Estimations and self-estimations are regarded as a specific group of tasks based on the ability to perform mental operations. The higher the ability, the more efficient are the process of solving tasks requiring estimations and self-estimations and the process of self-regulation of predictive behavior. Experiments conducted by the author with the help of a new apparatus technique developed together with Ya. A. Ponomariov proved the initial hypothesis and enabled the author to offer some recommendations concerning ways of overcoming difficulties in learning and education.