Proofs and refutations in lower secondary school geometry
Proofs and refutations in lower secondary school geometry
In this paper, we report on a teaching experiment in which we focused on students tackling 3D geometry problems in which, in general, they initially tended to produce 'primitive' conjectures by relying on visual images rather than geometrical reasoning. Following the work of Larsen and Zandieh (2008), we utilise the ideas of Lakatos (1976) on managing the refutation process and how the use of counter-examples can be important in promoting the growth of students' capability with geometrical reasoning and proof. We found that students’ primitive conjectures can cause an unexpected result and that this can trigger further reviewing (‘Monster-barring’) and modifications of the conjecture ('Exception-barring') amongst students. Whole classroom discussion followed by small group discussion allowed students to exchange various ideas and opinions and this process was important for their construction of a proof of their new conjecture (‘Proof-analysis’).
mathematics, education, geometry
660-669
European Society for Research in Mathematics Education
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Kunimune, Susumu
c1255c4f-6293-4a26-a8b6-ff02013e3192
Kumakura, Hiroyuki
e7b62c78-5b51-4ccb-85a5-f2dc3e94bee2
Matsumoto, Shinichiro
f4827c3f-9182-4a0c-9a7a-a13a31df1640
February 2011
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Kunimune, Susumu
c1255c4f-6293-4a26-a8b6-ff02013e3192
Kumakura, Hiroyuki
e7b62c78-5b51-4ccb-85a5-f2dc3e94bee2
Matsumoto, Shinichiro
f4827c3f-9182-4a0c-9a7a-a13a31df1640
Fujita, Taro, Jones, Keith, Kunimune, Susumu, Kumakura, Hiroyuki and Matsumoto, Shinichiro
(2011)
Proofs and refutations in lower secondary school geometry.
Pytlak, Marta, Rowland, Tim and Swoboda, Ewa
(eds.)
In Proceedings of the 7th Congress of the European Society for Research in Mathematics Education (CERME7).
European Society for Research in Mathematics Education.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
In this paper, we report on a teaching experiment in which we focused on students tackling 3D geometry problems in which, in general, they initially tended to produce 'primitive' conjectures by relying on visual images rather than geometrical reasoning. Following the work of Larsen and Zandieh (2008), we utilise the ideas of Lakatos (1976) on managing the refutation process and how the use of counter-examples can be important in promoting the growth of students' capability with geometrical reasoning and proof. We found that students’ primitive conjectures can cause an unexpected result and that this can trigger further reviewing (‘Monster-barring’) and modifications of the conjecture ('Exception-barring') amongst students. Whole classroom discussion followed by small group discussion allowed students to exchange various ideas and opinions and this process was important for their construction of a proof of their new conjecture (‘Proof-analysis’).
Text
Fujita-etc_proofs_refutations_school_geom_CERME7_2011
- Accepted Manuscript
More information
Published date: February 2011
Venue - Dates:
7th Congress of the European Society for Research in Mathematics Education, University of Rzeszów, Rzeszów, Poland, 2011-02-09 - 2011-02-13
Keywords:
mathematics, education, geometry
Identifiers
Local EPrints ID: 445837
URI: http://eprints.soton.ac.uk/id/eprint/445837
PURE UUID: 97303472-37bc-4de8-839d-16963cc0ae39
Catalogue record
Date deposited: 08 Jan 2021 17:32
Last modified: 16 Mar 2024 10:25
Export record
Contributors
Author:
Taro Fujita
Author:
Susumu Kunimune
Author:
Hiroyuki Kumakura
Author:
Shinichiro Matsumoto
Editor:
Marta Pytlak
Editor:
Tim Rowland
Editor:
Ewa Swoboda
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
