Title Epistemološka i didaktička analiza pojma polinoma Title (english) Epistemological and didactic analysis of the notion of a polynomial Author Jelena Pleština Mentor Željka Milin-Šipuš (mentor)Committee member Matija Bašić (predsjednik povjerenstva)Committee member Nikola Koceić Bilan (član povjerenstva)Committee member Aleksandra Čižmešija (član povjerenstva)Committee member Ana Katalenić (član povjerenstva)Granter University of Zagreb Defense date and country 2023-03-17, Croatia Scientific / art field, NATURAL SCIENCES Universal decimal classificationUDC ) 51 - Mathematics Abstract Polinom kao jedan od najfundamentalnijih pojmova u gotovo svim područjima matematike, ima istaknutu ulogu u predtercijarnom i tercijarnom matematičkom obrazovanju. Upravo to ga kvalificira da bude idealan objekt institucijskog i epistemološkog istraživanja o didaktičkim procesima. Potreba za takvim istraživanjem inducirana je: 1. na globalnoj razini, malobrojnim istraživanjima u kojima je polinom glavni objekt istraživanja te neodgovorenim pitanjima o razlozima različitog načina definiranja pojma polinoma u predtercijarnom obrazovanju [13,221]; 2. na lokalnoj razini, recentnim promjenama u znanju za podučavanje u predtercijarnom obrazovanju i mogućim efektima tih promjena na tercijarno obrazovanje. Odabrani teorijski okvir, Antropološka teorija didaktike (ATD), nudi alate koji omogućavaju istraživanje epistemoloških i institucijskih aspekata znanja za podučavanje. Stoga se alatima ATD-a analizira tranzicija prema studiju matematike, kroz studij, kao i inverzna tranzicija, ona koju nastavnici matematike prolaze kada počinju podučavati matematiku u predtercijarnom obrazovanju. Dakle, analizira se dvostruki Kleinov prekid i tranzicija kroz studij matematike s obzirom na pojam polinoma. Pojam matematičke prakseologije koristi se za modeliranje i analiziranje matematičkih sadržaja i aktivnosti. Diseminacija matematičkih prakseologija analizira se i modelira pojmom didaktičke prakseologije. Didaktička transpozicija, koja je istodobno alat i metodologija, omogućava analiziranje znanja unutar obrazovnih institucija u odnosu na znanje discipline matematike. Prvo se analiziraju geneza i razvoj pojma polinoma u disciplini matematike, tj. razvoj znanja o pojmu polinoma koja epistemološki legitimiraju znanja koja se podučavaju u predtercijarnim i tercijarnim obrazovnim institucijama. Uzima se u obzir i reforma Nove matematike koja je inducirana promjenom u disciplini matematike. Posebno se istražuje realizacije reforme u hrvatskom gimnazijskom obrazovnom sustavu, kao i njeni rudimenti i mogući efekti na aktualni obrazovni sustav. Dokumenti koji propisuju znanje za podučavanje u hrvatskom predtercijarnom obrazovanju podvrgnuti su prakseološkoj analizi, kao i najkorišteniji gimnazijski udžbenici u zadnjih dvadesetak godina, kako bi se dobio uvid u sekundarno-tercijarnu tranziciju (prvi Kleinov prekid) od kad je uveden Bolonjski proces. S obzirom na pojam polinoma, analizira se obrazovanje matematičara i nastavnika matematike na Prirodoslovno-matematičkom fakultetu Sveučilišta u Splitu. Promatra se i mogući efekti drugog Kleinov prekida na buduće nastavnike matematike.
Abstract (english) The polynomial, as one of the most fundamental notions in almost all areas of mathematics, has a prominent role in pre-tertiary and tertiary mathematics education. That qualifies it to be an ideal object of institutional and epistemological research on didactic processes. The need for such research was induced by: 1. at the global level, the few studies in which the polynomial is the main object of research, and the unanswered questions about the reasons for the different ways of defining the notion of a polynomial in pre-tertiary education [13,221]; 2. at the local level, recent changes in knowledge for teaching in Croatian pre-tertiary mathematics education and the possible effects of these changes on university mathematics education. The selected theoretical framework, the Anthropological Theory of the Didactic (ATD), offers tools that enable the investigation of epistemological and institutional aspects of knowledge for teaching. Therefore, ATD tools are used to analyse the transition towards the study of mathematics, through the study, as well as the inverse transition, the one that mathematics teachers go through when they start teaching mathematics in pre-tertiary education. Thus, Klein’s double discontinuity, and transition through the study of mathematics, are analysed concerning the notion of a polynomial. A mathematical praxeology is a tool that is used for modelling and analysing mathematical contents and activities. The dissemination of mathematical praxeologies is analysed and modelled by the notion of a didactic praxeology. A didactic transposition, which is both a tool and a methodology, enables the analysis of knowledge within educational institutions concerning the knowledge of the discipline of mathematics. First, the genesis and development of the notion of a polynomial in the discipline of mathematics are analysed, i.e. the development of the knowledge about the notion of a polynomial that epistemologically legitimises the knowledge taught in pre-tertiary and tertiary educational institutions. The reform of New Mathematics, which was induced by a change in the discipline of mathematics, is also taken into account. The implementation of the reform in the Croatian high school education system is especially investigated, as well as its rudiments and possible effects on the current education system. Documents prescribing knowledge for teaching in Croatian pre-tertiary education were subjected to praxeological analysis, as well as the most used secondary textbooks in the last twenty years, as would gain an insight into the secondary-tertiary transition (Klein’s first discontinuity) since the Bologna process was introduced. The education of mathematicians and mathematics teachers at the Faculty of Science, University of Split is analysed considering the notion of a polynomial. The possible effects of Klein’s second discontinuity on prospective pre-tertiary mathematics teachers are also observed.
Keywords
polinom
predtercijarno matematičko obrazovanje
sveučilišno matematičko obrazovanje
antropološka teorija didaktike
dvostruki Kleinov prekid
Keywords (english)
polynomial
pre-tertiary mathematics education
university mathematics education
anthropological theory of the didactic
Klein’s double discontinuity
Language croatian URN:NBN urn:nbn:hr:217:703003 Promotion 2023 Study programme Title: Mathematics Type of resource Text Extent x, 331 str. File origin Born digital Access conditions Embargoed access Terms of use Created on 2023-05-04 11:17:00
