Well-developed combinatorial abilities are an essential component of the professionalism of a modern primary school teacher. The goal of the present study is to search for methodological techniques for lessons on the methods of teaching mathematics in primary school that would activate the interconnection of logical thinking and several non- cognitive abilities of teachers in training. Said interconnection is viewed as a means allowing diagnosing and developing the combinatorial abilities of future primary school teachers. The study implements testing methods with consecutive mathematical processing. Assessment of the non-cognitive factors (the level of general cultural development, general humanitarian training, characteristics of the microenvironment, the level of general psychosocial development, etc.) involved the methods assessing academic success and psychosocial development level, as well as expert assessment of the level of general cultural development. These data were compared with the level of development of pedagogical university students’ logical thinking determined through Raven’s Progressive Matrices. The forming stage of the study involved original methodological techniques used to stimulate university students’ interest in creating compositions of textual mathematical problems for primary school students. The proposed methodological solutions to the problems of the diagnostics and development of combinatorial thinking in future teachers understood as a combination of logical thinking and several non-cognitive factors have shown themselves to be effective. The development of compositions of textual mathematical problems for primary school students is an effective means of developing future teachers’ combinatorial abilities.