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ERIC Number: EJ951262
Record Type: Journal
Publication Date: 2011-May
Pages: 14
Abstractor: ERIC
Reference Count: 16
ISBN: N/A
ISSN: N/A
What's 2 Got to Do with It? Using Dynamic Geometry Environments to Find Surprising Results and Motivate Proof
Martin, Tami; Cullen, Craig J.; Day, Roger
New England Mathematics Journal, v43 p49-62 May 2011
Dynamic geometry software (DGS), such as Geometer's Sketchpad[TM], Cabri Geometry[TM], and GeoGebra[TM] has become a widely used classroom technology. The broad availability of DGS has given students the opportunity to engage in many aspects of reasoning and proof, including exploration, conjecture development, and proof, in its many roles. By working in dynamic geometry environments (DGEs), students can explore properties, test conjectures, and discover new relationships. DGEs allow learners to explore a variety of visual representations that can serve as vehicles for further analysis, propelling learners to generalizations and formal proofs. In this article, the authors illustrate how questions posed in a DGE can engage students in a cyclic process of generating and testing conjectures followed by the justification of those conjectures. In particular, they illustrate that connections between measurement and geometric properties can be explored in a DGE, leading to surprising results and engendering the intellectual need to determine why a relationship exists. The activities presented in this article focused on exploring the relationship between the area and perimeter of a rectangle as one of its dimensions is fixed and the other is varied. This exploration generated discussion of measurement, comparison, variation, graphing, technology, and rates of change. The activity was carried out in a college mathematics course on geometric reasoning for non-majors. The activity is appropriate for high school mathematics students spanning a variety of courses. (Contains 7 figures.)
Association of Teachers of Mathematics in New England. Web site: http://www.atmne.net
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A