Numerical inversion is the ability to understand that addition is the opposite of subtraction and vice versa. Three-term arithmetic problems can be solved without calculation using this conceptual shortcut. To verify that this principle is used, inverse problems (a + b - b) can be compared with standard problems (a + b - c). If this principle is used, performance on inverse problems will be higher than performance on standard problems because no calculation is required. To our knowledge, this principle has not been previously studied in children with mathematical learning disabilities (MLD). Our objectives were (a) to study whether 10-year-olds with MLD are able to use this conceptual principle in three-term arithmetic problems and (b) to evaluate the impact of the presentation mode. A total of 64 children with or without MLD solved three-term arithmetic problems (inverse and standard) in two presentation modes (symbolic and picture). The results showed that even though children with MLD have difficulties in performing arithmetic problems, they can do so when the inverse problem is presented with pictures. The picture presentation mode allowed children with MLD to efficiently identify and use the conceptual inversion shortcut and thus to achieve a similar performance to that of typically developing children. These results provide interesting perspectives for the care of children with MLD.
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http://dx.doi.org/10.1016/j.jecp.2021.105343 | DOI Listing |
J Exp Child Psychol
April 2022
Centre de Recherche en Epidémiologie et Santé des Populations (CESP), INSERM U1018, UFR Médecine, Université Paris-Saclay, F-91190 Gif-sur-Yvette, France; Child and adolescent protection Centre, Assistance Publique-Hôpitaux de Paris, Centre Hospitalo-Universitaire de Bicêtre, Département médico-universitaire santé de l'enfant et de l'adolescent, F-94270 Le Kremlin-Bicêtre, France.
Numerical inversion is the ability to understand that addition is the opposite of subtraction and vice versa. Three-term arithmetic problems can be solved without calculation using this conceptual shortcut. To verify that this principle is used, inverse problems (a + b - b) can be compared with standard problems (a + b - c).
View Article and Find Full Text PDFBr J Dev Psychol
June 2018
McGill University and University of Regina, Regina, Saskatchewan, Canada.
Research suggests that children's conceptual understanding of multiplication and division is weak and that it remains poor well into the later elementary school years. Further, children's understanding of fundamental concepts such as inversion and associativity does not improve as they progress from grades 6 to 8. Instead, some children simply possess strong understanding while others do not.
View Article and Find Full Text PDFJ Integer Seq
December 2016
Computer Security Division, National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD, 20899-8930.
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose -coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle.
View Article and Find Full Text PDFCognition
April 2016
Indiana University, Bloomington, Indiana, United States.
The idea that cognitive development involves a shift towards abstraction has a long history in psychology. One incarnation of this idea holds that development in the domain of mathematics involves a shift from non-formal mechanisms to formal rules and axioms. Contrary to this view, the present study provides evidence that reliance on non-formal mechanisms may actually increase with age.
View Article and Find Full Text PDFJ Exp Child Psychol
June 2003
Centre for Research in Child Development, Department of Psychology, University of Alberta, Edmonton, Alberta, Canada T6G 2E9.
An important issue in the development of mathematical cognition is the extent to which children use and understand fundamental mathematical concepts. We examined whether young children successfully use the principle of inversion and, if so, whether they do so based on qualitative identity, length, or quantity. Twenty-four preschool children and 24 children in Grade 1 were presented with three-term inversion problems (e.
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