The Concepts in Secondary Mathematics and Science (CSMS) and Strategies and Errors in Secondary Mathematics (SESM) research projects based at Chelsa College, England, have shown the marked reluctance of secondary school students to use fractions when solving mathematical problems, even though they have been taught the topic for a number of years. One of the topics CSMS investigated was ratio and proportion; students appeared to have used the incorrect addition strategy identified by other researchers. SESM probed more deeply into such errors, and the meanings children give to a/b. For the first stage of the project, 23 children were interviewed individually about their reactions to tasks involving fractions. Then teaching modules were developed and evaluated with 59 children aged 13 and 14. Most children avoided using fractions on the pretest: they refused to acknowledge the existence of fractions. After instruction, about one-third of the children still avoided fractions in responding to test questions. Results are given for a variety of items, with the conclusion that the difficulties appeared to be fundamental. (MNS)