Summary:
The role and usefulness of generalization in sciences and more specifically in the field of
mathematics is undeniable. To formulate proposals, reasoning, and conclusions with generalized strength is one of the core components of the core of every science that uses mathematics. As far as didactics of mathematics are concerned, the majority of the research community agrees on the central role that generalization must hold in the classroom. In Greece, developing pupils' ability to generalize is a basic requirement of Mathematical Literacy, which is one of the ultimate goals of the educational system. However, it is noteworthy that there are many definitions of the concept of
generalization, and those definitions evolved simultaneously with the science of teaching
mathematics. A correspondingly large number of surveys are focused on the difficulties students encounter in generalizing, strategies to address these difficulties, and the role of the teacher in managing the concept of generalizing in the class environment. In the present study, we focused in two different cases of school classes in which each teacher followed different teaching practices, we identified the moments and the form in which the generalization appeared during the courses we attended, and finally we tried to demonstrate the way of its overall management by the teacher. Our results, combined with the individual discussions we had with the two teachers, highlight the strong
influence that the two teachers' personal goals and views had on shaping two significantly different school environments, which led to different forms of generalization in each class.
Keywords:
generalization, generalization strategies, algebraic thinking, realistic mathematics (RME), IBL, knowledge transfer, teaching styles
