Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that single operations of algebra are often represented as collections of parts which may have independent status. Second, operations seem to be connected, often inappropriately, with a general scheme for symbol manipulation. Third, various kinds of knowledge are brought into play to detect errors. Evidence about the role of these kinds of knowledge, found in the solutions and comments of college students, is discussed, and some implications for instruction are considered. (Author/MK)