The article deals with the problem-based learning (PBL) that combines theoretical knowledge and practice in the educational process. PBL is an effective learning method through which the students become responsible and initiative. PBL main goals, principles and steps of implementation are observed in the article. PBL is a constructive, self-directed, collaborative and contextual process and has the potential to prepare students more effectively for future learning and profession. The main objectives of PBL are described in the article: constructing an extensive and flexible knowledge base; developing effective problem-solving abilities; becoming effective collaborators; being motivated to learn, work and research. It is cleared up that PBL focuses on practical learning where students solve real life badly structured problems. It is shown that the educational process is organized around the interdisciplinary problems and it can help students to learn integrally. The participants of problem-based learning process have to plan, monitor and evaluate the learning process actively, interpret prior knowledge and experience and after their self-study and mutual interaction within the group, they are able to construct and reconstruct their knowledge networks. The author states that implementation of PBL in the educational process gives students a sense of ownership over their learning and empowers participants with valuable skills that motivate students to learn and ability to achieve good results.The main ways of implementation of PBL in Ukrainian higher educational institutions and some recommendations are given in the article.

The present paper provides the results of the feedback influence on students’ autonomous ESP learning. It is aimed to study the impact of feedback on autonomous learning outcomes of first-year students, who are studying a two-year university course of “English for Specific Purposes (ESP)”, the significant part of which is dedicated to self-regulated learning. The aim of the course is to improve the students’ proficiency in professionally oriented English communication to the level of B2 according to the Common European Framework of Reference for Languages (CEFR). The investigation has proved the importance of teachers’ support in students’ autonomous ESP learning. The outcomes of those students who received the feedback regularly signify that even being self-sufficient, students strive for teachers’ or peer observation and feedback in the educational process. In the article, the interdependence between the level of students’ autonomous ESP learning competence and students’ feedback literacy is presented. The results of the study suggest that students’ autonomous ESP learning outcomes are considerably influenced by supportive external written feedback if it is sought, and their feedback literacy level is at least moderate or higher. A higher level of students’ feedback literacy is observed among students with a more advanced level of autonomous ESP learning competence and who demonstrate better academic achievements in professionally oriented English communication. The coherence of the elaborated levels of Ukrainian students’ feedback literacy and the ways of its enhancing can be significant for educators in other countries.

The paper deals with theoretical substantiation and construction of the methodological system of autonomous learning of the course "English for Specific Purposes (ESP)" for prospective teachers of Mathematics. The purpose of the study is to prove theoretically the methodological system of autonomous ESP learning for prospective teachers of Mathematics and to test empirically the current students" level of autonomous learning competence. The main components of the methodological system are observed, among them: target component (social demand, requirements, goals, and objectives); methodological component (approaches and principles); procedure component (content and technologies); assessment component (control and results). The main features such as functionality, complexity, openness and conceptual positions of the methodological system are described in the paper. It is said that the designed methodological system of autonomous learning of ESP of prospective teachers of Mathematics can be implemented in the educational process effectively in the presence of grounded pedagogical conditions, among them: training of students" autonomy, pedagogical support, and effective learning environment. The analysis of the study results reveals that during the initial phase of the implementation of autonomous ESP learning, the students have a moderate level of autonomous learning competence and it needs improvement in the process of implementation of the developed system.

In the study, the technology of work with cases in quasi-professional training of prospective teachers was designed and the results of academic progress were monitored. The designed technology of work on cases was based on the principles of the competent education. The diagnostic methods were chosen in accordance with the goals of the study experiment that allowed monitoring the dynamics of the researched qualities. The expert evaluation was based on the developed scale of 10 in accordance with the cognitive levels: knowledge, understanding, application, analysis, synthesis and evaluation. The experiment has proved that forming and control the competencies with the help of designed technology are more productive that allows making a conclusion about its productivity as well as the effectiveness of created pedagogical conditions. The technology of work with cases in quasi-professional training of prospective teachers includes methods and forms of studying, the description of students’ and teacher’s activity, and has the following components: a target, tasks, the organizational and pedagogical conditions, the informative component, the diagnostics and control, the structure of interaction, the technological component, and the effectiveness. The realization of case technology can be presented at three stages: the preparatory stage, the executive stage, the reflexive stages, which are described by the target, methods and forms, the students’ activity, forming competencies, the teacher’s activity, and control of results. The experimental study of implementing technology of using the case method in the educational process was conducted on the basis of Vinnytsia Mykhailo Kotsiubynsky State Pedagogical University among pre-service teachers (96 participants) during two semesters while studying the course of Pedagogics.

The study intends to expand a methodology of shaping intending educators’ ethical culture. The examples of effective techniques that were used in a teacher-training process are provided. Some samples of authentic pedagogical cases created by teachers and students are presented. The main stages of work on the formulation of the “Teacher’s Code of Ethics” are revealed. Such interaction methods as “Brain Storming”, “Decision Tree” are given. Fragments of the lesson “Pedagogical techniques in the structure of pedagogical communication of a teacher” are described, where students analyze videos on pedagogical topics, identify phrases that violate the ethical norms of the teaching profession and choose alternatives.The excerpts from the works of intending educators, where students reflect on the teachers’ functions and responsibilities, are analysed. A structured set of traditional (lectures, tutorials, laboratory classes) and innovative (brainstorming, role-playing, case studies, decision tree, pedagogical marathon, etc.) methods, which accelerate students’ gradual progress to the highest creative level of ethic culture is presented. Such organization of the educational process reflects the developmental changes from intuitive actions in different situations on the basis of initial ethics knowledge to the willingness of intending educators to work independently, guided by high-minded principles and norms in professional situations.