Date of Award

1-1-2000

Thesis Type

Masters

Document Type

Thesis

Divisions

Faculty of Education

Department

-

Institution

Universiti Malaya

Abstract

This study explored concept images and concept definitions of college students on limits of functions. Their views concerning the attainability of the limit and the extent to which they understood the stand taken by the formal view on this matter were also probed on. The sample comprised 10 students who had completed the Calculus and Analytic Geometry 1 course in the School of American University Studies at a private college in the Klang Valley. A questionnaire on beliefs about limits was administered to them and 4 students were then selected for a task-based interview on the attainability of the limit. The students exhibited a variety of concept images on limits. Four students described limits in terms of the dynamic view and related limits to determining the slope of a tangent to a point on a curve. Only 1 student included the formal definition. This indicated that the formal definition was not a dominant aspect of the students' concept image on limits. Two students prcxluced a correct concept definition on the limit of a function, implying that many of these students had not understood the fonnal definition. Majority of the students agreed to both the infonnal views and fonnal view on limits. During the interviews, 2 students had related attainability of the limit to continuous functions, and 2 other students believed that the limit was unattainable. For the latter 2, one student viewed constant functions as an exception to the rule. The other student insisted that constant functions were no exception because limits pertained to a point of interest. He also believed that although continuous functions attained their limits, the process of approaching the limit was unrelated to the situation in which the function attained its limit. His view contradicted the concept of continuity. The findings imply that these students were unaware of the inconsistent and conflicting aspects of their concept images which were at variance with the formal view on the limits of functions. Alternative pedagogical strategics were proposed by considering the opportunity for students to explore the meanings of words used in communicating the limit concept. exposing them to the historical development of the limit concept, and discussing the attainability of the limit within the concept of continuity.

Initial

snms

Additional Information

Dissertation (M.A) -- Faculty of Education, Universiti Malaya, 2000.

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