Closing Observations

  • Arthur B. Powell


In the previous 16 chapters, we have witnessed ordinary students develop extraordinary mathematical ideas, forms of reasoning, and heuristics. Extraordinary are these students’ accomplishments since their mathematical behaviors emerged not from quickly parroting rules and formulae but rather from deliberately engaging their own discursive efforts. As Speiser (Chapter 7, this volume) notes, these students built fundamental mathematical understanding, over time, through extended task-based explorations.


Mathematics Education Mathematical Idea Sense Making Mathematical Behavior Focal Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Urban EducationRutgers UniversityNewarkUSA

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