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ERIC Number: EJ880027
Record Type: Journal
Publication Date: 2010
Pages: 38
Abstractor: As Provided
Reference Count: 66
ISBN: N/A
ISSN: ISSN-0737-0008
The Infinite Challenge: Levels of Conceiving the Endlessness of Numbers
Falk, Ruma
Cognition and Instruction, v28 n1 p1-38 2010
To conceive the infinity of integers, one has to realize: (a) the unending possibility of increasing/decreasing numbers (potential infinity), (b) that the cardinality of the set of numbers is greater than that of any finite set (actual infinity), and (c) that the leap from a finite to an infinite set is itself infinite (immeasurable gap). Three experiments probed these understandings via competitive games and choice tasks accompanied by in-depth interviews. Participants were children 6 to 15 years old and adults. The results suggest that roughly from about age 8 on, children grasp potential and actual infinity. However, for several additional years their conception of actual infinity is incomplete because the immeasurable gap between a finite and an infinite set is not entirely internalized. Even many adolescents and adults fail to appreciate this gap. Distinguishing between number concepts and their names facilitates conceiving aspects of infinity. Educational implications of these findings are discussed. (Contains 3 footnotes, 3 tables, and 3 figures.)
Routledge. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Publication Type: Journal Articles; Reports - Research
Education Level: Adult Education; Elementary Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A