Closing in on Proof

Autor/in	Coffland, David A.
Titel	Closing in on Proof
Quelle	In: Mathematics Teaching in the Middle School, 17 (2012) 8, S.494-500 (7 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1072-0839
Schlagwörter	Number Systems; Grade 7; Grade 8; Thinking Skills; Computation; Teaching Methods; Mathematics Teachers; Teacher Attitudes; Secondary School Mathematics; Middle School Students; Mathematical Logic; Validity; Mathematics Activities; Teacher Student Relationship + Suchen Sie Ihr Suchwort? Number system; Zahlensystem; School year 07; 7. Schuljahr; Schuljahr 07; School year 08; 8. Schuljahr; Schuljahr 08; Denkfähigkeit; Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Lehrerverhalten; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; Mathematical logics; Mathematische Logik; Gültigkeit; Teacher student relationships; Lehrer-Schüler-Beziehung
Abstract	The combined seventh-grade and eighth-grade class began each day with a mathematical reasoning question as a warm-up activity. One day's question was: Is the product of two odd numbers always an odd number? The students took sides on the issue, and the exercise ended in frustration. Reflecting on the frustration caused by this warm-up activity, the teacher understood that the question of parity ("even-ness" or "odd-ness") of the product of two odd numbers related do a basic axiom of the number system, specifically, the closure property of multiplication. Early in the year, the class studied basic axioms--commutative, associative, identity, inverse, closure, and distributive properties. Students identified computational uses for most properties but were unable to find applications for the closure properties of addition and multiplication. They concluded that the closure properties were necessary in the number system but were not useful for computation. The teacher recalled his dissatisfaction with the conclusion that closure properties "were not useful." To address these issues, he decided to create three days of activities, forming a mini unit exploring the closure property. The series of activities was also an opportunity for students to determine what was considered a valid proof and to become familiar with some categories of proof. This introduction to proof started students on a path of reasoning. (Contains 5 tables.) (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