JP6674708B2 - User-adaptive test program, apparatus and method with mixed questions based on different criteria - Google Patents

Description

  The present invention relates to a technology of an e-Learning system for determining the academic ability of a user (learner).

  According to the user-adaptive e-Learning system, it is possible to select and specify questions and contents suitable for learning comprehension for each user using a database that stores the past tendency of answers of many users as a history. it can. There is also a “testing” system that provides different problems and learning materials for each user by arranging an e-Learning system as a server on a network.

  It is very difficult to create a plurality of questions corresponding to the user's level of understanding. In particular, it is extremely difficult to make the difficulty level of each question constant and determine the level of understanding. On the other hand, there is an adaptive testing (computer-adaptive test) technique for estimating the parameters of an unanswered question according to a user's answer result and selecting the next question (for example, see Non-Patent Document 1). ).

  There is also a technique for determining a user's understanding level from test execution results using a test database (for example, see Patent Document 1, Non-Patent Documents 2 and 3). According to this technique, it is possible to select a question according to the probability of the user's understanding and give a question, and determine the user's academic ability with high accuracy even with a small number of questions. In particular, according to the technology described in Non-Patent Document 3, the problem of maximizing the amount of network-type information for a learning model using a Bayesian network is controlled as follows.

  In general, tests conducted at schools and study schools consist of multiple questions with different degrees of difficulty and points, and within a predetermined time, the total score calculated by correcting or incorrectly answering or partially adding or subtracting points is calculated. Then, the scholastic ability of each user is evaluated.

JP-A-2004-170842

Masaomi Ueno, "Evaluation of Learning in the New Era", Education Testing Research Center, 18th meeting report, June 18, 2010, [online], [Searched on December 21, 2016], Internet <https: / /www.cret.or.jp/files/dbd90c4cb469bf94ef5da2256616c7e7.pdf> Masaomi Ueno, Hitoshi Ohnishi and Norio Shigemasu, "Proposal of Test Theory with Stochastic Network", IEICE Technical Report, ET93-64, 55-62, 1993, [online], [Search December 21, 2016 ], Internet <http://ci.nii.ac.jp/naid/110003192386> Masaomi Ueno, Chiharu Kawatake, Jin Ohnishi, "Structural Optimization Method in Network-Based Test Theory", IEICE Technical Report, ET93-ET127, March 26, 1994, IEICE, Vol100, P50-P60, [online ], [Searched on December 21, 2016], Internet <URL: http://jglobal.jst.go.jp/public/20090422/200902114032577390> Norio Shigemasa, Masaomi Ueno, Yoichi Motomura, "Introduction to Bayesian Networks", Baifukan, first edition issued on July 21, 2006 "Amount of information", Wikipedia, [online], [Searched on December 21, 2016], Internet <URL: https://en.wikipedia.org/wiki/%E6%83%85%E5%A0%B1 % E9% 87% 8F>

  However, in the case of the user-adaptive e-Learning system, a considerable amount of time is required to repeat the question and answer determination until the user's academic level can be estimated from a wide range of learning contents. In addition, since the time required for answering differs depending on the difficulty level of the question level for the user, there are some users who have extra time and others who do not have enough time to perform the test within a certain time. In general, a user is "subjectively" aware of a good problem and a bad problem. That is, the user can immediately answer a question such as a questionnaire simply asking whether he is good or not with a short required time.

  On the other hand, the inventor of the present application thought that the number of questions and the time required for estimating the user's learning level could be reduced by the user's "subjective" questions and answers.

  Therefore, it is an object of the present invention to provide a user-adaptive test program, an apparatus, and a method that can reduce the number of questions and the time required until a user's learning level is estimated, regardless of the learning level.

According to the present invention, in a user-adaptive test program that causes a computer mounted on an apparatus to function,
It is a directed graph composed of "nodes" including understanding probabilities and arcs connecting the nodes, in which an item based on a first criterion for obtaining a subjective answer to a subjective question is associated with a node. Model storage means for storing in advance a model and a second model in which an item based on a second criterion for obtaining a test answer to a test question is associated with a node;
For the first model and the second model, and comprehension probability updating means based on the response of the user and recalculates the comprehension probability at other nodes not yet out of items associated to an item,
For the first model and the second model, the information amount calculation means for calculating a network information amount from comprehension probabilities of all nodes,
The method is characterized in that a computer functions as model switching means for switching to the second model when the network information amount becomes a predetermined condition while repeating the understanding level probability updating means and the information amount calculating means for the first model. I do.
In this specification, questions and questions for estimating the user's academic level are referred to as “items”, and answers to the questions and answers to subjective questions are referred to as “responses”.

According to another embodiment of the program of the present invention,
Preferably, the predetermined condition of the model switching means causes the computer to function such that the network information amount of the first model becomes equal to or less than the first threshold value.

