Functional Reasoning and working with Functions: Functions/mappings in mathematics teaching tradition in Hungary and Germany

摘要

After a short survey of the genesis of the ideas behind “functional reasoning” in mathematics education at the beginning of the 20th century, the development and implementation of these ideas in both parts of Germany and in Hungary in the second half of the 20th century are discussed and compared. The ideas of Felix Klein had a strong influence in both countries. However, from the 1950’s to the 1970’s (the period of “New Math”) an attempt was made to teach functions and mappings in a more sense, involving both elementary (real-valued) functions and geometric transformations. In the 1970’s and 1980’s there were lots of discussions about the notion and notation of functions. Finally, dynamic aspects of functions – one of the main ideas of the reforms at the beginning of the 20th century – came into focus again in the 1980’s and remained essential to this day.