On difficulties with fractions

A sample of less successful students (aged 12–15) was tested on the topic of fractions. The test paper presented diagrams, word problems, and computational questions. The analysis was designed to find out the specific difficulties and deficiencies of these children. It is shown that most of them are only able to apply remembered rules to the solution of the problems without knowing whether the rule works, i.e., their understanding is at most instrumental, but not relational.