Abstract
Focusing on the convention that the same literal symbol in the same expression takes the same number, this paper aims to clarify American students' understanding of algebraic expressions through a written survey and clinical interview. In the interview, subjects who had inconsistent ideas on understanding literal symbols were carefully matched. To identify such students a written task was conducted beforehand. The methodology of this purposeful identification of subjects for interview is one of the characteristic features of this study. The interview revealed that American students have the misconception that the same literal symbol does not necessarily stand for the same number. This tendency is consistent with the data for Japanese students. This phenomenon in both countries is considered as a lack of understanding of the "definite aspect" which is one of the key aspects of the concept of variables.
