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Teaching congruences in connection with diophantine equations

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dc.title Teaching congruences in connection with diophantine equations en
dc.contributor.author Ďuriš, Viliam
dc.contributor.author Gonda, Dalibor
dc.contributor.author Tirpáková, Anna
dc.contributor.author Pavlovičová, Gabriela
dc.relation.ispartof Education Sciences
dc.identifier.issn 2227-7102 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued 2021
utb.relation.volume 11
utb.relation.issue 9
dc.type article
dc.language.iso en
dc.publisher MDPI
dc.identifier.doi 10.3390/educsci11090538
dc.relation.uri https://www.mdpi.com/2227-7102/11/9/538
dc.subject congruences en
dc.subject residual classes en
dc.subject cryptography en
dc.subject relational algebra en
dc.subject prime numbers en
dc.subject discrete mathematics en
dc.subject survey en
dc.description.abstract The presented paper is devoted to the new teaching model of congruences of computer science students within the subject of discrete mathematics at universities. The main goal was to create a new model of teaching congruences on the basis of their connection with Diophantine equations and subsequently to verify the effectiveness and efficiency of the proposed model experimentally. The teaching of congruences was realized in two phases: acquisition of procedural knowledge and use of Diophantine equations to obtain conceptual knowledge of congruences. Experiments confirmed that conceptual understanding of congruences is positively related to increasing the procedural fluidity of congruence resolution. Research also demonstrated the suitability of using Diophantine equations to link congruences and equations. Among other things, the presented research has confirmed the justification of teaching mathematics in computer-oriented study programs. © 2021 by the authors. Licensee MDPI, Basel, Switzerland. en
utb.faculty Faculty of Humanities
dc.identifier.uri http://hdl.handle.net/10563/1010587
utb.identifier.obdid 43882703
utb.identifier.scopus 2-s2.0-85115145318
utb.identifier.wok 000699206400001
utb.source j-scopus
dc.date.accessioned 2021-10-10T09:47:59Z
dc.date.available 2021-10-10T09:47:59Z
dc.format.extent 14
dc.rights Attribution 4.0 International
dc.rights.uri https://creativecommons.org/licenses/by/4.0/
dc.rights.access openAccess
utb.ou Department of School Education
utb.contributor.internalauthor Tirpáková, Anna
utb.fulltext.affiliation Ďuriš Viliam 1 , Gonda Dalibor 2,* , Tirpáková Anna 1,3 and Gabriela Pavlovič1 Department of Mathematics, Faculty of Natural Sciences, Constantine The Philosopher University in Nitra, 1 Department of Mathematics, Faculty of Natural Sciences, Constantine The Philosopher University in Nitra, Tr. A. Hlinku 1, 94901 Nitra, Slovakia; vduris@ukf.sk (Ď.V.); atirpakova@gmail.com (T.A.); gpavlovicova@ukf.sk (G.P.) 2 Department of Mathematical Methods and Operations Research, Faculty of Management Science and Informatics, University of Žilina, Univerzitná 1, 01001 Žilina, Slovakia 3 Department of School Education, Faculty of Humanities, Tomas Bata University in Zlín, Štefánikova 5670, 760 00 Zlín, Czech Republic * Correspondence: dalibor.gonda@fri.uniza.sk; Tel.: +421-911-720-507ová1
utb.fulltext.dates Received: 30 July 2021 Accepted: 10 September 2021 Published: 14 September 2021
utb.fulltext.sponsorship This research received no external funding.
utb.wos.affiliation [Viliam, Duris; Anna, Tirpakova; Pavlovicova, Gabriela] Constantine Philosopher Univ Nitra, Fac Nat Sci, Dept Math, Tr A Hlinku 1, Nitra 94901, Slovakia; [Dalibor, Gonda] Univ Zilina, Fac Management Sci & Informat, Dept Math Methods & Operat Res, Univ 1, Zilina 01001, Slovakia; [Anna, Tirpakova] Tomas Bata Univ Zlin, Fac Humanities, Dept Sch Educ, Stefanikova 5670, Zlin 76000, Czech Republic
utb.scopus.affiliation Department of Mathematics, Faculty of Natural Sciences, Constantine The Philosopher University in Nitra, Tr. A. Hlinku 1, Nitra, 94901, Slovakia; Department of Mathematical Methods and Operations Research, Faculty of Management Science and Informatics, University of Žilina, Univerzitná 1, Žilina, 01001, Slovakia; Department of School Education, Faculty of Humanities, Tomas Bata University in Zlín, Štefánikova 5670, Zlín, 760 00, Czech Republic
utb.fulltext.projects -
utb.fulltext.faculty Faculty of Humanities
utb.fulltext.ou Department of School Education
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