JP6498106B2 - User-adaptive test program, apparatus and method for selecting model of problem group according to understanding probability - Google Patents

Description

  The present invention relates to a technique of an e-Learning system that determines the academic ability of a user (learner).

  According to the user-adaptive e-Learning system, using a database that accumulates the answer tendency of many past users as a history, for each user, select and clearly specify problems and contents suitable for the user's learning and understanding. can do. There is also a “testing” system that provides different problems and learning materials for each user by placing the e-Learning system as a server on the network.

  It is very difficult to create a plurality of problems corresponding to the user's level of understanding. In particular, it is extremely difficult to determine the level of comprehension by making the difficulty level of each question constant. On the other hand, there is an adaptive testing (computer adaptive test) technique that estimates the parameters of a problem that has not been issued and selects the next problem according to the answer result of the user (see, for example, Non-Patent Document 1). ).

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

  When operating a Bayesian network, it is necessary to prepare a storage memory space of a probability table (Conditional Probability Table) including probability values estimated based on given conditions in the computer. Here, when the estimated granularity is O and the number of nodes is n, it is known that the maximum number of elements in the probability table is On, and it is necessary to prepare enormous computer calculation resources. On the other hand, algorithms such as loopy belief propagation, a sampling method, and a Junction Tree method have been proposed as techniques for reducing computational resources (see, for example, Non-Patent Document 5).

JP 2004-170842 A

Masaomi Ueno, “Evaluation of Learning in the New Era”, Education Test Research Center 18th Research Group Report, June 18, 2010, [online], [Search April 21, 2015], Internet <https: / /www.cret.or.jp/files/dbd90c4cb469bf94ef5da2256616c7e7.pdf> Masaomi Ueno, Hitoshi Onishi, Kazuo Shigeki, “Proposal of Test Theory with Probability Network”, IEICE Technical Report, ET93-64, 55-62,1993, [online], [Search April 21, 2015 ] Internet <http://ci.nii.ac.jp/naid/110003192386> Masaomi Ueno, Chiharu Kawatake, Hitoshi Onishi, "Structural Optimization Method in Network Type Test Theory", IEICE Technical Report, ET93-ET127, March 26, 1994, IEICE, Vol100, P50-P60, [online ], [Search March 8, 2015], Internet <URL: http://jglobal.jst.go.jp/public/20090422/200902144032577390> Kazuo Hangeki, Masaomi Ueno, Yoichi Motomura, “Outline of Bayesian Network”, Baifukan, July 21, 2006 Yoichi Motomura, “Bayesian Network: From Introduction to Application to Human Modeling”, [Search July 30, 2015], Internet <URL: https://staff.aist.go.jp/y.motomura/paper/ BSJ0403.pdf> "Amount of information", Wikipedia, [online], [Search on 9th of April 2015], Internet <URL: https://en.wikipedia.org/wiki/%E6%83%85%E5%A0%B1 % E9% 87% 8F>

  However, when the next problem for determining the user's degree of understanding is selected using, for example, a Bayesian network, a large amount of calculation processing and storage memory space are required as described above. The greater the number of questions that can be selected, the greater the computational resources required to calculate the understanding probability.

  In addition, understanding of learning content realistic for the user does not simply proceed step by step according to the learning level (curriculum). For example, in an actual educational setting, when the first grader of junior high school has a low level of understanding of mathematics, it is not just an effort to improve the level of understanding of arithmetic by elementary school students. When a junior high school first grader's understanding level is low in mathematics "graphics", the arithmetic of elementary school students should also be judged from the understanding level based on "graphics". In this case, it is possible to reduce the overall number of questions as a result by determining the degree of understanding of the “graphic” problem of arithmetic by elementary school students.

  Therefore, the present invention provides a user-adaptive test program, apparatus, and method that can select the next problem from a group of problems that are not limited to the learning level (curriculum) and whose understanding level is ambiguous for the user. For the purpose.

