Development of Mathematical Knowledge in Young Children: Attentional Skill and the Use of Inversion

The principle of inversion, that a + b − b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya ( 2005...

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Published inJournal of cognition and development Vol. 15; no. 1; pp. 161 - 180
Main Authors Watchorn, Rebecca P. D., Bisanz, Jeffrey, Fast, Lisa, LeFevre, Jo-Anne, Skwarchuk, Sheri-Lynn, Smith-Chant, Brenda L.
Format Journal Article
LanguageEnglish
Published Colchester Taylor & Francis Group 01.01.2014
Psychology Press
Taylor & Francis
Taylor & Francis Ltd
Subjects
Attention Control
Biological and medical sciences
Canada
Child
Child development
Children & youth
Cognitive Ability
Computation
Computer Assisted Testing
Correlation
Developmental psychology
Elementary School Students
Foreign Countries
Fundamental and applied biological sciences. Psychology
Hypotheses
Knowledge
Longitudinal Studies
Mathematics
Mathematics Skills
Problem Solving
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Scores
Skill Development
Skills
Statistical Analysis
Validity
Canada
Human
School age
Arithmetics
Attention
Inversion
Cognition
Mathematics
Cognitive development
Child
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Abstract The principle of inversion, that a + b − b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya ( 2005 ). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion.
AbstractList The principle of inversion, that a + b -- b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion. [PUBLICATION ABSTRACT]
The principle of "inversion," that a + b - b "must" equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion.
The principle of inversion, that a + b − b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya ( 2005 ). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion.
Audience Grade 2
Grade 3
Grade 4
Elementary Education
Author Bisanz, Jeffrey
Skwarchuk, Sheri-Lynn
Fast, Lisa
LeFevre, Jo-Anne
Watchorn, Rebecca P. D.
Smith-Chant, Brenda L.
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Arithmetics
Attention
Inversion
Cognition
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Snippet The principle of inversion, that a + b − b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts...
The principle of "inversion," that a + b - b "must" equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts...
The principle of inversion, that a + b -- b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts...
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SubjectTerms Attention Control
Biological and medical sciences
Canada
Child
Child development
Children & youth
Cognitive Ability
Computation
Computer Assisted Testing
Correlation
Developmental psychology
Elementary School Students
Foreign Countries
Fundamental and applied biological sciences. Psychology
Hypotheses
Knowledge
Longitudinal Studies
Mathematics
Mathematics Skills
Problem Solving
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Scores
Skill Development
Skills
Statistical Analysis
Validity
Title Development of Mathematical Knowledge in Young Children: Attentional Skill and the Use of Inversion
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