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Cardinality and Cardinal Number of an Infinite Set : A Nuanced Relationship / Ami Mamolo.

This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls...

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Bibliographic Details
Online Access: Full Text (via ERIC)
Main Author: Mamolo, Ami
Format: eBook
Language:English
Published: [Place of publication not identified] : Distributed by ERIC Clearinghouse, 2014.
Subjects:
Mathematical Concepts.
Mathematical Logic.
Number Concepts.
Logical Thinking.
Abstract Reasoning.
Concept Formation.
Learning Theories.
College Students.
College Mathematics.
Majors (Students)
College Faculty.
Mathematics Teachers.
Mathematics Skills.
Cognitive Processes.
Knowledge Level.
Description
Summary:This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases shed new light on the nuances involved in encapsulating, and de-encapsulating, a set theoretic concept of infinity. Implications for further research are discussed. [For the complete proceedings, see ED597799.]
Item Description:Availability: North American Chapter of the International Group for the Psychology of Mathematics Education. e-mail: pmena.steeringcommittee@gmail.com; Web site: http://www.pmena.org/.
Abstractor: As Provided.
Educational level discussed: Higher Education.
Educational level discussed: Postsecondary Education.
Physical Description:1 online resource (8 pages)
Type of Computer File or Data Note:Text (Speeches/Meeting Papers)
Text (Reports, Research)
Preferred Citation of Described Materials Note:North American Chapter of the International Group for the Psychology of Mathematics Education, Paper presented at the Joint Meeting of the International Group for the Psychology of Mathematics Education (PME) (38th) and the North American Chapter of the Psychology of Mathematics Education (PME-NA) (36th, Vancouver, Canada, Jul 15-20, 2014).

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