Parentheses can be used in the context of integers, fractions, decimals, negative real numbers, or algebra in four different ways: to indicate the order of operations (e.g.,5x(3+2)=5x5), to represent the associative property (e.g.,(5+3)+2=5+(3+2)),to represent the distributive property(e.g.,5x(3+2)=5x3+5x2), and to represent the sign-change rule(e.g.,5-(3+2)=5-3-2). 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-operations rule but do not understand the other uses of parentheses. In the second phase, they understand only that parentheses mean〝do what is inside parentheses first〞(i.e.,they have some understanding that parentheses indicate the order of operations). In the third phase, children learn more about the uses of parentheses. However, this knowledge is incomplete and, as a result, frequently overapplied. In the fourth phase, children construct a more complete and interconnected understanding of the four uses, and , thus, no longer overapply them. In the fifth phase, children construct a relatively more complete and general understanding of the four uses in that they can apply them regardless of format. The aim of this study is to confirm this hierarchical learning model regarding the uses of parentheses. A stratified random sample of 120 fourth-graders from Taipei, Taiwan participated in this research. A latent class analysis supports the hierarchical learning model.