From the introduction: In this article I argue that there are a whole number of problems with using the \lq algebra as object\rq analogy, and give some alternative methods of teaching the simplification of algebraic expressions. To do this, first I give an example of what I consider to be a \lq good\rq analogy, that of merits / demerits for teaching negative number arithmetic, explain why I consider algebra as object to be a poor analogy for teaching purposes, and then look at a range of alternative ways of addressing this crucial point.