular diagram generator 48.

[0017] The user terminal 20 includes a UI screen 50 and a processor 60. The UI screen 50 displays a double triangular frame and movable parts representing two quantities, two relational quantities, and multiplication and division operations contained in the correct double triangular diagram 32. The learner can freely move these movable parts by touching the UI screen 50 or by operating a mouse (not shown). The processor 60 reads a computer program from storage (not shown) and operates as a part operation determination unit 62.

[0018] 3 is a flowchart of a double triangular diagram learning support method according to one embodiment of the present invention. The operation of each functional element operating in the processor 40 of the server 10 and the processor 60 of the user terminal 20 will be described with reference to the flowchart.

[0019] When the learning task of creating a double triangular diagram begins, first, the task presenter 42 presents, on the UI screen 50 of the user terminal 20, movable parts and a double triangular frame of the double triangular diagram, each representing four quantities (two quantities and two related quantities) and multiplications and divisions included in the correct double triangular diagram 32 (S1). Specifically, the task presenter 42 references the correct double triangular diagram 32 stored in the storage 30 and sends information about the two quantities and two related quantities included in the correct double triangular diagram, as well as information about the double triangular frame and arithmetic operators, to the user terminal 20. The user terminal 20 receives this information and displays, on the UI screen 50, the movable parts and double triangular frames for the two quantities, the two related quantities, and the multiplications and divisions.

[0020] 4 shows an example of a screen presentation for a learning task of creating a double triangular diagram. As shown, movable parts representing two quantities, two related quantities, two multiplications, and four divisions are presented on the UI screen 50. A double triangular frame is presented on the UI screen 50 as a fixed part that does not move.

[0021] The learner assembles a double triangular diagram by dragging and dropping the movable parts using a mouse or touching the UI screen 50 and placing them on the double triangular frame. When the learner has completed the double triangular diagram, he or she clicks the "Complete" button to notify the system that the task is complete.

[0022] Returning to FIG. 3, the user terminal 20 accepts the learner's operation to move the movable part and moves the movable part on the screen (S2). During this time, the part operation determination unit 62 determines that the movable part presented on the UI screen 50 has been operated and placed in a position in the double triangular frame where the movable part can be placed (S3). For example, one movable part representing multiplication and division can be placed on each side of each triangle in the double triangular frame. One movable part representing an abundance can be placed on each vertex of the base of each triangle. One movable part representing a relational quantity can be placed on the remaining vertices of each triangle.

[0023] When a movable part overlaps a part placement position in the double triangular frame through a drag-and-drop operation, the movable part being operated is highlighted, and when the learner stops the drag-and-drop operation at this point, the part operation determination unit 62 determines that the movable part has been placed in the double triangular frame. On the other hand, when a movable part placed in the double triangular frame is right-clicked with the mouse or tapped on the screen for an extended period of time, the part operation determination unit 62 determines that the movable part has been separated from the double triangular frame. A movable part separated from the double triangular frame can be moved again and placed in another position in the double triangular frame.

[0024] When the learner clicks the "Complete" button on the UI screen 50 to notify the system that the double triangular diagram is complete (yes in S6), the user terminal 20 transmits information about the double triangular diagram created by the learner to the server 10. Specifically, the information transmitted is the information about which moving parts are located at which positions in the double triangular frame.

[0025] When the server 10 receives information about the double triangular diagram created by the learner from the user terminal 20, the evaluation unit 46 evaluates the accuracy of the double triangular diagram created by the learner (S8). Specifically, the evaluation unit 46 compares the double triangular diagram created by the learner with the correct double triangular diagram 32 to evaluate the accuracy of the double triangular diagram created by the learner. If the answer is incorrect (no in S9), the evaluation unit 46 displays a message on the UI screen 50 indicating that the answer is incorrect, prompting the learner to correct the double triangular diagram, and the process returns to step S2. If the answer is correct (yes in S9), the process ends.

[0026] <<Adjusting the difficulty of tasks>> In step S1, the task presenter 42 may preliminarily place some of the movable parts in positions in the double triangular frame where the movable parts can be placed, and present the movable parts on the UI screen 50. For example, a movable part representing multiplication and division may be preliminarily placed in the double triangular frame to present the task. This can reduce the difficulty of the task.