According to another embodiment of the program of the present invention,
The predetermined condition of the model switching means is such that, even if the understanding level probability updating means and the information amount calculating means are repeated a predetermined number of times for the first model, the computer is set so that the network information amount does not fall below the first threshold value. It is also preferable to make it work.

According to another embodiment of the program of the present invention,
The model switching means causes the computer to switch to the first model when the network information amount becomes a predetermined condition while repeating the understanding level probability updating means and the information amount calculating means for the second model. Is also preferred.

According to another embodiment of the program of the present invention,
The model switching means causes the computer to switch to the first model when the network information amount of the second model does not become equal to or less than the second predetermined threshold value even after the switched second model is repeated a predetermined number of times. It is also preferred.

According to another embodiment of the program of the present invention,
Each node of the first model corresponds to one of the nodes of the second model,
It is also preferable that the model switching means causes the computer to function so as to convert the understanding probability of the node of the migration destination model into the understanding probability of the corresponding node of the migration source model and rewrite it.

According to another embodiment of the program of the present invention,
Item presenting means for selecting a node associated with an unlisted item for the first model and the second model, and presenting the item of the node;
For the first model and the second model, it is also preferable to make the computer further function as a response determination unit that determines whether the content of the response to the already-explained item is correct or incorrect.

According to another embodiment of the program of the present invention,
The understanding degree probability updating means assigns the understanding degree probability of the node in a stepwise manner from 0 to 1 in accordance with the contents of a plurality of subjective answers to the subjective question for the item based on the first criterion, It is also preferable to have the computer function to recalculate the understanding probability.

According to another embodiment of the program of the present invention,
Arcs in the model's directed graph are connected based on the understanding order relation between the nodes, and are weighted according to the degree of association between the nodes.
It is also preferable that the understanding probability updating means causes the computer to function so as to calculate the understanding probability of the node by Bayes' theorem.

According to another embodiment of the program of the present invention,
The information amount calculation means calculates the network information amount when the random variables X of all the nodes U in the model follow the probability distribution P by the following equation: H (X) = − Σ _x∈UP (X = x ) logP (X = x)
It is also preferable to make the computer function as described above.

According to the present invention, in an apparatus for performing a user-adaptive test,
It is a directed graph composed of "nodes" including understanding probabilities and arcs connecting the nodes, and a first item in which an item based on a first criterion for obtaining a subjective answer to a subjective question is associated with the node Model storage means for storing in advance a model and a second model in which an item based on a second criterion for obtaining a test answer to a test question is associated with a node;
For the first model and the second model, and comprehension probability updating means based on the response of the user and recalculates the comprehension probability at other nodes not yet out of items associated to an item,
For the first model and the second model, the information amount calculation means for calculating a network information amount from comprehension probabilities of all nodes,
When the network information amount becomes a predetermined condition during the repetition of the understanding probability updating means and the information amount calculating means for the first model, a model switching means for switching to the second model is provided.

According to the present invention, using the apparatus, a ruthenate stringent method to perform a test of the user-adaptive,
Device is a directed graph constructed in including physical Kaido probability a "node" and connecting it arcs nodes together, items based on the first reference to determine the subjective answer associated with node for subjective questions A first model and a second model in which items based on a second criterion for obtaining a test answer to a test question are associated with nodes,
The equipment is
For the first model and the second model, the first step of re-calculated based on the response of the user, the comprehension probability at other nodes not yet out of items associated to an item,
For the first model and the second model, running a second step of calculating the network information amount from comprehension probabilities of all nodes,
When the first information and the second information are repeated for the first model and the network information amount becomes a predetermined condition , the first model is switched to the second model.

ADVANTAGE OF THE INVENTION According to the user-adaptive test program, apparatus, and method of the present invention, the number of questions and the time required for estimating the learning level of the user can be reduced regardless of the learning level.
ADVANTAGE OF THE INVENTION According to this invention, a question whose answer level is ambiguous can repeat a question and an answer. This makes it possible to estimate the user's learning level by progressing the test question according to the user's subjective answer without making the content of the test question too difficult or too simple.

