Addressing Misconceptions in Secondary Geometry Proof

Autor/inn/en	Cirillo, Michelle; Hummer, Jenifer
Titel	Addressing Misconceptions in Secondary Geometry Proof
Quelle	In: Mathematics Teacher, 112 (2019) 6, S.410-417 (8 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Misconceptions; Geometry; Mathematical Logic; Validity; Geometric Concepts; Mathematics Instruction; Mathematics Teachers + Suchen Sie Ihr Suchwort? Missverständnis; Geometrie; Mathematical logics; Mathematische Logik; Gültigkeit; Elementare Geometrie; Mathematics lessons; Mathematikunterricht; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende
Abstract	Research suggests that teachers struggle to find effective ways to introduce proof. In 1940, in an article in this journal, Roland Smith argued that being aware of student misconceptions in geometry is the first step in preparing to address the fundamental challenges of learning to prove. Through careful study, he identified and analyzed "three serious learning difficulties" that students have in connection with (1) a lack of familiarity with geometric figures; (2) not sensing the meaning of the if-then relationship; and (3) an inadequate understanding of the meaning of proof (p. 100). Smith found that when these difficulties were attended to explicitly, student results improved. Years later, in 1985, Sharon Senk detailed findings from her study of 1520 students, in which she found that only 30 percent of students in a full-year geometry course that covered proof reached a 75 percent mastery of proof. Overall, 29 percent of the sample could not write a single valid proof. Consequently, Senk recommended (p. 455) that we must immediately look for more effective ways to teach proof in geometry, making the following suggestions: (1) pay special attention to teaching students to start a chain of reasoning; (2) place greater emphasis on the meaning of proof than we do currently; (3) teach students how, why, and when they can transform a diagram in a proof. Just as Smith found in his study, the authors had found that student results improve when they explicitly attend to misconceptions such as those described above. In the conclusion of this article, they offer some teacher perspectives on this approach; these perspectives provide evidence that attending to particular misconceptions supports both teachers and their students and yields greater student success and enjoyment of learning proof in geometry. (ERIC).
Anmerkungen	National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/publications/mathematics-teacher/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01