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The study shows that each of sources of achieving success in teaching is in many respects geared to the principles of empirical observation for education process efficiency. The present issue is unfolded to the full extent on the basis of teaching the basics of scientific and mathematical disciplines. However, its problematics is also expanded due to the fact the teaching should be founded on a checkable and verifiable basis. For this purpose, we have developed an equilibrium model that assesses all the possible risks of its application in project activities of higher education institutions of Emergency Situations Ministry of Russia. The work's relevance resides in the fact we have suggested an effective model for accounting of learning and checking knowledge regardless of subjective factors and standardised unverifiable assessment of educational process, since it is shown that only mathematical model can provide objective substantiation of research paradigm.