Children's Understanding of the Uses of Parentheses
Hsieh, Ju-Shan
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/80328
Description
Title
Children's Understanding of the Uses of Parentheses
Author(s)
Hsieh, Ju-Shan
Issue Date
1999
Doctoral Committee Chair(s)
Baroody, Arthur J.
Department of Study
Education
Discipline
Education
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Education, Elementary
Language
eng
Abstract
"Parentheses can be used in the context of whole numbers, fractions, decimals, integers (which include negative values), or algebra in four different ways: to represent the associative property (e.g., (5 + 3) + 2 = 5 + (3 + 2)), to represent the distributive property (e.g., 5 x (3 + 2) = 5 x 3 + 5 x 2), to represent the sign-change rule (e.g., 5 - (3 + 2) = 5 - 3 - 2), and to indicate the order of operations (e.g., 5 x (3 + 2) = 5 x 5). A curriculum analysis and preliminary study lead to the following model regarding the learning of these uses: During the first of five phases, children learn the basic operations and the order-of-operations rule but have no understanding about the use of parentheses. In the second phase, children understand only that parentheses mean ""do what is inside parentheses first."" In the third phase, children construct an incomplete understanding of the four principles and may overapply these uses. In the fourth phase, children construct a relatively complete and interconnected understanding of the four uses. In the fifth phase, children construct an even more complete understanding of the four principles and can apply them regardless of format (e.g., apply the sign-change rule in the subtractive type, 5 - (3 - 2) = 5 - 3 + 2, and the divisive type, 5 ÷ (3 x 2) = 5 ÷ 3 ÷ 2). The aim of this study was to confirm the learning model regarding the uses of parentheses. A stratified random sample of 120 fourth graders from Taipei, Taiwan participated in this research, and 12 of these students were interviewed. A latent class analysis and the interview data support the hierarchical learning model. Also examined were the effects of format, namely which operations were involved and the location of parentheses. The main implication of the hierarchical learning model and the results of this study is that teaching and assessment of the order-of-operations, the associative property, the distributive property, and the sign-change rule should be done in an integrated manner."
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
