Students’ Concept Definitions and Concept Images about Limit Concept

Limit is the concept that students have difficulties and is required to powerful mathematical thinking skill. To investigate students’ concept definitions and concept images about limit concept is important to reveal learning processes of limit concept. The purpose of the study is to determine students’ concept images, concept definitions and relationships between students’ concept images and formal definition about limit concept for one variable real valued functions. The study was conducted with 11 students who were selected from 31 students attending Analysis I course. Criterion sampling method that is a purposive sampling method was used in selection of the students. After teaching process of limit concept, a test which had open-ended questions was carried out to 31 students. Responses of students were analyzed qualitatively by researchers. With regard to analyses, the students were classified into eight groups using their concept images, concept definitions and relationships between their concept images and formal definition of limit as criterions. Eleven students were selected from groups according to group sizes to carry out clinical interviews. The clinical interviews were analyzed qualitatively by researchers. Consequently, it was found that both students’ concept images and concept definitions focused on the theorem about equality of right and left hand limits and dynamic form of limit. Moreover, the students had difficulties in explaining and using the formal definition of limit. In addition, students used their concept images to solve questions and most of them could not establish the relationship between their concept images and formal definition of limit.