摘要：The article presents the arguments in favor of the active use of programming as a modern method of formation of mathematical knowledge. Today it is possible to implement the previously invented algorithms in a variety of virtual environments, whether it is a programming environment or specialized system of computer mathematics. That is what opens the way for each student to find and implement solutions is not one particular, but a whole class of problems, empirical confirmation of the already known truths and to promote and test new hypotheses. This allows you to shift the emphasis in mathematics education with the establishment of computer skills and some limited training with a pencil and paper (chalk and blackboard) toward the use of various computer computing systems, not only as a tool environment to simplify the quantitative and qualitative studies of various processes and tools for release time from routine calculations on the research part of the problem, but at the same time, and as an instrument of knowledge, a monitoring tool and a tool to develop their own mathematical knowledge. Examples are given of the use of programming ideas in solving problems of some mathematical courses. Attention is accented on a using these ideas in the preparation of mathematics teachers as the main link in the mathematical education system.
