Abstract: The subject of the research is the psychological peculiarities of cognitive development and motivation of elementary school children demonstrated in the process of solution of covergent tasks under conditions of different motivational attitudes. Within the framework of this research, convergent tasks mean the tasks that have only one solution. Gavrilova analyzes what psychological peculiarities of cognitive development such as nonverbal intelligence and creativity and motivation such as leading motives, attributive style of explanation of successes and failures (Martin Seligman), leading motivation attitude (Carol Dweck) affect the success of convergent solutions most of all under the conditions of this or that motivational attitude created by the verbal instruction of an experimentor. The main research methods used by the author includes experiment and psychological tests. The experiment included three series of surveys depending on different motivational attitudes, neutral, competitive and negative. The psychodiagnostics allowed to define psychological peculiarities of cognitive development and motivation of children who participated in the research. The main conclusion of the research is that there are particular psychological features of cognitive development and motivation of elementary school students that predetermine success of solving convergent tasks under conditions of particular motivational attitudes. Noteworthy that there are factors that directly relate to the success of convergent solutions and there are factors that prove to be important when only one motivational attitude is used.