Triangles from Three Points

Autor/in	Nirode, Wayne
Titel	Triangles from Three Points
Quelle	In: Mathematics Teacher, 108 (2014) 1, S. 32-38 PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Forschungsbericht; Geometry; Mathematics Instruction; Secondary School Mathematics; Geometric Concepts; Honors Curriculum; Teaching Methods; Problem Solving; Computer Software; Computer Uses in Education; Educational Technology; High School Freshmen; Ohio + Suchen Sie Ihr Suchwort? Geometrie; Mathematics lessons; Mathematikunterricht; Elementare Geometrie; Teaching method; Lehrmethode; Unterrichtsmethode; Problemlösen; Computernutzung; Unterrichtsmedien
Abstract	Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the 12th International Congress on Mathematics Education. Jun referenced Wernick's (1982) original work in which he posed 139 unique problems. In each problem, three points are chosen from the following set of sixteen points--the three vertices of a triangle, the four classic points of concurrency (i.e., centroid, circumcenter, incenter, and orthocenter), the three midpoints, the three perpendicular feet, and the three feet of the angle bisectors The task is to locate, if possible, the three vertices of the triangle. For example, one possible version of the problem is to locate the other two vertices of a triangle given a vertex, the orthocenter, and the centroid. In this article Nirode describes how he implemented Wernick's problems in his instruction with his freshman honors geometry students in two distinct ways. First, he gave students numeric coordinates for three points and asked them to find the coordinates of the vertices of the triangle. Second, he followed Jun's suggestion to use dynamic geometry software (DGS) and gave students problems to complete as a project using The Geometer's Sketchpad® (GSP). (Other versions of DGS also could be used, such as GeoGebra, which is free.) (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/
Begutachtung	Peer reviewed
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10