Title: A computer-assisted environment for understanding geometry theorem proving problems and making conjectures

Authors: Wing-Kwong Wong, Chun-Wei Huang, Sheng-Kai Yin, Hsi-Hsun Yang, Po-Yu Chen, Sheng-Cheng Hsu, Shih-Hung Wu

Addresses: Department of Electronic Engineering, National Yunlin University of Science and Technology, No. 123, University Road, Section 3, Douliou, Yunlin 64002, Taiwan. ' Department of Electronic Engineering, National Yunlin University of Science and Technology, No. 123, University Road, Section 3, Douliou, Yunlin 64002, Taiwan. ' Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, No. 123, University Road, Section 3, Douliou, Yunlin 64002, Taiwan. ' Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, No. 123, University Road, Section 3, Douliou, Yunlin 64002, Taiwan. ' Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, No. 123, University Road, Section 3, Douliou, Yunlin 64002, Taiwan. ' Department of Information Management, Nan Kai University of Technology, No. 568, Chungcheng Road, Caotun, Nantou 542, Taiwan. ' Department of Computer Science and Information Engineering, Chaoyang University of Technology, No. 168, Jifong E. Road, Wufong, Taichung 413, Taiwan

Abstract: Many students do not perform well in geometry theorem proving. Researchers indicated that the construction of the figure of a geometry problem is fundamental in understanding the problem and producing a proof. We believe that the construction of the figure of a geometry problem is fundamental in understanding the problem and producing a proof. Current dynamic geometry environments are useful for illustrating invariant conditions when a figure is changed dynamically. However, they generally neither show the construction of a figure nor allow learner to make conjectures within the environments. To address these issues, we propose a system that shows how to construct the figure of a problem step by step and allows a learner to manipulate the figure dynamically and enter the properties of the figure that they discover. For the conjectures they enter, the system can test whether the conjectures are correct or not.

Keywords: dynamic learning environment; geometry learning; geometry theorem proving; intelligent information systems; geometry education.

DOI: 10.1504/IJIIDS.2009.027684

International Journal of Intelligent Information and Database Systems, 2009 Vol.3 No.3, pp.231 - 245

Published online: 07 Aug 2009 *

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