According to the present invention, a user-adaptive test program for causing a computer mounted on an apparatus to function is provided.
Specify the “node” that includes the probability of understanding, which is associated with the question and the answer,
A learning model storage unit that divides a plurality of nodes into a plurality of models (groups) based on different criteria, and stores a directed graph in which the nodes are connected by arcs for each model,
A next candidate model selecting means for calculating an average understanding probability that is an average value of the understanding probabilities for each model, and selecting a next candidate model based on the average understanding probability;
In the next candidate model, a problem presentation means for selecting a node associated with an unissued problem and presenting the problem,
Answer determination means for determining the correct / incorrect answer of the answer to the given question;
For each user, for each model in the learning model storage means, recalculate the comprehension probabilities at all other nodes associated with the unanswered question based on the already answered question and the correct / incorrect answer of the answer. The computer is made to function as an understanding degree probability update means.

According to another embodiment of the test program of the present invention,
The model is obtained by classifying a plurality of nodes based on a learning level and / or a learning category.
It is also preferred that the computer function so that the directed graph of the model is obtained by connecting nodes with arcs based on the learning order relationship.

According to another embodiment of the test program of the present invention,
The understanding probability update means records the problem in the learning model storage means with an understanding probability of the node of 1 when the answer is correct and an understanding probability of the node of 0 when the answer is incorrect. It is also preferred to have the computer function to recalculate the degree probability.

According to another embodiment of the test program of the present invention,
The understanding level probability update means preferably causes the computer to function to calculate the understanding level probability of the node by Bayes' theorem.

According to another embodiment of the test program of the present invention,
The next candidate model selection means is:
For each user, further calculate the standard deviation in understanding probabilities of multiple nodes for each model,
A model whose average value is within the range of the first predetermined threshold value from the median value of understanding probability (= 0.5) and whose standard deviation is equal to or larger than the second predetermined threshold value is selected as the next candidate model. It is also preferable to make the computer function.

According to another embodiment of the test program of the present invention,
The next candidate model selection means, when a plurality of next candidate models are selected,
The average information amount H (X) when the random variables X of all the nodes U included in the next candidate model follow the probability distribution P is calculated for each next candidate model by the following equation:
H (X) = − _Σx∈UP (X = x) logP (X = x)
It is also preferable to cause the computer to function so as to select the model having the highest average information amount H (X) as the next candidate model.

According to another embodiment of the test program of the present invention,
The problem presenting means presents a predetermined number or more of questions included in an unquestioned learning unit, and the answer determination means includes an understanding probability update means after the correct / incorrect answer results for the predetermined number or more of questions. It is also preferable to make the computer function so that the next candidate model selection means is executed.

According to the present invention, an apparatus for performing a user adaptive test comprising:
Specify the “node” that includes the probability of understanding, which is associated with the question and the answer,
A learning model storage unit that divides a plurality of nodes into a plurality of models (groups) based on different criteria, and stores a directed graph in which the nodes are connected by arcs for each model,
A next candidate model selecting means for calculating an average understanding probability that is an average value of the understanding probabilities for each model, and selecting a next candidate model based on the average understanding probability;
In the next candidate model, a problem presentation means for selecting a node associated with an unissued problem and presenting the problem,
Answer determination means for determining the correct / incorrect answer of the answer to the given question;
For each user, for each model in the learning model storage means, recalculate the comprehension probabilities at all other nodes associated with the unanswered question based on the already answered question and the correct / incorrect answer of the answer. Comprehension degree probability update means.

According to the present invention, there is provided a test method for a device for performing a user adaptive test,
Specify the “node” that includes the probability of understanding, which is associated with the question and the answer,
The apparatus divides a plurality of nodes into a plurality of models (groups) based on different criteria, and has a learning model storage unit that stores in advance a directed graph in which nodes are connected by arcs for each model,
The device
A first step of calculating an average comprehension probability that is an average value of the comprehension probabilities for each model, and selecting a next candidate model based on the average comprehension probabilities;
A second step of selecting a node associated with an unissued problem in the next candidate model and presenting the problem;
A third step of determining the correct / incorrect answer of the answer to the given question;
For each user, for each model in the learning model storage means, recalculate the comprehension probabilities at all other nodes associated with the unanswered question based on the already answered question and the correct / incorrect answer of the answer. And a fourth step.

