The integration of GeoGebra into ACODESA method also fostered some process aspects of mathematical reasoning (generalizing, conjecturing, and justifying) on parametric equations. It became apparent that the participants constructed parametric equations from existing knowledge of trigonometric identities, definition of function, and general form of the equation of a circle by making connections between algebraic and geometric representations. Results of the study indicate the use of GeoGebra in ACODESA method triggered a sense of understanding of parametric equations. ![]() The collected data were analysed based on Toulmin's model. For example, try moving the green point in the upper left corner closer to the black point in the lower left corner. Try dragging the corners of the rectangle around to restrict the domain. The left graphics window shows a rectangular domain of points (u, t). Data were collected through students' written productions, screen recorder software, and transcriptions of the students' argumentations for selected groups. The parametric equations and describe a torus. The participants of the study consist of 24 university students enrolled in a mathematics education programme at a state university in Turkey. ![]() This study examines how collective argumentation in the integration of the ACODESA method (collaborative learning, scientific debate and self-reflection) and GeoGebra can help students understand parametric equations. Topic: Parametric Curves Drag the points that control the parametric equations x (t), y (t), and z (t) and observe how the 3D curve (x (t), y (t), z (t) changes.
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