Heuristic arguments and rigorous proofs in secondary school education

A tétel rövid nézete
dc.contributor.authorFülöp, Zsolt
dc.date.accessioned2024-09-04T09:47:03Z
dc.date.available2024-09-04T09:47:03Z
dc.date.issued2014-12-01
dc.description.abstractIn this paper we are going to discuss some possible applications of the mechanical method, especially the lever principle, in order to formulate heuristic conjectures related to the volume of three-dimensional solids. In the secondary school educational processes the heuristic arguments are no less important than the rigorous mathematical proofs. Between the ancient Greek mathematicians Archimedes was the first who made heuristic conjectures with the methods of Mechanics and proved them with the rigorous rules of Mathematics, in a period, when the methods of integration were not known. For a present day mathematician (or a secondary school mathematics teacher) the tools of the definite integral calculus are available in order to calculate the volume of three dimensional bodies, such as paraboloids, ellipsoids, segments of a sphere or segments of an ellipsoid. But in the secondary school educational process, it is also interesting to make heuristic conjectures by the use of the Archimedean method. It can be understood easily, but it is beyond the normal secondary school curriculum, so we recommend it only to the most talented students or to the secondary schools with advanced mathematical teaching programme.en
dc.formatapplication/pdf
dc.identifier.citationTeaching Mathematics and Computer Science, Vol. 12 No. 2 (2014) , 167-184
dc.identifier.doihttps://doi.org/10.5485/TMCS.2014.0367
dc.identifier.eissn2676-8364
dc.identifier.issn1589-7389
dc.identifier.issue2
dc.identifier.jatitleTeach. Math. Comp. Sci.
dc.identifier.jtitleTeaching Mathematics and Computer Science
dc.identifier.urihttps://hdl.handle.net/2437/379764en
dc.identifier.volume12
dc.languageen
dc.relationhttps://ojs.lib.unideb.hu/tmcs/article/view/14954
dc.rights.accessOpen Access
dc.rights.ownerZsolt Fülöp
dc.subjectheuristic argumentsen
dc.subjectdeductive proofen
dc.subjectlever principleen
dc.titleHeuristic arguments and rigorous proofs in secondary school educationen
dc.typefolyóiratcikkhu
dc.typearticleen
dc.type.detailedidegen nyelvű folyóiratközlemény hazai lapbanhu
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Teaching Mathematics and Computer Science (DE-journals)