  According to the user-adaptive test program, apparatus, and method of the present invention, the next problem can be selected from a group of problems that are not limited to the learning level (curriculum) and whose understanding level is ambiguous for the user. As a result, the number of questions for determining the degree of understanding of the user can be reduced.

It is a functional block diagram of the test apparatus in this invention. 3 is a flowchart of the present invention. It is an example of the directed graph of the node memorize | stored in the learning model memory | storage part. It is explanatory drawing showing all the nodes in a learning model memory | storage part. It is explanatory drawing showing the model divided according to the learning level in a learning model memory | storage part. It is explanatory drawing showing the model divided according to the learning category in a learning model memory | storage part. It is the 1st explanatory view showing the directed graph and comprehension probability of a node at the time of initialization. It is a 2nd explanatory drawing showing the update of the comprehension probability of a node when answering the question of the node 6-5 correctly. It is a 3rd explanatory drawing showing the update of the comprehension probability of a node in the case of having answered the question of the node 6-8 incorrectly. It is the 4th explanatory view showing update of the comprehension probability of a node when answering a problem of node 6-4 incorrectly. It is the 5th explanatory view showing the update of the comprehension probability of a node when answering the question of node 6-13 correctly. It is a flowchart of the next candidate model selection part in this invention. It is the table | surface which computed the average comprehension probability and the standard deviation about each model for every user. It is a graph showing an average comprehension probability about each model for every user. It is a graph showing dispersion | distribution of an understanding degree probability for every user. It is a graph showing the relationship between generation | occurrence | production probability and information content. It is the table | surface which computed the element unit average information amount for every model, and the average value of element unit average information amount.

  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 that performs 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 apparatus 1 functions as a server for the terminal 2. Further, the functional configuration unit of the test apparatus 1 may be mounted on the terminal 2 so that the terminal alone functions as the test apparatus.

  1 includes a learning model storage unit 10, a next candidate model selection unit 11, a problem presentation unit 12, an answer determination unit 13, and an understanding level probability update unit 14. These functional components are realized by executing a program that causes a computer mounted on the apparatus to function. Further, the processing flow of these functional components can be understood as a user-adaptive test method as shown in FIG.

[Learning model storage unit 10]
The learning model storage unit 10 defines a “node” including a probability of understanding, in which a question and an answer are associated with each other. The problem may include not only text but also images, video, and sound. The learning model storage unit 10 divides a plurality of nodes into a plurality of models (groups) based on different criteria, and accumulates a directed graph in which the nodes are connected by arcs for each model.

  As an initial state, the learning model storage unit 10 is assumed to give comprehensive understanding probabilities for each node from the answer results for a large number of users. For example, the understanding degree probability in the initial state may be an average correct answer rate obtained from a large number of users. Of course, it may be set in advance manually or may be calculated using machine learning.

  The learning model storage unit 10 sets the node's understanding probability to 1 in the case of a correct answer, and sets the node's understanding probability to 1 in the case of a correct answer, after the question of the node has been set. Is recorded as 0.

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

  According to FIG. 3, a directed graph in one model is represented, and nodes are connected by arcs based on a learning order relationship. The learning order relationship means that the understanding probability of the preceding node affects the understanding probability of the subsequent node. For example, it is only necessary to be able to specify the relationship from front to back roughly according to the learning curriculum, such as April-> May for first graders.

  A set of words extracted by morphological analysis of question and answer texts associated with each node may be compared, and an arc may be a combination of those having high learning content similarity between nodes. Morphological analysis is a process that uses a grammar and word dictionary as an information source to divide a sentence written in a natural language into morphemes (Morpheme), which are the smallest units that have meaning as a language, and discriminate each part of speech. . Here, all the extracted words may be used, or only morphemes whose part of speech is a noun may be extracted.

