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. The participants of the study consist of 24 university students enrolled in a mathematics education programme at a state university in Turkey. Data were collected through students' written productions, screen recorder software, and transcriptions of the students' argumentations for selected groups. The collected data were analysed based on Toulmin's model. Results of the study indicate the use of GeoGebra in ACODESA method triggered a sense of understanding of 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. The integration of GeoGebra into ACODESA method also fostered some process aspects of mathematical reasoning (generalizing, conjecturing, and justifying) on parametric equations.