"All the Real Math To Which School (Including College) Refused Yo u Access."

[Alan Kay]

I think lots of insight can be gained by seeing what the "weighing 
angles" illustration is all about.

Notice that when the angle is 90? the scale will measure the full 
weight of the dumbell and wheels. When the angle is 0?, the scale 
will show zero weight. In between, the scale will show the weight of 
the dumbell and wheels in the direction down the inclined plane. 
"Weight" is actually defined as the mass of an object times the force 
of gravity on it ( w = mg ). So what we are seeing on the scale is 
the differential effect of gravity down inclined planes at different 
angles.

If we use a protractor to tilt the inclined plane (say) every 5? then 
we can write down the different forces down the plane. If we divide 
these numbers by the maximum weight when the angle is 90, we will get 
numbers between 0 and 1. These numbers can be put into a holder as a 
table of values and used in a wide variety of projects, including 
making a roller coaster. So there is no need to use the idea of 
"sine" -- and this makes projects that need these ratios -- like 
roller coasters -- much more in the range of 5-7th graders.

Cheers,

Alan



At 11:49 AM -0400 4/17/03, John Voiklis wrote:
>Hello Alan,
>
>You hit it right on the mark with "vectors," but thinking back on it, the
>breakdown in communication may have been over the concepts themselves
>(despite claims to the contrary). I was discussing this with fellow computer
>club mentors and I seem to remember that even the illustrations you sent and
>your references to "weighing angle" and "'down track' forces" were greeted
>with blank looks. Without dwelling on this sad state of affairs, I simply
>want to point out that in "proselytizing" about Squeak we need to keep in
>mind that adults, even those in the biz, need the models just as much as
>kids; we can't assume an understanding even of simple math and physics.
>
>Best,
>
>J
>-----Original Message-----
>From: owner-squeakland at squeakland.org
>[mailto:owner-squeakland at squeakland.org]On Behalf Of Alan Kay
>Sent: Thursday, April 17, 2003 10:22 AM
>To: squeakland at squeakland.org
>Subject: RE: "All the Real Math To Which School (Including College)
>Refused Yo u Access."
>
>
>Thanks John --
>
>It would be great if you could list the "language stuff" that causes
>the glazing. Do you mean terms like "vectors"? What other terms are
>offputting?  One of the reasons this stuff works so well with the
>kids is that they just do the models, we don't employ terminology
>with them.
>
>Cheers,
>
>Alan
>
>At 8:29 PM -0400 4/16/03, John Voiklis wrote:
>>While I did not ask the original question, I thank you, Alan, for these
>>helpful hints to the pendulum problem.
>>
>>Getting back to the imagined book in the subject line and my earlier
>>question about whether such a resource exists: the reaction I have gotten
>>from all the people with whom I have shared this problem and the hints is
>>that they can understand the concepts but not the terminology...at least in
>>this instance, it is the language that makes their eyes glaze over. I don't
>>present this as a criticism, but, as someone concerned with explaining such
>>things to people, it is definitely an important observation; one at least
>>that I should keep in mind.
>>
>>Best,
>>
>>John
>
>
>--


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