In education there are two elementary systems: the students and society, and one auxiliary, intermediary system: the teacher. The construction of aims in mathematical instruction requires a previous description of the most important educational proprieties and needs of both society and the student who is being gradually included in it. It follows from that: 1. the basic subject of school education is the individual student and the essence of the educational process should be based on learning; where as the teacher and the student's nearest environment (i.e. school) should be the organizer of learning, 2. school education should be a solid foundation for further education (including self-education), which equips the learner with relatively long-lasting and useful knowledge as well as with the skill of the widening and applying the knowledge. Student's intellectual development is possible only in the process of active and directed work containing receipting, gaining, transformating and applying the information. So it should be "education trough using mathematics, not only mathematics for itself "- the students should build their own cognitive schemas.