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ERIC Number: EJ1053536
Record Type: Journal
Publication Date: 2015-Mar
Pages: 5
Abstractor: ERIC
ISSN: ISSN-0025-5769
Recursive Averaging
Smith, Scott G.
Mathematics Teacher, v108 n7 p553-557 Mar 2015
In this article, Scott Smith presents an innocent problem (Problem 12 of the May 2001 Calendar from "Mathematics Teacher" ("MT" May 2001, vol. 94, no. 5, p. 384) that was transformed by several timely "what if?" questions into a rewarding investigation of some interesting mathematics. These investigations led to two conclusions: (1) Developing generalizations from patterns can be as rewarding to obtain as they are hard to discern; and (2) Sometimes the most productive question to pose is, "Can this result be generalized?". Although Smith did not prove the general case in his own investigation, he writes here that he thought it was still satisfying to uncover patterns and discover that these patterns were themselves considered by others in the mathematics community.
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: High Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A