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ERIC Number: EJ1052140
Record Type: Journal
Publication Date: 2015-Feb
Pages: 9
Abstractor: ERIC
ISSN: ISSN-1073-5836
Count on It: Congruent Manipulative Displays
Morin, Joe; Samelson, Vicki M.
Teaching Children Mathematics, v21 n6 p362-370 Feb 2015
Representations that create informative visual displays are powerful tools for communicating mathematical concepts. The National Council of Teachers of Mathematics encourages the use of manipulatives (NCTM 2000). Manipulative materials are often used to present initial representations of basic numerical principles to young children, and it is through these early developmental experiences that children frequently receive their first introduction to formal mathematics. Manipulative displays are well suited to serve as proxies for real-world problems, taking on the role of representing quantities. Teachers intuitively assemble manipulative displays to construct such representations, often attaching language to scaffold the real-world connections they are trying to portray. Many children prosper from the interaction; however, others do not. For the latter, confusion can result when the arrangement of the display is not clearly connected to the concept being taught (Garcia- Mila, Marti, and Teberosky 2004). The aims of this article are to: (1) identify the rationale for using manipulative displays as tools for communicating concepts; (2) describe the desired attributes teachers should consider when selecting and implementing manipulatives; (3) define conceptual congruence; and (4) offer some suggestions for helping teachers achieve greater congruence between the numerical concepts and procedures they are teaching and the manipulative displays they are using to represent them. The authors also present an example of a 1 x 10 ten-frame display to use as a tool to facilitate conceptual congruence. A bibliography is included.
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
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A