Educational Studies in Mathematics

, Volume 96, Issue 2, pp 229–248 | Cite as

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

  • Lianghuo FanEmail author
  • Chunxia Qi
  • Xiaomei Liu
  • Yi Wang
  • Mengwei Lin


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 Geometric transformation Auxiliary lines Intervention-based study 



The authors wish to thank Mr. Xianfeng Shi and Ms. Hong Li for their assistance in conducting this study and the anonymous reviewers for their helpful comments. The study was supported in part by a research grant from Beijing Advanced Innovation Centre for Future Education (Project No. BJAICFE2016SR-008).

Supplementary material

10649_2017_9772_MOESM1_ESM.pdf (540 kb)
ESM 1 (PDF 539 kb)
10649_2017_9772_MOESM2_ESM.pdf (711 kb)
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10649_2017_9772_MOESM3_ESM.pdf (260 kb)
ESM 3 (PDF 260 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Southampton Education SchoolUniversity of SouthamptonSouthamptonUK
  2. 2.Faculty of EducationBeijing Normal UniversityBeijingChina
  3. 3.Institute of Basic Education Development and ResearchCapital Normal UniversityBeijingChina
  4. 4.Beijing Hepingjie No. 1 Middle SchoolBeijingChina

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