  As a method for calculating the learning content similarity between nodes, for example, a TF-IDF (Term Frequency-Inverse Document Frequency) method may be used. According to this method, TFi, j calculated from the number and frequency of occurrence of the word wi in the learning content of the node j and the number mi of the nodes where the word wi appears among all the nodes j = 1 to N are obtained. The calculated IDFi is used as a weight for the word wi included in the node j. For each node, the learning content is expressed by Bag-of-Words, and the components of each vector are weighted by the corresponding value of TF × IDFi. Bag-of-Words expresses learning text as a feature vector defined by the frequency of one word, and derives similarity between sentences using IDFs derived in advance based on sentence sets as word weights. is there. Then, a cosine distance is calculated between the two vectors, and this is used as the similarity between the learning contents.

  Nodes whose learning content similarity is equal to or greater than a predetermined threshold are connected by arcs of a directed graph. For example, it is considered that the probability of understanding the problem of the node after being connected by the arc also changes according to the level of understanding probability of the problem of the previous node.

  This directed graph may be created manually by considering the relationship between the nodes based on the learning guidance policy. Moreover, it may be automatically created based on the learning start time from the similarity 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, the single subject “mathematics” is applied. However, the subject may extend over a plurality of subjects, or may be based on highly specialized qualification education or corporate education.

  FIG. 4 is an explanatory diagram showing all nodes in the learning model storage unit. FIG. 4 shows nodes as learning units from the fourth grader to the third grader. The learning unit from the fourth grade to the sixth grade in elementary school is represented by 49 nodes, and the learning unit for junior high school students is represented by 21 nodes.

  5 and 6 divide a plurality of nodes into a plurality of models (groups) based on different criteria. The model is obtained by classifying a plurality of nodes on the basis of a learning level and / or a learning category. Also, the granularity may be different within the same learning level and / or learning category.

  FIG. 5 is an explanatory diagram showing a model divided according to the learning level in the learning model storage unit. According to FIG. 5, nodes are divided for each grade as a learning level.

  FIG. 6 is an explanatory diagram showing a model divided according to the learning category in the learning model storage unit. According to FIG. 6, the nodes are divided for each learning category. For example, nodes are divided across multiple grades, elementary school students, and junior high schools by learning categories such as “number and calculation”, “quantity / graphic”, and “quantity”.

For example, the model m20 has a total of 15 nodes (4 nodes in elementary school 5, 3 nodes in elementary school 6, 3 nodes in middle one, 3 nodes in elementary school, with “number and calculation” of elementary school students and “number and formula” of junior high school as learning areas. 2 nodes in the middle 2 and 3 nodes in the middle 3).
In addition, according to the models m22 and m23, the “quantity relationship” of elementary school students develops into “functions” of junior high school students and “use of materials”. For this reason, the models m22 and m23 have the same elementary school node but different junior high school student nodes.

According to FIG. 1, the problem presentation unit 12, the answer determination unit 13, and the understanding level probability update unit 14 are executed in units of next candidate models extracted by the next candidate model selection unit 11. Here, the following three embodiments can be assumed.
(1) Embodiment 1
For each subsequent candidate model, the problem presentation unit 12, the answer determination unit 13, and the understanding level probability update unit 14 are repeatedly executed a predetermined number or more. In this case, it is possible to reduce the amount of calculation for selecting the next candidate model in order to repeat a predetermined number of questions / answers in the next candidate model for the user. Further, since the next candidate model is fixed for a predetermined number of problems, problems within the learning level and / or the learning category are continuously presented.
(2) Embodiment 2
Each time the question presentation unit 12, the answer determination unit 13, and the understanding level probability update unit 14 are executed, the next candidate model is reselected from all models. In this case, the calculation amount increases in order to select the optimal next candidate model each time, but it is possible to exhaustively answer questions outside the learning level and / or the learning category.
(3) Embodiment 3
The above-described first and second embodiments are combined, and after repeating a predetermined number of questions / answers in the next candidate model, the next candidate model is selected again. According to the first embodiment, the amount of calculation for selecting the next candidate model can be reduced moderately, and the second embodiment can comprehensively ask questions outside the learning level and / or the learning category.

