View in EDS PDF Full Text

Teaching the Conceptual Revolutions in Geometry

Saved in:
Bibliographic Details
Title: Teaching the Conceptual Revolutions in Geometry
Language: English
Authors: Carson, Robert N., Rowlands, Stuart
Source: Science & Education. Oct 2007 16(9-10):921-954.
Availability: Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Peer Reviewed: Y
Physical Description: PDF
Page Count: 34
Publication Date: 2007
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Symbols (Mathematics), Concept Formation, Geometry, Mathematics Instruction, History, Mathematical Concepts, Cognitive Processes
DOI: 10.1007/s11191-006-9041-y
ISSN: 0926-7220
Abstract: Mathematics begins in human experience thousands of years ago as empirical and intuitive experiences. It takes the deliberate naming of concepts to help crystallize and secure those observations and intuitions as abstract concepts, and to begin separating the concept of number from specific instances of objects. It takes the creation of compact symbols to enable efficient calculation and to begin raising a consciousness of this activity we call mathematics. And it takes the sustained development and discussion of mathematical conventions and practices to create entire domains of mathematical thought, such as we find in geometry. The major innovations and conceptual reformulations are few in number, but these represent perhaps the greatest challenges to learners. Historically significant transformative events have their counterpart in the cognitive growth of the individual. This article examines the interplay between these big ideas in cultural history and the deliberate processes of cognitive change that are their counterpart in the educational process.
Abstractor: As Provided
Number of References: 45
Entry Date: 2011
Accession Number: EJ924536
Database: ERIC
FullText Links:
  – Type: pdflink
    Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwHSn5Zsqu9Q2wcXw8h9ISWqAAAA4jCB3wYJKoZIhvcNAQcGoIHRMIHOAgEAMIHIBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDGF4lzEmAZPQ__0xPQIBEICBmhABDlglYp02bNfxSr9YWg416qxYFbRSXHSsKNp9h_HIx6kI_rThBH4yBlg-uFQUyaCKP15Vfd1VNAQroDaVvje0VkBUWkuNxk9TKCYSIjdj-s_03dpOLeizfnCfWUHPeMnkhvBAtEtCXwVZo1LWOmLW7Pk8_0b7GtYIOSHJ1SU7dQKFwdIeVI0UWM8sbEUUFM-y0Kjbl5b-0Vc=
Text:
  Availability: 0
Header DbId: eric
DbLabel: ERIC
An: EJ924536
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Teaching the Conceptual Revolutions in Geometry
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Carson%2C+Robert+N%2E%22">Carson, Robert N.</searchLink><br /><searchLink fieldCode="AR" term="%22Rowlands%2C+Stuart%22">Rowlands, Stuart</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Science+%26+Education%22"><i>Science & Education</i></searchLink>. Oct 2007 16(9-10):921-954.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: PhysDesc
  Label: Physical Description
  Group: PhysDesc
  Data: PDF
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 34
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2007
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Evaluative
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Symbols+%28Mathematics%29%22">Symbols (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Concept+Formation%22">Concept Formation</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22History%22">History</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Concepts%22">Mathematical Concepts</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Processes%22">Cognitive Processes</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1007/s11191-006-9041-y
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0926-7220
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Mathematics begins in human experience thousands of years ago as empirical and intuitive experiences. It takes the deliberate naming of concepts to help crystallize and secure those observations and intuitions as abstract concepts, and to begin separating the concept of number from specific instances of objects. It takes the creation of compact symbols to enable efficient calculation and to begin raising a consciousness of this activity we call mathematics. And it takes the sustained development and discussion of mathematical conventions and practices to create entire domains of mathematical thought, such as we find in geometry. The major innovations and conceptual reformulations are few in number, but these represent perhaps the greatest challenges to learners. Historically significant transformative events have their counterpart in the cognitive growth of the individual. This article examines the interplay between these big ideas in cultural history and the deliberate processes of cognitive change that are their counterpart in the educational process.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: Ref
  Label: Number of References
  Group: RefInfo
  Data: 45
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2011
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ924536
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ924536
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s11191-006-9041-y
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 34
        StartPage: 921
    Subjects:
      – SubjectFull: Symbols (Mathematics)
        Type: general
      – SubjectFull: Concept Formation
        Type: general
      – SubjectFull: Geometry
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: History
        Type: general
      – SubjectFull: Mathematical Concepts
        Type: general
      – SubjectFull: Cognitive Processes
        Type: general
    Titles:
      – TitleFull: Teaching the Conceptual Revolutions in Geometry
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Carson, Robert N.
      – PersonEntity:
          Name:
            NameFull: Rowlands, Stuart
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 10
              Type: published
              Y: 2007
          Identifiers:
            – Type: issn-print
              Value: 0926-7220
          Numbering:
            – Type: volume
              Value: 16
            – Type: issue
              Value: 9-10
          Titles:
            – TitleFull: Science & Education
              Type: main
ResultId 1