WO2021240685A1 - スキル可視化装置、スキル可視化方法およびスキル可視化プログラム - Google Patents

スキル可視化装置、スキル可視化方法およびスキル可視化プログラム Download PDF

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WO2021240685A1
WO2021240685A1 PCT/JP2020/020927 JP2020020927W WO2021240685A1 WO 2021240685 A1 WO2021240685 A1 WO 2021240685A1 JP 2020020927 W JP2020020927 W JP 2020020927W WO 2021240685 A1 WO2021240685 A1 WO 2021240685A1
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skill
state
learner
visualization
learning
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French (fr)
Japanese (ja)
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浩嗣 玉野
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NEC Corp
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NEC Corp
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Priority to JP2022527356A priority patent/JP7355240B2/ja
Priority to PCT/JP2020/020927 priority patent/WO2021240685A1/ja
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    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B7/00—Electrically-operated teaching apparatus or devices working with questions and answers
    • G09B7/02—Electrically-operated teaching apparatus or devices working with questions and answers of the type wherein the student is expected to construct an answer to the question which is presented or wherein the machine gives an answer to the question presented by a student
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B19/00—Teaching not covered by other main groups of this subclass
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B7/00—Electrically-operated teaching apparatus or devices working with questions and answers
    • G09B7/02—Electrically-operated teaching apparatus or devices working with questions and answers of the type wherein the student is expected to construct an answer to the question which is presented or wherein the machine gives an answer to the question presented by a student
    • G09B7/04—Electrically-operated teaching apparatus or devices working with questions and answers of the type wherein the student is expected to construct an answer to the question which is presented or wherein the machine gives an answer to the question presented by a student characterised by modifying the teaching program in response to a wrong answer, e.g. repeating the question or supplying a further explanation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/044—Recurrent networks, e.g. Hopfield networks
    • G06N3/0442—Recurrent networks, e.g. Hopfield networks characterised by memory or gating, e.g. long short-term memory [LSTM] or gated recurrent units [GRU]
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B19/00—Teaching not covered by other main groups of this subclass
    • G09B19/02—Counting; Calculating
    • G09B19/025—Counting; Calculating with electrically operated apparatus or devices

Definitions

  • the present invention relates to a skill visualization device, a skill visualization method, and a skill visualization program that visualize changes in a learner's skill.
  • Knowledge tracing visualizes the learner's skills to grasp the learning situation in real time, predicts whether or not the problem can be solved, and provides the optimum problem for the learner.
  • the proficiency level of each student's learning content is grasped in detail to support effective review, and the exercises optimized for the proficiency level of each student's learning content are optimized.
  • the test creation server that creates the collection is described.
  • Non-Patent Document 1 describes a method of performing knowledge tracing in real time. The method described in Non-Patent Document 1 uses a recurrent neural network (RNN) to model student learning.
  • RNN recurrent neural network
  • Non-Patent Document 2 describes interpretable knowledge tracing by a probabilistic model having a non-compensated item response model.
  • AI Artificial Intelligence
  • a learning method in which the learner can independently decide what to study while interacting with the AI that is, a learning method in which the learner can independently master the AI.
  • a learning method in which the learner can independently master the AI it is necessary to feed back information so that the learner can make a learning plan while grasping the transition of his / her own skill over the long term.
  • the test creation server described in Patent Document 1 has " ⁇ (a circle indicating all correct answers)” and “ ⁇ (some incorrect answers) according to the ratio of the number of correct answers to the number of questions given in the small unit.
  • the learning achievement rate is displayed in three stages: “(triangle indicating)” and “x (cross indicating all incorrect answers)”.
  • the display content described in Patent Document 1 only displays the actual results of correct or incorrect answers, it is possible to grasp how much the skill for solving the question is satisfied. It is not possible.
  • Non-Patent Document 1 and Non-Patent Document 2 the probability of solving the problem at the present time can be predicted based on the estimated learner's skill.
  • the methods described in Non-Patent Document 1 and Non-Patent Document 2 do not consider predicting future changes in skills as learning progresses. Ultimately, it is preferable to obtain information on how to proceed with learning and how to improve skills in the future, rather than information on whether or not a specific problem can be solved.
  • an object of the present invention is to provide a skill visualization device, a skill visualization method, and a skill visualization program that can visualize a learner's long-term changes in skills.
  • the skill visualization device has a learning plan input unit that accepts input of a learning plan, which is information in which problems to be solved by a learner are arranged in chronological order, and solves each problem planned in the learning plan in chronological order. It is characterized by having a state estimation unit that estimates the state of the learner's skill at each time in the future and a state visualization unit that visualizes the state of the learner's skill at each estimated time point.
  • the skill visualization method accepts input of a learning plan, which is information in which the problems to be solved by the learner are arranged in chronological order, and each future problem when each problem planned in the learning plan is solved in chronological order. It is characterized by estimating the state of the learner's skill at a time point and visualizing the state of the learner's skill at each estimated time point.
