Supporting students to overcome circular arguments in secondary school mathematics: the use of the flowchart proof learning platform
Supporting students to overcome circular arguments in secondary school mathematics: the use of the flowchart proof learning platform
The extent to which students are competent in identifying circular arguments in mathematical proofs remains an open question, as does how it might be possible to enhance their competency. In this paper we report on a study of learners encountering logical circularity while tackling geometry proof problems using a web-based proof learning support environment. The selected episodes presented in the paper illustrate how learners who have just started learning to construct mathematical proofs make various mistakes, including using circular arguments. Using the feedback supplied by the web-based proof learning support environment, and with suitable guidance from the teacher on the structural aspects of a proof, learners can start bridging the gap in their logic and thereby begin to overcome circular arguments in mathematical proofs.
mathematics, education, proof
353-360
International Group for the Psychology of Mathematics Education
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
10 July 2011
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro, Jones, Keith and Miyazaki, Mikio
(2011)
Supporting students to overcome circular arguments in secondary school mathematics: the use of the flowchart proof learning platform.
Ubuz, Behiye
(ed.)
In Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (PME35).
vol. 2,
International Group for the Psychology of Mathematics Education.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
The extent to which students are competent in identifying circular arguments in mathematical proofs remains an open question, as does how it might be possible to enhance their competency. In this paper we report on a study of learners encountering logical circularity while tackling geometry proof problems using a web-based proof learning support environment. The selected episodes presented in the paper illustrate how learners who have just started learning to construct mathematical proofs make various mistakes, including using circular arguments. Using the feedback supplied by the web-based proof learning support environment, and with suitable guidance from the teacher on the structural aspects of a proof, learners can start bridging the gap in their logic and thereby begin to overcome circular arguments in mathematical proofs.
Text
Fujita-etc_overcome_circular_arguments_PME35_2011
- Accepted Manuscript
More information
Published date: 10 July 2011
Venue - Dates:
35th Conference of the International Group for the Psychology of Mathematics Education, Middle East Technical University, Ankara, Turkey, 2011-07-10 - 2011-07-15
Keywords:
mathematics, education, proof
Identifiers
Local EPrints ID: 445901
URI: http://eprints.soton.ac.uk/id/eprint/445901
ISSN: 0771-100X
PURE UUID: a30320db-7b41-4ed4-a2fa-ed589f7d0238
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Date deposited: 13 Jan 2021 17:31
Last modified: 16 Mar 2024 10:25
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Contributors
Author:
Taro Fujita
Author:
Mikio Miyazaki
Editor:
Behiye Ubuz
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