**ERIC Number:**EJ1160109

**Record Type:**Journal

**Publication Date:**2017-Oct

**Pages:**6

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

**EISSN:**N/A

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.

Descriptors: Mathematics Instruction, Secondary School Mathematics, High Schools, Standards, Mathematical Concepts, Concept Formation, Misconceptions, Algebra, Elementary School Mathematics, Equations (Mathematics)

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/

**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