This chapter discusses that students' moving across different notations enhances and complexifies their understandings even further. It focuses on what Marti E. and Pozo J. I. have called external systems of representation, to differentiate from mental representations. The chapter explores ways in which children's understanding about a certain problem and the functions associated with it can be enhanced by moving across different notations for the problem. It provides a detailed description of the kinds of thinking and understanding highlighted by different notations, as children progress through different steps in solving a linear function best deal problem. The chapter illustrates both the research and the policy suggestions and recommendations for the use of multiple representations. Brenner M. E. and her colleagues have explored students' abilities to translate among representations in the area of algebra. They carry out training experiments with students and explore the impact on their algebraic understanding of being able to move across representations.