The development of school teaching systems to enable effective adaptive communication of information requires specific pedagogical solutions to several important theoretical and methodological problems .These include 1) the discernment of basic characteristics needed to diagnose and improve the quality of subject preparation for schoolchildren, 2) clarifying the role of the teacher in the structure of adaptive learning process, and 3) finding ways to integrate adaptive content into the framework of courses on mathematics. The purpose of our study was to determine theoretical and methodological foundations of teaching mathematics to schoolchildren taking into account their level of ability with the consequent development of appropriate adaptive content. The basic characteristics that underpin the concept of adaptive learning which contributes to both individual profiles of student ability to learn and subsequent success outcomes are: proficiency, motivation to learn and level of mathematical knowledge. The evaluation of individual profile structure of schoolchildren determines the choice of methodologies for presentation of adaptive content in ways allowing development and motivation. The system of educational process management developed in this way includes both content-methodical and procedural-technological components. This makes it possible to automatically evaluate the level of each students' mathematical training (knowledge, motivation, development) and to ensure continuous improvement. This system can also be used by secondary teachers of mathematics as a part of extracurricular activities, or as a distance learning support. In addition, the recommendations for structuring multi-level problem material can be used by mathematics teachers to self-construct adaptive sets tasks at various stages of teaching mathematics. As a result, students have the opportunity to improve their own profile of learning success, particularly by solving a chain of tasks.

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The conditions of modern labor market dictate the need for highly qualified specialists who creatively approach the performance of their professional activities, independently making competent productive decisions. In search of a solution to this problem, higher education institutions resort to the use of modern educational technologies. The article presents the forms of implementation of discussion technologies, their peculiarity, considers their importance and specificity of use in the conditions of personality-centered training and defines the goals of discussion technologies implementation in the course study. The study revealed an increase in the level of students’ training. The use of discussion technologies allowed them to study the topics of the course more deeply.

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