Supervisors info:
Κα Χρυσαυγή Τριανταφύλλου, Επίκουρη Καθηγήτρια, Μαθηματικό, ΕΚΠΑ
Summary:
Periodicity is a concept that relates not only to the regular phenomena of everyday life and the physical world, but also to abstract mathematical concepts. Although is central to many disciplines, there is a limited number of researches focusing on its understanding. In Greece, periodicity is taught for the first time to students in high school. Ιn mathematics in algebra in the 11th grade, and in physics in the 11th, and 12th grades of high school through periodic movements and periodically varying quantities.
In this paper we will describe an application to 45 9th Grade students, who worked in groups to solve an open problem with realistic content presenting the movement of a Ferris wheel. We analyzed the strategies developed by the students in their attempt to model the problem and how they conceptualized elements of the concept of periodicity.
The students developed two modeling cycles, the first concerned the static characteristics of the wheel such as its radius, height and circumference, and the second the dynamic elements of the wheel's motion such as the period of circular motion and the interaction of time and height of a wagon during movement.
Some of the strategies developed by the students in the two cycles were the use of proportional sums, the use of reference points, and the use of trigonometry. Students conceptualized aspects of the concept of periodicity. They perceived the period as the minimum time to repeat a movement but also as a forecast tool.
We conclude that the intervention framework ie. the open problem in a realistic context and the cooperation between pupils favored the development of a rich mathematical activity.
Keywords:
Open-ended problem, Modeling, Realistic framework, Periodic behavior
