Universität zu Köln

Godau, Claudia, Haider, Hilde, Hansen, Sonja, Schubert, Torsten, Frensch, Peter A. and Gaschler, Robert (2014). Spontaneously spotting and applying shortcuts in arithmetic - a primary school perspective on expertise. Front. Psychol., 5. LAUSANNE: FRONTIERS MEDIA SA. ISSN 1664-1078

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Abstract

One crucial feature of expertise is the ability to spontaneously recognize where and when knowledge can be applied to simplify task processing. Mental arithmetic is one domain in which people should start to develop such expert knowledge in primary school by integrating conceptual knowledge about mathematical principles and procedural knowledge about shortcuts. If successful, knowledge integration should lead to transfer between procedurally different shortcuts that are based on the same mathematical principle and therefore likely are both associated to the respective conceptual knowledge. Taking commutativity principle as a model case, we tested this conjecture in two experiments with primary school children. In Experiment 1, we obtained eye tracking data suggesting that students indeed engaged in search processes when confronted with mental arithmetic problems to which a formerly feasible shortcut no longer applied. In Experiment 2, children who were first provided material allowing for one commutativity-based shortcut later profited from material allowing for a different shortcut based on the same principle. This was not the case for a control group, who had first worked on material that allowed for a shortcut not based on commutativity. The results suggest that spontaneous shortcut usage triggers knowledge about different shortcuts based on the same principle. This is in line with the notion of adaptive expertise linking conceptual and procedural knowledge.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Godau, Claudia UNSPECIFIED UNSPECIFIED UNSPECIFIED Haider, Hilde UNSPECIFIED UNSPECIFIED UNSPECIFIED Hansen, Sonja UNSPECIFIED UNSPECIFIED UNSPECIFIED Schubert, Torsten UNSPECIFIED UNSPECIFIED UNSPECIFIED Frensch, Peter A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gaschler, Robert UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-435898
DOI:	10.3389/fpsyg.2014.00556
Journal or Publication Title:	Front. Psychol.
Volume:	5
Date:	2014
Publisher:	FRONTIERS MEDIA SA
Place of Publication:	LAUSANNE
ISSN:	1664-1078
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MATHEMATICS; SKILL; PERFORMANCE; FLEXIBILITY; INSTRUCTION; KNOWLEDGE Multiple languages Psychology, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/43589