Resources and Tools for Elementary Math Specialists and Teachers
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Making Mathematics Reasonable in School

This 19-page article (pdf) by Deborah Loewenberg Ball and Hyman Bass is a chapter from A Research Companion to Principals and Standards for School Mathematics, published by NCTM. The authors discuss the foundations of mathematical reasoning and proof and support their position that it is central to understanding and using mathematics. Two episodes from a third grade class help illustrate how children can develop the ability to reason. Ball and Bass suggest teaching practices that foster this development.
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Contributed by: National Council of Teachers of Mathematics - Publisher, Deborah Loewenberg Ball - Author, Hyman Bass - Author
This resource is included in the following PD Collection(s):
CCSS Practice Standard 3This collection assists teachers as they integrate Mathematical Practice Standard 3 into their classroom routines. Encouraging productive student conversations about mathematics builds the foundation that supports this practice. These resources will help teachers learn methods for creating an environment where constructing arguments and critiquing the reasoning of peers is a common occurrence. Additional resources may be found in a companion classroom collection.
CCSS Practice Standard 2This collection aims to shed light on Practice Standard 2: Reason abstractly and quantitatively, and offers instructional strategies for helping students make sense of quantities and their relationships in problem situations. These resources provide meaningful ways to support children as they learn to represent problem contexts with numbers and symbols, and then re-interpret the numbers and symbols in terms of the original problem. A companion Classroom Collection includes resources to help teachers develop this practice with their students.
Math TopicMathematical Practices, Mathematical Processes
Grade Level2, 3, 4, 5, 6+
Resource TypeReference Materials, Article

  • Additional Information
    • AudienceEducator
    • LanguageEnglish (USA)
    • Education TopicProfessional development, Teacher preparation, Teaching strategies
    • Interdisciplinary Connection
    • Professional DevelopmentYes
    • ContributorNational Council of Teachers of Mathematics - Publisher, Deborah Loewenberg Ball - Author, Hyman Bass - Author
    • Publication Date2003
    • Rights(c) 2003 National Council of Teachers of Mathematics, Inc.
    • AccessFree access
  • Standards
    • Common Core State Standards for Mathematics

      Select a standards document: