The development of soft skills in pre-service teachers helps to improve the quality of teaching, create a positive classroom environment and ensure an individualized approach to learning. The integration of soft skills, in particular flexibility and adaptability to change, helps teachers to respond effectively to new teaching methods, technological innovations and the requirements of the modern educational environment. The authors of this article aimed to investigate the possibilities of developing soft skills within the educational components of the training programme for pre-service mathematics and physics teachers. The methodological basis of the study was the analysis of scientific literature, synthesis, formalization of scientific sources, description, comparison, and theoretical generalization of own pedagogical experience of teaching the course “Olympiad Mathematics”. The results of the study reveal some ways of developing soft skills of future masters of secondary education of Sumy State Pedagogical University named after A.S. Makarenko in the process of studying the course “Olympiad Mathematics”. At the same time, among the various topics of the course, the topic “Proof of Inequalities” was singled out. The peculiarities of applying the following methods and techniques to the proof of inequalities in the context of development of soft skills are revealed: the method of strengthening (weakening) of inequality, the method of mathematical induction, the Malikov's method, the method of transforming the common term in sums and its evaluation, the method of evaluating the terms of the product and introducing an additional factor, the method of applying the properties of functions to the proof of inequalities, the method of using the properties of the definite integral of a certain function on a segment. It has been found that the most common methods of proving inequalities have wide possibilities in the context of development of soft skills. Each of the methods of proving inequalities discussed in the article is illustrated by relevant examples with detailed explanations. It is proved that this topic opens up wide opportunities for the acquisition and development of a number of soft skills. The research allows identifying specific ways to improve soft skills in pre-service mathematics and physics teachers, which are practically significant for further development of these professions when studying specific topics of the “Olympiad Mathematics” course: using group work formats during seminars, problem-based learning in mathematics, applying digital technologies in the study of Olympiad Mathematics, self-analysis and reflection, using mentoring support technology, public speaking during seminars with presentations of own solutions
Shyshenko et al. (Mon,) studied this question.