Students’ mathematical thinking of the tree concept: an integration of APOS with Tall’s three worlds of mathematics

Abstract

In this study, we investigate students’ mathematical thinking of the tree concept, a fundamental concept in graph theory, using a combination of the APOS theory and Tall’s three worlds of mathematics. The qualitative research describes here is a phenomenological study drawing on task-based interviews with 18 undergraduate mathematics students. The findings indicate that students preferred to think in the embodied world when solving tasks related to the tree concept. This type of thinking, despite its great value, should not prevent students from thinking in the symbolic and formal worlds. Furthermore, the findings indicate that almost half of the participants had difficulties with the acyclicity and connectivity concepts, which are necessary prior knowledge to help students develop Process and Object for the tree concept. The results also suggest that more opportunities could be provided for students to engage with tasks that related to Process and Object in the three mathematics worlds.