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Individual differences in the effect of relevant concreteness on learning and transfer of a mathematical concept
Institution:1. Department of Obstetrics and Gynecology, Division of Reproductive, Endocrinology and Infertility, McGill University Health Centre, Royal Victoria Hospital, Montreal QC;2. Department of Radiology, McGill University Health Centre, Royal Victoria Hospital, Montreal QC;1. Department of Child and Adolescent Psychiatry, Hospital General Universitario Gregorio Marañón, CIBERSAM, IiSGM, School of Medicine, Universidad Complutense, Madrid, Spain;2. Department of Child and Adolescent Psychiatry and Psychology, Institut Clinic of Neurosciences, IDIBAPS, SGR-1119, Hospital Clínic (Barcelona). Department of Psychiatry and Psychobiology, University of Barcelona, CIBERSAM, Spain;3. Department of Psychiatry, Hospital Universitario de Alava (Santiago), University of the Basque Country EHU/UPV Vitoria, CIBERSAM, Spain;4. Orygen Youth Health Research Centre, Centre for Youth Mental Health, The University of Melbourne, Victoria, Australia;5. Melbourne Neuropsychiatry Centre, The University of Melbourne, Parkville, Australia;6. Department of Child and Adolescent Psychiatry, Institute of Psychiatry, King''s College London, London, UK;7. Section of Child and Adolescent Psychiatry and Psychology, Hospital Infantil Universitario Niño Jesus, CIBERSAM, Madrid, Spain;8. Child Psychiatry Unit, Hospital Universitario Marqués de Valdecilla, CIBERSAM, Santander, Spain;9. National Distance Education University (UNED), Spain;1. University of Kiel, Germany;2. University of Hamburg, Germany
Abstract:The concreteness of training materials influences learning and—perhaps more importantly—transfer. Building on prior research finding abstract representations best facilitated transfer to a game task, we conducted a similar study using training figures varying in concreteness but directly assessed transfer to modular arithmetic problems. Training figures: (a) were purely abstract, (b) were abstract but with features relevant to the transfer task, or (c) included additional concrete-relevant features. We hypothesized that concreteness—or number of relevant features—would be positively correlated with learning and transfer—especially among younger and/or lower-ability students. Although there was no overall difference in initial learning, the concrete-relevant and abstract-relevant features independently facilitated near-transfer, where concrete-relevant features supported lower-reasoning students. For far-transfer, eighth-graders benefited from the abstract-relevant features, whereas sixth-graders required additional concrete-relevant features. These findings suggest that concreteness interacts with learner and task characteristics to produce learning and transfer outcomes.
Keywords:Abstract problem features  Concrete problem features  Transfer  Mathematics  Learning
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