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Analysis of factors influencing the understanding of the concept of infinity

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Abstract

The article discusses the understanding of infinity in children, teachers and primary teacher students. It focuses on a number of difficulties that people cope with when dealing with problems related to infinity such as its abstract nature, understanding of infinity as an ongoing process which never ends, understanding of infinity as a set of an infinite number of elements and understanding of well-known paradoxes. In the empirical section of the article, a study is described that was conducted at the Faculty of Education, University of Ljubljana, Slovenia. It encompassed 93 third-year students of the Primary Teacher Education study programme with the aim of researching their understanding of the concept of infinity. The focus was on finding out how primary teacher students who received no in-depth instruction on abstract mathematical content understand different types of infinity: infinitely large, infinitely many and infinitely close, what argumentation they provide for their answers to problems on infinity and what their basic misunderstandings about infinity are. The results show that the respondents’ understanding of infinity depends on the type of the task and on the context of the task. The respondents’ justifications for the solutions are based both on actual and on potential infinity. When solving tasks of the types ‘infinitely large’ and ‘infinitely many’, they provide justifications based on actual infinity. When solving tasks of the type ‘infinitely close’, they use arguments based on potential infinity. We conclude that when they feel unsure of themselves, they resort to their primary method of dealing with infinity, that is, to potential infinity.

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Notes

  1. The Bologna Process is named after the Bologna Declaration, which was signed in the Italian city of Bologna on 19 June 1999 by ministers in charge of higher education from 29 European countries. Today, the Process unites 47 countries—all party to the European Cultural Convention and committed to the goals of the European Higher Education Area. The overarching aim of the Bologna Process is to create a European Higher Education Area based on international cooperation and academic exchange that is attractive to European students and staff as well as to students and staff from other parts of the world (see http://www.ond.vlaanderen.be/hogeronderwijs/bologna/about/).

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  1. Faculty of Education, University of Ljubljana, Ljubljana, Slovenia

    Vida Manfreda Kolar & Tatjana Hodnik Čadež

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  1. Vida Manfreda Kolar
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  2. Tatjana Hodnik Čadež
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Correspondence to Vida Manfreda Kolar.

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Manfreda Kolar, V., Hodnik Čadež, T. Analysis of factors influencing the understanding of the concept of infinity. Educ Stud Math 80, 389–412 (2012). https://doi.org/10.1007/s10649-011-9357-7

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