Developing and Measuring an Understanding of the Concept of the Limit of a Sequence

摘要

This study investigates understanding of limits. The concept of limits is one of the fundamental ideas in mathematics. The limit concept is a broad one. Thus, to establish a focus for this study, the researcher concentrated on limits of sequences. The limit concept is the foundation upon which differential and integral calculus are built. The all important question of whether an infinite series converges or diverges rests with limits of sequences of partial sums. The entire study was related to characterizing and measuring understanding of the concept of the limit of a sequence. The major purposes were: To develop a meaning of the understanding of the limit of a sequence based upon students' behavior; and To measure the meaning of the understanding of the limit of a sequence. This was to be done by constructing an instrument that is valid, reliable, objective, and suitable for measuring this understanding. The related topic was: To investigate specific subskills that might be related to understanding the concept of the limit of a sequence.