Some psychological conditions of introduction of the notion of magnitude in teaching are dealt with. Proceeding from analysis of mathematical concepts of magnitude the author sets forth a hypothesis that this notion is semiotic in nature as are the operations operative in instructional introduction of it. Only within this framework complementarity of operations of transformation and comparison (which comprise the basis of the notion of magnitude) is present in children's problem solving. Results of experimental approbation of methods designed to establish correspondence of children's activity to the nature of the notion of magnitude are given (the methods are based on reversal of the objects comparison task).