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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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