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1 | In article given the problem of readiness of the teacher for activity on development of mathematical abilities of pupils in a context of its formation in conditions of in qualification improvement system of professional skills is considered, the tasks of course preparation within the limits of which the teacher creatively realizes the potential and solves problems of professional development are defined. The basic directions and the factors influencing on the condition of readiness of the teacher for activity on development of pupils abilities are analyzed and the structurization of system of readiness elements is offered | 891 |