The Use of 3D-Printing Technology in Calculus Education: Concept Formation Processes of the Concept of Derivative with Printed Graphs of Functions

Abstract

3D-printing technology has become increasingly important in recent years, offering many possibilities for mathematics teaching and learning. From our point of view, the field of calculus seems to be particularly suitable for the use of 3D-printing. Using the example of 3D-printed graphs of functions, the use of this technology in calculus is discussed within the three approaches of Grundvorstellungen, Subjective Domains of Experience and Empirical Theories. An empirical study, based on the qualitative content analysis according to Philipp Mayring, examines the influence of the models on concept formation processes in the context of derivatives. The focus is on the following research question: "What are the characteristics of concept formation processes of the concept of derivative in the context of 3D-printed graphs of functions?" Keywords 3D-printing. Derivative. Calculus. Grundvorstellung. Subjective domains of experience. Printed graphs of functions 3D-Printing in Mathematics Education 3D-printing technology is a relatively new tool with potential for mathematics education. It can be described as an additive manufacturing method allowing for digital models constructed with CAD-software to be transformed layer by layer into a real model made out of liquid plastic (see Gibson et al. 2014). Witzke and Hoffart (2018) detail three options for using the 3D-printing technology in the classroom. First, there is the possibility to reproduce Digital Experiences in Mathematics Education

Edge Models with the CAD Software: Creating a New Context for Mathematics in Elementary School

“…Recent research indicates how 3D printing technology can be implemented in mathematics classes in (upper) secondary school, for example, to explore central concepts of calculus (Dilling & Witzke, 2020a). Furthermore, Dilling and Witzke (2020b) describe how primary students use 3D printing technology, combined with the CAD program SketchUp, in a learning unit about tessellation in geometry lessons and state that digital media could raise various challenges (i.e., virtual enactivity and technical problems), in addition to different advantages, such as precision (p. 90).…”

“…By empirical contexts, we mean that, in mathematics classes, mathematical knowledge is usually developed in empirical contexts, especially drawings and application frameworks(Dilling & Witzke, 2020a). Subsequently, teaching mathematics at school often involves an empirical belief system shaped by material and illustrations.…”

Fostering Spatial Ability Through Computer-Aided Design: a Case Study

“…In a qualitative analysis, it could be observed that the students developed a deep understanding of the relationship between changes of the linear dimensions of the objects and their volumes through the use of Tinkercad and 3D printers. Dilling and Witzke (2020b) have qualitatively examined the effects of a specific learning environment from the field of calculus with the use of 3D printing technology on the understanding of concepts of differential calculus. It turned out that the students developed ideas about covariation and the slope of a tangent of a graph.…”

Exploring the use of 3D printing in mathematics education: A scoping review

“…In recent years, research has documented the impacts of 3D printing on mathematics education which was not possible in the past. First, 3D printing helps students visualize concepts and proofs (e.g., geometry, calculus, area/volume) that enables them to develop mathematical, abstract, and spatial thinking (e.g., Dilling & Witzke, 2020; Ng & Ye, 2022). For example, Ng and Ferrara (2020) have reported how primary students used 3D printing pens to create their own prisms and pyramids to learn the geometric properties and cross-sections.…”

“…For example, Ng and Ferrara (2020) have reported how primary students used 3D printing pens to create their own prisms and pyramids to learn the geometric properties and cross-sections. Dilling and Witzke (2020) conducted an empirical study to engage students to derive concepts about functions and calculus in middle school. Furthermore, as creativity is the essence of mathematics, 3D printing enables students’ creative exploration and design (e.g., Chien & Chu, 2018; Ng, 2017).…”