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Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division.

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Title: Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division.
Authors: Milton, Jessica H., Flores, Margaret M., Moore, Alexcia J., Taylor, Ja'Lia J., Burton, Megan E.
Source: Learning Disability Quarterly. Feb2019, Vol. 42 Issue 1, p32-45. 14p.
Subjects: Students with disabilities, Learning disabilities, Mathematics, Psychology of school children, Qualitative research, Teaching methods, Psychology
Abstract: To meet increasingly complex mathematics standards in late elementary school, students must conceptually understand and be fluent in the operations of multiplication and division. This includes understanding the operations' inverse relation. The purpose of the study was to investigate the effects of alternating concrete–representational–abstract (CRA) multiplication and division instruction on students' mastery of unknown facts and on their conceptual understanding. Fourth through sixth-grade students with learning disabilities who had failed to master all multiplication facts participated in the study. The researchers used a mixed method design, measuring accuracy and fluency of facts with a multiple probe across students design and qualitative methods to capture changes in students' explanations of their computation. The researchers demonstrated a functional relation between CRA instruction and accuracy and fluency in multiplication and division. Qualitative results indicated differences in students' understanding of the operations. Implications of the results will be discussed further. [ABSTRACT FROM AUTHOR]
Copyright of Learning Disability Quarterly is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Psychology and Behavioral Sciences Collection
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  Data: Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division.
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  Data: <searchLink fieldCode="JN" term="%22Learning+Disability+Quarterly%22">Learning Disability Quarterly</searchLink>. Feb2019, Vol. 42 Issue 1, p32-45. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Students+with+disabilities%22">Students with disabilities</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+disabilities%22">Learning disabilities</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Psychology+of+school+children%22">Psychology of school children</searchLink><br /><searchLink fieldCode="DE" term="%22Qualitative+research%22">Qualitative research</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+methods%22">Teaching methods</searchLink><br /><searchLink fieldCode="DE" term="%22Psychology%22">Psychology</searchLink>
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  Data: To meet increasingly complex mathematics standards in late elementary school, students must conceptually understand and be fluent in the operations of multiplication and division. This includes understanding the operations' inverse relation. The purpose of the study was to investigate the effects of alternating concrete–representational–abstract (CRA) multiplication and division instruction on students' mastery of unknown facts and on their conceptual understanding. Fourth through sixth-grade students with learning disabilities who had failed to master all multiplication facts participated in the study. The researchers used a mixed method design, measuring accuracy and fluency of facts with a multiple probe across students design and qualitative methods to capture changes in students' explanations of their computation. The researchers demonstrated a functional relation between CRA instruction and accuracy and fluency in multiplication and division. Qualitative results indicated differences in students' understanding of the operations. Implications of the results will be discussed further. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Learning Disability Quarterly is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1177/0731948718790089
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        Text: English
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      – SubjectFull: Mathematics
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              Text: Feb2019
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