Project teaching developed in parallel with the development of the history of didactics and education. The didactic literature shows that the execution of teaching tasks dates from the middle of the 19th century. It is mentioned that W. T. Harris initiated a didactic plan. Project-based learning is a long tradition in American public schools, and the originators of the project method are William Heard Kilpatrick and John Deweya. Traditional teaching methods in schools cannot properly provide the important potential of intellectual advancement in students ’ability to master new knowledge and technologies. Project teaching is a form of problem-based and research-oriented teaching, in which emphasis is placed on independent student research work. The project method like no other method provides an opportunity for a wise combination of theory and practical application of knowledge in real life. In addition, the project method allows to deepen students' self-confidence, their self-awareness, helps them understand the importance of group work. The project method signifies a serious role in cooperation in the process of performing creative exercises, it forms research skills. It influences them to apply knowledge and skills to define and solve problems. The role of teachers and students is extremely important. Joint synergies with the aim of solving problems are important. Research learning is associated with John Dewey and is thought to have been the first to use the term. Research work means a cognitive style of work in which students independently or with the support of a mentor come to information, solve a problem using the necessary, adequate to them scientific methods and steps. Both methods have their advantages and disadvantages, forms, types, goals and stages that will be written about in the paper. The purpose of this research is to define two key teaching methods in teaching and to present modeling of teaching processes within methodological approaches.