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Lec 2 | MIT 5.95J Teaching College-Level Science and Engineering, Spring 2009

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    Ok, teaching equations, and how to teach equations in a way that promotes
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    long lasting learning and understanding.
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    Ok. So. The first example.
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    I'm going to give you two choices for starting the example.
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    So the first choice, the example is —
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    So this is example one for teaching equations.
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    And it's —
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    This is Hardy-Weinberg Equilibrium.
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    So, here's one way you could start.
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    So if a locus has n alleles
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    and the organism is polyploid
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    So that means it has say "c" copies of chromosomes
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    Okay so, and the, so there is "n" alleles
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    and the allele frequencies are.
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    So the allele frequencies are "p1" through "pn."
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    Then, we're going to deduce the genotype frequencies
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    so this is the multinomial coefficient
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    c choose k1, k2, k3 all the way to kn.
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    And k1 through kn are the number of copies of each allele.
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    With k1 plus, blah blah blah, kn all equal to c.
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    So, you could, actually state that,
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    and then prove it, that's option A.
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    So now I'll give you option B
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    for starting the same topic.
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    Options B,
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    So option B, is, from Hardy
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    so in Hardy's Mathematicians apology
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    he writes, I've never done anything useful.
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    No discovery of mine has made,
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    or is likely to make,
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    directly or indirectly,
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    for good or ill,
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    the least difference to the amenity of the world.
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    And that's a very interesting,
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    very bold statement.
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    And amazingly for such a brilliant mathematician, its wrong.
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    And today, what we're going to do
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    is we're going to look at an example
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    that. Of a discovery by Hardy
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    Hardy-Weingberg Equilibrium.
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    That does make a difference to the amenity of the world.
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    and helps you actually understand genetics.
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    Ok so the option B is to quote
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    Hardy and then show the,
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    point out
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    and then point out the contradiction
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    between what he said and what we're going to do
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    now also, in option B,
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    you can also go a bit farther,
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    you can say,
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    well why would Hardy have said something like that?
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    Well indeed why would he have said something like that, in his apollogy?
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    Well, it's, actually probably hard to appreciate
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    on this side of the Atlantic
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    because we've never actually had
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    Well since the Civil War, we've never had
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    a war that just basically devastated
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    entire countries, on our own soil.
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    Whereas in Europe,
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    the memories of World War One
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    are very strong are very strong.
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    So if anyones from Europe you know that.
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    In, you know in every English Chapel
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    there's names on the wall
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    of all the people who died
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    in the quote Great War.
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    So, it's World War One
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    had a very strong effect
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    on European society.
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    And one of the effects was on
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    European science.
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    And people's attitude toward science.
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    So, poison gas was invented
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    partly by a German Chemist, Haber,
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    was one of them.
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    And in the end
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    he committed suicide
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    partly maybe because of what he had done.
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    He was, so, did he?
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    Yeah, I think he.
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    No sorry, his wife committed suicide.
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    I forget now, I should check that.
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    But, basically people were, in the family were so unhappy
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    about what had happened
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    just there that there was a suicide
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    and furthermore science after that was
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    considered you know World War One was considered
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    The Chemist's War
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    So there was a wish to distance one's self
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    from those kinds of horrible effects
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    so the quote from Hardy is a reflection
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    of that. He himself was actually very anti-war
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    he left Cambridge because Cambridge
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    fired Bertrand Russell for protesting World War One.
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    So Hardy left Cambridge for professorship at Oxford
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    And only came back basically
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    12 or 13 years later
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    to Cambridge. So that statement
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    of his is partly a wish
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    that he's hoping that nothing he's has any effect on the world
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    becausein his mind, maybe most effects are bad.
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    Well, but actually he did have an effect,
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    the effect is Hardy Weinberg
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    even if you discount everything he did in number theory
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    there's Hardy-Weinberg
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    and it has an effect amd we're going to look at it.
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    So let me ask you
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    a rhetorical question,
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    if you're a student,
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    which would you find more engaging,
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    more inviting?
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    This one or this one?
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    Who votes for that one?
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    Okay, who votes for that one?
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    Yeah, now, why?
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    So now think of,
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    so the question i'm going to ask you
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    to think about in, just for a minute
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    in with one or two of your neighbors is
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    why?
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    So, yeah this is definitely
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    more engaging.
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    In terms of the principle we talked about last time,
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    what makes this way of introducing it
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    more engaging, more likely to bring students in,
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    more likely to want to learn
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    about Hardy Weinberg?
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    Okay so find a neighbor or two
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    and think about
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    the principles behind option B.
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    Okay so...
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    I'll rudely interupt you.
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    And good thing I did
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    the voice excercise so I
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    can project all the way to the back.
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    So, what reasons for option B?
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    Or again stops your name
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    which is the same thing.
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    Yes, could you tell me your name?
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    I'm going to, Bryan, I'm going to try to learn people's names.
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    So go ahead,
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    That's right, through the mount wave
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    or in fact maybe even
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    so yeah, I'm activating the ability of the students to
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    basically take dictation.
