EJMT Abstract

Studies have shown that students’ angle “Grundvorstellungen” (basic ideas) often do not reflect the definitions of angles properly and only some of the possible views on angles are being held. Students develop a sustaining misconception of angle in relation to Euclidean distance, an idea which is even supported by most traditional measuring instruments in Germany. In close connection to this it can be shown, that a revision of already existing protractors is inevitable for the development of an appropriate angle understanding. Dynamic views on angles like rotation and turning propose a solution for this problem but are rarely integrated in German math lessons or current textbooks. An IGS (interactive geometry software) and its dynamic approach in particular can be utilized to support a deeper understanding of the angle concept with respect to the rotational angle aspect. Thus, it should be integrated into an IGS angle measurement tool. To reach this goal, mathematical, didactical and design aspects of an IGS are being analysed for angle measurements. As a result, a tangible tool for angular measurements related to the rotational aspect of the angle concept has been developed. Since the development of digital geometrical tools takes place in the area between mathematics and its didactic, computer science and cognitive psychology, one must simultaneously consider the implementation in all other disciplines. Therefore, the development of such a tool is not a linear process but rather an iterative one after developing the presumptions. A starting point for this article should be the mathematical definition of the term angle which directed by the mathematic-didactical circumstances supports a first concept of the angular measurement tool. Only then should design decisions contribute to the completion.