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ERIC Number: EJ876167
Record Type: Journal
Publication Date: 2010-Mar
Pages: 9
Abstractor: ERIC
Reference Count: 0
ISSN: ISSN-1073-5836
Identifying Logical Necessity
Yopp, David
Teaching Children Mathematics, v16 n7 p410-418 Mar 2010
Understanding logical necessity is an important component of proof and reasoning for teachers of grades K-8. The ability to determine exactly where young students' arguments are faulty offers teachers the chance to give youngsters feedback as they progress toward writing mathematically valid deductive proofs. As defined, logical necessity is the condition for which conclusions follow necessarily from premises. One way to reinforce the concept of logical necessity is to examine arguments that have a lapse in logical thinking. The activities presented in this article suggest ways that prospective elementary school teachers can sharpen this skill. The activities on logical necessity were not stand-alone instruction but part of a larger instructional effort that embedded proof and reasoning--in particular, evaluating arguments--in weekly and often daily instruction. The logical necessity criterion became part of classroom discourse on argument evaluation that originated from prospective teachers within the classroom community. [Additional tasks: "Twos and Fives" and "Mathematical Arguments" accompany the online version of this article at] (Contains 6 figures.)
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education; Grade 1; Grade 2; Grade 3; Grade 4; Grade 5; Grade 6; Grade 7; Grade 8; Kindergarten
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A