This is much worse because it presents mathematics as a subject without contact or interest in a real world. Secretary Clinton`s ethics agreement at the time [she took office] did not exclude other State Department officials from attending or contacting the Clinton Foundation. This can be applied to higher mathematics. For students (and therefore also for teachers), the transformation of mathematicians into human beings can make science more tangible, it can make research interesting as a process (and as work?) and this can be a starting point/entry point for real mathematics. Therefore, stories can make math stickier. Stories cannot replace conventional approaches to mathematics teaching. But they can improve it. However, a one-sided answer to the question leads to unilateral approaches to what should be taught in mathematics. And indeed, if you look at the second diagnosis, if for the keyword “mathematics”, the images that come to mind do not go beyond an “a”{2} – b`{2} – it {2}`) scribbled in chalk on a board – why should mathematics be attractive again as a subject, science or profession? Of course, it is a difficult task to work with outstanding issues at school.

None of the major outstanding issues can be resolved with an elementary mathematical toolbox; Many of them are not even accessible as questions. The great fear of discouraging students is therefore justified. On the other hand, why not study mathematics by showing how questions often arise along the way? Asking questions in mathematics and mathematics could lead to interesting answers, especially to the question: “What is mathematics, really?” None of this is totally false, but it is not satisfactory either. Suffice it to say that the fact that there is no agreement on the definition of mathematics, as part of a definition of mathematics, puts us in logical difficulties that may have made Godel smile.1 On the other hand, the first and second diagnosis of the quote by Mendick et al. (2008) include: Mathematicians are part of “What is mathematical”! By stories, we are not only talking about biographies, but also about how mathematics is created or discovered: Jack Edmonds`s report (Edmonds, 1991) that he found that the flower shrinking algorithm is a great story about how mathematics is actually done. Think of Thomas Harriot`s problem of stacking cannonballs in a storage room and what Kepler did with them: the emergence of a mathematical problem. Sometimes scientists even lock themselves into stories: see z.B. Leslie Lamports Byzantine general (Lamport, Shostak – Pease, 1982). Mathematicians look for models (Highland – Highland, 1961, 1963) and use them to make new assumptions. Mathematicians solve truth or falsification of conjectures by mathematical evidence. If mathematical structures are good models of real phenomena, then mathematical thinking can provide insights or predictions about nature.

Using abstraction and logic, mathematics developed from the counting, calculation, measurement and systematic study of the shapes and movements of physical objects. Practical mathematics was a human activity for as far as written recordings exist. The research needed to solve mathematical problems can take years or even centuries of research. How to avoid double discontinuity is of course a big challenge for the design of university programs for math teachers. However, one important aspect is related to the question “What is mathematics? ” : an image/concept of mathematics very common in high school, as illustrated by school curricula, mathematics consists of subjects presented by the high school curriculum, i.e. the (elementary) geometry of algebra (in the form of arithmetic, and perhaps polynomies), plus perhaps the elementary probability, calculation (differentiation and integration) in a variable