The role of representations in students’ intuitive thinking about infinity

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Initial investigations suggest that students’ intuitive decisions concerning the equivalency of two given infinite sets are largely determined by the way these sets are represented. So far the effects of two types of representations were investigated: the numerical-horizontal and the numerical-vertical representations. Our study was mainly aimed at determining which representations (numerical-horizontal, numerical-vertical, numerical-explicit or geometric) yielded higher percentages of one-one correspondence reactions. For these purposes, 189 middle class 10th to 12th graders were asked to react to 14 problems dealing with comparing infinite sets. The problems presented different representations of the same infinite sets. It was found that one-one correspondence justifications were mainly elicited by numerical-explicit and by geometric representations. The discussion suggests ways of adjusting these findings to two different approaches to teaching: analogy and conflict.

Original languageEnglish
Pages (from-to)33-40
Number of pages8
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number1
StatePublished - 1996


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