FIG. 2 is a functional configuration diagram of a test device according to the present invention. It is a flowchart of this invention. 5 is an example of a directed graph of nodes stored in a model storage unit. FIG. 4 is an explanatory diagram illustrating a model stored in a model storage unit. It is the 1st explanatory view showing the digraph of a node and the understanding degree probability at the time of initialization. FIG. 14 is a second explanatory diagram illustrating updating of the understanding degree probability of the node when the answer to the test question of the node 5 is correct. FIG. 13 is a third explanatory diagram illustrating updating of the understanding probability of the node when the test question of the node 8 is incorrectly answered. FIG. 14 is a fourth explanatory diagram showing an update of the understanding probability of the node when the test question of the node 4 is incorrectly answered. FIG. 14 is a fifth explanatory diagram illustrating updating of the understanding level probability of the node when the answer to the test question of the node 13 is correct. FIG. 4 is an explanatory diagram illustrating switching of nodes in a model. It is explanatory drawing showing the time required for a subjective answer and a test answer. It is a flowchart showing a predetermined condition of model switching. It is explanatory drawing showing the switch of a model. It is explanatory drawing showing the application object of the understanding degree probability of a 1st model. It is explanatory drawing showing the method of application and calculation of the understanding degree probability of a 2nd model. It is explanatory drawing showing the application object of a 2nd model understanding degree probability. FIG. 9 is an explanatory diagram illustrating a method of applying and calculating an understanding degree probability of a first model.

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

FIG. 1 is a functional configuration diagram of a test apparatus according to the present invention.
FIG. 2 is a flowchart of the present invention.

  According to FIG. 1, a test apparatus 1 for executing user-adaptive testing and a terminal 2 (for example, a tablet terminal) operated by a user to be learned are connected via a network. The test device 1 functions as a server for the terminal 2. Further, the functional components of the test apparatus 1 may be mounted on the terminal 2 so that the terminal alone functions as the test apparatus.

  According to the test apparatus 1 of FIG. 1, the test apparatus 1 includes a model storage unit 100, an item presentation unit 101, a response determination unit 102, an understanding probability update unit 11, an information amount calculation unit 12, and a model switching unit 13. . These functional components are realized by executing a program that causes a computer mounted on the device to function. Further, the flow of processing of these functional components can be understood as a user-adaptive test method as shown in FIG.

[Model storage unit 100]
The model storage unit 100 stores a model of a directed graph composed of “nodes” including understanding probability and arcs connecting the nodes. A node is associated with a certain item, and may include not only text but also images, videos, and sounds.

  FIG. 3 is an example of a directed graph of nodes stored in the model storage unit.

  According to FIG. 3, a directed graph in one model is represented, and nodes are connected by an arc based on the understanding order relationship. The understanding order relationship means that the understanding probability of the preceding node affects the understanding probability of the subsequent node. For example, it is sufficient if the relationship from the front to the back can be roughly specified according to the learning curriculum, such as from April to May of the first year of junior high school.

  Nodes whose relevance of learning content is equal to or greater than a predetermined threshold are connected by an arc of a directed graph. For example, it is conceivable that the user's understanding probability for the node connected by the arc changes according to the level of the understanding degree for the previous node. For example, in the case of FIG. 3, the understanding probability of the node 8 changes according to the understanding probabilities of the nodes 2, 4, and 6, and the node 12 changes accordingly. That is, the change of the understanding degree probability is linked.

  This directed graph may be manually created based on the learning guidance policy while considering the relevance between nodes. Further, it may be automatically created based on the learning start time from the degree of relevance of the learning content in the learning unit of each node. For example, if the dependency of each learning unit in the same subject is clear, it can be determined relatively easily. According to FIG. 3, a single subject “mathematics” is applied. However, the subject may be applied to a plurality of subjects, or may be based on qualification education or corporate education with high specialty.

  Understanding the learning content that is realistic for the user does not simply proceed step by step according to the learning level (curriculum). For example, in an actual educational setting, if a first-grade junior high school student has a low level of understanding of mathematics, it is not merely a matter of improving elementary school children's understanding of mathematics. When a first-year junior high school user has a low level of understanding of mathematical "figures", the degree of understanding based on "figures" should be considered even in elementary school students' arithmetic. In this case, even if the question corresponding to the node of the "graphic" of the elementary school student's arithmetic is added, the learning level of the user can be optimally estimated as a result.

  FIG. 4 is an explanatory diagram illustrating a model stored in the model storage unit.

The model storage unit 100 stores a plurality of models as described below.
A first model in which items based on a first criterion are associated with nodes; a second model in which items based on a second criterion are associated with nodes;

The node of the first model based on the first criterion is to calculate the understanding probability from the subjective answer to the subjective question, and the node of the second model based on the second criterion is the test answer to the test problem. The probability of understanding may be calculated from the following. Below, the subjective question and the subjective answer, the test question and the test answer are respectively illustrated.
<Subjective questions and subjective answers>
Question 1 Answer whether you can calculate the expression 7a-b-5 (a-2b) using characters.
1. Can calculate correctly.
2. I am confident in calculating correctly.
3. I don't have the confidence to calculate correctly.
4. Cannot calculate correctly.
<Test questions and test answers>
Question 1 Calculate and answer Equations 7a-b-5 (a-2b) using letters.
1.2a-11b
2.2a + 11b
3.2a-9b
4.2a + 9b

  The node of the first model based on the first criterion is for obtaining an understanding degree probability from the test answer to the test question in the first subject, and the node of the second model based on the second criterion is The understanding probability may be obtained from a test answer to a test question in the second subject.

