关于经典的无穷大悖论及其相关函数

IF 1.1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Teaching Mathematics and Its Applications Pub Date : 2021-02-01 DOI:10.1093/teamat/hrab001

Chanakya Wijeratne;Rina Zazkis

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引用次数: 0

摘要

在这项研究中，我们考虑了一个经典的无穷大悖论及其变体，并建议如何使用函数一致收敛的概念来分析误导直觉的来源。然后，我们研究了六名数学荣誉学生是如何参与悖论的变体的。尽管他们接受了高级数学训练，但参与者在解决出现的矛盾情况方面遇到了相当大的困难。根据书面回复和个人访谈的数据，我们描述了学生的方法，试图将他们的直觉与数学计算相协调。

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On the classic paradox of infinity and a related function

In this study we consider a classic paradox of infinity and its variations and suggest how the sources of misleading intuition can be analysed using the concept of uniform convergence of functions. We then examine how six mathematics honour students engage with a variation of the paradox. Despite their advanced mathematical training, the participants experienced considerable difficulty in addressing the presented paradoxical situation. Drawing on data from written responses and individual interviews, we describe the students’ approaches in an attempt to reconcile their intuitive perceptions with their mathematical computations.

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来源期刊

Teaching Mathematics and Its Applications EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

2.40

自引率

25.00%

发文量

期刊介绍： The journal provides a forum for the exchange of ideas and experiences which contribute to the improvement of mathematics teaching and learning for students from upper secondary/high school level through to university first degree level. A distinctive feature of the journal is its emphasis on the applications of mathematics and mathematical modelling within the context of mathematics education world-wide. The journal"s readership consists of mathematics teachers, students, researchers and those concerned with curriculum development and assessment, indeed anyone concerned about the education of users of mathematics.