Modernization of modern higher education in general and military education, in particular, is largely associated with the transformation of Russian society, with its socio-economic changes and complex geopolitical situation, requiring, first of all, military specialists of high quality, capable of making quick decisions in a situation of sharply changing operational environment.

The problem and the goal. The article focuses on the development of intellectual and mathematical abilities of schoolchildren that function within the digital educational environment. Two sides of the abilities being formed are highlighted: cognitive and emotional-value ones developed due to the dialogical format of discussing the search for solutions to complex mathematical problems. The purpose of the study is to present ways to motivate schoolchildren to solve complex mathematical problems using a dialogical learning format.