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Can you give references to articles/books that contain interesting metaphors for what is wrong in mathematics education from the point of view of mathematicians?

An example for what I am searching:

A mathematician's lament

In this article, the author compares mathematics education to music education where children are taught to translate sheet music from one key to another without ever listening to music or singing because this is considered an advanced topic for college that has to be preceded by good routine practice of the language of music.

Now, this metaphor has some strength and some weaknesses and this is not the right place to discuss them, so I just ask you for links to other metaphors.

I think that this could be a useful and interesting collection, but I will certainly accept if you think otherwise and close this question.

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    $\begingroup$ You're aware that there's a book that's an extended version of Lockhart's essay? $\endgroup$ – J. M. isn't a mathematician May 9 '11 at 13:46
  • $\begingroup$ @JM I wasn't. Thanks for the link. $\endgroup$ – Willie Wong May 9 '11 at 13:58
  • $\begingroup$ No, I was not aware of that. Thanks. $\endgroup$ – Phira May 9 '11 at 13:59
  • $\begingroup$ You might be interested in the videos here and here. $\endgroup$ – Shahab May 9 '11 at 15:01
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There are a number of metaphors for mathematics from classic philosophy:

  • Plato's Cave (text here)

  • Socrates' dialog with Meno, where Socrates 'pulls out' a proof from Meno's slave presumably uneducated slave.

  • Another Socratic dialog named Theaetetus, where the metaphor of a midwife is given (to ideas and by extension to imparting ideas to others).

These aren't directly metaphors of problematic aspects of mathematical education which is what is asked for, but rather metaphors of just the education, so presumably problems discussed in the analogies are problems for mathematics education.

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