Universität zu Köln

Suemmermann, Moritz Lucius, Sommerhoff, Daniel and Rott, Benjamin ORCID: 0000-0002-8113-1584 (2021). Mathematics in the Digital Age: The Case of Simulation-Based Proofs. Int. J. Res. Undergrad. Math. Educ., 7 (3). S. 438 - 466. CHAM: SPRINGER INT PUBL AG. ISSN 2198-9753

Full text not available from this repository.

Abstract

Digital transformation has made possible the implementation of environments in which mathematics can be experienced in interplay with the computer. Examples are dynamic geometry environments or interactive computational environments, for example GeoGebra or Jupyter Notebook, respectively. We argue that a new possibility to construct and experience proofs arises alongside this development, as it enables the construction of environments capable of not only showing predefined animations, but actually allowing user interaction with mathematical objects and in this way supporting the construction of proofs. We precisely define such environments and call them mathematical simulations. Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs along the dimensions of interactivity and formality. Furthermore, we give an analysis of the functions of proofs that can be satisfied by simulation-based proofs. Finally, we provide examples of simulation-based proofs in Ariadne, a mathematical simulation for topology. The results of the analysis show that simulation-based proofs can in theory yield most functions of traditional symbolic proofs, showing promise for the consideration of simulation-based proofs as an alternative form of proof, as well as their use in this regard in education as well as in research. While a theoretical analysis can provide arguments for the possible functions of proof, they can fulfil their actual use and, in particular, their acceptance is of course subject to the sociomathematical norms of the respective communities and will be decided in the future.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Suemmermann, Moritz Lucius UNSPECIFIED UNSPECIFIED UNSPECIFIED Sommerhoff, Daniel UNSPECIFIED UNSPECIFIED UNSPECIFIED Rott, Benjamin UNSPECIFIED orcid.org/0000-0002-8113-1584 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-573619
DOI:	10.1007/s40753-020-00125-6
Journal or Publication Title:	Int. J. Res. Undergrad. Math. Educ.
Volume:	7
Number:	3
Page Range:	S. 438 - 466
Date:	2021
Publisher:	SPRINGER INT PUBL AG
Place of Publication:	CHAM
ISSN:	2198-9753
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Education & Educational Research Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/57361