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This chapter is part of a book that is no longer available to purchase from Cambridge Core

5 - Cognitive Issues

Steven G. Krantz
Steven G. Krantz
Affiliation:
Washington University in St. Louis
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Summary

Mathematical maturity is when you're grown up enough to handle a 2ϵ

Michael Sharpe (mathematician)

A method in mathematics is a trick that is used more than once.

Ron Getoor (mathematician)

Everything is trivial when you know the proof.

David V. Widder (mathematician)

Obvious is in the eye of the beholder.

Ron Getoor (mathematician)

If we accept that mathematics is a sort of language, then I suppose that developing mathematical maturity is akin to becoming fluent in the language.

Harold Boas (mathematician)

When we were children, we used to think that when we were grown-up we would no longer be vulnerable. But to grow up is to accept vulnerability… To be alive is to be vulnerable.

Madeleine L'Engle (author)

Chapter Overview

“Nature versus nurture” is a very old question in the study of child development. Do children become scholastically gifted because of good genes, or because of a supportive environment at home (and at school), or both? Since the math teacher is more a part of the latter aspect than the former, it is natural for teachers to want to understand this dialectic.

There are many different types of learning: rote learning, learning by trial and error, learning by attacking difficult problems, learning by imitating a master, learning by exploration, learning by experimentation. Which of these is most relevant to developing mathematical maturity? Which is inimical to mathematical maturity?

If we are to be effective mathematics teachers, we should endeavor to understand students' values and students' goals. Not to mention their motivations.

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A Mathematician Comes of Age , pp. 77 - 106
Publisher: Mathematical Association of America
Print publication year: 2011

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  • Cognitive Issues
  • Steven G. Krantz, Washington University in St. Louis
  • Book: A Mathematician Comes of Age
  • Online publication: 05 March 2012
  • Chapter DOI: https://doi.org/10.5948/UPO9781614445111.006
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  • Cognitive Issues
  • Steven G. Krantz, Washington University in St. Louis
  • Book: A Mathematician Comes of Age
  • Online publication: 05 March 2012
  • Chapter DOI: https://doi.org/10.5948/UPO9781614445111.006
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Cognitive Issues
  • Steven G. Krantz, Washington University in St. Louis
  • Book: A Mathematician Comes of Age
  • Online publication: 05 March 2012
  • Chapter DOI: https://doi.org/10.5948/UPO9781614445111.006
Available formats
×