  • the skill visualization program has a learning plan input process that accepts input of a learning plan, which is information in which the problems to be solved by the learner are arranged in chronological order, and each problem scheduled in the learning plan in chronological order. It is characterized by executing a state estimation process for estimating the state of the learner's skill at each future time point when solved, and a state visualization process for visualizing the state of the learner's skill at each estimated time point. ..
  • FIG. 1 is a block diagram showing a configuration example of an embodiment of the learning device according to the present invention.
  • the learning device 100 of the present embodiment includes a storage unit 10, an input unit 20, a learning unit 30, and an output unit 40.
  • the storage unit 10 stores various information such as parameters, setting information, and log data used for processing by the learning device 100 of the present embodiment. Specifically, the storage unit 10 stores a learning record (hereinafter referred to as a learning correctness log) indicating whether or not a certain problem has been answered correctly. The contents of the learning correctness log will be described later. Further, the storage unit 10 may store each model generated by the learning unit 30 described later.
  • a learning correctness log indicating whether or not a certain problem has been answered correctly. The contents of the learning correctness log will be described later.
  • the storage unit 10 may store each model generated by the learning unit 30 described later.
  • the learning device 100 may be configured to acquire various information from another device (for example, a storage server) via a communication network.
  • the storage unit 10 does not have to store the above-mentioned information.
  • the storage unit 10 is realized by, for example, a magnetic disk or the like.
  • the input unit 20 receives input of various information used for processing by the learning unit 30.
  • the input unit 20 may acquire various information from the storage unit 10, for example, or may accept input of various information acquired via the communication network.
  • the input unit 20 accepts the input of the learner's time-series learning correctness log as learning data indicating the learning results. Specifically, the input unit 20 inputs learning data including data in which a problem and the correctness of the problem are associated with information representing a learner's characteristics (hereinafter, may be referred to as a user characteristic). accept.
  • FIG. 2 is an explanatory diagram showing an example of learning data.
  • the learning data illustrated in FIG. 2 shows that the learners 1 to N are associated with the correctness ( ⁇ , ⁇ ) for each problem.
  • the user characteristics indicating the characteristics of each user may be held separately from the learning data.
  • the learning unit 30 includes a first knowledge model learning unit 31 and a second knowledge model learning unit 32.
  • the first knowledge model learning unit 31 generates a time-series change in the learner's skill state (hereinafter referred to as a skill state sequence) by machine learning using the learner's learning results.
  • the state of the learner's skill is, for example, the proficiency level of the learner's skill.
  • the first knowledge model learning unit 31 may generate a skill state sequence by using, for example, the method described in Non-Patent Document 2. Specifically, the first knowledge model learning unit 31 may generate a state in which the posterior probability is maximized under the given learning correctness log as a skill state column.
  • the first knowledge model learning unit 31 may generate a feature of the problem used for learning (hereinafter, referred to as a problem feature vector).
  • the first knowledge model learning unit 31 may generate a problem feature vector by using the method described in Non-Patent Document 2 as in the generation of the skill state sequence.
  • the problem feature vector can be generated without depending on the learning results.
  • a problem feature vector can be generated as a vector for problem i, where the i-th entry is 1 and the other entries are 0.
  • This problem feature vector is a so-called one-hot vector ([0, ..., 1, ..., 0]) that identifies each problem.
  • the first knowledge model learning unit 31 does not have to generate the problem feature vector.
  • the skill state sequence of the present embodiment corresponds to the state transition probability (and the initial state probability) in the generation model of the uncompensated time series IRT (item response theory) described in Non-Patent Document 2. Therefore, the first knowledge model learning unit 31 may generate a skill state sequence by learning the model defined by the following equation 1. It should be noted that Equation 1 is a model for transitioning to the next state z j (t + 1) by the linear transformation D when the state z j (t) of the user j at the time t is given. Note that z j (t) is a random variable.
  • Di (j, t) represents a linear transformation that changes the state according to the problem i solved by user j at time t
  • ⁇ i (j, t + 1) represents Gaussian noise
  • the second term on the right side is a bias term, which is a term representing a feature amount of the user j that can affect the state transition.
  • x j, k (t + 1) is a covariate of state transitions, and any feature related to the learner is used as the user feature.
  • user characteristics for example, the learner's attributes (for example, age, gender), motivation (whether or not he / she is interested in the subject), and the elapsed time since the learner j last learned the problem including skill k are assumed.
  • Forgetting rate 2 ⁇ ( ⁇ / h) (where ⁇ is the elapsed time and h is the half-life) and the like.
  • aggregated information of performance series may be used.
  • the aggregated information for example, the number of answers up to 5 consecutive correct answers for each skill, information indicating the speed of acquisition, the result of the past test, and the like can be mentioned.
  • ⁇ k T is a coefficient representing the characteristics of each skill, and for example, a large negative value is set for the coefficient of a skill that is easy to forget.
  • ⁇ 0 and P 0 represent the mean and variance of the Gaussian distribution in the initial state of the learner, respectively.
  • the vector containing a i and b i are included in the output probabilities described in Non-Patent Document 2 corresponds to the problem feature vectors of the present embodiment.
  • a i is a vector representing the discriminating power of each skill in question i (slope)
  • b i is the difficulty in question i. Therefore, the first knowledge model learning unit 31 may generate a problem feature vector by learning the model defined by the following equation 2.