  Below, after explaining the problem presentation part 12, the answer determination part 13, and the understanding degree probability update part 14 performed for every model, the next candidate model selection part 11 is demonstrated.

[Problem Presentation Unit 12 (S12)]
The problem presentation unit 12 selects, for each user, a node associated with an unissued problem in the next candidate model and presents the problem. When the test apparatus 1 is a server, the problem presentation unit 12 transmits the problem content to the terminal 2 operated by the user.

[Answer determination unit 13 (S13)]
The answer determination unit 13 determines the correct / incorrect answer of the answer to the given question for each user. Since each node includes a question and an answer, the correct answer / wrong answer is determined by comparing the user's answer with the answer of the question. The determination result is reflected in the learning model storage unit 10.

  According to the present invention, the problem presentation unit 12 presents a predetermined number or more of questions included in the unquestioned learning unit, and the answer determination unit 13 displays the correct / incorrect answer results for the predetermined number of questions. It is preferable to execute an understanding probability update unit 14 and a next candidate model selection unit 11 which will be described later. After the understanding level probabilities for the predetermined number of nodes are calculated, it is possible to select the optimum model to be asked next as much as possible.

  According to FIG. 4 described above, answers have already been made for 10 nodes. These nodes are already assigned either 1 (correct answer) or 0 (incorrect answer) as the degree of understanding probability. According to the present invention, the model to be asked next is then selected, and the node corresponding to the unsolved problem of that model is selected.

[Understanding Level Probability Update Unit 14 (S14)]
The comprehension probability update unit 14 associates, for each user (learner), an unissued question with respect to each model in the learning model storage unit 10 based on the existing question and the correct / incorrect answer of the answer. Recalculate understanding probabilities (likelihoods) at all other nodes.
The user answers the questions to be answered sequentially, and the answer determination unit 13 described later sets the understanding probability of the node to 1.0 in the case of a correct answer, and sets the understanding probability of the node in the case of an incorrect answer. 0.0. For each correct / incorrect answer result, the comprehension probability stored in the learning model storage unit 10 is recalculated. As a result, it is possible to update the comprehension probability of an unquestioned question using the answer result of the question that has already been set.

  The understanding degree probability of the node included in each model, which is updated by the understanding degree probability update unit 14, may be, for example, using a “Bayesian network”. A Bayesian network is a graphical network that describes a causal relationship between nodes by probability (see, for example, Non-Patent Document 4). The network in the present invention refers to a graph structure having “nodes” in which a problem and an answer are associated with each other and the similarity given to arcs between the nodes as “weights”. A Bayesian network is a model of probabilistic reasoning that expresses inference of causal relations between a plurality of nodes by a directed acyclic graph structure and expresses a relation between individual variables by a conditional probability. A directed acyclic graph structure is one in which an arrow is attached to an arc (directed), and the path of the arrow does not circulate through a node. By using a Bayesian network, the correct answer rate (understandability probability) of uncertain events (correct answers / incorrect answers) for the nodes associated with unanswered questions from the correct answers / incorrect answers of each node already answered. Can be estimated quantitatively.

For a Bayesian network, for example, consider a case of parent node A-> child node B, parent node A-> child node C as a directed graph between nodes A, B, and C.
A comprehension probability: P (A)
B comprehension probability: P (B)
C comprehension probability: P (C)
C comprehension probability when A answers correctly = P (C | A)
C comprehension probability when B answers correctly = P (C | B)
C comprehension probability when A answers correctly and then B answers correctly
= P (C | A = 1, B = 1)
Every time an answer result of a question that has been given is obtained, the understanding probabilities of all the unanswered nodes (learning units) are recalculated. As a result, even in a complex system, it is possible to model a probabilistic dependency relationship in a problem to be presented subsequently using the understanding probability (conditional probability) at each node.

