Resources and Tools for Elementary Math Specialists and Teachers
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Halves, Pieces, and Twoths

This qualitative research article examines teachers' choices of instructional representations and their bearing on student learning. Through the context of teaching fractions, the author examines the importance of, and complexities in, teacher choices when representing mathematical concepts in the classroom in order to teach those concepts. Teachers' pedagogical content knowledge is explained as the basis for these choices.
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Contributed by: Deborah Ball - Author, National Center for Research on Education - Initiator, National Center for Research on Teacher Learning - Publisher
This resource is included in the following PD Collection(s):
CCSS Practice Standard 4This collection supports teachers as they integrate Practice Standard 4 into their classroom routines. In these articles, videos, and lesson studies, teachers will see strategies that help guide students to use concrete, pictorial, and symbolic representations to describe mathematical situations in everyday life. Additional resources for immediate use in the classroom can be found in a companion classroom collection.
Math TopicNumber Sense, Fractions, Number Concepts, Mathematical Practices, Mathematical Processes
Grade Level
Resource TypeReference Materials, Article

  • Additional Information
    • AudienceEducator, Researcher
    • LanguageEnglish (USA)
    • Education TopicEducational environment, Instructional materials, Misconceptions, Professional development, Teacher content knowledge, Teacher preparation, Teaching strategies
    • Interdisciplinary Connection
    • Professional DevelopmentYes
    • ContributorDeborah Ball - Author, National Center for Research on Education - Initiator, National Center for Research on Teacher Learning - Publisher
    • Publication Date1990
    • Rights(c) Deborah Ball
      http://www.eric.ed.gov/PDFS/ED324226.pdf
    • AccessFree access
  • Standards
    • Common Core State Standards for Mathematics

      Select a standards document: