The paper addresses concept formation processes of a student in the field of geometry. More precisely, the paper deals with the question of how to assist a student in a mathematical concept formation process – in the context of area calculations in triangles – with a specially designed learning environment based on the usage of 3D printed objects. Methodologically, we use the descriptive framework of the concept of Domains of Subjective Experience for the analysis of our case study. The objective is to describe the use of a learning environment to initiate targeted, theoretical concepts with a student. The student develops an empirical notion of bases and heights in triangles (with respect to the calculation of surface areas), using 2D drawings and 3D printed objects. In this article we argue, teaching mathematics consistently in an object-oriented and practical (visual) way, and additionally promoting the development of concept formation as a mathematical activity, brings a student in a situation where he develops hypotheses, tries them out, and transfers them to other fields of application; thus engages in concept formation processes.
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