Universität zu Köln

Hansen, Sonja Maria, Haider, Hilde ORCID: 0000-0001-7293-3166, Eichler, Alexandra, Godau, Claudia, Frensch, Peter A. and Gaschler, Robert ORCID: 0000-0002-8576-5330 (2015). Fostering Formal Commutativity Knowledge with Approximate Arithmetic. PLoS One, 10 (11). SAN FRANCISCO: PUBLIC LIBRARY SCIENCE. ISSN 1932-6203

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Abstract

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hansen, Sonja Maria UNSPECIFIED UNSPECIFIED UNSPECIFIED Haider, Hilde UNSPECIFIED orcid.org/0000-0001-7293-3166 UNSPECIFIED Eichler, Alexandra UNSPECIFIED UNSPECIFIED UNSPECIFIED Godau, Claudia UNSPECIFIED UNSPECIFIED UNSPECIFIED Frensch, Peter A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gaschler, Robert UNSPECIFIED orcid.org/0000-0002-8576-5330 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-387053
DOI:	10.1371/journal.pone.0142551
Journal or Publication Title:	PLoS One
Volume:	10
Number:	11
Date:	2015
Publisher:	PUBLIC LIBRARY SCIENCE
Place of Publication:	SAN FRANCISCO
ISSN:	1932-6203
Language:	English
Faculty:	Faculty of Human Sciences
Divisions:	Faculty of Human Sciences > Department Psychologie
Subjects:	Psychology
Uncontrolled Keywords:	Keywords Language PROCEDURAL KNOWLEDGE; CONCEPTUAL KNOWLEDGE; NUMBER; INSTRUCTION; MATHEMATICS; REPRESENTATIONS; FLEXIBILITY; STRATEGIES Multiple languages Multidisciplinary Sciences Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/38705