Actually, what the 10 and 11 year olds do is:
1. measure from the bottom of a ball to the bottom of the ball in the next frame using the height of a rectangle that is stretched to fit.
2. They stack up the rectangles to see that the incremental change in height is constant. They know this is constant accelleration because they have played with it using their painted cars a few months previously.
3. they paint a small simulated ball
4. they then adapt the script they wrote for the cars to drop the ball in the vertical direction with constant accelleration:
5. ball drop ticking ball's speed increase by -1 ball's y increase by ball's speed
6. then they tinker with the constant to find the accelleration that matches what is happening in the movie
7. Then they figure out a way to "prove" that they have "captured gravity" a. one way is to leave a little mark at each position of the real ball b. another way is to run the movie and their simulation frame by frame to show that the simulated ball tracks the movie
In other words, these children actually derive the dynamic relationship of (very near) constant accelleration near the surface of the earth in the form of a discrete 2nd order differential equation. It is quite remarkable to see this (especially for me, since I designed this project for 9th through 12th graders).
The key here is to spread out the various ideas and parts that have to be learned over several months in the midst of doing other things.
Cheers,
Alan
At 7:25 PM +0200 4/21/03, G.J.Tielemans@dinkel.utwente.nl wrote:
Yes Alan, falling object on movieframes: I saw something the same with eggs from Mark Guzdial on Georgia Tech. But where are the student-created-time-connected-graphs?
-----Oorspronkelijk bericht----- Van: Alan Kay [mailto:Alan.Kay@squeakland.org] Verzonden: maandag 21 april 2003 0:08 Aan: squeakland@squeakland.org Onderwerp: RE: "All the Real Math To Which School (Including College) Refuse d Yo u Access."
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