The Incorporation of Generalization in Teaching Units

Abstract

"Mathematization" is a term used to extend the educational philosophy of mathematical teaching and learning as an active and creative process. It is Wittmann's Teaching Units that have brought the idea of design science into the didactical practice of mathematization. His Teaching Units, however, do not have a diachronic design of how the lesson in the classroom should be developed over time, although they contain the fundamental design such as objectives, materials, problems, and background. On the other hand, mathematization can be regarded as a typical symbolization process in the sense of Peirce which is called semiosis, and in this context the Dörfler's generalization model, which starts from the activity and constructs the generalization process, is quite thought-provoking. It is therefore possible to design, practise and evaluate the Teaching Units of Wittmann in the teaching-learning context in terms of the generalization model by Dörfler. This is the objective as well as the result of this research. The methodology is to employ a teaching experiment called 'Star Patterns' based on the above theoretical framework, and to prove its effectiveness through the analysis of results based on Dörfler's model.