Scaffolding Mathematical Prerequisites to STEM Students by Solving Non-Traditional Problems

In public opinion, "Mathematics = Calculations". In a more meticulous formulations, the same opinion is expressed by making it indistinguishable from abstraction, symbolic representation, and symbolic manipulation. Such opinions lower its important role in our social life and, consequently, build an inappropriate starting point for education - not only in Mathematics but in a wide range of other subjects. In this contribution, we open door for a different educational basis using arguments from Knowledge Management. The above opinions do not consider that all our knowledge requires extensive amount of tacit knowledge. In the present course, tacit knowledge is oriented "inside" i.e. to optimal execution of formal operations. Here we demonstrate how to build "external" tacit knowledge i.e. learners' comprehension of links between Mathematics and real world. To evoke their interest, non-traditional ("absurd") problems in are used. The simple examples demonstrate Mathematics' power, limits and role in society. The paper also calls for creating similar problems in other disciplines in order to prepare STEM students for their effective participation in multidisciplinary teams.