Multiple Proof Approaches and Mathematical Connections

Autor/inn/en	Jiang, Zhonghong; O'Brien, George E.
Titel	Multiple Proof Approaches and Mathematical Connections
Quelle	In: Mathematics Teacher, 105 (2012) 8, S.586-593 (8 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Geometric Concepts; Mathematics Instruction; Secondary School Mathematics; Preservice Teachers; Mathematics Teachers; Mathematical Logic; Validity; Mathematics Education; Technology; Trigonometry + Suchen Sie Ihr Suchwort? Elementare Geometrie; Mathematics lessons; Mathematikunterricht; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Mathematical logics; Mathematische Logik; Gültigkeit; Mathematische Bildung; Technologie; Trigonometrie
Abstract	One of the most rewarding accomplishments of working with preservice secondary school mathematics teachers is helping them develop conceptually connected knowledge and see mathematics as an integrated whole rather than isolated pieces. To help students see and use the connections among various mathematical topics, the authors have paid close attention to selecting such problems as the Three Altitudes of a Triangle problem. They presented the problem to preservice teachers (referred to here as "students") in their Geometry for Teachers class. Using technology to explore the Three Altitudes of a Triangle problem, students devise many proofs for their conjectures. After all the proof approaches were presented and discussed in class, students were excited about what they had learned and felt ownership of the proofs. They commented that they not only understood how to prove that the three altitude lines of any triangle are concurrent but also saw connections between this problem situation and various mathematical topics. In addition, their explorations of multiple approaches to proofs led beyond proof as verification to more of illumination and systematization in understandable yet deep ways (de Villiers 1999); expanded their repertoire of problem-solving strategies; and developed their confidence, interest, ability, and flexibility in solving various types of new problems. These benefits, in turn, will be passed on to their own students. (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