In this paper, we propose a new self-organizational machine learning system, called Dual-Schemata model. This model is based on Piaget's schema theory, which is well known theory in developmental psychology. In our model, we divide Piaget's original schema into two parts; one is a perceptional schema and the other is an intentional schema. By this division, we can describe both adaptation and learning processes of a human and/or of an autonomous robot more simply and more effectively. Further, we show a series of experiments, in which a facial-robot with our Dual-Schemata model attempts to chase movements of a colored ball, and then we present that a robot gets to obtain some inner symbols concerning with those ball movements.