The Use of 3D-Printing Technology in Calculus Education: Concept Formation Processes of the Concept of Derivative with P
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The Use of 3D-Printing Technology in Calculus Education: Concept Formation Processes of the Concept of Derivative with Printed Graphs of Functions Frederik Dilling 1 & Ingo Witzke 1 # The Author(s) 2020
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 * Frederik Dilling [email protected]–siegen.de Ingo Witzke [email protected]
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Mathematics Education, University of Siegen, Herrengarten 3, 57072 Siegen, Germany
Digital Experiences in Mathematics Education
existing manipulatives. Another option is the development of manipulatives by the teacher (and also in co-operation with students). This enables their adaption according to the individual requirements of the students. If the students are also involved in the printing process and detect the structure of the printed object, the development of black boxes can be avoided. Finally, the students can also develop 3D-printed objects on their own. In relation to inquiry-based learning, this third option is the most interesting application for education. In mathematics education, several articles on this last option have been published. Most of them examine the relationship between the use of 3D-printing and the learning of geometry. Panorkou and Pratt (2016) investigate the potential of CAD-software for developing ideas about dimensions. The results show that even young students can develop adequate ideas of directions, positions, orientations and containment of parameters in dealing with the software. Ng (2017) explains the benefits of 3D-printing technology for learning about the volume of solids. For this study, qualitative data was collected in a c
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