Last modified: 2023-02-15

#### Abstract

*This study aims to provide an overview of the change in thinking skills from mathematics in high school to mathematics at university about the limit of indefinite forms. Mathematics in universities is shifting towards mathematical proofs and formal frameworks of thinking. Changes in the way of thinking are reviewed with the framework of three mathematical worlds, namely conceptual-embodied based on perception, action and experiment; proceptual-symbolic based on algebraic computation and manipulation; and axiomatic-formal based on the concept of mathematical definitions and proofs. The descriptive quantitative research method consists of the stages of preparation, data collection, data transcription, data analysis. A total of 20 first year graduate students in mathematics education were given a math problem sheet, containing two numbers regarding the limit of indefinite forms. The results of students work are grouped based on the concept of three worlds. As many as 18 students or 90% are in the proceptual-embodied world, and two students or 10% are in the axiomatic-formal world. No student is in a conceptual-embodied world. From each group, one student was selected to conduct semi-structured interviews as research triangulation. The results of the interview show that students' thinking abilities are still influenced by the knowledge they previously acquired while in high school and further research is needed to improve their thinking skills in accordance with the real world of mathematics in university.*