The Research on Graduate Students’ Understanding of Three Basic Limit Concepts

Abstract

This research adopted the methods of semi-structured interviews and questionnaires, chose 40 first year graduate students as participants, studied what opinions they held about the relationship between the three limits which are limit of a sequence，limit of a function at a point and limit of a function at infinity. The study shows that most of students’ understanding of the concept of limits is incomplete. They believe that three limit concepts are distinct but related, and cannot be integrated into a limit concept. Misconceptions and cognition obstacle of the limit exist extensively in the mind of graduate student, and it is very difficult to overcome for them. It is necessary for both teachers and textbooks to clarify the "common" of the three limits and provide a unifying organizational framework to all three concepts of limit for students. These new findings expand and deepen the current research about students’ understanding of three limits.