Geometry + Technology = Proof

Autor/inn/en	Lyublinskaya, Irina; Funsch, Dan
Titel	Geometry + Technology = Proof
Quelle	In: Mathematics Teacher, 105 (2012) 6, S.448-454 (7 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Educational Technology; Algebra; Geometry; Geometric Concepts; Computer Software; Secondary School Mathematics; Mathematics Instruction; Computer Uses in Education; Validity; Mathematical Logic; Teaching Methods + Suchen Sie Ihr Suchwort? Unterrichtsmedien; Geometrie; Elementare Geometrie; Mathematics lessons; Mathematikunterricht; Computernutzung; Gültigkeit; Mathematical logics; Mathematische Logik; Teaching method; Lehrmethode; Unterrichtsmethode
Abstract	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.) (ERIC).
Anmerkungen	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/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10