Universität zu Köln

Gaschler, Robert, Vaterrodt, Bianca, Frensch, Peter A., Eichler, Alexandra and Haider, Hilde (2013). Spontaneous Usage of Different Shortcuts Based on the Commutativity Principle. PLoS One, 8 (9). SAN FRANCISCO: PUBLIC LIBRARY SCIENCE. ISSN 1932-6203

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Abstract

Based on research on expertise a person can be said to possess integrated conceptual knowledge when she/he is able to spontaneously identify task relevant information in order to solve a problem efficiently. Despite the lack of instruction or explicit cueing, the person should be able to recognize which shortcut strategy can be applied - even when the task context differs from the one in which procedural knowledge about the shortcut was originally acquired. For mental arithmetic, first signs of such adaptive flexibility should develop already in primary school. The current study introduces a paper-and-pencil-based as well as an eyetracking-based approach to unobtrusively measure how students spot and apply (known) shortcut options in mental arithmetic. We investigated the development and the relation of the spontaneous use of two strategies derived from the mathematical concept of commutativity. Children from grade 2 to grade 7 and university students solved three-addends addition problems, which are rarely used in class. Some problems allowed the use of either of two commutativity-based shortcut strategies. Results suggest that from grade three onwards both of the shortcuts were used spontaneously and application of one shortcut correlated positively with application of the other. Rate of spontaneous usage was substantial but smaller than in an instructed variant. Eyetracking data suggested similar fixation patterns for spontaneous an instructed shortcut application. The data are consistent with the development of an integrated concept of the mathematical principle so that it can be spontaneously applied in different contexts and strategies.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gaschler, Robert UNSPECIFIED UNSPECIFIED UNSPECIFIED Vaterrodt, Bianca UNSPECIFIED UNSPECIFIED UNSPECIFIED Frensch, Peter A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Eichler, Alexandra UNSPECIFIED UNSPECIFIED UNSPECIFIED Haider, Hilde UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-475718
DOI:	10.1371/journal.pone.0074972
Journal or Publication Title:	PLoS One
Volume:	8
Number:	9
Date:	2013
Publisher:	PUBLIC LIBRARY SCIENCE
Place of Publication:	SAN FRANCISCO
ISSN:	1932-6203
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ADDITIVE COMMUTATIVITY; CHILDRENS ADDITION; KNOWLEDGE; INVERSION; YOUNG; PRESCHOOLERS; FLEXIBILITY; MATHEMATICS; EXPERTISE; SKILL Multiple languages Multidisciplinary Sciences Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47571