ÖzetLimit, güçlü bir matematiksel düşünme becerisi gerektiren, öğrencilerin öğrenmede zorlandıkları bir kavramdır. Öğrencilerde limit kavramına yönelik, kavram imajlarının ve kavram tanımlarının araştırılmasının, limit kavramının öğrenilme süreçlerinin belirlenmesine katkı getireceği düşünülmektedir. Bu çalışmada, tek değişkenli reel AbstractLimit 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.

In this study the effectiveness of an arrow diagram which can help students apply the Chain Rule was investigated. Different variations of this diagram were used as mnemonic devices for applying the Chain Rule. For the investigation two instruments were developed, diagnostic test and post-test. The diagnostic test was developed to determine the students' difficulties with the Chain Rule and to create matched groups. It was administered to 76 students taking the Advanced Calculus Course. By matching according to the results of the diagnostic test, the sample of 24 pairs of subjects is obtained. The results of the post-test, administered after the teaching program, indicated that the arrow diagram had positive effects on applying the Chain Rule.