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ERIC Number: EJ1152317
Record Type: Journal
Publication Date: 2017-May
Pages: 9
Abstractor: As Provided
ISSN: ISSN-1072-0839
Refining Concepts: Half Isn't Always Less
Carter, Cynthia J.
Mathematics Teaching in the Middle School, v22 n9 p524-532 May 2017
The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing and critiquing viable arguments, supported by choosing and using an appropriate mathematical tool (CCSSI 2010) helped them refine their understanding. It also describes a mental image that can inspire or interfere with reasoning and is neither misconception nor lack of knowledge. [This article was written with Ellen Prince and Zachary Schwartz.]
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: Middle Schools
Audience: Teachers
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Identifiers - Location: Massachusetts
Grant or Contract Numbers: 0917958