The Higher Education by Propaedeutic Cycles is a very complex problem. Government Regulations have affected the governability of the Superior Institutions in Colombia and similarly the student dropout in tertiary education, is more then 50%. Lot of problems sitting in front of Higher Education Institutions, to mention some of them: - Colombia by Higher Education student dropout loses annually a value close to USD $300.000,000. - The need to increase students' cognitive productivity. It is well know that few ICT-based techniques are applied for this purpose. - It is also necessary to increase the productivity of lecturers as knowledge rebuilders to generate contents in virtual environments; - A great problem is related to the Academic and pedagogical governance due to environmental demands by the Industry and the same Economy while recognizing state regulatory pressures. - Financial sustainability as the funding of universities is increasingly precarized. - Finally the low competitivity of the tertiary education We present a alternative reply solution to face the national problem: A governability model based in the Leontief Model is presented pari passu with an intelligent coach for concept and knowledge verification in order to face these complex problems national wide. The knowledge architecture of the mathematical model is presented with the composition of the linear programming with the Leontief Matrix of Input/Output as an analytical tool of the academic knowledge and economic study of an university institution in the space of the knowledge government and management. This knowledge architecture seems appropriate for universities to enter in the Knowledge Society. The latter has been heralded in the Government Plan 2010—2014.