Copyright © Lucas Amiras 2020



In most schoolbooks and university textbooks on geometry the meaning of the primitive notions “plane (surface)” and “straight (line)” is dismissing. In few exceptions there is an effort to convey their meaning by  using activities where concrete handicraft realisations of planes and straight lines are used. But after that, nobody comes over to an explanation of the properties named by “plane” or “straight” imposed on physical objects.

Peter Bender and Alfred Schreiber  publish since 1978 two articles discussing didactical aspects of the operational approach in the foundations of geometry on the basis of the work of Dingler and Lorenzen . The outcome of this discussion is an operational didactics of geometry with a didactical “operative concept formation principle” as the core conception. Finally, in a book on “Operative genesis of geometry” (Bender/Schreiber 1984)  they contribute a thorough discussion of philosophical and especially didactical aspects of the approach.

In the same extensive plans for introducing elementary notions of geometry in classroom by Dieter Volk and by Konrad Krainer are designed (in German). These proposals are discussed in (Amiras 2014). In this book several suggestions for introducing elementary notions of geometry on the basis of protogeometry  can also be found.

At the present time most of literature on the subject is accessible only in German . In English there is only one article by Bender/Schreiber.

However, forthcoming an article on a protogeometric proposal for teaching elementary notions of geometry in classroom (a translation from an existing article in German with additions). A little popular scientific book on protogeometry is in planning.