title: Spontaneously spotting and applying shortcuts in arithmetic-a primary school perspective on expertise.
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.
authors: Department of Psychology, Humboldt-Universität zu Berlin Berlin, Germany ; Cluster of Excellence: Image Knowledge Gestaltung, an Interdisciplinary Laboratory Berlin, Germany.
authors: Claudia
authors: C
authors: Godau
authors: Department of Psychology, Universität Köln Köln, Germany.
authors: Hilde
authors: H
authors: Haider
authors: Department of Psychology, Universität Köln Köln, Germany.
authors: Sonja
authors: S
authors: Hansen
authors: Department of Psychology, Humboldt-Universität zu Berlin Berlin, Germany ; Cluster of Excellence: Image Knowledge Gestaltung, an Interdisciplinary Laboratory Berlin, Germany.
authors: Torsten
authors: T
authors: Schubert
authors: Department of Psychology, Humboldt-Universität zu Berlin Berlin, Germany ; Cluster of Excellence: Image Knowledge Gestaltung, an Interdisciplinary Laboratory Berlin, Germany.
authors: Peter A
authors: PA
authors: Frensch
authors: Cluster of Excellence: Image Knowledge Gestaltung, an Interdisciplinary Laboratory Berlin, Germany ; Department of Psychology, Universität Koblenz-Landau Landau, Germany.
authors: Robert
authors: R
authors: Gaschler
keywords: arithmetic; commutativity; expertise; numerical cognition; spontaneous strategy application