Using rules blindly

Some students find it difficult to know which procedure to apply in a particular situation. A lack of understanding of how and why a procedure works is usually the underlying cause.

There appear to be three common pathways to students establishing a pattern of applying a procedure inappropriately. These are:

• learning a useful and effective strategy for one type of task, then not realising that when the task changes, the strategy must also change (e.g. comparing unit fractions by just comparing the denominators, then applying the same strategy to comparing non-unit fractions)
• encountering an unfamiliar situation and drawing on a familiar strategy that seems to have some connection to the new situation (e.g. trying to add fractions by treating the numerators and denominators as whole numbers, and adding them)
• being taught to use a new procedure, and allowing it to supersede all previous strategies (e.g. when finding a common denominator, always multiplying the two denominators, even when there is a much simpler relationship between the denominators such as one being a multiple of the other).