Methods of teaching inverse and incorrect problems to students in the context of informatization of education
- Authors: Kornilov V.S.1
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Affiliations:
- Moscow Сity University
- Issue: Vol 17, No 4 (2020)
- Pages: 315-322
- Section: INNOVATION PEDAGOGICAL TECHNOLOGIES IN EDUCATION
- URL: https://journal-vniispk.ru/2312-8631/article/view/321257
- DOI: https://doi.org/10.22363/2312-8631-2020-17-4-315-322
- ID: 321257
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Abstract
Problem and goal. Computer technologies are now widely used in applied research aimed at obtaining new scientific knowledge. These studies used the method of computer modeling and computing experiment, from which it is possible to study the properties of remote or inaccessible objects, processes and phenomena of different nature. The above mentioned is directly related to teaching students applied mathematics in general, and, in particular, to teaching students of physical and mathematical training areas inverse and ill-posed problems, which are the scientific direction of applied mathematics. It is obvious that in the process of teaching students inverse and ill-posed problems, it is advisable to use computer technologies. However, the use of computer technology should be appropriate and correct. Methodology. The process of finding solutions to inverse and ill-posed problems is usually time-consuming, since such mathematical problems are non-linear in their formulation and may have a non-unique and unstable solution. These circumstances pose a mathematical difficulty in the proof of the theorems of existence, uniqueness and stability of solutions to inverse and ill-posed problems. Computer technologies help to overcome mathematical difficulties associated with routine transformations, analysis of information about solving such mathematical problems. Results. Using computer technologies, students gain experience in mobile research of various inverse and ill-posed problems, as well as in identifying the capabilities of computer technologies in solving various applied mathematical problems, and develop ICT competence. Conclusion. When using multimedia and computer technologies in the process of teaching students inverse and ill-posed problems, didactic principles of teaching are implemented, which allow students to acquire deep scientific knowledge on inverse and ill-posed problems, and develop their information culture.
About the authors
Viktor S. Kornilov
Moscow Сity University
Author for correspondence.
Email: vs_kornilov@mail.ru
doctor of pedagogical sciences, candidate of physical and mathematical sciences, full professor, professor of the department of informatization of education
29 Sheremetyevskaya St, Moscow, 127521, Russian FederationReferences
- Belov YuA, Lyubanova ASh, Polynceva SV, Sorokin RV, Frolenkov IV. Obratnye zadachi matematicheskoj fiziki [Inverse problems of mathematical physics]. Krasnoyarsk: SFU Publ.; 2008.
- Vabishevich PN. Vychislitel'nye metody matematicheskoj fiziki. Obratnye zadachi i zadachi upravleniya [Computational methods of mathematical physics. Inverse problems and management problems]. Moscow: Vuzovskaya kniga Publ.; 2019.
- Vatulyan AO, Belyak OA, Suhov DYu, Yavruyan OV. Obratnye i nekorrektnye zadachi [Inverse and ill-posed problems]. Rostov-on-Don: Izd-vo Yuzhnogo federal'nogo universiteta Publ.; 2011.
- Kornilov VS. The inverse problems in the content of training applied mathematics. Bulletin of Peoples’ Friendship University of Russia. Series: Informatization in Education]. 2014;(2):109–118.
- Kornilov VS. Training students to inverse problems for differential equations as the factor of forming competence in the field of applied mathematics. Bulletin of Peoples’ Friendship University of Russia. Series: Informatization of Education. 2015;(1):63–72.
- Kornilov VS. Realizaciya nauchno-obrazovatel'nogo potenciala obucheniya studentov vuzov obratnym zadacham dlya differencial'nyh uravnenij [Realization of scientific and educational potential of teaching university students inverse problems for differential equations]. Kazanskij pedagogicheskij zhurnal [Kazan pedagogical journal]. 2016; (6):55–59.
- Kornilov VS. Teoriya i metodika obucheniya obratnym zadacham dlya differencial'nyh uravnenij [Theory and method of teaching inverse problems for differential equations]. Moscow: OntoPrint; 2017.
- Petrov YuP, Sizikov VS. Korrektnye, nekorrektnye i promezhutochnye zadachi s prilozheniyami [Correct, incorrect and intermediate tasks with applications]. Saint Petersburg: Politekhnika Publ.; 2003.
- Romanov VG. Ustojchivost' v obratnyh zadachah [Stability in inverse problems]. Moscow: Nauchnyj mir Publ.; 2005.
- Grinshkun VV. Sushchestvuyushchie podhody k ispol'zovaniyu sredstv informatizacii pri obuchenii estestvennonauchnym disciplinam. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Seriya: Informatika i informatizacija obrazovanija [Bulletin of the Moscow City Pedagogical University. Series: Informatics and Informatization of Education]. 2014;4 30):8–13.
- Boronenko TA, Fedotova VS. Formirovanie IKT-kompetentnosti nauchno-pedagogicheskih kadrov v trekhurovnevoj sisteme vysshego obrazovaniya [Formation of ICT competence of scientific and pedagogical personnel in the three-level system of higher education]. Obrazovanie i nauka [Education and science]. 2016;(1): 95–106.
- Buzhinskaya NV. Metodika ocenki urovnya IKT-kompetentnosti studentov pedagogicheskih vuzov [Methodology for assessing the level of ICT competence of students of pedagogical universities]. Vestnik Bryanskogo gosudarstvennogo universiteta [Bulletin of the Bryansk State University]. 2016;1(27):319–324.
- Goloskokov DP. Uravneniya matematicheskoj fiziki. Reshenie zadach v sisteme Maple [Equations of mathematical physics. Solving problems in the Maple system]. Saint Petersburg: Piter Publ.; 2004.
- Kornilov VS. Psychological aspects of training higher school students to fractal sets. Bulletin of Peoples’ Friendship University of Russia. Series: Informatization of Education. 2011;(4):79–82.
- Edvards ChG., Penni DE. Differencial'nye uravneniya i kraevye zadachi: modelirovanie i vychislenie s pomoshch'yu Mathematica, Maple i Matlab [Differential equations and boundary value problems: modeling and computation using Mathematica, Maple and Matlab]. Moscow: Vil'yams Publ.; 2008.
- Ivashchenko AV, Gagarin AV, Stepanov SA. Cennostnyj podhod k formirovaniyu professional'no-ekologicheskoj kul'tury budushchego specialista [Value approach to the formation of professional and environmental culture of the future specialist]. Vestnik Moskovskogo gosudarstvennogo gumanitarnogo universiteta imeni M.A. Sholohova [Bulletin of the Moscow State University for the Humanities named after M.A. Sholokhov]. 2012;1(1):58–67.
- Muravyova EV. Ekologicheskoe obrazovanie studentov tekhnicheskogo vuza kak bazovaya sostavlyayushchaya strategii preodoleniya ekologicheskogo krizisa [Ecological education of technical university students as a basic component of the strategy for overcoming the ecological crisis] (dissertation of the doctor of pedagogical sciences). Kazan; 2008.
- Fajrushina SM. Formirovanie ekologicheskoj kul'tury studentov pedagogicheskih vuzov v processe izucheniya estestvennonauchnyh discipline [Formation of ecological culture of students of pedagogical universities in the process of studying natural science disciplines] (dissertation of the candidate of pedagogical sciences). Kazan; 2007.
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