## Why Use the Array?

Being able to recognize and manipulate information in the multiplication array is a crucial step along the math continuum because it represents the transition from concrete, situation-specific representations of multiplication to more abstract models that students can use to think

However, students often struggle with this concept because it involves several new types of abstract thinking that can be difficult to master. For example, many children have difficulty understanding how one square can represent both a row and a column. Although this concept is challenging, it is important because it is foundational not only for multiplication, but also for understanding area, geometry, and the Cartesian coordinate system (Fosnot & Dolk, 2001, p. 37; Battista et al. 1998, p. 531). The understanding of these rows and columns also helps represent the scalar nature of multiplication, where the first number scales the second number (Wallace & Gurganus, 2005; Otto, 2011). In addition, the patterns created by the rows and columns of the multiplication table can help students see and understand important foundational math principles such as the commutative and distributive properties (Otto, 2011;

Harries & Barmby, 2008). Many of these concepts are difficult to grasp without the help of a model such as the array.

*about*multiplication (Fosnot & Dolk, 2001; Battista et al. 1998; Otto, 2011; Wallace & Gurganus, 2005).However, students often struggle with this concept because it involves several new types of abstract thinking that can be difficult to master. For example, many children have difficulty understanding how one square can represent both a row and a column. Although this concept is challenging, it is important because it is foundational not only for multiplication, but also for understanding area, geometry, and the Cartesian coordinate system (Fosnot & Dolk, 2001, p. 37; Battista et al. 1998, p. 531). The understanding of these rows and columns also helps represent the scalar nature of multiplication, where the first number scales the second number (Wallace & Gurganus, 2005; Otto, 2011). In addition, the patterns created by the rows and columns of the multiplication table can help students see and understand important foundational math principles such as the commutative and distributive properties (Otto, 2011;

Harries & Barmby, 2008). Many of these concepts are difficult to grasp without the help of a model such as the array.