 [ Article ]
Journal of Educational Research in Mathematics - Vol. 30, No. 2, pp.307-328
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 May 2020
Received 07 Apr 2020 Revised 07 May 2020 Accepted 13 May 2020

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

Sunwoo, Jin*
*Teacher, YoungDuk Elementary School, South Korea camy17@naver.com

## 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

## Acknowledgments

본 연구 결과의 일부는 2019 수학교육관련학회 연합국제학술대회(2019.12.13.~12.15.)에서 발표하였음.

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