Promoting Mathematical Connections Using Three-Dimensional Manipulatives

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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).


Edited by Jennifer Eli,, of the University of Arizona, Tucson, and Despina Stylianou,, of the City College of New York. Readers are encouraged to visit to submit manuscripts that take research findings and translate them into practical outcomes, strategies, or tips that directly inform teachers' classroom practice.

Contributor Notes

Farshid Safi,, is an assistant professor of mathematics education at the University of Central Florida in Orlando. He focuses on developing teachers' conceptual understanding of K–grade 12 mathematics and content knowledge for teaching, as well as connecting essential topics in professional development through the use of multiple representations and technology.

Siddhi Desai,, is a senior mathematics secondary education major at The College of New Jersey in Ewing Township. She is interested in studying the use of technology and manipulatives in helping students develop a conceptual understanding of school mathematics.

(Corresponding author is Safi author is Desai
Mathematics Teaching in the Middle School


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