This study examined the links students are able to make between formal expressions and situations to which they might refer. Students' understanding of a basic set of transformational rules in elementary algebra sign changes in addition and subtraction expressions with parentheses was assessed, exploring: (1) informal intuitive understanding of situations in which instances of the sign-change principles were implicit; (2) knowledge of the formal rules applied to numerical expressions; and (3) ability to link the two. Students from grades 5, 7, and 9 from parochial schools in the Pittsburgh, Pennsylvania area participated; 28 students from each grade participated in the main study. The situations and the interviews are described, followed by the results, which are categorized under informal understanding of principles, sign change rules applied to formal expressions, and linking of expressions and situations. It is concluded that increasing students' understanding of referential meaning of formal symbol systems may facilitate the learning of formal rules and the application of mathematics to problem solving and learning more advanced mathematics. (MNS)