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ERIC Number: EJ1160109
Record Type: Journal
Publication Date: 2017-Oct
Pages: 6
Abstractor: ERIC
ISSN: ISSN-0025-5769
Circumventing High School Rules That Expire
Dougherty, Barbara J.; Bush, Sarah B.; Karp, Karen S.
Mathematics Teacher, v111 n2 p134-139 Oct 2017
The perpetuation of mathematical rules that expire (Karp, Bush, and Dougherty 2014; 2015), or rules that are taught in previous grades that no longer hold true, suggests that many secondary students harbor misconceptions from their elementary and middle-grades mathematics experiences as they progress to mathematics classes that are more sophisticated. High school students, particularly students who are struggling in mathematics class, often try to use these familiar but short-lived "rules" as strategies when attempting increasingly challenging tasks and find that their rules backfire. Such experiences can be discouraging and can foster the idea that mathematics is a set of tricks and tips to memorize rather than a network of integrated concepts. Here, the authors discuss fifteen mathematical rules that expire to highlight how these "rules"-- which they have found prevalent in their many years working in schools, on websites, or in some cases, have taught and later regretted--can cause long-term problems. For each rule that expires, the authors: (1) state the rule; (2) discuss how students overgeneralize it; (3) provide counterexamples; and (4) state the point at which the rule begins to fall apart. A bibliography is included.
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A