  It is assumed that the model storage unit 100 comprehensively gives, as an initial state, an understanding degree probability for each node from results of answers or answers to a large number of users. For example, the probability value in the initial state may be an average frequency of answers obtained from a large number of users or an average correct answer rate of answers. Of course, it may be manually set in advance, or may be calculated using machine learning.

[Item presentation unit 101 (S101)]
The item presenting unit 101 selects, for each user, an item associated with an unappeared node for the first model or the second model (currently selected model), and performs a subjective question or test question on the item and Present a test answer. When the test device 1 is a server, the item presenting unit 101 transmits a subjective question or a test question for the item to the terminal 2 operated by the user.

[Response Determination Unit 102 (S102)]
The response determination unit 102 determines, for each user, a response to an existing node or item for the first model or the second model (currently selected model). Each item can be compared to the user's response to include subjective questions and subjective answers, or test questions and test answers. The result of the determination is reflected in the model storage unit 100.

  Note that the item presenting unit 101 presents a subjective question or a test question for a predetermined number or more of nodes or items included in the unanswered learning unit, and the response determination unit 102 provides an answer for the predetermined number or more of the nodes or items. After the determination of the correct answer / wrong answer, an understanding degree probability updating unit 11, an information amount calculating unit 12, and a model switching unit 13, which will be described later, may be executed.

[Understanding Degree Probability Update Unit 11 (S11)]
The understanding probability updating unit 11 performs a user (learning) on a node or an item (a subjective question or a test question) for the first model (a subjective question model) or the second model (a test question model) in the model storage unit 100. ) Is recalculated based on the response (subjective answer or test answer) of the other person. The understanding probability is calculated by Bayes' theorem.

  The user sequentially responds to the items to be set, changes the understanding probability of the node based on the determination of the response determination unit 102, and recalculates the understanding probability of another node. As a result, it is possible to update the understanding probability of the node associated with the unlisted item according to the response of the already-listed item.

For example, when there are a plurality of subjective answers to the subjective question, the understanding degree probability of the node is gradually assigned from 0.0 to 1.0.
<Subjective answer> [Probability of understanding]
1. Can calculate correctly. -> 1.0
2. I am confident in calculating correctly. -> 0.7
3. I don't have the confidence to calculate correctly. -> 0.3
4. Cannot calculate correctly. -> 0.0
Further, for example, when there is one correct answer to the test question, 0.0 or 1.0 is assigned to the understanding degree probability of the node.
<Test answer> [Probability of understanding]
1.2a-11b-> 0.0
2.2a + 11b-> 0.0
3.2a-9b-> 0.0
4.2a + 9b-> 1.0

Note that, when a predetermined time or more elapses before a test answer for a test question, a hint for the test question may be presented to the user. In that case, the understanding degree probability and the probability of the item may be applied according to the number of times (or contents) of the hint.
(1) When one hint is presented and the "correct answer" is given, the probability of understanding is-> 0.75
(2) When the two hints are presented and the "correct answer" is given, the probability of understanding is-> 0.60

  In addition, when a predetermined time or more elapses before a test answer for a test question, the acceptance of the test answer is terminated, and the probability of understanding of the item is set to 0.0. May be presented.

  The understanding probability of the nodes included in each model, which is updated by the understanding probability update unit 11, may use, for example, a “Bayesian network”. A Bayesian network is a graphical network that describes a causal relationship between nodes using probabilities (for example, see Non-Patent Document 4). The network according to the present invention has a “node” in which items and responses are associated with each other, and refers to a graph structure in which the degree of association given to arcs between nodes is given as “weight”. The Bayesian network is a probabilistic inference model that expresses a causal relationship between a plurality of nodes by using a directed acyclic graph structure and expresses a relationship between individual variables by conditional probability. The directed acyclic graph structure refers to a structure in which an arrow is given to an arc (directed) and the path of the arrow does not go around a node. By using the Bayesian network, the correct answer rate (probability of understanding) of an uncertain event (correct answer / wrong answer) is quantitatively determined for the node associated with an unlisted item from the response content of each node that has already appeared. Can be estimated.

Regarding the Bayesian network, for example, consider a case where parent node A-> child node B and parent node A-> child node C as a directed graph between nodes A, B, and C.
Probability of understanding A: P (A)
Probability of understanding B: P (B)
Probability of understanding C: P (C)
Probability of understanding level of C when A answers correctly = P (C | A)
Probability of understanding of C when B answers correctly = P (C | B)
C's comprehension probability when A answers correctly and then B answers correctly
= P (C | A = 1, B = 1)
Each time a response to the question item is obtained, the comprehension degree probability of another node (learning unit) that has not appeared is recalculated. As a result, even if the system is complicated, the probabilistic dependency of the item to be subsequently presented can be modeled using the understanding degree probability (conditional probability) at each node.

