The article considers basic concepts of data science. The technologies of Machine Learning and Data Mining and the corresponding free software and data sources suitable for use in the educational process are analyzed. Elements of the methodology of teaching the basics of Data Science to future computer science teachers and computer scientists are offered. Article’s purpose is to select appropriate free Data Mining tools and develop some components of the methodology of teaching disciplines of the cycle of professional training of future computer science teachers and computer scientists. Methodology. Study and analysis of scientific publications, educational and methodical publications, comparative analysis of software, generalization of experience of specialists in education and computer science, modeling and synthesis of components of teaching methods, a systematic approach to teaching computer science. Scientific novelty. Appropriate freely available Data Mining tools have been selected, and some components of the methodology for teaching future computer science teachers and computer scientists have been developed. Conclusions. The main concepts and terms of modern technologies of processing and analysis of big data such as Data Science, Machine Learning, Data Mining are considered in the article. Machine learning algorithms are analyzed, sources of educational data are reviewed, freely distributed tools are selected, and methodological approaches to training Data Mining and Machine Learning of future computer science teachers and computer science specialists are presented. These methodological approaches to teaching modern methods and tools for processing large data are aimed at forming in future professionals the special competencies needed for effective modeling, design, development, maintenance, implementation and training of information technology in professional activities. Such formation can be carried out at studying courses «Information and communication technologies», «Programming in Python», «Fundamentals of artificial intelligence and data mining», «Introduction to Data Science and machine learning», which actualizes the subjects of these courses.