The importance of moving between embodied, symbolic and formal worlds of mathematical thinking: The case of the tree concept

International audience ; In this study, we investigate university students’ mathematical understanding of the tree concept, a fundamental concept in graph theory using Tall’s theory of three worlds of mathematical thinking. The qualitative research described here is a phenomenological study drawing on task-based interviews with 18 undergraduate mathematics students. The findings highlight the importance of moving between the embodied, symbolic and formal worlds of mathematical thinking to be a successful mathematical problem solver in graph theory. We identified that students moved between these worlds in three situations: Thinking in the embodied world as a guide to thinking in symbolic and formal worlds; evaluating thinking in one world by thinking in another world; and moving from one world to another when thinking in one world is unsuccessful. Lecturers could highlight such movements in teaching to encourage students to move between these worlds during problem-solving.