  • Qi (j, t) and k in Equation 2 indicate the correspondence between the problem i and the skill k, and if the skill k is necessary to solve the problem i, it becomes 1, and if it is not necessary, it becomes 0.
  • the first knowledge model learning unit 31 may generate the problem feature vector as shown in Equation 3 below. For example, when problem 1 requires skill 1 and skill 2, the first knowledge model learning unit 31 sets 0 for the vector shown by the following equation 3 except for a 1 , a 2 , b 1 , and b 2. It suffices to generate such a feature vector.
  • FIG. 3 is an explanatory diagram showing an example in which a problem and a necessary skill are associated with each other.
  • a problem and a skill required to solve the problem are associated in a table format is shown.
  • one skill may be required for each problem, or two or more skills may be required.
  • the correspondence between the problem and the necessary skill is set in advance by the user or the like.
  • the first knowledge model learning unit 31 may generate a skill state sequence by using, for example, the method described in Non-Patent Document 1.
  • Skill status column of the present embodiment corresponds to the vector y t of the prediction probability of the time series described in Non-Patent Document 1.
  • Y t described in Non-Patent Document 1 is a vector of length equal to the number of issues, each entry represents the probability that the learner correct the problem.
  • the first knowledge model learning unit 31 may generate a vector y t of the prediction probability of the time series as a skill state column.
  • the one-hot vector described in Non-Patent Document 1 corresponds to the problem feature vector of the present embodiment.
  • the i-th entry can be generated as a vector of 1
  • the other entries can be generated as a vector of 0.
  • the one-hot vector ([0, ..., 1, ..., 0]) that identifies each problem may be generated in advance as the problem feature vector.
  • the first knowledge model learning unit 31 does not have to generate the problem feature vector.
  • the method of generating the skill state sequence and the problem feature vector by using the methods described in Non-Patent Document 1 and Non-Patent Document 2 has been described above.
  • the method of generating the skill state sequence and the problem feature vector is not limited to the learning methods described in Non-Patent Document 1 and Non-Patent Document 2.
  • the second knowledge model learning unit 32 generates a model that predicts the future skill state of the learner by machine learning using the skill state sequence and the problem feature vector. Specifically, the second knowledge model learning unit 32 learns a model in which the problem feature, the user feature, and the time information are the explanatory variables, and the skill state of the user is the objective variable.
  • the skill status can be acquired from the skill status column generated by the first knowledge model learning unit 31.
  • the problem feature may be acquired from the problem feature vector generated by the first knowledge model learning unit 31, and may be acquired from information generated by an arbitrary method based on the problem (for example, one-hot vector). May be good.
  • the user characteristics are the same as the user characteristics when the first knowledge model learning unit 31 uses it for learning.
  • the time information is information indicating the time when the learner solved the problem.
  • the mode of the time information is arbitrary, and may be, for example, time information expressed in the format of YYYYMMDDHHM, such as the elapsed time from a certain time t-1 to t.
  • the first knowledge model learning unit 31 may generate a skill state sequence that maximizes the posterior probability as a skill state column.
  • the first knowledge model learning unit 31 is described below in a state where specific values of the user j's actual results y j (1) , ..., Y j (Tj) indicated by the learning correctness log are obtained.
  • the mode of the model learned by the second knowledge model learning unit 32 is arbitrary, and the second knowledge model learning unit 32 may learn RNN, which is often used in the prediction of time series data, for example.
  • RNN a general RNN may be used, or an LSTM (Long short-term memory), a GRU (Gated Recurrent Unit), or the like may be used.
  • the learning of the model for performing the knowledge trace is generally performed using the learner's correctness data (learning correctness log) as in the learning performed by the first knowledge model learning unit 31.
  • the second knowledge model learning unit 32 of the present embodiment is learning a model for performing knowledge tracing without directly using the correctness data of the learner, the second knowledge model learning unit 32 is learning the model. This can be called a knowledge trace model without correct / incorrect data.
  • the output unit 40 outputs the model (knowledge trace model without correct / incorrect data) generated by the second knowledge model learning unit 32.
  • the output unit 40 may store the generated model in the storage unit 10, or may store the generated model in another storage medium (not shown) via the communication network.
  • the input unit 20, the learning unit 30 (more specifically, the first knowledge model learning unit 31 and the second knowledge model learning unit 32), and the output unit 40 are computer processors (more specifically, a computer processor that operates according to a program (learning program)). For example, it is realized by a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit).
  • CPU Central Processing Unit
  • GPU Graphics Processing Unit
  • the program is stored in the storage unit 10, the processor reads the program, and according to the program, the input unit 20 and the learning unit 30 (more specifically, the first knowledge model learning unit 31 and the second knowledge model learning unit). 32) and may operate as the output unit 40. Further, even if the functions of the input unit 20, the learning unit 30 (more specifically, the first knowledge model learning unit 31 and the second knowledge model learning unit 32) and the output unit 40 are provided in the SaaS (Software as a Service) format. good.
