International Journal of Early Childhood Education
2013, Vol. 19 No. 1, 153-170
Kindergarteners’ Understanding of
Base-Ten Notation through Formal and
Informal Instructions: A Comparative
Study of the United States and Korea
Young-Mi Lee
Hanyang Women’s University, Korea
3)
Su-Jeong Wee
Purdue University Calumet, USA
Abstract
The present study examines kindergarteners' understanding of the base-ten number
system through formal and informal instructions in the United States and South Korea.
A total of 69 kindergarteners (30 in the U.S. and 39 in Korea) and their head teachers
participated in this study over the course of one semester. Experimental groups in
both countries were provided with various formal and informal instructions, whereas
control groups were not. The math activities for formal instruction and concrete materials
for informal instruction, which were designed to support Korean children's development
of base-ten understanding, were provided to the experimental groups in the U.S. and
Korea for one semester. Pre-tests and post-tests were conducted with all participating
children at the beginning and at the end of the semester to examine changes in
the children's understanding of base-ten notation over time. The findings indicate no
differences in terms of children's performance on base-ten tasks during the pre-test
between the experimental and the control groups in each country. Comparison between
the countries showed that Korean children exhibited better understanding of base-ten
notation than their peers in the U.S. even before any math instruction was provided.
During the post-test, children in the experimental groups in both countries showed
Correspondence and requests for reprints should be sent to Young-Mi Lee, Hanyang Women’s University,
200 Salgoji-gil, Seongdong-gu, Seoul, 133-817, Korea.
E-mail: [email protected]
This study was funded in part by Hanyang Women’s University in the first semester of 2011.
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Lee & Wee
better understanding of base-ten notation than children in the control groups. Overall,
Korean children in the experimental group achieved the highest scores in understanding
the base-ten system. This paper discusses the elements that affected the children's
understanding of base-ten notation in the U.S. and Korea, including numerical language
systems and the types of instruction provided.
[Key words]
cross-national, base-ten number system, kindergarteners, Korea, United States
INTRODUCTION
The base-ten number system is a foundational math concept that children must
grasp during early childhood (Main, 2012) in order to perform successfully in higher
levels of math. While learning mathematics skills, children must build on this concept
to perform basic computations, such as multi-digit addition and subtraction, and to
develop logical thinking abilities. Competence in understanding the base-ten number
system emerges among children as early as at kindergarten age; thus, proper guidance
during early childhood is critical to intellectual development (Lee, 2008; Miura et al.,
1998).
Understanding the base-ten system requires children to grasp an abstract relationship
among number words, Arabic multi-digit numerals, and quantities (Cotter, 2000; Uy,
2003). Upon comprehending the base-ten system and place value notation concepts,
children can extend their number knowledge to larger numbers, such as hundreds and
thousands, without the need to count successively. Differentiating the values of 2s in
the number 22 appears to be a complex process for most kindergarteners. Learning to
do this involves (1) building connections between key ideas of place value, such as quantifying
sets of objects by grouping by 10, (2) treating the groups as units, and (3) using the
structure of the written notation to capture this information about grouping (Silva, 1999,
p. 10). As a child learns to count to 22, initially the child can only understand that
the number 22 represents a collection of 22 objects. To know that the digit on the right
represents two 1s and the digit on the left represents two 10s, the child must transform
ten 1s mentally into one 10.
Many studies (e.g., Gonzales et al., 2004; OECD PISA, 2004; Wang & Lin, 2005)
have consistently reported that Asian children surpass their counterparts in the U.S.
in various domains of mathematical achievement, including computational skills. Asian
children’s superiority in these skills has been observed as early as kindergarten age (Burger,
2010; Fuson & Ho, 1998; Miller et al., 1995; Zhou, Peverly, & Lin, 2005). This disparity
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