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The aim of the article is to study the basic structural and semantic qualities of two-component complex sentences with object clauses functioning in mathematical works in English and French. The works of outstanding modern mathematicians in the field of differential geometry and algebraic topology served as a material for the research. Using the technique of continuous sampling the authors extracted the sentences to be studied. The basic principles of communicative grammar, structural and semantic analysis, as well as statistical methods to process the extracted material, were applied. For the difficult material to be apprehended properly the language of mathematical works must obey some definite syntactical laws. Complex sentences with clear subordination of clauses favor to a great extent the logical consecutive statement of the mathematical text. Having a more complicated structure than simple sentences they are more evident in semantic facilitating apprehension of the information being conveyed. Constructions with object clauses are highly productive among the complex sentences of the inseparable type. As a rule, it is the subordinate clause that contains somewhat new that promotes the advancement of the course of reasoning whereas the main clause is assigned only an auxiliary part. The article covers such important features of the studied sentences as the position and construction of the main and subordinate clauses, their means of connection, morphological and semantic properties of the subordinating word, etc. In the course of analysis of these structures in the two languages, some common features (for example, the absolute predominance of the preposition of the main clause), as well as considerable differences (for example, the absence of a conjunction in English) are revealed, which should be taken into account at working with the texts of mathematical works in these languages.

The authors examine the pros and cons of games in the context of increasing students' creativity and scientific competence. Research materials and methods consisted of two tests. The first included the use of 7 pedagogical methods that are valid for the mental diagnosis of students: speed of thinking; method of thinking flexibility; method of determining the level of imagination and others. After the first testing, the training program included techniques for playing chess (in the classroom and online) and sand animation (in the classroom). Re-testing was carried out to assess the effectiveness of the programs. The study results showed that play activities improve the quality of student learning both in the classroom and online and enhance the functioning of many processes, including the speed and flexibility of thinking, memory capacity and attentiveness. This study demonstrates that play activities used in the educational process can play a positive role in teaching students. Further research needs to focus on studying the role of age, gender and race in play activities and determine how these factors affect performance.   Keywords: chess, cognitive processes, natural science education, pedagogical methods, performance, play activity, thinking

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