The process of development in schoolchildren of mental operations underlying the process of transformation of algebraical expressions has been studied under conditions of experimental teaching. A programme produced for this aim comprized theoretical information on general principles of the algebraical transformation and a system of didactical tasks included in order to organize the process of learning those principles. It has been possible as a result to increase the generality, flexibility, and reflectedness of corresponding mental operations, to promote higher independence of thinking, to stimulate self-control and interest in the subject. At the same time stable individual differences between the children have been observed along a wide range of the experimental material. Some explanations of the phenomenon are provided.