ABSTRACT
The debate among British mathematicians in the first half of the 19th century about the nature of algebra draws attention to another important aspect of algebra—an epistemological problem. H. Freudenthal points out that the traditional teaching of algebra places on students the demand to become fluent in handling the formal algebraic language, while at the same time understanding how this language may be used to solve meaningful problems. An inspection of school algebra textbooks shows that most of the problems they contain, whether "real" or artificial, would be better handled, and certainly better understood, if treated as problems to be solved by arithmetic. The central importance of the function concept to algebra courses in school is one of the assertions that need to be looked at carefully. Mathematics education research should be sensitive to context, and particularly to didactical intention, as a significant contextual element.
