This study proposes the use of dynamic software that will enable students to explore a specific kind of parametric equation at the tertiary level. Firstly, it was aimed at visualizing the basic cycloid curve which is the trajectory of a point on the circle rolling along x-axis. Then, the mathematical meaning of the design process, which is mostly based on the syntax, was tried to be drawn out. It was explained however, that this meaning, produced the parametric equation of basic cycloid. Lastly, it explained the abstraction of more specific cycloids, which are called epicycloids and hypocycloid, from the mathematical analysis of first design. The entire abstraction process is defined as an example of how a model plays cyclic role between mathematics and the real world.
Key words: Dynamic mathematics software, abstraction process, cycloids, mathematical modeling, multiple representations, tertiary level.
**A short version of this paper was presented orally at the12th International Congress on Mathematical Education Seoul, South Korea.
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