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    Or, as someone said,
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    teaching is an excellent way
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    to transfer material from
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    the notes of the teacher to
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    the notes of the student
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    without it passing through
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    the minds of either.
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    So I'll call that 'not a.'
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    So, this is the 'not' symbol.
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    'not a' is.
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    So I'm promoting dictation
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    which doesn't necessarily.
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    I'm, basically asking to do dictation
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    which doesn't necessarily
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    lead to any kind of learning.
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    It could for example
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    copy all of that down,
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    but not really understand any of it.
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    Okay, other...
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    Yes, could you tell me your name?
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    Susanna, yeah?
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    Yeah.
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    Okay so,
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    right and so B is a story.
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    Or, I'll
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    I'll. You know, so here's an
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    I'll give you an example
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    of how stories can be so powerful.
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    And just even the word.
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    So a, a big commercial publisher,
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    this was several years ago,
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    they wanted me
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    to write a freshman physics textbook.
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    I'd actually, I'd just put up a proposal on the web saying
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    you we shoudl write up a freshman physics textbook
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    that is based of history and science
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    and they saw it and they thought,
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    "ohh that's great"
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    so they flew me from
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    England to California to talk to them.
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    And, they liked it mostly
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    but they said, "hmm, history."
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    So there was the word.
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    They liked the idea as I talked about it
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    but the word history really frightened them.
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    And then, I'm still amazed as how
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    I had this amazing insight
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    of just two letters.
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    I thought, "ohh wait, I can actually explain to them what i mean."
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    I said, "well actually, if you just take away that part,
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    what I'm really talking about is that."
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    And it was interesting
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    as soon as they saw the word story,
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    everybody.
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    And they saw that, well history doesn't have to be
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    names, dates, facts.
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    I think that's what they were seeing it as.
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    They saw it as 'story' which is actually
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    its origin in French or Latin, 'histoire.'
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    They all of a sudden were totally convinced.
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    They said, "ohh yeah that's exactly how we should do the textbook."
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    And for various reasons, basically because
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    I want it to be a freely licensed,
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    want it to be a freely licensed book,
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    we didn't actually sign a contract.
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    But, it's an example of how powerful 'story' is
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    and how people who actually spend their lives thinking about
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    teaching and reaching students.
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    This educational publisher
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    knew the importance of story.
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    But if you present it as just dry history,
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    it's not so interesting.
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    So, 'story.'
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    Yeah, so it's, let's see.
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    Who haven't I heard from?
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    Adrian, yeah.
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    Okay, so there's a contradiction.
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    The contradiction creates some kind of tension.
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    Right so that tension creates interest.
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    So. Right so every good story needs some kind of tension.
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    You know, so the tension here,
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    the contradiction is that, you know,
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    Hardy wanted to do nothing that could harm people basically.
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    So he was like, "Okay well anything can be used, could be used, even if it's for good for ill.
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    So let me just back off from all that
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    say I'm not going to do anything that has an effect, an application.
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    I'm a pure mathematician."
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    His most famous book is of course, Pure Mathematics.
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    Well maybe his most book famous is that book, which I quoted from,
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    A Mathematician's Apollogy.
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    But his most famous math book is,
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    probably the Course of Pure Mathematics.
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    And that's what he wanted to be known for.
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    And that's in contradiction with the fact
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    that, no, even Hardy couldn't help an application.
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    An actually very very common one,
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    it's taught in every single Introductory Biology course probably.
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    Okay so you need tension.
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    Now, that's a general principle of learning there.
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    You know the idea of story and tension
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    and paradox.
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    So you.
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    The one way that as a undergraduate in physics
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    that I learned a ton of physics,
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    me and my friends were doing problem sets together
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    and you know lots of the problems were,
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    just grinding through math.
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    So we didn't learn a hell of a lot from that.
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    But, we were in the library late at night,
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    you know, the physics library,
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    and ordering pizza and trying to do our problem set
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    and we just got to making up physics paradoxes.
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    You know perpetual motion machines.
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    We'd invent perpetual motion machines
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    and try to get the other person
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    to figure out what was wrong with it.
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    Sometimes we didn't even know what was wrong with it,
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    we'd both try to figure it out.
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    So, from that kind of tension,
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    tension is almost in a way self-teaching.
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    Beacuse, as long as the tension's there you know you're not at the end of the story.
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    Right so you know there's more to do.
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    So the same thing,
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    as long as there was perpetual motion going on,
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    and we hadn't found the reason,
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    we knew weren't done with the problem.
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    We didn't have to ask the teacher,
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    "Well, is this right?"
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    Because it was basically self-teaching
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    as long as the tension was there
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    we knew that we weren't finished.
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    Okay so, yeah,
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    another general principle stories of tension.
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    Let's see there was a comment over...
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    Yes, tell me your name.
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    Wing, Wing-ho.
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    Right.
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    Okay so, yeah the, it, the teacher makes himself more human
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    and makes the person who invented,
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    or one of the people who invented the Hardy-Weinberg Equilibrium more human.