  The directed graph of the present invention is a network that specifies an understanding order relationship between learning units. Therefore, when a correct answer is given for an arbitrary node, the understanding probability of other nodes connected to that node also increases according to the correct answer. On the other hand, when a wrong answer is given for an arbitrary node, the understanding degree probability of another node connected to that node also decreases according to the wrong answer.

  5 to 9 show a process of updating the understanding probability of the node in the model. Here, it shows how the understanding probability changes depending on the correct / wrong answer of the test answer to the test question.

FIG. 5 is a first explanatory diagram showing a directed graph and an understanding degree probability of a node at the time of initial setting.
The understanding probability of each node at the time of the initial setting may be an average frequency of answers obtained from a large number of users or an average correct answer rate of answers. Of course, it may be manually set in advance, or may be calculated using machine learning.
According to FIG. 5, first, the node 5 closest to the median value 0.5 (understanding degree probability is 0.52) is selected, and a test question associated with the node is given to the user.

FIG. 6 is a second explanatory diagram illustrating updating of the understanding level probability of the node when the “answer” is given to the test question of the node 5.
According to FIG. 6, the user has answered the test question of node 5 correctly. The understanding probability of the node 5 is updated to 1.00, and the understanding probability is recalculated by the Bayesian network for other nodes other than 1.00 or 0.00.

FIG. 7 is a third explanatory diagram showing the update of the understanding probability of the node when the test question of the node 8 is “wrongly answered”.
According to FIG. 7, the user has incorrectly answered the test question of node 8. The understanding probability of the node 8 is updated to 0.00, and the understanding probability is recalculated by the Bayesian network for other nodes other than 1.00 or 0.00.

FIG. 8 is a fourth explanatory diagram showing the update of the understanding probability of the node when the test question of the node 4 is “wrongly answered”.
According to FIG. 8, the user has incorrectly answered the test question of node 4. The understanding probability of the node 4 is updated to 0.00, and the understanding probability is recalculated by the Bayesian network for the other nodes having the understanding probability other than 1.00 or 0.00.

FIG. 9 is a fifth explanatory diagram illustrating updating of the understanding level probability of the node when the “answer” is given to the test question of the node 13.
According to FIG. 9, the user has answered the test question of the node 13 correctly. The understanding probability of the node 13 is updated to 1, and the understanding probability is recalculated by the Bayesian network for other nodes other than 1.00 or 0.00.

[Information amount calculation unit 12]
The information amount calculation unit 12 calculates the information amount from the node understanding level probability and the network information amount from all node information amounts for the first model or the second model.

The average information amount Hi (X) when the probability of the node i is p can be calculated by the following binary cross entropy.
Hi (X) =-plogp- (1-p) log (1-p)
The average information amount Hi (X) is an index indicating the likelihood or difficulty of a certain event.
A node closer to the understanding probability of 0.5 has a higher average information amount Hi (X), and it is difficult to determine whether the node understands or does not understand.
If the event always occurs (occurrence probability is 0.0 or 1.0)-> average information amount H (X) is minimum If the occurrence probability is 1/2 (occurrence probability is 0.5)-> average information The quantity H (X) is maximum

The information amount calculation unit 12 calculates, for each model (currently selected model), the “network information amount H (X)” when the random variables X of all the nodes U included in the model follow the probability distribution P, using the following equation. (For example, see Non-Patent Document 5).
H (X) = _-Σx∈UP (X = x) logP (X = x)

  FIG. 10 is an explanatory diagram illustrating switching of nodes in the model.

According to FIG. 10A, the switching of the nodes in the subjective question model is shown.
First, a subjective question associated with the node 11 having an understanding degree probability of 55% (average information amount 0.99) is selected. It is assumed that “no confidence in calculating correctly” is answered as a subjective answer to the question of the subjective question of the node 11. In this case, the understanding degree probability based on the node 11 is changed to “30%”. As a result, the understanding probability of other nodes also changes.
Next, a subjective question associated with node 8 having an understanding degree probability of 55% (average information amount 0.99) is selected. It is assumed that "subject to correct calculation" is answered as a subjective answer to the subjective question of the node 8. In this case, the understanding degree probability based on the node 8 is changed to “70%”. As a result, the understanding probability of other nodes also changes.
Next, a subjective question associated with the node 9 having an understanding degree probability of 50% (average information amount 1.00) is selected. Suppose that “I am confident in calculating correctly” is answered as a subjective answer to the question of the subjective question of the node 9. In this case, the understanding probability based on the node 9 is changed to “70%”. As a result, the understanding probability of other nodes also changes.
Thus, the subjective question and the subjective answer are repeated.

