Abstract
Objectives In this study, we developed instructional materials that allow students to explore the mathematical internal connections of quadratic curves using a technology tool, and analyzed the results of students to understand how students perceived the mathematical internal connections of quadratic curves. Also, we tried to find out what the hindrance factors were for perceiving the mathematical internal connections. Methods For this purpose, we developed instructional materials for 16 first-year students attending S gifted school located in a small city to explore the mathematical internal connections using GeoGebra. Moreover, the developed instructional materials were applied to the students, and the students' results were analyzed in terms of the mathematical internal connections between algebraic representations and geometric representations and between different mathematical objects. Results As a result of analyzing the results of the students, the students were able to understand the quadratic curves well in the process of connecting geometric expressions based on the definition of the quadratic curves, and had a motivation to find other tasks on their own. In the process of connecting different quadratic curves, the students constructed algebraic expressions from definitions and understood the connections of different quadratic curves in the process of finding common math expressions between each expression. In addition, students came to understand the connections of quadratic curves through the process of plotting graphs by inputting common expressions into GeoGebra. However, in some cases, students' prior learning acted as a hindrance to their exploration of mathematical intenal connections. Conclusions Using the materials developed in this study, students were able to explore the mathematical internal connections of quadratic curves with a technology tool. In addition, the mathematical knowledge learned in advance before lessons could act as a hindrance factor in exploring the mathematical internal connections.
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