Concept Formation Processes regarding Height and Base in Triangles

Abstract

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.

Description of the activated mathematical knowledge of the triangle concept in three empirical contexts

“…Anna takes a ruler, paper and pencil and starts drawing her triangle. Anna draws a triangle (Figure 2) with one side of the triangle parallel to the edge of the leaf (see also Pielsticker, 2021).…”

“…with issues relating to 3D printing, 3D pen or dynamic geometry software (DGS) (for example GeoGebra) in mathematics lessons (e.g. Dilling & Witzke, 2020;Elschenbroich, 2018;Elschenbroich & Seebach, 2018;Kaenders & Schmidt, 2014;Ng, 2017;Ng et al, 2018;Panorkou & Pratt, 2016;Pielsticker, 2021). Thus, manipulatives that relate to this world are an essential element of teaching practice, as they can motivate, illustrate and justify mathematical relationships.…”

Tinkercad Circuits Platform-Based Learning Experiences of Gifted Students in the Emergency Distance Education Process

“…Compared to other programs of this type, Tinkercad includes a particularly intuitive approach to directly modeling three-dimensional (3D) objects and provides easy access to such software for first-time users such as primary school students. As several research projects have already shown, this program provides students of all ages with a good start in 3D printing technology (Dilling & Vogler, 2021; Ng et al, 2018; Pielsticker, 2021).…”