  • SaaS Software as a Service
  • the input unit 20, the learning unit 30 (more specifically, the first knowledge model learning unit 31 and the second knowledge model learning unit 32), and the output unit 40 are each realized by dedicated hardware. You may. Further, a part or all of each component of each device may be realized by a general-purpose or dedicated circuit (circuitry), a processor, or a combination thereof. These may be composed of a single chip or may be composed of a plurality of chips connected via a bus. A part or all of each component of each device may be realized by the combination of the circuit or the like and the program described above.
  • each component of the input unit 20, the learning unit 30 (more specifically, the first knowledge model learning unit 31 and the second knowledge model learning unit 32) and the output unit 40 is a plurality of information processing devices.
  • a plurality of information processing devices and circuits may be centrally arranged or distributed.
  • the information processing device, the circuit, and the like may be realized as a form in which each is connected via a communication network, such as a client-server system and a cloud computing system.
  • FIG. 4 is a flowchart showing an operation example of the learning device 100 of the present embodiment.
  • the learning unit 30 (more specifically, the first knowledge model learning unit 31) generates a skill state sequence by machine learning using the learning results (step S11). Then, the learning unit 30 (more specifically, the second knowledge model learning unit 32) learns a model in which the problem feature, the user feature, and the time information are used as explanatory variables, and the state of the learner's skill is used as the objective variable. (Step S12).
  • the first knowledge model learning unit 31 generates a skill state sequence by machine learning using the learning results
  • the second knowledge model learning unit 32 has problem features, user features, and so on. Then, a model is learned in which the time information is used as an explanatory variable and the learner's skill state is used as an objective variable. Therefore, it is possible to learn a model that predicts changes in the learner's long-term skills.
  • the knowledge tracing model is learned based on the learner's time-series learning correctness log. That is, the model described in Non-Patent Document 2 is not a model suitable for long-term prediction because the correct / incorrect result of solving the problem is required as learning data.
  • the second knowledge model learning unit 32 learns a model in which the problem feature, the user feature, and the time information are used as explanatory variables, and the learner's skill state is used as the objective variable. Therefore, it becomes possible to make long-term predictions of learners.
  • Embodiment 2 Next, a second embodiment of the present invention will be described.
  • the learning plan in the present embodiment is information indicating which problem the learner solves when and in what order, and is information in which the problems to be solved by the learner are arranged in chronological order.
  • a method of visualizing how the state of one's skill changes when one problem is solved will be described.
  • the method of estimating the change in the skill state and visualizing the estimation result will be appropriately described using the model learned in the first embodiment.
  • the method of estimating the change in the state of the skill is not limited to the method using the model learned in the first embodiment.
  • FIG. 5 is a block diagram showing a configuration example of an embodiment of the visualization system according to the present invention.
  • the visualization system 1 of the present embodiment includes a learning device 100 and a visualization device 200. Since the content of the learning device 100 of the present embodiment is the same as that of the learning device 100 of the first embodiment, detailed description thereof will be omitted.
  • the storage unit 10 included in the learning device 100 of the first embodiment may be provided in a device different from the learning device 100.
  • the visualization device 200 acquires a model learned by the learning device 100 (that is, a knowledge trace model without correct / incorrect data).
  • a model learned by the learning device 100 that is, a knowledge trace model without correct / incorrect data.
  • the information used for processing by the visualization device 200 for example, the knowledge trace model without correct / incorrect data
  • a storage device for example, a storage unit 10
  • the visualization device 200 does not have to be connected to the learning device 100.
  • the visualization device 200 includes a learning plan input unit 210, a state estimation unit 220, and a state visualization unit 230.
  • the learning plan input unit 210 accepts the input of the learning plan.
  • the learning plan input unit 210 may display a learning plan input screen on a display device (not shown) and interactively accept input of the learning plan from the learner.
  • FIG. 6 is an explanatory diagram showing an example of a screen for inputting a learning plan.
  • the learning plan input unit 210 displays a calendar-style input screen 211 as illustrated in FIG. 6, and is a learning plan input by the learner via an appropriate input interface (for example, a touch panel, a pointing device, a keyboard, etc.). May be accepted.
  • an appropriate input interface for example, a touch panel, a pointing device, a keyboard, etc.
  • the display device may be provided in the visualization device 200, or may be realized by a device different from the visualization device 200 connected via a communication line.
  • the learning plan input unit 210 may accept input of the learning plan described in a file or the like.
  • the state estimation unit 220 estimates changes in the skill state based on the learning plan. Specifically, the state estimation unit 220 estimates the change in the state of the learner's skill when each problem set in the learning plan is solved in time series.
  • the proficiency level of each skill that is estimated to be improved when the problem is solved is predetermined, and the state estimation unit 220 adds the proficiency level corresponding to the solved problem according to the learning plan (for example, addition). , Multiply, etc.) You may estimate changes in the state of the skill. Further, the state estimation unit 220 may reduce the skill proficiency level according to a certain function (forgetting curve) with the passage of time.
