Abstract
Mathematics teachers at the secondary education in the 21st century must be able to move the students by scientific subtleness of mathematics and also be able to convince them of the usefulness of mathematics in life and work. In order to achieve this aim, the teachers are required to be well-cultured in Logos and Ars. For instance, they should be aware that the mathematics education is an art where they do play the major role and should know how are changing the trends and methodology of mathematics, particularly of applied mathematics, together with current science and technology in general, as we describe below. In order to meet these changes, there are many things to do, while we here only propose to make the approach in the secondary mathematics double-tracked in a good balance of the following two paths, locally and globally: one track Logos-emphasizing and the other Ars-oriented. In the final section, some topics selected from the ordinary syllabus are mentioned, each of which is significant either for theoretical thinking or for applicable literacy.
