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View Diary: Weekly Physics: Equations of Motion (63 comments)

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  •  I'm not talking about rigor (5+ / 0-)
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    linkage, craiger, guyeda, drache, whiteclover

    I meant develop the intuition first.  Otherwise you risk losing the audience.  Just an opinion,  That and about $4 will get you a Starbucks.

    •  could you explain more please? (6+ / 0-)

      I am not trying to be difficult but I always like hearing constructive criticism of my writing as I know I'm not the best writer and am always trying to better myself.

      What do you mean develop intuition first? In your view should I start with an example?

      A song about life
      Why aren't you more like Gandhi? Why aren't I?

      by drache on Sat Jun 06, 2009 at 08:24:35 PM PDT

      [ Parent ]

      •  Not a bad idea, here's a good place (4+ / 0-)

        Starting with an example and working in the physics seems like a good idea.

        This part seems like a good place for an intro:

        Well let's think about what exactly happens to the ball after it is thrown. Initially it has a positive velocity and is slowly or quickly slowed by the earths gravity.

        I liked this section, it builds from experience, makes you think about what is actually happening.  

        Here's an idea, hacked together very quickly:

        The ball goes up and  slows.  Why?   Why does the velocity change?  What does constant velocity mean?  We're getting into the counter-intuitive, we're moving from Aristotle to Newton.  

        Next we see that the ball goes up only so far and then it stops.  Now you have everything you need to understand the equations by putting together everything you already know. You have the initial conditions for velocity and position, you have the acceleration, you have the observed behavior...etc.

      •  How about starting closer to the beginning ... (4+ / 0-)
        Recommended by:
        BentLiberal, linkage, guyeda, drache

        Maybe something like:

        The equations of motion enable us to determine and describe the location and speed of a moving object at any point in time.  For example, if you are driving on the interstate and you got on at mile/exit 200 and drove for 1/2 hour at 60 miles per hour, you would be at either mile marker 170, or 230 depending on which direction you were heading.  This is an example of constant velocity motion.  There is a formal equation for this which is s = s0 + vt, where s is current location, s0 is starting location, v is velocity, and t is time.  Things get a little more complicated when we add in the concept of speeding up and slowing down - positive and negative acceleration.

      •  what would help me is.... (2+ / 0-)
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        guyeda, drache spell out each equation in common English right below it, and explain it right there as well.  (I'm dyslexic so I have trouble reading equations, but I'm actually quite good with this stuff on the conceptual level and I even use it in ordinary conversation among my (yes, geeky) friends.)  

        For example,

        "v = v0 +at is read, v equals v subscript zero, plus a t.  The first term "v" is for final velocity at a chosen end-point in time; the term "v subscript zero" refers to initial velocity at some hypothetical starting-point in time that we'll call zero; the term "a" refers to acceleration and "t" refers to time.  Thus, final velocity equals initial velocity plus acceleration times time."  

        The place where the dyslexia is a real pain in the butt, is where we start getting into parentheses, brackets, etc., and a bunch of subscript and superscript.  Reading that stuff is like trying to spell out words in alphabet soup while it's being stirred.  One thing that helps for that, is to use lots of space between the various groups of terms.  

        For example instead of   a=(bc(de)),  do this:  a = ( bc  (de)  ).  

        Also, commas in multi-digit numbers are essential:  1234567 is nasty, but 1,234,567 is legible.  

        If there was a way to set off subscripts and superscripts in color, that might also be highly useful.  For example, superscripts in red, subscripts in blue.  I don't even know if that can be done on this site, but it could be helpful in other kinds of teaching materials.

        I suspect that a lot of the trouble people have with the math that goes along with this stuff, is actually something similar to dyslexia but not diagnosable as such.  This is supported by research by Bell Labs that led to the formatting used with telephone numbers, and the use of color to differentiate numerals (red) from letters (black) on early telephone dial: these steps reduced wrong numbers, many of which are what we would call dyslexic errors in processing alphanumeric character strings.  

      •  criticisms, hopefully constructive (3+ / 0-)
        Recommended by:
        guyeda, drache, xgy2

        The other day, I made a similar comment in your diary about vectors.  You drew some vectors and talked about how to perform abstract operations on vectors, but you didn't develop first why a vector would be an interesting notion or what kind of real-world problems vectors would help you solve.  Same sort of problem tonight.

        It's like reading the instruction manual for a compound miter saw without understanding how a picture frame is put together and what kind of tools might make the job easier.  Math is a tool.  Show us a an interesting problem first, and then develop the tools to solve it.

        Also, you already introduced vectors and velocity is absolutely a vector, but you didn't build on that concept and thereby give it some continuing relevance, even though you wrote about reversal of direction as a ball at the peak of its arc.  I think this plays into the common notion held by math-phobes that math is a collection of unrelated trivia to be memorized.  At every appropriate opportunity, concepts should be tied together and shown to be related.

        My 2¢.

        "They let 'em vote, smoke, and drive -- even put 'em in pants! So what do you get? A -- a Democrat for President!" ~ Faster, Pussycat! Kill! Kill!

        by craiger on Sun Jun 07, 2009 at 12:59:45 AM PDT

        [ Parent ]

        •  well I think I understand your position better (0+ / 0-)

          a lot better now.

          I say your comment and didn't necessarily disagree I just did not see how to do that with vectors.

          But now I see that if I want this series to work I will have to try to do that. And I will have to introduce questions, examples or even problems at the start, talk about the physics, introduce people to the equations and then show how the physics works on what was previously introduced.

          Thank you for your thoughts and I certainly appreciate it.

          A song about life
          Why aren't you more like Gandhi? Why aren't I?

          by drache on Sun Jun 07, 2009 at 07:56:59 AM PDT

          [ Parent ]

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