Designing Tasks of Introductory Real Analysis to Bridge a Gap between Students' Intuition and Mathematical Rigor: The Case of The Convergence of a Sequence

The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students' intuition and mathematical rigor. In particular, we focus on a task, called the e-strip activity, designed for the convergence of a sequence. Data were collec...

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Bibliographic Details
Published in:International Journal of Research in Undergraduate Mathematics Education 2017-04, Vol.3 (1), p.34-68
Main Authors: Roh, Kyeong Hah, Lee, Yong Hah
Format: Article
Language:English
Subjects:
Calculus
College Students
Concept Formation
Convergence
Difficulty Level
Educational Experiments
Grounded Theory
Instructional Design
Introductory Courses
Intuition
Mathematical analysis
Mathematical Logic
Strip
Students
Task Analysis
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Summary:The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students' intuition and mathematical rigor. In particular, we focus on a task, called the e-strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom teaching experiment for a semester-long IRA course. Fischbein's notion of secondary intuition was employed to elucidate the development of student intuition throughout the e-strip activity. We discuss how the e-strip activity played a role in developing students' intuition and how it impacted students' learning of the subsequent topics in the course, including definitions and theorems about convergence.
ISSN:2198-9745
2198-9753
DOI:10.1007/s40753-016-0039-9