  • the state estimation unit 220 estimates the change in the skill state using the model learned in the first embodiment (knowledge trace model without correct / incorrect data). You may. That is, the state estimation unit 220 uses problem features representing the characteristics of the problem used by the learner for learning, user characteristics representing the characteristics of the learner, and time information representing the time when the learner solved the problem as explanatory variables. , A change in the skill state may be estimated using a prediction model with the learner's skill state as the objective variable.
  • the prediction model has a skill state sequence representing a time-series change in the state of the learner's skill, which is generated by machine learning using the learning results of the learner, and a skill state sequence.
  • This is a model learned using data including feature quantities based on a problem feature vector representing the features of the problem used by the learner for learning.
  • the state visualization unit 230 visualizes the estimated state of the learner's skill.
  • FIG. 7 is an explanatory diagram showing an example of visualizing the state of the skill. As illustrated in FIG. 7, a line graph in which the time is set on the horizontal axis and the skill state (proficiency level) is set on the vertical axis, even if the learner's skill state at each time point is visualized in chronological order. good.
  • the state visualization unit 230 may visualize the correct answer probability of the learner at a designated time for each problem.
  • FIG. 8 is an explanatory diagram showing an example of visualizing the probability of solving a problem.
  • the correct answer probability is visualized by the bar graph 311 for each problem summarized for each unit.
  • the state visualization unit 230 may estimate the state of the learner's skill at a certain point in time using, for example, a knowledge trace model without correct / incorrect data, and calculate the correct answer probability based on the estimated skill. For example, when the method described in Non-Patent Document 2 is used, the state visualization unit 230 may calculate the correct answer probability of each problem by using the formula 2 shown above and visualize the calculation result. Specifically, the state visualization unit 230 may visualize the average in the distribution of correct answer probabilities calculated using Equation 2 as the correct answer probability in the bar graph 311 and represent the variance as the degree of uncertainty by the line 312.
  • the state visualization unit 230 may visualize the state of each skill of the learner at a certain point in time in more detail.
  • the state visualization unit 230 may, for example, visualize the learner's skill assumed at a designated time point for each skill required for solving the target problem.
  • FIG. 9 is an explanatory diagram showing an example in which the state of each skill is output as a graph.
  • the graph illustrated in FIG. 9 is a graph that visualizes the state of the learner's skill for each skill required to solve a certain problem. Further, in the example shown in FIG. 9, it is assumed that, for example, the problem provider has given two types of labels (A-level and B-level) according to the level of the problem.
  • a problem a problem with the label "A-level” (hereinafter referred to as "A problem”) is referred to as a standard problem, and a problem with the label "B-level” (hereinafter referred to as “B problem”). ) Is a development problem.
  • the threshold value of each level of the skill is shown by a boundary line
  • the boundary line 321 is the threshold value of the skill state where it is assumed that all the A problems can be solved
  • the boundary line 322 is all the B problem. It is the threshold of the skill state that is supposed to be solved.
  • the state of each skill at a certain time point is represented by a bar graph 323, and the uncertainty of the state of the skill is represented by a circled line 324.
  • Non-Patent Document 2 When associating skills with a certain problem, it is common to say that it can be solved by satisfying all of those skills.
  • Such a model described in Non-Patent Document 2 is called an uncompensated model in multidimensional item response theory. It can be said that the explanation of the reason for prediction using this uncompensated model is natural.
  • the model that predicts the correct answer probability is represented by the product of each skill.
  • the prediction model can be expressed as follows using the sigmoid function ⁇ .
  • the explanation is high because it is interpreted that "the above problem cannot be solved without knowledge of fractions and equations".
  • a model representing the probability that the learner can solve the problem i when the learner's state z and the problem i are given can be defined by, for example, the following equation 4 which is a simplification of the above equation 2. That is, the model exemplified in Equation 4 is a model represented by a combination of skills k required by the learner to solve the problem i, and the probability of solving the problem is calculated by the product of each skill.
  • the learner's state z represents the proficiency level of each skill k possessed by the learner at a certain point in time.
  • bi and k represent the difficulty level of the skill k used in the problem i
  • ai and k represent the degree of rise (slope) of the skill k related to the problem i, as in the above formula 2. It is a parameter. That is, Equation 4, b i, the higher the skill level z k skills than difficulty indicating k is, indicating that a problem with a high probability can be solved.
  • FIG. 10 is an explanatory diagram showing an example of the likelihood function of the correct answer probability.
  • the vertical axis (z-axis) shows the probability of correct answer
  • the other axes (x-axis and y-axis) show the proficiency level of the skill required to solve the problem.
  • the likelihood function illustrated in FIG. 10 is represented by the equation 4 exemplified above. For example, suppose that two skills are required to solve a problem, as illustrated in FIG. In this case, it is shown that the correct answer probability does not increase even if only one skill is high, but the correct answer probability increases when both skills are high.
  • FIG. 11 is an explanatory diagram schematically showing information on the uncompensated model.
  • the x mark 113 shown at the lower left of the graph indicates the state of the learner's skill at the present time.
  • the ellipse 114 surrounding the x mark 113 indicates a contour line of the probability when the distribution of the learner's skill state follows the Gaussian distribution. In this case, the position of the learner's skill state corresponds to the mean in the Gaussian distribution.
