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

Abstract

A 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.

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“…In fact, Zbiek and Conner (2006) have indicated that modeling specifically contributes to the understanding of known mathematical concepts, to the learning of new mathematical concepts, to establishing interdisciplinary relationships, and to both the conceptual and procedural development of students through the detailed demonstration of the applicability of mathematical concepts in real-life. There are various studies demonstrating the importance of dynamic geometry software and computer algebra systems as tools for realistic mathematics education (Aktümen, 2013;Aktümen, Baltaci, & Yildiz, 2011;Kabaca & Aktümen, 2010;Widjaja & Heck, 2003). In addition to these, numerous studies have been performed on real-life problems in mathematics education (Aydin & Monoghan;Aydin-Unal & Ipek, 2009;Fauzan, Slettenhaar, & Plomp, 2002;Kwon, 2002;Oldknow & Taylor, 2008;Van Den Heuvel-Panhuizen, 2000).…”

“…Furthermore, there are a gradually increasing number of studies investigating real-life problems with DGS Gecü & Özdener, 2010;Gittinger, 2012;Kabaca & Aktümen, 2010;Widjaja & Heck, 2003). At the same time, there are also studies in the literature regarding threedimensional modeling with DGS (Aktümen, 2013;Aktümen, Baltaci, & Yildiz, 2011;Aktümen, Doruk, & Kabaca, 2012;Oldknow, 2009;Oldknow & Tetlow, 2008).…”

Modeling and Visualization Process of the Curve of Pen Point by GeoGebra

“…Furthermore, there are a gradually increasing number of studies investigating real-life problems with DGS Gecü & Özdener, 2010;Gittinger, 2012;Kabaca & Aktümen, 2010;Widjaja & Heck, 2003). At the same time, there are also studies in the literature regarding threedimensional modeling with DGS (Aktümen, 2013;Aktümen, Baltaci, & Yildiz, 2011;Aktümen, Doruk, & Kabaca, 2012;Oldknow, 2009;Oldknow & Tetlow, 2008).…”

“…In fact, Zbiek and Conner (2006) have indicated that modeling specifically contributes to the understanding of known mathematical concepts, to the learning of new mathematical concepts, to establishing interdisciplinary relationships, and to both the conceptual and procedural development of students through the detailed demonstration of the applicability of mathematical concepts in real-life. There are various studies demonstrating the importance of dynamic geometry software and computer algebra systems as tools for realistic mathematics education (Aktümen, 2013;Aktümen, Baltaci, & Yildiz, 2011;Kabaca & Aktümen, 2010;Widjaja & Heck, 2003). In addition to these, numerous studies have been performed on real-life problems in mathematics education (Aydin & Monoghan;Aydin-Unal & Ipek, 2009;Fauzan, Slettenhaar, & Plomp, 2002;Kwon, 2002;Oldknow & Taylor, 2008;Van Den Heuvel-Panhuizen, 2000).…”

The Modelling Process of a Paper Folding Problem in GeoGebra 3D

“…There are several studies on modeling the real life situations in GeoGebra [2,3,4,5]. In this research, a problem situation has been suggested and modeling process in GeoGebra has been explained.…”