Publication Date

2007

Document Type

Dissertation/Thesis

First Advisor

Zollman, Alan, 1951-

Degree Name

Ph.D. (Doctor of Philosophy)

Department

Department of Mathematical Sciences

LCSH

Limit theorems (Probability theory)--Study and teaching

Abstract

This study is designed to improve student performance on the concept of limit by promoting reflective abstraction through instructor, peer, curriculum and individual initiates. It is based on Piaget’s notion of reflective abstraction. It examines Piaget’s four constructs of reflective abstraction, which are interiorization, coordination, encapsulation, and generalization. In addition it includes the notion of reversal, which is originally discussed by Piaget and refined into a construct of reflective abstraction by Dubinsky. This study examined the performance of two sections of first-semester calculus students at a midwestem community college. One section of students studied an experimental curriculum designed to promote evidence that implies reflective abstraction occurs through the five constructs. These students completed problems in collaborative groups. They were required to identify the connections among the various topics and they were given several opportunities to reflect on and write about their understanding of the concepts. A second section of students studied a traditional curriculum. Students in both sections examined the same examples and completed the same homework exercises. Data for the study included pretest scores and posttest scores for all students in the study. Data also included transcribed interviews, homework sets, and classroom observations for a subgroup of 12 students. The pretest-posttest scores showed that the students in the reflective abstraction section scored significantly higher than the students in the traditional section on a posttest of limits. An examination of the subgroup of students showed that the students in the reflective abstraction section scored significantly higher than the students in the traditional section on a measure of written communication. Further analysis of the data shows that successful students, regardless of assigned section, engaged in activities that imply reflective abstraction more often than the less successful students.

Comments

Includes bibliographical references (pages [131]-139).

Extent

vii, 251 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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