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monika hardy

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scottaaronson.com/blog

mathmathematicians_lament

shared by monika hardy on 23 Jun 09 - Cached
  • maa.org?
  • You know when you’ve taught math properly to a student, because the student feels more powerful and confident than before (just like a successful student of carpentry or basketball). That feeling of power is what inspired me and, I imagine, many others to pursue mathematics or science as a vocation. My belief is that the vast majority of math professors and math teachers don’t see how to “empower” their students in this way, and indeed it is a very hard thing to do. So we settle for either a “cultural understanding” of mathematics or a demonstration of some rote skills.
  • n art portrayed as a cold heartless bureaucracy.
  • ...12 more annotations...
  • What Lockhardt and I advocate teaching is not “New Math”, not “Back-to-Basics Math”, but something much more radical than either: math.
  • I concluded that brains come in different types Stop doing research, and just teach. It may be a crime to the research community, but it will be an endless boon to people who actually want to learn.
  • The only analogy that seemed to work is that mathematicians are like the tool and die makers of the world: everyone needs what we produce, almost no one is interested in what we do, and even fewer understand just how hard it is.
  • Perhaps we should simply accept that math is going to be like literature or art. A small percent will have the desire and interest to pursue it in highschool and we should just try to avoid turning off the rest enough they might return in their own time
  • We don’t have the resources (name your resource) to even approach the periphery of what Lockhart envisions. It will never happen. You guys live in another world. However, I can tell you this: things are better than ever before, and it is people like you and places like this that make it better.
  • We have so little to lose by sacrificing the current highschool curriculum in favor of discussing actual mathematical ideas (i.e. posing questions, trying to come up with answers). O
    • monika hardy
      monika hardy on 23 Jun 09
       
      so little to lose really edupunk isn't so risky really
  • The potentially valuable aspect of studying high school math isn’t learning to solve certain random types of problems. It’s learning to think clearly about deceptively-simple concepts. In doing this you learn to attack problems, generalize techniques, define concepts, make convincing arguments, and find counterexamples. If you need to know the quadratic formula for some weird reason, then all you need to do is look it up. The skills listed above aren’t just useful to scientists, but to lawyers, writers, doctors, etc
  • his comes from
    • monika hardy
      monika hardy on 23 Jun 09
       
      read later - good examples - and need to delve into assessment section more
  • The point is you don’t start with definitions, you start with problems. Nobody ever had an idea of a number being “irrational” until Pythagoras attempted to measure the diagonal of a square and discovered that it could not be represented as a fraction. Definitions make sense when a point is reached in your argument which makes the distinction necessary. To make definitions without motivation is more likely to cause confusion
    • monika hardy
      monika hardy on 23 Jun 09
       
      great thoughts for an ebook
  • The problem, I think, is that the authors aim to prove rather than to communicate.
    • monika hardy
      monika hardy on 23 Jun 09
       
      beware of goals, why are we writing an ebook?
  • Math books should be written, if not in the order the math was actually created, then in the order in which the ideal mathematician might conceivably discover it.
  • pointing out the wrong ways we teach and inspire by writing such a mind numbing repetitive article is quite ironic.
    • monika hardy
      monika hardy on 23 Jun 09
       
      that's the way a lot of us do ed. we talk about new things and changes in the same old way
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