FIG. 10B shows the switching of nodes in the test question model.
First, a test question associated with node 8 having an understanding degree probability of 50% (average information amount 1.00) is selected. It is assumed that the test answer to the test question of the node 8 is “correct answer”. In this case, the understanding degree probability based on the node 8 is changed to “100%”. As a result, the understanding probability of other nodes also changes.
Next, a test question associated with the node 11 having an understanding degree probability of 55% (average information amount 0.99) is selected. Assume that the test answer to the test question of the node 11 is “wrong answer”. In this case, the understanding probability based on the node 11 is changed to “0%”. As a result, the understanding probability of other nodes also changes.
Next, a test question associated with node 9 having an understanding degree probability of 55% (information amount 0.99) is selected. Assume that the test answer to the test question of the node 9 is “correct answer”. In this case, the understanding probability based on the node 9 is changed to “100%”. As a result, the understanding probability of other nodes also changes.
Thus, the test question and the test answer are repeated.

  The “average” and “variance difference” in FIGS. 10A and 10B are indices indicating a change in the distribution of the information amount before and after the question, and are updated with the content of the response each time the question is asked.

  FIG. 11 is an explanatory diagram showing the time required for the subjective answer and the test answer.

Here, the response cost ratio for each question is expressed as follows.
Response cost ratio = (time required from presentation of an average test question to answering the test) /
(Time required from presentation of average subjective question to subjective answer)
Also, the time required for the "correct answer" and the "wrong answer" of the test answer are different.
According to FIG. 11, the cost of the subjective answer to the user (the required time) is substantially constant. On the other hand, as for the cost of the test answer to the user, the higher the difficulty of the test question, the higher the cost of the test answer.

[Model switching unit 13]
The model switching unit 13 controls switching to the second model or the first model according to the amount of network information in the first model or the second model (currently selected model).

  FIG. 12 is a flowchart showing a predetermined condition for switching models.

Here, the predetermined conditions of the model switching unit 13 include the following two embodiments.
(First embodiment)
While repeating the understanding degree probability updating unit 11 and the information amount calculating unit 12 for the first model, when the network information amount becomes a predetermined condition, the network is switched to the second model.
According to FIG. 12A, when the network information amount of the first model becomes equal to or less than the first threshold, the first model is switched to the second model.
According to FIG. 12B, even if the understanding level probability updating unit 11 and the information amount calculating unit 12 are repeated a predetermined number of times (for example, 20 times) for the first model, the network information amount of the first model is equal to the first model. If the value does not fall below the threshold, the first model is switched to the second model.

  Regarding the switching from the first model to the second model, the first model and the understanding probability updated by the understanding probability update unit 11 are converted into the understanding probability of the node mutually corresponding to the second model to be switched. Convert and rewrite.

(Second embodiment)
While repeating the understanding degree probability updating unit 11 and the information amount calculating unit 12 for the switched second model, when the network information amount of the second model becomes a predetermined condition, the second model is switched to the first model.
According to FIG. 12C, even if the understanding level probability updating unit 11 and the information amount calculating unit 12 are repeated a predetermined number of times (for example, three times) with respect to the switched second model, the network information amount of the second model is reduced. If it does not fall below the second threshold, it switches to the first model.

  Regarding switching from the second model to the first model, the second model and the understanding probability updated by the understanding probability update unit 11 are converted into the understanding probability of the node mutually corresponding to the first model that is the switching destination. Convert and rewrite.

  The switching from the first model to the second model or the switching from the second model to the first model may be performed a plurality of times. In this case, for example, a plurality of third and fourth thresholds may be used in addition to the first threshold and the second threshold.

  FIG. 13 is an explanatory diagram illustrating model switching.

<About User A>
First, using a subjective question model (first model), a subjective question associated with a node having a large amount of network information is presented. Then, the probabilities of understanding of other nodes are changed according to the subjective answer, and the amount of network information is calculated. Until the amount of network information becomes equal to or less than the first threshold = 6.7, a subjective question associated with a node having a large amount of network information is presented using a subjective question model. By the subjective answer to the node 6 presented at the ninth time, the network information amount becomes 6.5, and it is switched to the test problem model (second model).
Next, a test problem is presented from a node having a large amount of network information using a test problem model (second model).

