Analogija u geometriji

master's thesis

• Title (english): Analogy in geometry
• Author: Mateja Colussi
• Mentor: Matija Bašić (mentor)
• Committee member: Matija Bašić (predsjednik povjerenstva)
• Committee member: Hrvoje Planinić (član povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Zaključivanje na temelju analogije javlja se kako u običnom jeziku svakodnevnog života tako i u matematici i nekim drugim znanostima. U matematici analogija označava da smo uočili sličnost izmedu nekih objekata i na temelju te sličnosti zaključili da objekti imaju još neka zajednička svojstva. U ovome radu objasnili smo što je analogija i koliko je važan alat u matematičkom zaključivanju te ju povezali s ostalim oblicima mišljenja i zaključivanja. U prvom dijelu rada opisali smo što je analogija općenito, dali primjere lažne analogije te rekli koju riječ o Leonhardu Euleru. Potom smo proučavali na temelju čega se u matematici zaključivanje po analogiji može provoditi. Davali razne primjere i poseban naglasak stavili na analogiju i generalizaciju. Drugi dio rada posvetili smo analogiji u geometriji, s naglaskom na analogiju izmedu planimetrije i stereometrije. Treći dio rada posvetili smo analogiji u samoj nastavi matematike (posebno geometrije). Rekli smo pokoju riječ o njenoj važnosti u školskom obrazovanju, miskoncepcijama učenika, cilju upotrebe tehnologije te na samom kraju dali tri aktivnosti koje se mogu primijeniti u nastavi matematike.

Abstract (english)

Conclusions based on analogy occur both in the ordinary language of everyday life and in mathematics, as well as in some other sciences. In mathematics, analogy means that we have noticed a similarity between some objects and based on this similarity we have concluded that the objects have some other properties in common. In this work, we explained what analogy is and how important of a tool it is in making mathematical conclusions as well as connected it with other forms of thinking and deductioning. In the first part of the work, we described what analogy is in general, gave examples of false analogy and said a few words about Leonhard Euler. Then we studied the basis on which concluding using analogy can be carried out in mathematics. Then gave various examples and put special emphasis on analogy and generalization. We devoted the second part of the work to analogy in geometry, with an emphasis on the analogy within planimetry and stereometry. We devoted the third part of the work to analogy within teaching of mathematics (especially geometry). We said a few words about its importance in school education, students’ misconceptions, the purpose of analogy within technology and at the very end we gave three activities that can be applied in mathematics lessons.

• Keywords: lažne analogije; Leonhard Euler; planimetrija; stereometrija; nastava matematike
• Keywords (english): false analogies; Leonhard Euler; planimetry; stereometry; mathematics teaching
• Language: croatian
• URN:NBN: urn:nbn:hr:217:529488
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-10-26 07:59:21