Diskussion:The Klein Project

Special attention: Teachers' College math programs I believe a special note should be put in the project on the population of students preparing to be math teachers.One "neglected" subject seems to me to requier a special attention: Number Systems. This subject is usually not covered in regular math programs. I believe that a prospective secondary-high school teacher should be exposed to a systematic construction of all number systems one after the other starting with Peano axioms and ending in a solid precalculus construction of real numbers. The approach of such a course should be inquisitive (i.e. not just a list of definitions and properties but an enqeiry as to why do we define it this way - a combination of applicational and mathematical reasoning). The prerequisits of such a course should be solely basic Set Theory (equivalence relation, order, etc), the course supplies "the missing link" to a proper calculus course. It would be nice, I believe, to give an exposition of such a course (with a good list of references) in the materials of the project. In the proceedings of the last ICME meeting one can see papers dealing with precalculus introduction of real numbers.