In the paper problems which organizers of Olympiads are faced considered. The approach to solve this problems suggested. This approach is based on activity theory and includes using rather simple constructive problems as a first step to more complicated theoretical ones. The experience of implementing this approach within the framework of the Olympiad in Discrete Mathematics and Theoretical Informatics is described. The focus is set on computer manipulators -interactive dynamic models of mathematical and informatical object.
Конструктивные задачи возникают во всех областях математики. Они очень важны в работе со школьниками и студентами, так как являются одним из самых простых способов стимуляции продуктивной деятельности учащихся. Эта работа посвящена роли конструктивных задач в дистанционных олимпиадах по математике и информатике. Также задачи подобного рода могут быть использованы для мониторинга интеллектуальной деятельности учащихся в образовательном процессе. Ключевые слова: математические олимпиады, конструктивные задачи, дистанционное обучение, конструктивная деятельность, компьютерные средства, предметные манипуляторы. неинвазивный мониторинг.
The development of information technologies makes it possible to record a large amount of data in the learning process, both on the results of performing educational operations and on the psychophysical characteristics of students. In this regard, a number of ethical, pedagogical and methodological problems arise. Among them are the disproportionate control actions to the volume and properties of information retrieved during monitoring and problems associated with ensuring the information security of the student. In contrast to natural monitoring, monitoring the management of teaching has as an object of training a person, who can be considered, from the point of view of management, as a highly organized information system. The article is devoted to the study of the problem of non-invasive monitoring, involving the redirection of most of the monitoring information to the student himself. As a definition of non-invasive monitoring, the following is proposed: non-invasive monitoring is a type of pedagogical feedback that is used exclusively for correcting the student’s actions and is prohibited from using to control the effectiveness and transfer the results outside class. The article analyzes 15 different teaching paradigms, which are explicitly or implicitly adhered to by teachers, organizing the educational process, from the point of view of compliance with the tasks of non-invasive monitoring. The methodological aspects of the implementation of non-invasive monitoring from the point of view of computer support of the learning process are also analyzed. It is shown how non-invasive monitoring can be supported by software that provides active interaction of the student with the subject environment and gives the teacher more freedom in planning and achieving strategic goals of managing the educational process.
Constructive tasks are very important and appear in every branch of mathematics. This work is devoted to some experiments with constructive tasks held within the education and assessment process. Firstly, some remote constructive tasks were given to students within a course of Mathematical Logic and Theory of Algorithms. The tasks served only as a support tool and students were not obliged to solve them. Secondly, tasks of the same types were given to elder students which had already passed the course with an additional request to log their intellectual activity while solving the tasks. The third experiment was held during the written exam. Constructive tasks which were given to the students appeared as “the reverse” to the tasks they had solved during the semester.
The paper discusses a certain type of competitions based on distance interaction of a participant with simulation models of concepts from discrete mathematics and computer science. One of them is the "Construct, Test, Explore" (CTE) competition, developed by the authors, the other is the Olympiad in Discrete Mathematics and Theoretical Informatics (DM&TI). The tasks presented in this paper are generally devoted to the concept of a graph isomorphism. Most of the tasks are verified automatically.
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