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

  7 to 11 show a process in which the node understanding probability is updated in the selected model.

FIG. 7 is a first explanatory diagram showing a directed graph and understanding probability of a node at the time of initial setting.
The understanding level probability of each learning unit at the time of initial setting may be an average value obtained from the answer results of past correct / incorrect answers of many users. Moreover, the average information amount obtained from the answer result may be sufficient. In the case of the average value, it is relatively difficult to determine “understand” or “understand” as the node is closer to the understanding probability 0.5.
First, the node 6-5 closest to the median value of 0.5 (understanding probability is 0.52) is selected, and the problem associated with that node is presented to the user. In the case of the average information amount, the larger the average information amount value is, the more difficult it is to determine “I understand” or “I don't understand”.

  FIG. 8 is a second explanatory diagram showing the update of the understanding probability of the node when the question of the node 6-5 is answered correctly. According to FIG. 8, the user has correctly answered the question of the node 6-5. The comprehension probability of the node 6-5 is updated to 1, and the comprehension probability is recalculated for all nodes other than 1 or 0 by the Bayesian network.

  FIG. 9 is a third explanatory diagram illustrating the update of the understanding probability of the node when the problem of the node 6-8 is erroneously answered. According to FIG. 9, the user has answered the problem of node 6-8 incorrectly. The comprehension probability of the node 6-8 is updated to 0, and the comprehension probability is recalculated for all nodes other than 1 or 0 by the Bayesian network.

  FIG. 10 is a fourth explanatory diagram showing the update of the understanding probability of the node when the problem of the node 6-4 is erroneously answered. According to FIG. 10, the user has wrongly answered the problem of node 6-4. The comprehension probability of the node 6-4 is updated to 0, and the comprehension probability is recalculated for all nodes other than 1 or 0 by the Bayesian network.

  FIG. 11 is a fifth explanatory diagram illustrating the update of the understanding probability of the node when the question of the node 6-13 is correctly answered. According to FIG. 11, the user has correctly answered the question of the node 6-13. The understanding level probability of the node 6-13 is updated to 1, and the understanding level probability is recalculated for all nodes other than 1 or 0 by the Bayesian network.

[Next Candidate Model Selection Unit 11 (S11)]
The next candidate model selection unit 11 calculates an average understanding degree probability that is an average value of the understanding degree probabilities for each model, and extracts a next candidate model based on the average understanding degree probability. Specifically, an average understanding probability that is closest to the median (= 0.5) may be extracted as the next candidate model, and further, the next candidate model is extracted using the standard deviation. It may be a thing.

  FIG. 12 is a flowchart of the next candidate model selection unit in the present invention.

(S111) The next candidate model selection unit 11 first calculates, for each user, an average value and a standard deviation of understanding probabilities of a plurality of nodes for each model.

  FIG. 13 is a table in which average comprehension probabilities and standard deviations are calculated for each model for each user. It is calculated for each model of learning level (grade classification) and learning category (learning area).

  FIG. 14 is a graph showing the average understanding probability for each model for each user. When the average understanding probability for each model is equal to or greater than a predetermined threshold, the user can determine that the learning content of the model is familiar.

  Note that models that have not been taken by the user are not subject to distribution grasping. For example, the user A who is a second grader of junior high school excludes the model m9 including the learning content of the third grader of junior high school. In addition, for example, the user B who is a sixth grader does not include models m7, m8, and m9 including learning contents of junior high school students.

(S112) Then, the next candidate model selection unit 11 has an average understanding probability within the range of the first predetermined threshold value from the median value (= 0.5), and the standard deviation is the second predetermined threshold value. A model that is equal to or greater than (allowable threshold) is extracted as the next candidate model. Here, for each model, 1 is set as the flag of the next candidate model.

