Cognitive dissonance and consonance are largely approached from the perspective of argumentation, and for the purposes to use it for the study of thinking and creativity of primary school-aged children playing chess as well. Standard psychological conditions for dissonance and consonance to appear in the argumentation sphere of primary school-aged children are analyzed. Having compared data of two personality dimensions by Hans Eysenck (“neuroticism – emotional stability” and “extraversion – introversion”) and five factor model the author identified dominating personality traits of primary school-aged children manifesting themselves in the process of argumentation in cognitive work. When giving psychological analysis of the game of chess during counseling after the game, children’s personality traits should be taken into account to study specific character of argumentation.