The article grounds the author's model of preparing future teachers of mathematics to the development of the intellectual culture of pupils, which presents by four interdependent blocks: target block, content block, organizationally-active block and result block. The target block of the model reflects the aim and tasks of the research. The aim of the elaborated model is defined as the formation of the readiness of future teachers of mathematics to the development of the intellectual culture of secondary school pupils. The content block includes methodological approaches and principles, on the basis of which grounds the formation of the the readiness of future teachers of mathematics to the development of the intellectual culture of pupils. The intellectual culture of the future teacher of mathematics is defined as an important and necessary prerequisite for the formation and development of the mentioned culture of secondary school pupil and included in the content of the concept of the readiness to the realization of the investigated process. In our research the readiness of future teachers of mathematics to the development of the intellectual culture of pupils look as the totality of three components: motivational readiness, which is determined by the formation of the motivational component of the intellectual culture of student and realization of the importance of implementing the development of this culture among pupils; theoretical readiness, which is characterized by the formation of the content component of the intellectual culture of the future teacher and the availability of firm knowledge of the bases of organization of the process of developing the intellectual culture of pupils; practical readiness, which is expressed by the formation of the operational-activity and communicative components of the intellectual culture of students and the ability to effectively develop the specified culture among the pupils. The organizationally-active block of the model includes the pedagogical conditions, forms, methods, means and technologies of the formation of the the readiness of future teachers of mathematics to the development of the intellectual culture of pupils. The result block of the elaborated structural-functional model is presented by our criteria and levels of readiness.