According to FIGS. 12 and 13, for example, the first predetermined threshold is 0.1, and the second predetermined threshold is 0.45.
In this case, for user A, the following four models are extracted as the next candidate model.
[Average comprehension probability] [Standard deviation]
Model m7 0.44 0.48
Model m8 0.41 0.53
Model m10 0.55 0.60

  FIG. 15 is a graph showing the variance of understanding probability for each user.

For example, the standard deviation difference σdiff is given by σmax−σmin.
Maximum difference in standard deviation of user A: σAdiff_max = σAm6−σAm4
Maximum difference in standard deviation of user B: σBdiff_max = σBm6−σBm4
At this time, when the allowable value of the standard deviation for the understanding probability is σconst, it can be determined whether or not the standard deviation for the understanding probability of the user exceeds the allowable value.
The standard deviation allowable value may be different for each learning level or learning category model, or may be the same value.

(S113) Next, the next candidate model selection unit 11 determines whether the number of next candidate models is one or more. If there is one next candidate model, it is only necessary to select that model.

(S114) When a plurality of next candidate models are selected, the next candidate model selection unit 11 calculates an average information amount H (X) for each next candidate model.
The average information amount H (X) is an index indicating the likelihood or difficulty of occurrence of a certain event, and is defined as follows.
H (X) =-plogp- (1-p) log (1-p)

FIG. 16 is a graph showing the relationship between the occurrence probability and the information amount. According to FIG. 16, it has the following relationship.
When an event always occurs (occurrence probability is 0 or 1)-> average information amount H (X) is minimum When an occurrence probability is half (occurrence probability is 0.5)-> average information amount H (X) is the maximum

The next candidate model selection unit 11 calculates, for each next candidate model, the average information amount H (X) when the random variables X of all the nodes U included in the next candidate model follow the probability distribution P. (For example, refer nonpatent literature 6).
H (X) = − _Σx∈UP (X = x) logP (X = x)

(S115) Then, the next candidate model selection unit 11 selects the model having the highest average information amount H (X) as the next candidate model.

  The next candidate model selection unit 11 calculates, for each next candidate model, an element unit average information amount in units of level and category, and an average value of the element unit average information amount.

  FIG. 17 is a table in which the element unit average information amount and the average value of the element unit average information amount are calculated for each model. According to FIG. 17, from the models m7, m8, and m10, m8 (understanding probability is 0.529) with the maximum average information amount is finally selected.

  As described above in detail, according to the user-adaptive test program, apparatus, and method of the present invention, it is possible to reduce the calculation resources and not only to the learning level (curriculum) but also to various understanding levels that are low for the user. The next question can be selected from the problem group based on the category. As a result, the number of questions for determining the user's comprehension level itself can be reduced by selecting the next question to be asked from the category having a low user comprehension level.

For example, when 429 nodes are configured as one probability model from first grade to third grade, the maximum number of elements in the conditional probability table (CPT) is 1.39 × 10 ¹¹⁹ (= 2 to the 429th power). ) It becomes a piece. In contrast, according to the present invention, by dividing into a plurality of models (groups) based on the learning level and / or learning category, the number of nodes constituting one model is reduced to a range of 34 to 75, for example. Thus, the maximum number of CPT elements can be 3.77 × 10 ²² (= 2 to the 75th power).

  Various changes, modifications, and omissions of the above-described various embodiments of the present invention can be easily made by those skilled in the art. The above description is merely an example, and is not intended to be restrictive. The invention is limited only as defined in the following claims and the equivalents thereto.