  • the state visualization unit 230 calculates the threshold value.
  • the threshold value calculated here corresponds to the threshold value indicated by the boundary line 321 exemplified in FIG.
  • FIG. 12 is an explanatory diagram showing an example of a process for calculating a threshold value.
  • the state visualizing unit 230 calculates the coordinate z k * for each dimension.
  • the state visualization unit 230 calculates z k * using, for example, the following equation 5 based on the above equation 4.
  • Equation 5 represents the correctness probability
  • a i and b i are similar to Equation 4, respectively, showing the slope and difficulty. Since it is assumed that the proficiency level is such that all the A problems can be solved, the most difficult problem i may be selected from the A problems.
  • the z k * calculated here corresponds to the coordinates of the plane tangent from the outside to the likelihood function illustrated in FIG. 10, and corresponds to the long chain lines 121 and 122 in FIG.
  • ⁇ is the difference between z k * and z ⁇ calculated for each dimension.
  • the z ⁇ calculated here corresponds to the coordinates of the surface in contact with the likelihood function illustrated in FIG. 10 from the inside, and corresponds to the coordinates of the point 123 in FIG.
  • the state visualization unit 230 repeats the following two processes when calculating the coordinates z ⁇ .
  • the status visualization unit 230 based on the z k, calculates the value of each delta k.
  • status visualization unit 230 as a second processing, the dimension k for the largest delta k, updating shown in Equation 6 below.
  • ⁇ is a parameter and is predetermined.
  • the status visualization unit 230 a z kmax updated and z ', the dimension k for the smallest delta k, updating shown in Equation 7 below.
  • the state visualization unit 230 repeats these two processes until a predetermined condition (for example, the amount of change is less than the threshold value, a predetermined number of times, etc.) is satisfied.
  • the state visualization unit 230 approximates the region to a rectangle by calculating (z ⁇ k ⁇ z k *) / 2 for each k.
  • the values calculated here correspond to the coordinates of the dashed lines 124 and 125 in FIG.
  • the state visualization unit 230 outputs a bar graph based on the ratio of the learner's skill proficiency to the value indicated by the rectangular approximated coordinates. Specifically, the state visualization unit 230 may output a bar graph based on the ratio of the coordinates 126 indicating the state of the learner's skill to the coordinates indicated by the broken lines 124 and 125. In this way, the state visualization unit 230 associates the proficiency level of the skill (that is, the threshold value) required for solving the target problem with the proficiency level of the skill assumed to be possessed by the learner. Output. The same applies to the threshold value of problem B.
  • FIG. 13 is an explanatory diagram showing an example of a process for visualizing the result. For example, if the learner's skill state for skill 1 (integer subtraction) is estimated to be z 1 2 and the variance ⁇ ⁇ of the skill state in the Gaussian distribution is z 1 1 and z 1 3 respectively. do. Then, the coordinates of the broken line 124 is calculated as z 1 4 in FIG. At this time, status visualization unit 230, a proficiency skills 1 learner, ⁇ (a i, 1 ( z 1 2 -b i, 1)) / ⁇ (a i, 1 (z 1 4 -b i , 1 )).
  • the state visualization unit 230 may output the variance of the Gaussian distribution as the uncertainty of the proficiency level by using the distribution indicating the state of the learner's skill estimated by the Gaussian distribution. Specifically, the state visualization unit 230 sets the uncertainty range to ⁇ ( ai, 1 (z 1 1 ⁇ bi , 1 )) / ⁇ ( ai, 1 (z 1 4 ⁇ bi, 1)). 1)) and ⁇ (a i, 1 (z 1 3 -b i, 1)) / ⁇ (a i, is calculated by 1 (z 1 4 -b i, 1)). The same applies to skill 2 (absolute value).
  • the state visualization unit 230 calculates the relative skill proficiency and uncertainty when the threshold value is 1. That is, the state visualization unit 230 expresses the proficiency level and the uncertainty level of the current learner's skill with respect to the threshold value as relative values in association with the skill name. Therefore, the excess or deficiency of the learner's skill can be presented based on the skill name that the learner can understand. Further, the state visualization unit 230 can improve the learner's sense of conviction by expressing the uncertainty of each skill together.
  • the state visualization unit 230 has a proficiency level of the learner's skill assumed at a designated time point and a problem included in the target group (for example, a labeled group) (for example, problem A). , B problem) is visualized in association with the threshold value indicating the proficiency level of the skill required to solve. Therefore, since the group specified by the problem provider is associated with the estimated difficulty level, it becomes easy to grasp the situation of the learner's skill.
  • the problem in the group may be one or multiple.
  • the state visualization unit 230 may output a candidate problem that requires the specified skill as a "recommended problem". Specifically, the state visualization unit 230 identifies a candidate for a problem that requires a specified skill from a table that associates the problem as illustrated in FIG. 3 with the skill required to solve the problem. You may.
  • FIG. 14 is an explanatory diagram showing an output example of the recommended problem.
  • status visualization unit 230 for skills "Tsubun” problems which require that skill candidates: the (Recommend problem Q 13, Q 18, Q 31 , Q 33), its It is shown that the skills are ordered according to the required degree (that is, proficiency level, difficulty level) and output in association with the expected learner's skill.
