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ERIC Number: EJ981841
Record Type: Journal
Publication Date: 2012-Feb
Pages: 7
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0025-5769
EISSN: N/A
Available Date: N/A
Geometry + Technology = Proof
Lyublinskaya, Irina; Funsch, Dan
Mathematics Teacher, v105 n6 p448-454 Feb 2012
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been brought to bear on applying dynamic geometry software (DGS) to the educational process. DGS allows students to discover results for themselves, formulate conjectures and intermediate results, examine special cases, and generate new ideas. GeoGebra and TI-Nspire[TM] computer algebra systems have dynamic geometry capabilities and a built-in computer algebra system (CAS); however, CAS does not have the capability to establish algebraic relationships between geometric objects and their properties. Geometry Expressions[TM] (GE), developed by Saltire Software, is the first of a new class of interactive symbolic geometry system. This software takes a geometric configuration and outputs algebraic expressions for quantities measured from the model. Integrating geometric and algebraic explorations could be a powerful tool for helping students develop reasoning skills in the inductive exploration-based approach. GSP, GeoGebra, and TI-Nspire all allow students to explore geometric objects visually and dynamically and to generate and confirm conjectures on the basis of their observations. This is an important step in developing proofs, and the value of these software packages cannot be underestimated. These software packages provide a geometric approach to strengthening reasoning skills. GE, on the other hand, has the capability to produce symbolic algebraic outputs for geometric objects, thus providing opportunities for developing an algebraic approach to proofs. In this article, the authors discuss several examples of how symbolic geometry can be used to guide students as they develop strategies for proofs. The accompanying examples of student work illustrate this process. (Contains 10 figures.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A