PROGRAPH Diagrams--A New Old System for Teaching Functional Modelling

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to explain these combinations effectively. The basic idea of a function, composition of functions or returning values of a function can be shown impressively. It is also possible to find easily nested diagrams for recursive functions. So the mathematical insights into topics which can be handled through functions gets opened up and the possibilities for working with functions increase. With the help of a selection of examples the idea of this type of diagram becomes clearer and through its implementation with CAS the effective use of functions is demonstrated. Hence the combination of PROGRAPH diagrams and CAS allows an understanding of and insight into functions so that the Black-Box-Principle is eliminated. For modern and effective education Functional Modelling is absolutely necessary. With the combination of graphical representation and CAS, learners are able to see and learn the common foundation of mathematical ideas and applications. (Contains 7 figures.)