Modelling the learning process in Petri net notation for effective managerial decision making

Abstract


The authors propose a model of the testing process in the notation of colored Petri nets. Before starting the simulation, the information flows of the process of mastering the discipline «Informatics» in IDEF3 notation by students of the Department of Applied Information Technologies of the ION RANEPA were studied. In the process of building the model, the following task was solved:let's give a Petri net consisting of a set of positions P = {p1, p2, ..., pn} and a set of transitionsT = {t1, t2, ..., tm}. The network simulates the testing process. Then there are such states of positions P that the following conditions are met for each transition T in the network:1. ∀ti ∈ T: (∀pi' ∈ Pred(tj): pi'(pj) = 1) → T(P) = 1, where Pred(tj) is the set of all preceding transition positions ti. 2. ∀tj ∈ T: tj(pj) = 1 → (∀p' ∈ Succ(tj): pj'(pj) = 1), where Succ(tj) is the set of all the following transition positions tj.That is, it is necessary to formalize the educational process using a colored Petri net. Find a labeling that can be achieved in a given colored Petri net that satisfies the following condition: there is a sequence of transitions (transactions) starting from the initial labeling, such that each subsequent labeling is obtained by applying the corresponding transition to the previous labeling. I.e.: ∃ M0: (initial labeling) → M*, where → M* denotes the reflexive and transitive closure of the transition relation in the Petri net.Solving the problem of the reachability of network labeling gave the concept of an optimal scenario for monitoring the development of competencies in the discipline: Some tasks and questions do not have to be included in the testing. Various scenarios for monitoring student progress are presented using the example of discipline testing. For example, one of the variants of the test scenario assumed the presence of a common resource with questions and assignments on the five topics under study. There were 50 questions in the database. The answer to each question can be rated from zero to 10 points. The test is considered passed if the student scored at least 41 points. The numbers of completed tasks and questions with the correct answer were also recorded.Another test option: 10 questions for each topic and the response time to the question (task) was recorded.A matrix analysis of the model was carried out. The vector of the initial marking μ(pi) = {47,1,1,1,0,0,0,0} and μk = {30, 0, 0, 0, 0, 0, 0, 41} at the end of testing. The analysis of the reachability of the μk marking allowed us to obtain one of the sequences of triggering transitions U k-1 = (t1, t3, t4, t3, t3, t4). Where transitions t1 – t4 fix the beginning and end of an elementary process (for example, the beginning of testing – the end of testing).The analysis of the model allowed us to investigate the dynamics of studying the topics of the discipline « Informatics »: how many times the student returned to re-reading the module materials, how many times he turned to additional material. Monitors attached to the transitions made it possible to determine the time for each operation and draw up protocols for studying the discipline.

Full Text

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About the authors

A. I Fedoseev

Russian Academy of National Economy and Public Administration under the President of the Russian Federation, Institute of Social Sciences

L. A Ponomareva

Russian Academy of National Economy and Public Administration under the President of the Russian Federation, Institute of Social Sciences

V. S Zabolotnikova

Russian Academy of National Economy and Public Administration under the President of the Russian Federation, Institute of Social Sciences

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