Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on Expertise
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 ma...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2014-06-01
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| Series: | Frontiers in Psychology |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2014.00556/full |
| _version_ | 1811218073381765120 |
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| author | Claudia eGodau Hilde eHaider Sonja eHansen Torsten eSchubert Robert eGaschler |
| author_facet | Claudia eGodau Hilde eHaider Sonja eHansen Torsten eSchubert Robert eGaschler |
| author_sort | Claudia eGodau |
| collection | DOAJ |
| description | 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 eyetracking 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. |
| first_indexed | 2024-04-12T07:03:33Z |
| format | Article |
| id | doaj.art-54d2053331174393912c59d1e292c1c1 |
| institution | Directory Open Access Journal |
| issn | 1664-1078 |
| language | English |
| last_indexed | 2024-04-12T07:03:33Z |
| publishDate | 2014-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Psychology |
| spelling | doaj.art-54d2053331174393912c59d1e292c1c12022-12-22T03:42:53ZengFrontiers Media S.A.Frontiers in Psychology1664-10782014-06-01510.3389/fpsyg.2014.0055691979Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on ExpertiseClaudia eGodau0Hilde eHaider1Sonja eHansen2Torsten eSchubert3Robert eGaschler4Humboldt Universität zu BerlinUniversität KölnUniversität KölnHumboldt Universität zu BerlinUniversität Koblenz-LandauOne 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 eyetracking 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.http://journal.frontiersin.org/Journal/10.3389/fpsyg.2014.00556/fullExpertiseNumerical cognitionArithmeticCommutativityspontaneous strategy application |
| spellingShingle | Claudia eGodau Hilde eHaider Sonja eHansen Torsten eSchubert Robert eGaschler Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on Expertise Frontiers in Psychology Expertise Numerical cognition Arithmetic Commutativity spontaneous strategy application |
| title | Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on Expertise |
| title_full | Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on Expertise |
| title_fullStr | Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on Expertise |
| title_full_unstemmed | Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on Expertise |
| title_short | Spontaneously Spotting and Applying Shortcuts in Arithmetic – A Primary School Perspective on Expertise |
| title_sort | spontaneously spotting and applying shortcuts in arithmetic a primary school perspective on expertise |
| topic | Expertise Numerical cognition Arithmetic Commutativity spontaneous strategy application |
| url | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2014.00556/full |
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