Positions from the game of "Kalakh" served as an experimental material on which transformation of thought processes connected with the computer-facilitated decision-making was studied. Analysis of the reasoning aloud and of registered dialogues with the computer enabled the author to reveal different indicators of the process of restructuring of thinking's inner supports (of visualization forms in their number) during the decision-making process. It is shown that new understanding and new vision of a situation are achieved only through functional introduction of the computer-supplied data into the intermediate units of analysis.