for secundary schools we use a system called video-measuring (IP-coach) Children make a video of a phenomena and then play it back picture-by-picture. On each picture they put a cross-mark for the place of the moving object. In a graph interface the resulting place-time graph is depicted.

-----Oorspronkelijk bericht----- Van: Alan Kay [mailto:Alan.Kay@squeakland.org] Verzonden: zondag 20 april 2003 2:56 Aan: squeakland@squeakland.org Onderwerp: Re: "All the Real Math To Which School (Including College) Refused Yo u Access."

Hi Bert --

At 6:57 PM +0200 4/19/03, Bert Freudenberg wrote:

Am Donnerstag, 17.04.03 um 21:24 Uhr schrieb 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 ).

If I were picking nits I'd point out that actually weight is a force (measured in Newtons), not gravity. Force is mass times acceleration (Newton's second law). So in this special case, weight is mass times gravitational *acceleration*. Weight is only another term for gravitational force. But you knew that ;-)

...

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.

What do you think of measuring the forces in the Etoy itself (for example, by taking the vertical extent of a rotated line)? Of course, I can see the value of using real-world data.

I think this is really important at this stage. This is one of the relatively few phenomena that is both very interesting, useful, and measurable by the kids. This "weighing angles" idea cuts through a lot of steps and gets right to a way to determine the differential accelleration down the plane by directly referring to the phenomena.

Do you think it's too large a step to "see" the height of the angle, which is proportional to the force?

It shouldn't be too hard for adults ... heh heh. But kids are just learning about proportions (in the US they generally don't learn proportions successfully and operationally). I think this is a very good thing to point out after they have their simulated cars successfully going down different planes at the correct accellerations (Note that this can be done via one of the touch tests between the sim car and the sim plane.)

Cheers,

Alan

-- Bert