[0027] Alternatively, the movable parts representing quantities and the movable parts representing relational quantities may be placed at any vertex of each triangle in the double triangular frame. This forces learners to create a double triangular diagram while being aware of the difference between quantities and relational quantities, thereby increasing the difficulty of the task. In addition, the task itself can be modified to increase the difficulty. Some examples are described below.

[0028] (adding dummy amounts) In step S1, the task presenter 42 may present on the UI screen 50 a movable part that represents a dummy quantity of existence or a relation quantity.

[0029] Figure 5A shows an example of a screen presentation for a double triangular diagram creation task that includes dummy quantities. In this example, extra movable parts representing the dummy quantities "4 apples" and "8 plates" are presented. In addition, two extra movable parts representing multiplication are presented. In this way, by presenting movable parts for the dummy quantities, the learner must select the correct quantity that is consistent with the relational quantity, thereby increasing the difficulty of the task.

[0030] Figure 5B shows an example of a screen presentation for a double triangular diagram creation task that includes dummy relational quantities. In this example, extra moving parts for the dummy relational quantities "1 / 2 apple per plate" and "2 plates per apple" are presented. In addition, two extra moving parts for multiplication are presented. In this way, by presenting the moving parts for the dummy relational quantities, the learner must select the correct relational quantity that is consistent with the quantity present, thereby increasing the difficulty of the task.

[0031] (missing information) In step S1, the task presenter 42 may present a movable part with some information about the two quantities and the two relational quantities missing on the UI screen 50. Then, in step S2, the part operation determination unit 62 may accept information input from the learner and use the accepted information to fill in the missing information in the movable part.

[0032] Figure 6A shows an example of a screen presentation for a double triangular diagram creation task where the quantity of abundance is unknown. In this example, the movable parts representing the quantity are presented as "# plates" and "# apples." Therefore, in order to complete the double triangular diagram, learners must fill in the unknown quantity of abundance while looking at the information on the related quantities, which increases the difficulty of the task.

[0033] Figure 6B shows an example of a screen presentation for a double triangular diagram creation task in which the quantity of the related quantity is unknown. In this example, the moving parts representing the related quantity are presented as "? apples per plate" and "? plates per apple." This means that in order to complete the double triangular diagram, learners must fill in the unknown quantity of the related quantity while looking at the quantity information, which increases the difficulty of the task.

[0034] To further increase the difficulty of the task, in step S1, the task presenter 42 may present on the UI screen 50 a movable part from which all information about the two quantities present or the two relational quantities is missing.

[0035] Figure 7A shows an example of a screen display for a double triangular diagram creation task in which all information about abundance is omitted. In this example, all information about the concept name, quantity, and unit of the moving part representing the abundance is expressed in square brackets, and an example of creating an abundance is shown. Therefore, in order to complete the double triangular diagram, learners must fill in the concept name, quantity, and unit of the abundance while looking at the information about the related quantities, which makes the task more difficult.

[0036] Figure 7B shows an example of a screen display for a double triangular diagram creation task in which all information about the related quantities is omitted. In this example, the names of two concepts, their units, and all information about the related quantities are shown in square brackets in the moving parts that represent the related quantities, and an example of creating a related quantity is shown. Therefore, in order to complete the double triangular diagram, learners must fill in the two quantities, their units, and the related quantities while looking at the quantity information, which makes the task more difficult.

[0037] <Automatic generation of double triangular diagrams> The correct double triangular diagram 32 can be created manually by the instructor and the information registered, or if there is an abundance table that stores the conceptual names of any abundances and the units used to count them, and a combination table that stores information about combinations of two abundances that have a mathematical relationship, the double triangular diagram generation unit 48 can refer to these tables to automatically generate the correct double triangular diagram.

[0038] For example, the double triangular diagram generation unit 48 refers to the combination table to select a combination of abundance ID1 and abundance ID2, and further refers to the abundance table to obtain [Concept 1] and [Unit 1] as the concept name and unit of abundance ID1, and [Concept 2] and [Unit 2] as the concept name and unit of abundance ID2. Next, the double triangular diagram generation unit 48 appropriately sets [Quantity 1] as the quantity of abundance 1 and [Quantity 2] as the quantity of abundance 2, and combines these to generate the following two abundances 1 and 2: Abundance 1: [Concept 1] [Quantity 1] [Unit 1] Abundance 2: [Concept 2] [Quantity 2] [Unit 2]