  • the state visualization unit 230 may output the question corresponding to the number.
  • the state visualization unit 230 may visualize changes in the state of the skill, including the degree of uncertainty.
  • FIG. 15 is an explanatory diagram showing another example of visualizing the change in the state of the skill.
  • the state visualization unit 230 is a line graph in which the time is set on the horizontal axis and the skill proficiency level is set on the vertical axis. It may be visualized in chronological order. At that time, the state visualization unit 230 may also visualize the boundary line 332 of the labeled problem as shown above.
  • the state visualization unit 230 may visualize changes in the state of a plurality of skills.
  • FIG. 16 is an explanatory diagram showing still another example of visualizing the change in the state of the skill.
  • the line graph 341 shows the transition of the states of the plurality of skills.
  • the state visualization unit 230 shows the correctness of the problem solved at each time point in a bar graph 342 (for example, upward if the answer is correct, so that the transition of the skill can be grasped in relation to the learning performance. If the answer is incorrect, it may be visualized downward).
  • the learning plan input unit 210, the state estimation unit 220, and the state visualization unit 230 are realized by a computer processor that operates according to a program (visualization program).
  • the program is stored in a storage unit (not shown) included in the visualization device 200, and the roseser reads the program and operates as a learning plan input unit 210, a state estimation unit 220, and a state visualization unit 230 according to the program. You may.
  • the functions of the learning plan input unit 210, the state estimation unit 220, and the state visualization unit 230 may be provided in the SaaS format.
  • the learning plan input unit 210, the state estimation unit 220, and the state visualization unit 230 may each be realized by dedicated hardware. Further, a part or all of each component of each device may be realized by a general-purpose or dedicated circuit (circuitry), a processor, or a combination thereof. These may be composed of a single chip or may be composed of a plurality of chips connected via a bus. A part or all of each component of each device may be realized by the combination of the circuit or the like and the program described above.
  • each component of the learning plan input unit 210, the state estimation unit 220, and the state visualization unit 230 is realized by a plurality of information processing devices, circuits, or the like, a plurality of information processing devices. , Circuits, etc. may be centrally arranged or distributed.
  • the information processing device, the circuit, and the like may be realized as a form in which each is connected via a communication network, such as a client-server system and a cloud computing system.
  • FIG. 17 is a flowchart showing an operation example of the visualization device 200 of the present embodiment.
  • the learning plan input unit 210 accepts the input of the learning plan (step S21).
  • the state estimation unit 220 estimates the state of the learner's skill at each future time point when each problem set in the learning plan is solved in time series (step S22).
  • the state visualization unit 230 visualizes the state of the learner's skill at each estimated time point (step S23).
  • the visualization mode is, for example, the contents shown in FIGS. 7 to 9 and 13 to 16.
  • the learning plan input unit 210 receives the input of the learning plan, and the state estimation unit 220 solves each problem set in the learning plan in chronological order at each future time point. Estimate the state of the learner's skill in. Then, the state visualization unit 230 visualizes the state of the learner's skill at each estimated time point. Therefore, it is possible to visualize changes in the learner's long-term skills.
  • FIG. 18 is a block diagram showing an outline of the skill visualization device according to the present invention.
  • the skill visualization device 90 (for example, the visualization device 200) according to the present invention is a learning plan input unit 91 (for example, a learning plan input unit) that accepts input of a learning plan which is information in which problems to be solved by a learner are arranged in chronological order. 210) and a state estimation unit 92 (for example, a state estimation unit 220) that estimates the state of the learner's skill at each point in the future when each problem planned in the learning plan is solved in time series. It is provided with a state visualization unit 93 (for example, a state visualization unit 230) that visualizes the state of the learner's skill at each time point.
  • a state visualization unit 93 for example, a state visualization unit 230
  • the state visualization unit 93 may visualize the learner's skill assumed at a designated time point for each skill required for solving the target problem (for example, the graph illustrated in FIG. 9). ).
  • the state visualization unit 93 is required to solve the problem of the target and the proficiency level of the learner's skill assumed at a specified time point (for example, the bar graph 323 illustrated in FIG. 9). It may be visualized in association with a threshold value indicating the skill proficiency level (for example, the boundary line 322 exemplified in FIG. 9).
  • the state visualization unit 93 sets the proficiency level of the learner's skill assumed at the designated time point and the target group (for example, the group of problems to which the label "A-level” is given). It may be visualized in association with a threshold indicating the proficiency level of the skill required to solve the included problem (for example, the A problem) (for example, the graph illustrated in FIG. 9). With such a configuration, the group specified by the problem provider is associated with the estimated difficulty level, so that it becomes easier to grasp the situation of the learner's skill.
  • the state visualization unit 93 may visualize changes in the state of one or more skills in chronological order (for example, the graphs exemplified in FIGS. 7, 15, and 16).
  • the state visualization unit 93 may visualize the correct answer probability for each problem at a designated time point (for example, the graph illustrated in FIG. 8).