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    So it's actually something much more easy,
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    easy for the students to connect to.
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    Yes, could you tell me your name?
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    Gregory.
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    mhm.
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    Okay so, so Gregor's point which is a good one
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    is that B doesn't have the same quantitative depth as A.
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    And, well actually what I'm going to show you
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    is a way to get to get to this
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    starting from here,
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    and using to the principles that were talking about
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    so that by the time you ger here or to something like this
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    it actually makes sense to the students.
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    Okay so that you can have both.
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    So, that's a promise and,
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    hopefully I'll deliver on it for you.
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    Okay does that?
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    But does that address what you're talking about?
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    That B doesn't have the quantitative depth.
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    And that's true.
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    You, well so you so the,
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    the point made is that
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    if you want to get here you do have to
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    say this at some point.
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    And you know you can't just say the story for an hour.
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    Well, it depends on the purpose of the class.
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    If the purpose is the history of Biology,
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    maybe you would continue with the story
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    or the history of science and war.
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    But if you know you want the students
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    to be able to solve problems in gentics
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    you know maybe you need to go here.
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    Or, what we'll find is the next.
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    I'll continue with option B
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    moving towards A
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    and show you how you can get there
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    without and still have
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    the opening of B preserved.
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    Okay so let's see,
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    there was yes.
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    Yes, can you tell me your name?
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    Okay.
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    Yeah okay, okay so B is, new.
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    Right, A is actually.
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    So against A, A is very familiar and common.
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    So in fact yeah I chose this,
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    I mean i didn't really make a strong ???man??? here.
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    This is how alot of things are introduced
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    for example, in mathematics class
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    theorem proof.
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    Right so the theorem will be introduced
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    without any of the struggle, the wondering,
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    that lead to the theorem.
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    Like, why would anyone care about such a thing?
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    Or if they cared about it,
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    why would they come up with something like that?
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    You know, how can you see that?
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    The, so yeah A is seen very familiar
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    and therefore maybe not as interesting.
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    Although it may also be intrinsically less interesting.
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    For the other reasons, but I take your point too
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    that it could just be familiarity.
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    Yes, can you tell me your name?
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    Meg, yeah.
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    mhm.
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    Okay.
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    Okay so your, your point which is an excellent one aswell
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    is that, you, B doesn't preclude the quatitative.
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    What you could do is you could talk about
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    the history.
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    Start with the history of Hardy saying that
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    which is not chronological because he said that in 1940
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    but that's okay, it doesn't have to be chronological
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    just because it's history.
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    Go to 1940 and then backtrack,
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    to well how did this problem
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    actually come to Hardy's attention
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    which is actually, turns out to be quite
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    an interesting story.
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    And then talk about how they solved it
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    and what was the ???public, date in history???
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    All the quantitative ideas would come out
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    in that way
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    and it would be
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    an almost backwards from the usual way.
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    In one way is that the usual way well,
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    the usual way here is completely general
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    and that's probably not the way
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    it was first figured out.
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    And, the advantage of
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    telling about it that way
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    is that you're preparing students themselves
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    for a research career.
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    Because, they're not,
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    nobody comes up with theorems
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    full blown you know like seen
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    out of the head of Zeus.
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    You come through it from struggle
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    and wondering, "hmm I wonder."
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    Everything comes, has some historical background to it.
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    So the, it's called the, you could say it,
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    the Genetic approach.
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    So in, in Biology, there's a slightness,
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    not misconception, but a saying that
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    ???oncology recapitulates via logically.???
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    In other words, that the organism,
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    as it develops in the womb
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    goes through all the evolutionary stages
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    that it went through
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    over the last 200 millions years,
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    or whatever it took to become,
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    say, a person.
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    You're first a fish
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    and then maybe you're a monkey
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    and then a person.
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    So roughly speaking,
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    it's not exactly true.
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    But there's alot of truth to that
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    for learning ideas.
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    That you have to recapitulate the history
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    of ideas to really understand where we are now,
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    the ideas today.
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    So a great example of that
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    is the Newton's Second Law of Motion.
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    The idea that force and acceleration,
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    are connected.
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    So for thousands of years,
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    millions of years, people thought
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    that force and velocity were connected.
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    And it's actually force and acceleration.
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    So actually you can guide people
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    to the understanding of force and acceleration being connected
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    by showing them the history of how people
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    thought it was force and velocity,
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    because, for those same reasons,
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    those are the reasons the student will think it too.
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    So you're actually helping them overcome their misconceptions.
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    So the history actually
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    generally speaking,
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    helps overcome misconceptions.
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    So I'll put that here.
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    And the history is actually quite interesting.
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    I think it was Punnett, from Punnett squares.
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    He played cricket with Hardy,
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    and Hardy loved cricket
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    and he just asked him about this problem
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    and Hardy said, "Ohh yeah I know, it's just this."
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    And sent off a paper to science or nature.
Title:
Lec 2 | MIT 5.95J Teaching College-Level Science and Engineering, Spring 2009
Video Language:
English
Duration:
02:14:58

English subtitles

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