[0039] Furthermore, the double triangular diagram generating unit 48 calculates [Quantity 2] / [Quantity 1] as [Relationship 1] and [Quantity 1] / [Quantity 2] as [Relationship 2], and combines these to generate the following two relations: Quantity 1 and Quantity 2. Note that " / " indicates division. Relationship 1: [Concept 1] 1 [Unit 1] per [Concept 2] [Relationship 1] [Unit 2] Relationship 2: [Concept 2] 1 [Unit 2] per [Concept 1] [Relationship 2] [Unit 1]

[0040] For example, if [Concept 1] = "apple", [Concept 2] = "plate", [Quantity 1] = "8", [Quantity 2] = "4", [Unit 1] = "piece", and [Unit 2] = "piece", the double triangular diagram generation unit 48 will generate two quantities and two relation quantities in the double triangular diagram shown in Figure 1(a). Abundance 1: "8 apples" Abundance 2: "4 plates" Quantity 1: "1 apple = 1 / 2 plate" Quantity 2: "2 apples per plate"

[0041] Furthermore, by transferring the automatic double triangular diagram generation function to the evaluation unit 46, the evaluation unit 46 can evaluate the correctness of the double triangular diagram created by the learner by verifying the mathematical consistency between the two quantities present and the two relational quantities in the double triangular diagram created by the learner, without comparing the double triangular diagram created by the learner with the correct double triangular diagram 32.

[0042] Effect This embodiment can support the learner in creating a double triangular diagram. The difficulty level of the assignment can be freely adjusted, and assignments can be automatically created and the correctness of the double triangular diagrams created by the learner can be automatically evaluated.

[0043] <<Variations>> The double triangular diagram learning support system 100 is not limited to a client / server system, but can also be implemented in a standalone environment using only the user terminal 20. In this case, the task presenter 42, evaluator 46, and double triangular diagram generator 48 can be configured to run on the processor 60 of the user terminal 20. The correct double triangular diagram 32 can be stored in the memory of the user terminal 20 or in external storage.

[0044] The shape and orientation of the double triangular frame are arbitrary. For example, the triangles may be acute isosceles triangles or may be other than isosceles triangles. The triangles may also be arranged symmetrically. Furthermore, the bases of the two triangles may be displayed overlapping each other.

[0045] As described above, the embodiments have been described as examples of the technology of the present invention. For this purpose, the accompanying drawings and detailed description have been provided. Therefore, the components described in the accompanying drawings and detailed description may include not only components essential for solving the problem, but also components that are not essential for solving the problem in order to exemplify the above technology. Therefore, the fact that these non-essential components are described in the accompanying drawings or detailed description should not be interpreted as immediately indicating that these non-essential components are essential. Furthermore, because the above-described embodiments are intended to exemplify the technology of the present invention, various modifications, substitutions, additions, omissions, etc. may be made within the scope of the claims or their equivalents. [Explanation of symbols]

[0046] 100 Double Triangle Diagram Learning Support System 10 Servers 20 User terminal 32 Correct Double Triangle 42 Assignment presentation section 46 Evaluation Department 48 Double Triangular Diagram Generation Unit 50 UI screens 62 Part operation determination unit

Claims

1. A learning support system in which a learner creates, on a UI screen, a double triangular diagram consisting of two quantities, two related quantities that are reciprocal of each other and represent the relationship between these quantities, and multiplications and divisions that hold among the three quantities of the two quantities and any one of the related quantities, a task presenting unit that presents on the UI screen a double triangular frame in which movable parts representing four quantities and multiplications / divisions of the two quantities and the two related quantities included in the correct double triangular diagram and two triangles that illustrate the relationship between the three quantities are symmetrically arranged; a part operation determination unit that determines whether the movable part is placed at a position where the movable part can be placed in the double triangular frame on the UI screen or whether the movable part is removed from the position; and an evaluation unit that evaluates the correctness of the double triangular diagram created by the learner by operating the movable parts. A double triangular diagram learning support system characterized by:

2. 2. The double triangle diagram learning support system according to claim 1, wherein the task presenting unit pre-positions some of the movable parts in positions in the double triangle frame where the movable parts can be placed and presents them on the UI screen.

3. The double triangular diagram learning support system according to claim 1 , wherein the task presenting unit presents a movable part representing a dummy abundance or a dummy relation amount on the UI screen.

4. the problem presenting unit presents, on the UI screen, the movable part from which information about the two quantities of existence or the two quantities of relationship has been partially or completely deleted; 2. The double triangle diagram learning support system according to claim 1, wherein the part operation determination unit receives information input from the learner and uses the received information to supplement missing information in the movable part.

