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ERIC Number: EJ1152201
Record Type: Journal
Publication Date: 2017-Apr
Pages: 5
Abstractor: ERIC
ISSN: ISSN-1072-0839
Promoting Mathematical Connections Using Three-Dimensional Manipulatives
Safi, Farshid; Desai, Siddhi
Mathematics Teaching in the Middle School, v22 n8 p488-492 Apr 2017
"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of representations should continually develop in complexity and scope. "[Students] will need to be able to convert flexibly among these representations. Much of the power of mathematics comes from being able to view and operate on objects from different perspectives" (NCTM 2000, p. 361). In fact, when students represent, discuss, and make connections among different mathematical ideas by using different methods, they engage in deeper sense making and improve their problem-solving skills while refining their mathematical understanding (Fuson, Kalchman, and Bransford 2005; Lesh, Post, and Behr 1987). Recently, researchers have worked to connect lessons learned from their scholarship that can then be used by teachers in the classroom to empower students' understanding of mathematics. Teachers are encouraged to devote time connecting algebra to arithmetic before transitioning to the structural ideas of algebra. They are also encouraged to promote experiences and interactions with physical objects and manipulatives to set the foundation for future abstraction (Kieran 1992). The primary goal of this article is to promote connections in the teaching and learning of algebraic thinking as recommended by current mathematics standards and to illustrate the coherence of mathematics by linking algebraic and geometric representations (Garofalo and Trinter 2012). (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: Middle Schools
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A