Characterizing University Students’ Geometric Thinking Through Dialogues with Generative Artificial Intelligence in Geometry Transformation Learning

Generative Artificial Intelligence (GenAI) has emerged as a promising technology for supporting mathematical dialogue, feedback, and reasoning in mathematics education. However, research has paid limited attention to how university students’ geometric thinking develops through sustained interaction with GenAI, particularly in geometry transformation learning. This study aims to develop a Dialogic Geometric Thinking Framework that characterizes the dimensions and progression of university students’ geometric thinking during sustained dialogue with ChatGPT. A qualitative exploratory design was employed involving undergraduate mathematics education students enrolled in a Geometry Transformation course at an Indonesian public university. Data were collected from student–ChatGPT dialogue transcripts, students’ written solutions, and reflective interviews. The data were analyzed thematically using reflexive thematic analysis to identify recurring characteristics and relationships among dimensions of geometric thinking and to synthesize them into an integrated framework. The findings identified five interrelated dimensions of geometric thinking: conceptual reasoning, representational coordination, procedural justification, reflective regulation, and mathematical elaboration. These dimensions illustrate how students progressively articulate mathematical concepts, coordinate representations, justify solution procedures, evaluate their reasoning, and extend mathematical ideas during AI-mediated dialogue. The study resulted in a Dialogic Geometric Thinking Framework that provides a process-oriented perspective on the development of university students’ geometric thinking during interaction with GenAI. The framework offers an initial theoretical foundation for understanding and further investigating geometric thinking in AI-mediated mathematics learning. Keywords: geometric thinking, generative artificial intelligence, chatGPT, geometry transformation, mathematical dialogue.