Avni Yildiz

Calculating the surface area of the water in a rolling cylinder and visualization as two and three dimensional by means of GeoGebra

real life problem was created in this study and ellipse equations and integral concept were used in the solution of this problem. As a real life problem, the change in the surface area of the water in a cylinder half of which was full of water and situated vertically was examined in a process in which it was tilted until it became parallel to the floor. In the study, piecewise function which gave the surface area of the water for the angle that the floor and the cylinder built was constructed. This process was visualized as two and three dimensional using GeoGebra which is a dynamic mathematics software program. As this problem situation overlaps with the principles of Realistic Mathematics Education approaches, it is believed that it will guide the teachers in classroom activities.

İLKÖĞRETİM MATEMATİK ÖĞRETMEN ADAYLARININ GEOMETRİK OLASILIK PROBLEMLERİNİ ÇÖZME SÜREÇLERİNİN ANALİTİK DÜŞÜNME BAĞLAMINDA İNCELENMESİ

Olasilik uzerine yapilan calismalar incelendiginde; tutum ve basari, kavram yanilgilari, olasilik problemlerini cozme ve kurma boyutlarina odaklanildigi gorulmektedir. Fakat geometrik olasilik problemlerinin cozum surecinin ilkogretim matematik ogretmen adaylari tarafindan nasil gerceklestiginin halen yanit bulamadigini soylenebilir. Ustelik bu surec, son zamanlarda uzerinde onemle durulmaya baslanan analitik dusunme baglaminda incelenmistir. Bu nedenle arastirmada, ilkogretim matematik ogretmen adaylarinin geometrik olasilik problemlerini analitik dusunme baglaminda nasil cozduklerinin surec olarak incelenmesi amaclanmistir. Ozel durum calismasi yonteminin kullanildigi arastirmanin katilimcilarini, 3 ogretmen adayi olusturmaktadir. Verilerin toplanmasinda klinik mulakat kullanilmistir. Verilerin analizinde ise nitel veri analiz yontemlerinden faydalanilmistir. Arastirmanin sonucunda, problemi sadece bir ogretmen adayinin cozebildigi tespit edilmistir. Fakat o ogretmen adayi, bulmus oldugu sonucu rastlanti ile bulmadigini belirtememistir. Ayrica calismaya katilan her ogretmen adayinin problemi cozerken bir algoritma izledikleri, problemin cozumune yeterince zaman harcadiklari ve tahmin - deneme yanilma gibi yontemleri pek kullanmadiklari tespit edilmistir. Anahtar Kelimeler: Analitik dusunme, geometrik olasilik, ilkogretim matematik ogretmen adaylari, klinik mulakat, problem cozme.