CHI TIẾT NGHIÊN CỨU …

Tiêu đề

Paradoxes as a window to infinity

Tác giả

Mamolo A.; Zazkis R.

Năm xuất bản

2008

Source title

Research in Mathematics Education

Số trích dẫn

DOI

10.1080/14794800802233696

Liên kết

https://www.scopus.com/inward/record.uri?eid=2-s2.0-77950320370&doi=10.1080%2f14794800802233696&partnerID=40&md5=6af54f17d040a1379472dddb1ad604b4

Tóm tắt

This study examines approaches to infinity of two groups of university students with different mathematical background: undergraduate students in Liberal Arts Programmes and graduate students in a Mathematics Education Master’s Programme. Our data are drawn from students’ engagement with two well-known paradoxes - Hilbert’s Grand Hotel and the Ping-Pong Ball Conundrum - before, during, and after instruction. While graduate students found the resolution of Hilbert’s Grand Hotel paradox unproblematic, responses of students in both groups to the Ping-Pong Ball Conundrum were surprisingly similar. Consistent with prior research, the work of participants in our study revealed that they perceive infinity as an ongoing process, rather than a completed one, and fail to notice conflicting ideas. Our contribution is in describing specific challenging features of these paradoxes that might influence students’ understanding of infinity, as well as the persuasive factors in students’ reasoning, that have not been unveiled by other means. © 2008, Taylor & Francis Group, LLC. All rights reserved.

Từ khóa

Cognitive conflict; Infinity; Paradoxes

Tài liệu tham khảo

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