5. 5. A double triangular diagram learning support system as described in any one of claims 1 to 4, comprising a double triangular diagram generation unit that sets any two concept names and any two quantities, combines the concept names and quantities to generate two quantities of abundance, and generates two relational quantities that are reciprocal of each other and represent the relationship between the quantities of abundance from the two quantities generated, thereby generating the correct double triangular diagram.

6. A server; a user terminal that is capable of communicating with the server; the task presenter, the evaluator, and the double triangular diagram of the correct answer are arranged on the server; 5. The double triangle diagram learning support system according to claim 1, wherein the UI screen and the part operation determination unit are arranged on the user terminal.

7. A server; a user terminal that is capable of communicating with the server; the double triangular diagram generation unit, the task presentation unit, the evaluation unit, and the correct double triangular diagram are arranged on the server; The double triangle diagram learning support system according to claim 5 , wherein the UI screen and the part operation determination unit are arranged on the user terminal.

8. A method for supporting learning in which a learner creates, on a UI screen, a double triangular diagram consisting of two quantities, two related quantities that are reciprocal of each other and represent the relationship between these quantities, and multiplications and divisions that hold among the two quantities and any one of the related quantities, automatically presenting on the UI screen a double triangular frame in which two triangles are symmetrically arranged to represent the four quantities and multiplication / division of the two quantities and the two related quantities included in the correct double triangular diagram, and the relationship between the three quantities; automatically determining, on the UI screen, that the movable part has been placed at a position in the double triangular frame where the movable part can be placed, or that the movable part has been removed from the position; and automatically evaluating the correctness of the double triangular diagram created by the learner by manipulating the movable parts. A double triangular diagram learning support method characterized by the above.

9. A program that causes a computer to function as a learning support system that communicates with a user terminal and allows a learner to create, on a UI screen, a double triangular diagram consisting of two quantities, two related quantities that are reciprocals of each other and represent the relationship between these quantities, and multiplications and divisions that hold among the three quantities of the two quantities and any one of the related quantities, means for automatically presenting on the UI screen a double triangular frame in which movable parts representing four quantities and multiplications / divisions of the two quantities and the two related quantities included in the correct double triangular diagram and two triangles symmetrically arranged to illustrate the relationship between the three quantities; and a means for automatically evaluating the correctness of the double triangular diagram created by the learner by operating the movable parts; and The user terminal The UI screen; a part operation determination unit that determines whether the movable part is placed at a position where the movable part can be placed in the double triangular frame on the UI screen or is removed from the position. A double triangle diagram learning support program characterized by:

10. A program that causes a computer to function as a learning support system that communicates with a server and allows a learner to create, on a UI screen, a double triangular diagram consisting of two quantities, two related quantities that are reciprocals of each other and represent the relationship between these quantities, and multiplications and divisions that hold among the three quantities of the two quantities and any one of the related quantities, The server a task presenting unit that presents on the UI screen a double triangular frame in which movable parts representing four quantities and multiplications / divisions of the two quantities and the two related quantities included in the correct double triangular diagram and two triangles that illustrate the relationship between the three quantities are symmetrically arranged; an evaluation unit that evaluates the correctness of the double triangular diagram created by the learner by operating the movable part, means for automatically determining, on the UI screen, whether the movable part has been placed at a position in the double triangular frame where the movable part can be placed, or whether the movable part has been removed from the position; A double triangle diagram learning support program that makes the computer function as a.

11. A program that causes a computer to function as a learning support system in which a learner creates, on a UI screen, a double triangular diagram consisting of two quantities, two related quantities that are reciprocals of each other and represent the relationship between these quantities, and multiplications and divisions that hold among the three quantities of the two quantities and any one of the related quantities, means for automatically presenting on the UI screen a double triangular frame in which movable parts respectively represent four quantities and multiplications / divisions of the two quantities and the two related quantities included in the correct double triangular diagram, and two triangles that illustrate the relationship between the three quantities are symmetrically arranged; means for automatically determining, on the UI screen, whether the movable part has been placed at a position in the double triangular frame where the movable part can be placed or whether the movable part has been removed from the position; and means for automatically evaluating the correctness of the double triangular diagram created by the learner by operating the movable parts; A double triangle diagram learning support program that makes the computer function as a.

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