This study was designed to determine whether (1) rules are more easily memorized when stated in mathematical symbolism or when stated verbally, and whether (2) the ability to use constituent symbols correctly, assuming mastery of the underlying grammar, is a necessary and/or sufficient condition for applying a learned rule statement. Twenty-four…

A concrete and a symbolic approach to learning multiplication in the second grade are studied. The results, indicating that children using the symbolic model performed at a higher level than those using a concrete model, are discussed. (DT)

The author emphasizes the importance of concepts and mathematical form in a discussion of understanding mathematics. (MN)

Discussion about the nature and varieties of mathematical understanding is presented. Symbolic understanding is defined as a mutual assimilation between a symbol system and a conceptual structure, that is dominated by the conceptual structure. (MP)