Universität zu Köln

Hock, Tobias, Heitzer, Johanna and Schwank, Inge ORCID: 0000-0003-1546-3369 (2016). Axiomatic Thinking and Working in Teaching Mathematics. J. Math.-Didakt., 37 (1). S. 181 - 209. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1869-2699

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Abstract

This article is motivated by the conviction that understanding the axiomatic method is a necessary component of an appropriate picture of mathematics. Therefore, it points out ways to investigate the role of axioms and proofs as well as the particular epistemological status of mathematical theorems as an additional topic at Sekundarstufe II. This includes recognising the necessity of axioms for a foundation of mathematical proofs, knowing the classical content-related and modern formalistic view on axioms as well as discussing general strategies for justifying mathematical theories. After sketching the historical development of the axiomatic method and of associated views in the philosophy of mathematics, we outline the most important pros and cons of dealing with axiomatics at school from a didactical perspective. We then delineate a concept of how the most important learning goals with respect to axiomatic aspects can be achieved by means of suitable topics. A teaching sequence from one of these topics, Kolmogoroff's axioms of probability, is presented in more detail.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hock, Tobias UNSPECIFIED UNSPECIFIED UNSPECIFIED Heitzer, Johanna UNSPECIFIED UNSPECIFIED UNSPECIFIED Schwank, Inge UNSPECIFIED orcid.org/0000-0003-1546-3369 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-283769
DOI:	10.1007/s13138-016-0088-2
Journal or Publication Title:	J. Math.-Didakt.
Volume:	37
Number:	1
Page Range:	S. 181 - 209
Date:	2016
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1869-2699
Language:	German
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Education & Educational Research Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28376