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Does a transformation approach improve students' ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms

Does a transformation approach improve students' ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms
Does a transformation approach improve students' ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms
We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students’ ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were 130 eighth-grade students in two classes with a comparable background that were taught by the same teacher. A two-week intervention was implemented in the experimental class aiming to help students learn how to use geometric transformations to draw auxiliary lines in solving geometric problems. The data were collected from a teacher interview, video-recordings of the intervention, and pre- and post- tests. The results revealed that there was a positive impact of using geometric transformations on the experimental students’ ability in solving high-level cognitive problems by adding auxiliary lines, though the impact on the students’ ability in solving general geometric problems as measured using the overall average scores was not statistically significant. Recommendations for future research are provided at the end of the article.
Teaching of geometry , Geometric proof, Auxiliary lines ● Intervention-based study, Geometric transformation
0013-1954
229-248
Fan, Lianghuo
28afe582-cd04-4ddc-9acb-a12494af79e0
Qi, Chunxia
b0be4d5e-7550-4210-bbfd-62e289591f13
Liu, Xiaomei
66f3931e-5d98-4ec9-8912-242fbc32d918
Wang, Yi
b0ecf165-944d-4664-99e8-41f5c14068b3
Lin, Mengwei
5fe12c56-0366-44d8-9a8a-8c34074791f7
Fan, Lianghuo
28afe582-cd04-4ddc-9acb-a12494af79e0
Qi, Chunxia
b0be4d5e-7550-4210-bbfd-62e289591f13
Liu, Xiaomei
66f3931e-5d98-4ec9-8912-242fbc32d918
Wang, Yi
b0ecf165-944d-4664-99e8-41f5c14068b3
Lin, Mengwei
5fe12c56-0366-44d8-9a8a-8c34074791f7

Fan, Lianghuo, Qi, Chunxia, Liu, Xiaomei, Wang, Yi and Lin, Mengwei (2017) Does a transformation approach improve students' ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms. Educational Studies in Mathematics, 96 (2), 229-248. (doi:10.1007/s10649-017-9772-5).

Record type: Article

Abstract

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students’ ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were 130 eighth-grade students in two classes with a comparable background that were taught by the same teacher. A two-week intervention was implemented in the experimental class aiming to help students learn how to use geometric transformations to draw auxiliary lines in solving geometric problems. The data were collected from a teacher interview, video-recordings of the intervention, and pre- and post- tests. The results revealed that there was a positive impact of using geometric transformations on the experimental students’ ability in solving high-level cognitive problems by adding auxiliary lines, though the impact on the students’ ability in solving general geometric problems as measured using the overall average scores was not statistically significant. Recommendations for future research are provided at the end of the article.

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Submitted date: 12 December 2015
Accepted/In Press date: 17 May 2017
e-pub ahead of print date: 22 June 2017
Published date: October 2017
Keywords: Teaching of geometry , Geometric proof, Auxiliary lines ● Intervention-based study, Geometric transformation
Organisations: Southampton Education School, Mathematics, Science & Health Education

Identifiers

Local EPrints ID: 412012
URI: http://eprints.soton.ac.uk/id/eprint/412012
ISSN: 0013-1954
PURE UUID: f66aa246-b52f-43d0-ba1e-26d5f1c99d66

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Date deposited: 04 Jul 2017 16:31
Last modified: 26 Nov 2021 06:22

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Contributors

Author: Lianghuo Fan
Author: Chunxia Qi
Author: Xiaomei Liu
Author: Yi Wang
Author: Mengwei Lin

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