An Analysis of Third Graders' Understanding of the Principle of Computation Between Two-Digit Number and Two-Digit Number: Focused on the Array Model

Abstract

Along with the significance of distributive property playing a fundamental role in providing explanations for multi-digit multiplication of whole numbers, the array model has been widely used to teach distributive property effectively. Given this, the purpose of this study was to investigate how third graders could understand multiplication in (two digits) × (two digits) and how their understanding could be expanded and applied to algebraic ideas after being taught reconstructed units of multiplication using the array model. The results of this study showed that most students represented the principle of computation between two-digit number and two-digit number using the array model as well as reasoned which picture represented the product of two numbers. Also, the participating students successfully applied the principle to the computation between three-digit number and two-digit number, and some students represented the product of two numbers by using variables (e.g., □, △). This paper concludes with some implications on how to teach multiplication of whole numbers in elementary mathematics.

Keywords

• computation between two-digit and two-digit number
• distributive property
• array model
• generalization