We are seeing more and more depressing results concerning the abilities of students joining higher education in recent years. Their knowledge of mathematics is worse than it used to be, and it is not sufficient to support a successful professional training. The results of mathematics tests carried out among college freshman students reflect a decisive contribution of the knowledge acquired in high school to be successful in higher education. We are posing questions and forming the hypotheses for our proposed research in this talk. It is important to complement the traditional mathematical knowledge at the institutional level. In order to improve efficiency a differentiated treatment is required. Different courses with appropriate topics and syllabuses look promising. In my presentation I concentrate on the question marks and assumptions arising from my research in the above mentioned topic.