DESCRIPTION OF SYMBOLS 1 Test apparatus 10 Learning model memory | storage part 11 Next candidate model selection part 12 Problem presentation part 13 Answer determination part 14 Comprehension probability update part 2 Terminal

Claims (9)

A user-adaptive test program for causing a computer mounted on the apparatus to function,
Specify the “node” that includes the probability of understanding, which is associated with the question and the answer,
A learning model storage unit that divides a plurality of nodes into a plurality of models (groups) based on different criteria, and stores a directed graph in which nodes are connected by arcs for each model,
A next candidate model selecting means for calculating an average understanding probability that is an average value of the understanding probabilities for each model, and selecting a next candidate model based on the average understanding probability;
In the next candidate model, a node associated with an unissued problem is selected, and a problem presenting means for presenting the problem,
Answer determination means for determining the correct / incorrect answer of the answer to the given question;
For each user, for each model in the learning model storage means, recalculate the comprehension probabilities at all other nodes to which the unanswered question is associated, based on the already answered question and the correct / incorrect answer of the answer. A test program for causing a computer to function as an understanding probability update means. The model is obtained by classifying a plurality of nodes based on a learning level and / or a learning category.
The test program according to claim 1, wherein the directed graph of the model causes a computer to function so that nodes are connected by arcs based on a learning order relationship. The comprehension probability update means records the problem in the learning model storage means with an understanding probability of the node of 1 when the answer is correct and an understanding probability of the node of 0 when the answer is incorrect. The test program according to claim 1 or 2, wherein a computer is caused to function to recalculate the understanding probability. 4. The test program according to claim 1, wherein the comprehension probability update unit causes the computer to calculate the comprehension probability of the node according to Bayes' theorem. 5. The next candidate model selection means includes:
For each user, further calculate the standard deviation in understanding probabilities of multiple nodes for each model,
A model in which the average value is within the range of the first predetermined threshold value from the median value (= 0.5) of the understanding probability and the standard deviation is equal to or larger than the second predetermined threshold value is defined as a next candidate model. The test program according to claim 1, wherein the computer is caused to function so as to make a selection. The next candidate model selection means, when a plurality of next candidate models are selected,
The average information amount H (X) when the random variables X of all the nodes U included in the next candidate model follow the probability distribution P is calculated for each next candidate model by the following equation:
H (X) = − _Σx∈UP (X = x) logP (X = x)
6. The test program according to claim 1, wherein the computer is caused to function so as to select a model having the highest average information amount H (X) as a next candidate model. The question presenting means presents a predetermined number or more of questions included in an unquestioned learning unit, and the answer determination means includes the correctness probability after the result of correct / incorrect answers to the predetermined number of questions. 7. The test program according to claim 1, wherein the computer is caused to function so that the updating unit and the next candidate model selection unit are executed. A device for performing user-adaptive tests,
Specify the “node” that includes the probability of understanding, which is associated with the question and the answer,
A learning model storage unit that divides a plurality of nodes into a plurality of models (groups) based on different criteria, and stores a directed graph in which the nodes are connected by arcs for each model,
A next candidate model selecting means for calculating an average understanding probability that is an average value of the understanding probabilities for each model, and selecting a next candidate model based on the average understanding probability;
In the next candidate model, a node associated with an unissued problem is selected, and a problem presenting means for presenting the problem,
Answer determination means for determining the correct / incorrect answer of the answer to the given question;
For each user, for each model in the learning model storage means, recalculate the comprehension probabilities at all other nodes to which the unanswered question is associated, based on the already answered question and the correct / incorrect answer of the answer. And an understanding degree probability updating means. A device testing method for performing user-adaptive testing,
Specify the “node” that includes the probability of understanding, which is associated with the question and the answer,
The apparatus has a learning model storage unit that divides a plurality of nodes into a plurality of models (groups) based on different criteria, and stores a directed graph in which the nodes are connected by arcs in advance for each model,
The device is
A first step of calculating an average comprehension probability that is an average value of the comprehension probabilities for each model, and selecting a next candidate model based on the average comprehension probabilities;
A second step of selecting a node associated with an unissued problem in the next candidate model and presenting the problem;
A third step of determining the correct / incorrect answer of the answer to the given question;
For each user, for each model in the learning model storage means, recalculate the comprehension probabilities at all other nodes to which the unanswered question is associated, based on the already answered question and the correct / incorrect answer of the answer. And a fourth step of testing the apparatus.

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