In this episode of Room to Grow, our hosts discuss the importance of mathematical representations for students' deep learning of mathematics. The five representations described in NCTM's Principles to Actions include Physical, Visual, Symbolic, Verbal, and Contextual. Research shows that attending to and making connections between these multiple representations. National Research Council (2001), "Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas" (p. 94). Joanie and Curtis remind listeners that the purpose of attending to multiple mathematical representations is not simply to check a box, but rather to make connections between the representations, allowing students to recognize the underlying structures and generalities. This deeper level of connection is at the heart of understanding mathematics.

Finally, they consider how mathematical representations support students' development of mathematical discourse and language; after all, student need to understand their representations pretty well in order to explain them to someone else! By incorporating discourse and mathematical language in the classroom, students thinking is validated and they create ownership of the mathematics, both their approaches and those of their classmates.

Be sure to check out these resources, referenced in this episode:

• Math Assessment Project - Shell Center: Comparing strategies lesson (includes the pancake problem discussed in this episode) https://www.map.mathshell.org/download.php?fileid=1631
• Learn more about Using and Connecting Mathematical Representations in NCTM's Principles to Actions https://www.nctm.org/Store/Products/Principles-to-Actions--Ensuring-Mathematical-Success-for-All/
• Learn more about the Five Practices for Orchestrating Productive Mathematics Discussions https://www.nctm.org/Store/Products/5-Practices-for-Orchestrating-Productive-Mathematics-Discussions,-2nd-Edition/

Share your feedback, comments, and suggestions for future episode topics by emailing [email protected]. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.