Reflections on and benefits of uses of history in mathematics education exemplified by two types of student work in upper secondary school

It is not at all clear what the role of history in mathematics education is or should be. At conferences where designs of lessons, results, and experiences with using history in teaching situations, or claiming to do so, are presented two camps can often be distinguished during the discussions according to whether the emphasis is placed on a genuine approach to history or to teach a certain subject matter within mathematics. One camp often accuses activities aiming at using history as an effective tool for teaching a certain concept or method in mathematics of distorting history. The other camp often finds that activities aiming at introducing students to historical issues of the development of mathematics have no relevance for the mathematics that needs to be taught.