ABSTRACT
This chapter aims to provide part of that synthesis by reviewing the research on the initial learning of algebra. It begins with the statement that "much of school arithmetic is oriented towards 'finding the answer.'" This emphasis in the curriculum allows children to get by with informal, intuitive procedures. The chapter discusses the children's difficulties with the topics have been found to center on the meaning of letters, the shift to a set of conventions different from those used in arithmetic, and the recognition and use of structure. It explains studies related to these three areas of difficulty but emphasizes the last one—recognition and use of structure— for this is the core of high school algebra. Z. Usiskin has described some of these many uses of variable and has related them to the different purposes of algebra. Children's first experiences with manipulating strings of arithmetic symbols usually occur within the framework of solving open sentences— sometimes called "missing addend" problems.
