The aim of this research is to give an overview of the psycho-didactical model of Engineering Pedagogy, as the basis of effective STEAM (Science, Technology, Engineering, Arts (Design), Mathematics) teaching and instructional design. Attributes of engineering graduates and basic skills of 21st century graduates are presented. The competency model of Engineering Educators by the International Society for Engineering Pedagogy (IGIP) is introduced. Micro-credentials pedagogical continuing education programme for STEAM teachers and engineering educators is presented, ensuring the acquisition of competencies for effective STEAM teaching. Learning activity as a system with a large number of elements is introduced, which under certain conditions can also become subsystems, being interconnected, with integrative properties and with the function of achieving certain specific goals. A Psycho-Didactical Model of Engineering Pedagogy is introduced as the basis for a toolbox of effective teaching STEAM.