<About User B>
First, using a subjective question model (first model), a subjective question associated with a node having a large amount of network information is presented. Then, the probabilities of understanding of other nodes are changed according to the subjective answer, and the amount of network information is calculated. The subjective question is presented using the subjective question model until the network information amount becomes equal to or less than the first threshold value = 6.7. Since the network information amount does not become equal to or less than the first threshold value of 6.7 even by the subjective answer to the node 22 presented at the 19th time, it is switched to the test problem model (second model).
Next, a test problem is presented from a node having a large amount of network information using a test problem model (second model).

<About User C>
First, using a subjective question model (first model), a subjective question associated with a node having a large amount of network information is presented. Then, the probabilities of understanding of other nodes are changed according to the subjective answer, and the amount of network information is calculated. The subjective question is presented using the subjective question model until the network information amount becomes equal to or less than the first threshold value = 6.7. At the time of the subjective answer to the node 5 presented at the sixth time, since the network information amount has become 6.4, it is switched to the test problem model (second model).
Next, the user C is presented from a test question associated with a node having a large amount of network information using a test question model (second model). At the time of the test answer for the node 10 presented at the tenth time, even if the predetermined number of times is repeated three times, the network information amount does not become the second predetermined threshold = 6.0 or less. Switch.
Again, a subjective question model (first model) is used to present a subjective question associated with a node having a large amount of network information. The subjective question is presented using the subjective question model until the network information amount becomes equal to or less than the third threshold value = 6.2. At the time of the subjective answer to the node 14 presented at the fourteenth time, the network information amount becomes 5.9, so the test question model (the second model) is switched again.
Again, using the test problem model (second model), the test problem is presented from the test problem associated with the node having a large amount of network information.

  FIG. 14 is an explanatory diagram illustrating an application target of the understanding probability of the first model.

  According to FIG. 14, for user A, an object to which the understanding probability is applied when switching from the subjective question model (first model) to the test problem model (second model) is shown.

Using the subjective question model (first model), the subjective information for the node 6 presented at the ninth time makes the network information amount 6.5, and when switching to the test problem model (second model), An example of a first understanding probability application criterion for applying the understanding probability of the subjective question model (first model) to the corresponding node of the test problem model (second model) will be described below.
[Probability of understanding of first model] [Probability of understanding of second model]
0.0 or more and less than 0.20 0.0
0.20 or more and less than 0.81 Not applicable 0.81 or more to 1.0 or less 1.0

  FIG. 15 is an explanatory diagram illustrating a method of applying and calculating the understanding probability of the second model.

  According to FIG. 15, according to the first understanding probability probability application criterion, the understanding probability of the subjective question model (first model) is applied to the corresponding node of the test problem model (second model). , The understanding probability of the “not applied” node is calculated using the second model.

  FIG. 16 is an explanatory diagram illustrating an application target of the second model understanding degree probability.

  According to FIG. 16, for the user C, an object to which the understanding probability is applied when switching from the test question model (second model) to the subjective question model (first model) is shown.

Using the test problem model (second model), when the test answer to the node 10 presented at the tenth time is repeated a predetermined number of times = 3 times, the network information amount is equal to the second predetermined threshold = 6.0. When switching to the first model again to avoid the following, the second understanding in which the understanding probability of the test problem model (second model) is applied to the corresponding node of the subjective question model (first model) Examples of the degree probability application criteria are shown below.
[Probability of understanding of second model] [Probability of understanding of first model]
0.0 or more and less than 0.20 Understanding probability of the second model 0.20 or more and less than 0.80 Not applicable 0.80 or more to 1.0 or less Understanding probability of the second model

  FIG. 17 is an explanatory diagram illustrating a method of applying and calculating the understanding degree probability of the first model.

  According to FIG. 17, according to the second understanding probability applying criterion, the understanding probability of the test problem model (second model) is applied to the corresponding node of the subjective question model (first model). , The understanding probability of the “not applied” node is calculated using the first model.

As described above in detail, according to the user-adaptive test program, apparatus and method of the present invention, measurement can be performed within a limited test time regardless of the user's understanding and proficiency. .
ADVANTAGE OF THE INVENTION According to this invention, a test question can be advanced according to a user's subjective answer, and the user's learning level can be estimated, without the content of a test question being too difficult or too simple.
For example, when a Bayesian network is used, the following problem for determining the user's understanding level requires a large amount of computational processing and storage memory space. By narrowing down the number of subjective answers that can be selected, it is possible to reduce the calculation resources required for calculating the understanding probability.

  For the above-described various embodiments of the present invention, various changes, modifications, and omissions in the scope of the technical idea and viewpoint of the present invention can be easily performed by those skilled in the art. The foregoing description is merely an example, and is not intended to be limiting. The invention is limited only as defined by the following claims and equivalents thereof.

