Hansen, Sonja Maria, Haider, Hilde, Eichler, Alexandra, Godau, Claudia, Frensch, Peter A. and Gaschler, Robert (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:
CreatorsEmailORCIDORCID Put Code
Hansen, Sonja MariaUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Haider, HildeUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Eichler, AlexandraUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Godau, ClaudiaUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Frensch, Peter A.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Gaschler, RobertUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
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: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
PROCEDURAL KNOWLEDGE; CONCEPTUAL KNOWLEDGE; NUMBER; INSTRUCTION; MATHEMATICS; REPRESENTATIONS; FLEXIBILITY; STRATEGIESMultiple languages
Multidisciplinary SciencesMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/38705

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