The study deals with teaching Russian as a non-native language to Kazakh students from linguistic and cultural positions. The purpose of the study is to substantiate the efficiency of adapting the integrated technology of mastering a non-native language based on the psycholinguistic analysis of the basic values. As the research methods, the study employs the association experiment and Karaulov's matrix of the "semantic gestalt" along with the classic linguodidactic attitudes; based on these methods the study provides the commentary of the associative fields with the valuably marked incentives. Such material being used will promote the actual development of the basic ideological values with the students. The theoretical and experimental content of the paper testifies to the effectiveness of the integrative methods in teaching Russian as a non-native language. The materials of the Free Association Experiment are presented in the comparative commentary of the semantic gestalt stimulus "Azhe -- Grandmother"; the latter represents in the linguistic consciousness of Kazakhs and Russians the significance of the concept under study in the system of the basic human values in the lexical-semantic group "Kinship relations". The conclusion postulated in the paper is as follows: the heuristic potential of the complex usage of the psycholinguistic (associative) and linguodidactic innovations is included in the process of developing a non-native language. The results of the study allow speaking about the expediency and prospects of further integration of the selected material into the study of the humanities at school and university.