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One of the most important and long-standing goals of education is to promote constructive and positive relationships among heterogeneous students. This is true regardless of students' differences in ability level, sex, disability, ethnic membership, social class differences, or task orientation. The authors of the paper deal with psychological and pedagogical (methodology, motivation, content framework of training and organization) conditions, relevant for improving cooperative cognitive activity of students, which were identified and observed in the process of mathematical instruction at a technical University. The results of experimental testing their efficiency are provided as well. Inclusive pedagogical experiments are carried out, involving various groups of technical students. The groups to be tested consist of students from five countries with various native languages. The assessment of cooperative cognitive activity requires tests, observation, surveys, and application of mathematical statistics methods; both qualitative and quantitative data are taken into account. The experiment allows for a conclusion that cooperative cognitive activity of students supported by the modular object-oriented dynamic environment 'Moodle', including a project-oriented activity in conditions of a real company as well, guaranties the highest level of students' socialization and improves their motivation. The cooperative cognitive activity of technical students is efficient according to the research results. [ABSTRACT FROM AUTHOR]