ABSTRACT

One of the main functions of algebra is the representation of general relations and procedures in concise and unambiguous terms. This chapter examines the structural similarities between relations and problem situations to determine the relevance, and manipulate the algebraic elements into new configurations. The most obvious feature of algebra is its use of letters, its introduction of new notation and convention, and its focus upon the manipulation of terms and the simplification of expressions—in other words, its syntax. While the ability to manipulate symbols is important in algebra, it is clear that the critical aspect of work understands what the algebraic statements represent and what rationale and justification underlie the transformations allowed. The ability to work meaningfully in algebra, and thereby handle the notational conventions with ease, requires that students first develop a semantic understanding of arithmetic. One task for research is to examine the whole question of students' recognition and use of structure and how this recognition may develop.