  • the state visualization unit 93 may output problem candidates that require the specified skill in order according to the degree to which the skill is required, in association with the expected learner's skill. (For example, the "recommended problem" illustrated in FIG. 14).
  • the state estimation unit 92 provides problem features representing the characteristics of the problem used by the learner for learning, user characteristics representing the characteristics of the learner, and time information representing the time when the learner solved the problem.
  • a predictive model for example, "knowledge trace model without correct / incorrect data" in which the learner's skill state is used as an explanatory variable may be used to estimate the change in the skill state.
  • the prediction model is a skill state sequence that represents a time-series change in the state of the learner's skill, which is generated by machine learning using the learning results of the learner, and the learner uses it for the learning. It may be learned using data including a feature amount based on a problem feature vector representing the feature of the problem (for example, by the learning device 100).
  • FIG. 19 is a schematic block diagram showing a configuration of a computer according to at least one embodiment.
  • the computer 1000 includes a processor 1001, a main storage device 1002, an auxiliary storage device 1003, and an interface 1004.
  • the skill visualization device 90 described above is mounted on the computer 1000.
  • the operation of each of the above-mentioned processing units is stored in the auxiliary storage device 1003 in the form of a program (skill visualization program).
  • the processor 1001 reads a program from the auxiliary storage device 1003, expands it to the main storage device 1002, and executes the above processing according to the program.
  • the auxiliary storage device 1003 is an example of a non-temporary tangible medium.
  • non-temporary tangible media include magnetic disks, magneto-optical disks, CD-ROMs (Compact Disc Read-only memory), DVD-ROMs (Read-only memory), which are connected via interface 1004. Examples include semiconductor memory.
  • the program may be for realizing a part of the above-mentioned functions. Further, the program may be a so-called difference file (difference program) that realizes the above-mentioned function in combination with another program already stored in the auxiliary storage device 1003.
  • difference file difference program
  • a learning plan input unit that accepts input of a learning plan, which is information in which problems to be solved by a learner are arranged in chronological order, and a future when each problem planned in the learning plan is solved in chronological order.
  • a skill visualization device including a state estimation unit that estimates the state of the learner's skill at each time point, and a state visualization unit that visualizes the estimated state of the learner's skill at each time point.
  • the state visualization unit is a skill visualization device according to Appendix 1 that visualizes the learner's skills assumed at a specified time point for each skill required to solve the target problem.
  • the state visualization unit visualizes the learner's skill proficiency assumed at a specified time point in association with a threshold indicating the skill proficiency required to solve the target problem.
  • Skill visualization device according to Appendix 1 or Appendix 2.
  • the state visualization unit has a threshold indicating the learner's skill proficiency assumed at a specified time point and the skill proficiency required to solve the problem included in the target group.
  • the skill visualization device according to any one of Supplementary note 1 to Supplementary note 3 for visualizing in association with each other.
  • Appendix 5 The skill visualization device according to any one of Appendices 1 to 4, which visualizes changes in the state of one or more skills in chronological order.
  • the state visualization unit is the skill visualization device according to any one of Appendix 1 to Appendix 5 that visualizes the correct answer probability for each problem at a designated time point.
  • the state visualization unit orders problem candidates that require the specified skill according to the degree to which the skill is required, and outputs it in association with the expected learner's skill.
  • the skill visualization device according to any one of Supplementary note 6 to.
  • the state estimation unit is a problem feature representing the characteristics of the problem used by the learner for learning, a user characteristic representing the characteristics of the learner, and time information representing the time when the learner solved the problem.
  • the skill visualization device according to any one of Supplementary note 1 to Supplementary note 7, which estimates a change in the skill state by using a prediction model in which the learner's skill state is used as an explanatory variable and the learner's skill state as an objective variable.
  • the prediction model is a skill state sequence that represents a time-series change in the state of the learner's skill, which is generated by machine learning using the learning results of the learner, and is used by the learner for the learning.
  • the skill visualization device according to Appendix 8 which is learned using data including a feature amount based on a problem feature vector representing a problem feature.
  • a skill visualization method comprising estimating the state of a person's skill and visualizing the state of the learner's skill at each of the estimated time points.
  • Appendix 11 The skill visualization method according to Appendix 10, which visualizes the learner's skills assumed at a specified time point for each skill required to solve the target problem.
  • a learning plan input process that accepts input of a learning plan, which is information in which the problems to be solved by the learner are arranged in chronological order, and a case where each problem planned in the learning plan is solved in chronological order.
  • Program storage medium
  • Appendix 13 A skill visualization program for visualizing the skills of the learner assumed at a specified time in the state visualization process for each skill required to solve the target problem is stored in the computer.
  • a learning plan input process that accepts input of a learning plan, which is information in which the problems to be solved by the learner are arranged in chronological order, and a case where each problem planned in the learning plan is solved in chronological order.
  • a skill visualization program for executing a state estimation process for estimating the state of the learner's skill at each future time point and a state visualization process for visualizing the estimated state of the learner's skill at each time point.
  • Appendix 15 The skill visualization program according to Appendix 14 that visualizes the learner's skills assumed at a specified time point in the state visualization process for each skill required to solve the target problem.

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