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

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## 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.

## Keywords

Task design Web-based proof learning support system Strategic knowledge## Notes

### 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.

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