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Paul Lockhart

A Mathematician's Lament

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  • b8453453735fez uma citaçãohá 4 anos
    Observation and discovery are one thing, but explanation is quite another. What we need is a proof, a narrative of some kind that helps us to understand why this pattern is occurring
  • b8453453735fez uma citaçãohá 4 anos
    School has never been about thinking and creating. School is about training children to perform so that they can be sorted
  • b8453453735fez uma citaçãohá 4 anos
    it is far easier to test someone’s knowledge of a pointless definition than to inspire them to create something beautiful and to find their own meaning
  • b8453453735fez uma citaçãohá 4 anos
    the most valuable skill for a scientist or engineer is being able to think creatively and independently
  • b8453453735fez uma citaçãohá 4 anos
    Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.
  • b8453453735fez uma citaçãohá 4 anos
    We learn things because they interest us now, not because they might be useful later
  • b8453453735fez uma citaçãohá 4 anos
    It may be true that you have to be able to read in order to fill out forms at the DMV, but that’s not why we teach children to read. We teach them to read for the higher purpose of allowing them access to beautiful and meaningful ideas
  • b8453453735fez uma citaçãohá 4 anos
    Teaching is not about information. It’s about having an honest intellectual relationship with your students
  • b8453453735fez uma citaçãohá 4 anos
    Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions
  • b8453453735fez uma citaçãohá 4 anos
    If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful
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