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ERIC Number: EJ814974
Record Type: Journal
Publication Date: 2008
Pages: 18
Abstractor: As Provided
Reference Count: 0
ISSN: ISSN-0732-3123
Between Perception and Intuition: Learning about Infinity
Singer, Florence Mihaela; Voica, Cristian
Journal of Mathematical Behavior, v27 n3 p188-205 2008
Based on an empirical study, we explore children's primary and secondary perceptions on infinity. When discussing infinity, children seem to highlight three categories of primary perceptions: processional, topological, and spiritual. Based on their processional perception, children see the set of natural numbers as being infinite and endow Q with a discrete structure by making transfers from N to Q. In a continuous context, children are more likely to mobilize a topological perception. Evidence for a secondary perception of N arises from students' propensities to develop infinite sequences of natural numbers, and from their ability to prove that N is infinite. Children's perceptions on infinity change along the school years. In general, the perceptual dominance moves from sequential (processional) to topological across development. However, we found that around 11-13 years old, processional and topological perceptions interfere with each other, while before and after this age they seem to coexist and collaborate, one or the other being specifically activated by the nature of different tasks. (Contains 11 figures and 2 tables.)
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A