DESCRIPTION OF SYMBOLS 1 Test apparatus 100 Model storage unit 101 Item presentation unit 102 Response determination unit 11 Understanding probability update unit 12 Information amount calculation unit 13 Model switching unit 2 Terminal

Claims (12)

In a user-adaptive test program that causes a computer mounted on the device to function,
It is a directed graph composed of "nodes" including understanding probabilities and arcs connecting the nodes, in which an item based on a first criterion for obtaining a subjective answer to a subjective question is associated with a node. Model storage means for storing in advance a model and a second model in which an item based on a second criterion for obtaining a test answer to a test question is associated with a node;
For the first model and the second model, and comprehension probability updating means based on the response of the user and recalculates the comprehension probability at other nodes not yet out of items associated to an item,
For the first model and the second model, the information amount calculation means for calculating a network information amount from comprehension probabilities of all nodes,
Causing the computer to function as model switching means for switching to the second model when the network information amount becomes a predetermined condition while repeating the understanding level probability updating means and the information amount calculating means for the first model. A test program characterized by: The test program according to claim 1, wherein the predetermined condition of the model switching means causes the computer to function such that the network information amount of the first model is equal to or less than a first threshold. The predetermined condition of the model switching means is that the network information amount does not become equal to or less than the first threshold value even after repeating the understanding level probability updating means and the information amount calculating means for the first model a predetermined number of times. The test program according to claim 1, wherein the test program causes the computer to function as described above. The model switching unit is configured to switch to the first model when the network information amount becomes a predetermined condition while repeating the understanding level probability updating unit and the information amount calculating unit for the second model. The test program according to any one of claims 1 to 3, wherein the test program is operated. The model switching means, be repeated a predetermined number of times for the second model has been switched, when the network information of the second model is not less than a second predetermined threshold value, the computer to switch to the first model The test program according to any one of claims 1 to 4, wherein the test program is caused to function. Each node of the first model corresponds to one of the nodes of the second model,
The model switching means converts the understanding level probability of the node of the migration destination model into the understanding level probability of the corresponding node of the migration source model according to the first understanding level probability applying criterion or the second understanding level probability applying criterion. The test program according to any one of claims 1 to 5, wherein the test program causes a computer to function so as to rewrite the test program. For the first model and the second model, select the node that non-output item associated, and items presenting means for presenting the items in the node,
For the first model and the second model, claim 1, characterized in that the computer is further caused to function as a response determination means for determining a correct / incorrect answer for the contents of a response to the foregoing item 6 of 1 Test program described in section. The comprehension degree update means, for an item based on the first criterion, changes the comprehension degree of the node in a stepwise manner from 0.0 to 1.0 in accordance with the contents of a plurality of subjective answers to the subjective question. The test program according to any one of claims 1 to 7, wherein the test program causes the computer to function so as to recalculate the understanding level probability. Arcs in the directed graph of the model are connected based on the understanding order relationship between the nodes, and are weighted according to the degree of association between the nodes,
The comprehension probability updating means, test program according to any one of claims 1 to 8 for causing a computer to function so as to calculate the intelligibility of probability of the node by Bayes' theorem. The information amount calculating means, the network information amount in the case of a random variable X of all nodes U in the model according to the probability distribution P, and calculated by the following equation _{H (X) = - Σ x∈U} P (X = X) logP (X = x)
The test program according to any one of claims 1 to 9 , wherein the computer is caused to function as described above. In an apparatus for performing a user-adaptive test,
It is a directed graph composed of "nodes" including understanding probabilities and arcs connecting the nodes, in which an item based on a first criterion for obtaining a subjective answer to a subjective question is associated with a node. Model storage means for storing in advance a model and a second model in which an item based on a second criterion for obtaining a test answer to a test question is associated with a node;
For the first model and the second model, and comprehension probability updating means based on the response of the user and recalculates the comprehension probability at other nodes not yet out of items associated to an item,
For the first model and the second model, the information amount calculation means for calculating a network information amount from comprehension probabilities of all nodes,
A model switching unit for switching to a second model when the network information amount becomes a predetermined condition while repeating the understanding degree probability updating unit and the information amount calculating unit for the first model. And equipment. Using the apparatus, a ruthenate stringent method to perform a test of the user-adaptive,
The device is a directed graph constructed in including physical Kaido probability a "node" and connecting it arcs nodes together, item correspondence to the node based on the first reference to determine the subjective answer to subjective questions The first model obtained in advance and a second model in which an item based on a second criterion for obtaining a test answer to a test question is associated with a node are stored in advance,
The device comprises:
For the first model and the second model, the first step of re-calculated based on the response of the user, the comprehension probability at other nodes not yet out of items associated to an item,
For the first model and the second model, running a second step of calculating the network information amount from comprehension probabilities of all nodes,
In that the first model repeating the first step and the second step, when the network information amount has reached a predetermined condition, characteristics and be ruthenate strike method to switch to the second model.