This is why this summer I'd like to collaboratively have us generate

a sample curriculum for 4th through 6th (or possibly even through

8th) grade.

The way I have this in my imagination is to think of the deep

knowledge ahead and to try to build the deep intuitions that are

needed to understand that knowledge when it is encountered.

So, to me, I would like to have "math" be "real math", and (a)

have the emphasis be on learning how to do mathematical reasoning on

the one hand, and (b) for the kids to learn vectors and geometry as

the main ways they have to think about numbers and arithmetic, and

for them to learn how to use differential (tiny little) vectors that

can be pasted together to make complex mathematical structures of

many kinds.

Similarly, I'd like to have "science" be "real science", and to

(a) have the emphasis be on learning the scientific ways to look at

the world and also the limitations of trying to "know" that world,

and (b) for them to make real contact with some of the deep

scientific ideas that can be made completely understandable to them

at various ages.

So my first pop at any curriculum design is always to think about

these ideas and how they might be taught using the best pedagogy and

most fruitful materials. The computer is just one of these, and it is

best used for the parts of a curriculum where it is quite superior to

physical media. We have a friend at the Exploratorium (Modesto Temez)

who is a positive genius in organizing science learning just using

easily obtainable junk in the outside world. This is where science

learning has to start. The computer can be useful in motivating and

being the instrument of the "mathematical music of science".

I will try to put out sketches of curriculum ideas for math and

science on the squeakland list over the next few weeks to stimulate

discussion.

A sketch at the computer part of the curriculum can be done by just

organizing the etoys as "starters" that have progressions to more

complex versions. For example, it's a good idea to do uniform motion

before doing accellerated motion (and this obtains for all the

different motions: in space, though images, audio samples, etc.).

In the accellerated motion examples we have experimented with,

the progression seems to be: model the dropping of a water balloon,

then model shooting it (shoot the alien), then do the Lunar Lander

game, then do the roller coaster. Then do Spacewar. Then do orbits of

planets and spaceships. A progression like this might extend over

more than one year of school, etc.

I think the tricky part of doing a math and science curriculum in

elementary school that really looks ahead to the "deep content" of

both these areas, is the amount and kind of teacher coaching that

needs to be done to help elementary school teachers who may not have

concentrated on math or science (in my experience, most have not).

From Alan Kay email

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