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Web-Based Task Design Supporting Students’ Construction of Alternative Proofs

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Proof Technology in Mathematics Research and Teaching

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 14))

Abstract

This study explores how a proving task with technology can be designed to develop students’ strategic knowledge of how to construct alternative proofs to the same problem, and how the designed task enriched their strategic knowledge in proving in the context of geometrical proof. The designed task had three components; open problem with flow-chart proofs, learning environment with web-based proof learning support system, and process of expressing strategic knowledge of how to reconstruct proofs. By analyzing experimental lessons with a grade 8 class (students aged 13–14), we found that these task components, and their interactions, contributed to developing students’ strategic knowledge. Using open problems with flow-chart proofs in a web-based proof learning support system enabled students to find alternative proofs to the same problem, and promoted the process of them expressing their strategic knowledge of how to reconstruct proofs.

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Acknowledgements

This research was supported by the Grant-in-Aid for Scientific Research, Ministry of Education, Culture, Sports, Science, and Technology, Japan. Special thanks to Mr. Yasuyuki Matsunaga for data collection, and Mr. Daisuke Ichikawa for practicing the lessons.

Author information

Authors and Affiliations

  1. Shinshu University, Nagano, Japan

    Mikio Miyazaki

  2. University of Exeter, Exeter, UK

    Taro Fujita

  3. University of Southampton, Southampton, UK

    Keith Jones

Authors
  1. Mikio Miyazaki
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  2. Taro Fujita
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  3. Keith Jones
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Corresponding author

Correspondence to Mikio Miyazaki .

Editor information

Editors and Affiliations

  1. Ontario Institute for Studies in Education, University of Toronto, Toronto, ON, Canada

    Gila Hanna

  2. AG Didaktik, Fachbereich 3, Universität Bremen, Bremen, Germany

    David A. Reid

  3. Faculty of Education, Stellenbosch University, Stellenbosch, South Africa

    Michael de Villiers

Appendices

Appendix 1: Worksheet of Lesson 4 to Express Ideas on Reconstructing Proofs

figure a

Appendix 2: Post-test After the 4th Lesson

figure b

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Miyazaki, M., Fujita, T., Jones, K. (2019). Web-Based Task Design Supporting Students’ Construction of Alternative Proofs. In: Hanna, G., Reid, D., de Villiers, M. (eds) Proof Technology in Mathematics Research and Teaching . Mathematics Education in the Digital Era, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-28483-1_14

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  • DOI: https://doi.org/10.1007/978-3-030-28483-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28482-4

  • Online ISBN: 978-3-030-28483-1

  • eBook Packages: EducationEducation (R0)

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