Title Asimptota i asimptotsko ponašanje - didaktička transpozicija objekta znanja u gimnazijskom obrazovanju u Republici Hrvatskoj Title (english) Asymptote and asymptotic behavior - didactic transposition in general secondary education in Croatia Author Ana Katalenić Mentor Aleksandra Čižmešija (mentor)Mentor Željka Milin-Šipuš (komentor)Committee member Ljiljana Arambašić (predsjednik povjerenstva)Committee member Zdenka Kolar-Begović (član povjerenstva)Committee member Zvonimir Šikić (član povjerenstva)Granter University of Zagreb Defense date and country 2017-03-15, Croatia Scientific / art field, NATURAL SCIENCES Universal decimal classificationUDC ) 51 - Mathematics Abstract Asimptota i asimptotsko ponašanje objekti su matematičkog znanja prisutni u različitim područjima matematike. Asimptotsko ponašanje istaknuto je svojstvo nekih funkcija i krivulja te važan alat za opisivanje i rješavanje raznovrsnih matematičkih i izvanmatematičkih problema. Različitost pristupa kojima se ostvaruje te širok spektar sadržaja i područja nastave matematike s kojima se može povezati, odnosno u kojima je relevantan objekt znanja, asimptotu čine zanimljivim objektom istraživanja. U
... More ovom doktorskom radu istražena je i opisana didaktička transpozicija tog objekta znanja u gimnazijskom obrazovanju u Republici Hrvatskoj. Teorijski okvir unutar kojega je provedeno ovo istraživanje jest antropološka teorija didaktike (ATD), koju je razvio francuski matematičar Yves Chevallard početkom 1980-tih godina za potrebe istraživanja matematičkog obrazovanja. Pregled relevantne svjetske znanstvene literature ukazuje na to da su malobrojna istraživanja fokusirana na opisivanje asimptote kao objekta znanja. Osobito nedostaje onih u kojima se sagledavaju različiti aspekti tog matematičkog pojma te njihov međusobni utjecaj, odnosno različiti konteksti u kojima je taj pojam relevantan. Osim toga, ovo je prvo istraživanje u Republici Hrvatskoj kojim se tema iz gimnazijskog matematičkog obrazovanja teorijski utemeljeno adresira i povezuje s inicijalnim sveučilišnim obrazovanjem nastavnika matematike. Istraživanje je provedeno u skladu s odabranim teorijskim okvirom i obuhvaća tri faze: analizu udžbenika, upitnike sa studentima nastavničkog smjera matematike i intervju sa znanstvenicima. Izgrađen je referentni epistemološki model za objekt znanja asimptote koji je usklađen sa zahtjevima znanja za poučavanje te podržan akademskim znanjem i saznanjima epistemoloških istraživanja. Less Abstract (english) Introduction: Asymptote and asymptotic behaviour are bodies of knowledge that have an important role in many traditional and modern mathematical disciplines and are supported by a rich and well-established abstract theory. Asymptotic behaviour is a significant property of some functions and curves and a tool for describing and solving various problems in theoretical and applied mathematics. Some basic aspects of these concepts must be utilized already in elementary mathematics as powerful
... More tools in graphing and analyzing behaviour of elementary functions at infinity and near singularities and in graphing simple plane curves such as hyperbola. Therefore, this body of knowledge is a common part of upper secondary mathematics curricula worldwide. The notion of an asymptote appears as a theoretical concept, a part of a procedure or as a self-sufficient task in different contexts and different educational cycles. Hence, connection with a wide range of teaching contents and mathematical bodies of knowledge makes it an interesting object of research. This doctoral thesis investigates and elaborates the didactic transposition of asymptote as a body of knowledge in general secondary education in Croatia. The research is conducted within the theoretical framework of the anthropological theory of the didactic (ATD), developed by a French mathematician Y. Chevallard especially for research in mathematics education. Scientific literature review shows that studies focused on describing the body of knowledge asymptote are scarce within ATD and other theoretical frameworks. Corpus of scientific research especially lacks those that consider various aspects of this body of knowledge, their mutual influences and connections or various contexts in which this body of knowledge is relevant. Further, research conducted within this thesis pioneers in mathematics education research in Croatia since it addresses and connects, in a theoretically founded manner, initial university education of mathematics teachers and general secondary education. The main idea of ATD is to determine the relation R I ( p , O ) O p I [ T , τ , θ , Θ ] T τ θ Θ A R B ( p , A ) R S ( p , A ) R M ( p , A ) B S M Less Keywords
asimptota
asimptotsko ponašanje
gimnazijsko obrazovanje
matematičko obrazovanje
didaktička transpozicija
antropološka teorija didaktike
ATD
referentni epistemološki model
REM
Keywords (english)
Asymptote
asymptotic behaviour
secondary education
mathematical education
didactical transposition
anthropological theory of the didactics
ATD
reference epistemological model
REM
Language croatian URN:NBN urn:nbn:hr:217:695091 Study programme Title: Mathematics Type of resource Text Extent 154 str. File origin Born digital Access conditions Open access Terms of use Created on 2019-03-14 11:57:40
