In this work the concept of formation of methodological knowledge and skills of future mathematics teachers in the process of teaching disciplines of mathematical cycle has been built and scientifically proved. The structural- functional model of the specified process that contains four blocks: methodological-target, content, organizational active and diagnostic has been built on the basis of the formulated conceptual ideas. A thorough analysis of the terminological aspect of the research problem has been made. The structure of the methodological activity has been clarified and it has been established that this structure contains five components: logical, external, motivationaltarget, internal and time. The content of the different levels (philosophical, general scientific, specifically scientific and technological) of mathematics methodology has been offered. It has been established that the methodological knowledge of the future mathematics teachers is structured in accordance with generally accepted levels of methodology and has four levels: philosophical, general scientific, concrete scientific, technological. The philosophical level of methodological knowledge includes the knowledge about philosophical laws, categories, principles; the questions about the subject of mathematics, the relation between mathematics and the real world, the structure and truth of mathematical knowledge; the problems of justification of mathematics; the place of mathematics in the sciences system. The general scientific level is formed by the general scientific methods of cognition. The content of methodological knowledge of the concrete scientific level consists of the knowledge about the subject and concrete scientific methods of studying the training course; fundamental concepts, fundamental theoretical facts (axioms, theorems) and fundamental relations between them; the connection with other disciplines of the mathematical cycle; the limits of the applicability of knowledge and the history of their development. The technological level is connected with research practice and also it includes the knowledge about the computer programs which are used for mathematics learning.
It has been proposed to combine methodological skills into four groups: 1) general methodological; 2) mathematical-methodological; 3) organizational-methodological; 4) communicative-methodological. It has been established that giving content to methodological knowledge and skills of future mathematics teachers depends on the academic discipline, in the process of studying which the mastering of methodological knowledge and the formation of methodological skills take place. Therefore, for future mathematics teachers the methodological knowledge of the different levels and methodological skills groups corresponding to them have been defined in the context of specific academic mathematical disciplines. Their contents have been revealed. It has been shown that the process of formation of methodological knowledge and skills has a cross-cutting character, takes place in three stages (propaedeutic, educationalactive, evaluative- reflexive) and continues throughout the training of future mathematics teachers. The expediency of conducting of methodological knowledge propaedeutics in the first-year students has been proved, and the ways and means of propaedeutic acquaintance of students with methodological knowledge and skills has been specified, in particular, the methodical provision for the organization of the work of the mathematical group "Propedeutics of methodological knowledge and skills in first year students" has been developed and introduced into the practice of training the future mathematics teachers. It has been established that in the content of the mathematical cycle disciplines there is a considerable potential for formation of methodological knowledge of all levels and corresponding methodological skills. But while studying these disciplines, not for all elements of methodological knowledge and skills are realized all three stages of the formation of methodological knowledge and skills. Extension, generalization and systematization of methodological knowledge of all levels take place during the study of the discipline "History and Methodology of Mathematics". The methodological supply for learning the discipline "History and Methodology of Mathematics" has been developed and implemented in the practice of preparing the future mathematics teachers. The methodology for forming methodological knowledge and skills of future mathematics teachers in the process of teaching the disciplines of the mathematical cycle, which is based on author's structural- functional model, has been developed, theoretically substantiated and experimentally verified.
