[IAEP] An example on statistical

[Alan Kay]

Hi Greg --

It is reported that when the Pharaoh got impatient during his math lesson, Euclid said to him "Sire, there is no royal road to geometry".

We attempt to make roads that have as few gratuitous difficulties as possible, but the real and important difficulties remain (it is the surmounting of the real difficulties that has caused the big changes in how human beings are able to think and act). The important areas include learning to read and write fluently, "think and do" real mathematics and real science.

Programming per se doesn't do it, but Seymour's insight was that programming done thoughtfully in certain ways could act as a new kind of mathematics that would greatly aid understanding.

And mathematics per se doesn't do it, because though it can be used as the language of science, like most languages of power, too much can be said and claimed. Science is the outlook that helps math and then programming behave well enough to be powerful and useful.

Long before we get to Yoshiki's particles and a piston supported by "gas" particles, the 5th grade children learn about velocity and acceleration, first mathematically using the computer, and then by looking at movement in the real world. This culminates in their dropping objects from the roof of their school, taking videos of the actions, and using what they've learned to figure out what kind of motion is going on, derive the 2nd order discrete DEs (as programs that are very much like the ones they used when playing around with motion on the computer earlier), making a simulated ball that is moved by these programs, and then matching up the simulation they've made with the videos they took to see how well their model works with the real world actions.

This is described in http://www.vpri.org/pdf/etoys_n_learning.pdf and I suggest that you read it and other writings that explain some of this.

An important point is that the experiment described above -- which is sometimes called "Galilean Gravity" -- is a real problem for college students (surveys over the last 30 years have shown that only 30% of American college students are able to understand this after taking the course as taught in most colleges -- and they are given the formulas, they do not have to derive them). In contrast, about 90% of the 11 year old children who use this different approach are able to not just understand the models, they actually derive the equations of motion and make the models.

This illustrates many important points about science, math, learning, pedagogy and curriculum design.

To be too brief: real math can be done with the aid of a computer, but real science has to be done in the actual world. The math is the "mapping language" for relating what is actually going on, to what we can observe and deduce, to what our poor brains can understand. Making simulations is a way to do active mathematics and can be very useful. For instance, as Einstein occasionally would point out, it helps to do thought experiments using math before looking at the real world because it can greatly help focus on what needs to be observed closely. So the playing around by simulating cars and particle systems can help thinking about what to look for in the real world. But it isn't science. But giving children simulations to "change variables with" in our experience seems to be both anti science and anti math in many important respects. However, children making simulations, both before and after observations, seems to really help in many ways.

An important side note about teaching children real science... I take pains in public talks to try to help the audience understand what real science is all about (it's not what most of them think). Then I try to show them the delicate balance between children's science as "real science" and "not quite like adult science". It's critical that children's science be real science (the above is an example), but virtually all of it winds up being done at a somewhat different level than adult science. Part of this is because the kinds of mathematics that can be used is more limited in range and depth, even though (as above) this way of looking at calculus is perfectly valid and very within the range of the ways children can think.

Another side note is that most adults are very impatient about lots of things. So, where we would never show a child a finished project with "gas" particles bouncing around -- we want to help them think through these and make them by themselves -- adults want to cut to the results and rarely are patient enough to go through the process. So we've made quite a few sample projects drawn from children and from our pedagogy so adults can get a little of the gist of what gets made. It's interesting to see the extent to which adults are willing to express opinions about things they are not inclined to learn -- including the pharaoh's impatience that it isn't easier -- and this is a problem that Seymour, we, Mitchel, and others who have been working in this area for many years, etc., have been dealing with for many decades.

Best wishes,

Alan







----- Original Message ----
From: Greg Smith (gregmsmi) <gregmsmi at cisco.com>
To: its.an.education.project at tema.lo-res.org
Sent: Friday, May 23, 2008 6:12:27 AM
Subject: Re: [IAEP] An example on statistical

Hi Yoshi,

Sorry, I didn't realize that your eToys version of this was already
available. I thought you were proposing a possible idea for a future
educational application. That was the perspective of my comments and I
didn't mean to say anything disparaging.

I'll open eToys and take a look at it as soon as I have a chance, but it
may take week or so. If you have a URL to it that may save me time. It
looked familiar from when I scanned the eToys sites but I thought you
were suggesting something new.

I'm still not completely clear on what this is teaching. Is it teaching
physics, chemistry, math, eToys, the Combined Gas Law or something else?

What did the teachers say about it? Did they have any suggestions on how
the application could be improved?

FYI on my perspective, I like to think I can program but I rarely do. I
hope I can figure out how to tweak variables in an eToys application but
I'm impatient and very time constrained so don't count on me for
improvements that will be robust enough for general use. My specialty is
talking to users and trying to define the software requirements that
will best address their needs. Then I try to convince a programmer to
implement what we think the user wants :-)

I'll put some time in to this one and try to give you a more informed
comment in the next round.

Thanks,

Greg S

***************** 
Date: Thu, 22 May 2008 13:48:23 -0700
From: Yoshiki Ohshima <yoshiki at vpri.org>
Subject: Re: [IAEP] [Its.an.education.project] An example on
    statistical    dynamics on XO
To: <its.an.education.project at tema.lo-res.org>
Message-ID: <ud4nef4ko.wl%yoshiki at vpri.org>
Content-Type: text/plain; charset=US-ASCII

  Hi, Greg,

> - I'm not familiar with the formula  PV = nRT. I can't say that the 
> sample app taught me it either :-( Is it Pressure * Volume = a 
> material constant (n) * R (?) * Temperature?

  Yes, basically.  n represents "amount of substance", and the form is
what learned as the "Boyle-Charles's law", but probably the variation of
the same idea is taught slightly different form around the world.
R is the constant also that depends on the unit system you use.  (And,
it looks like "k" is commonly used.)

http://en.wikipedia.org/wiki/Combined_gas_law

> I can look it up, but tried to learn
> from the description and 10 minutes with the app. If the formula is 
> the central point, put the variables names and values on the screen.

  Yes, that is a good idea.  Can you make a good one^^;?

> Understanding ratios is not trivial. Two variables in a linear 
> relationship is about all I can hold in my head. Seeing the numbers 
> change on screen may help.

  The numbers are all available, except volume.  Pull out ceilingpos
variable's watcher from the KedamaWorld's tab to see the volume on
screen.
  
> - In general, I suggest you start with the phenomenon and not the 
> equation. Show something happening and then let the user discover the 
> relevant variables and how they interact.

  Yes.  In physics and science, that should be done off computer.

  My example is after people see/learn about the real phenomenon.

> Historically speaking, how was
> the formula originally derived?  Start from there and see if you can 
> update it to some modern day activity.  Mentos in a coke bottle is the

> latest buzz on home experimentation in my house:
> http://www.youtube.com/watch?v=hKoB0MHVBvM

  Well, I guess that wasn't the latest buzz^^;

> If you could simulate that by changing the pressure rapidly it would 
> tie it to the real world.

  That kind of non-linear change might be hard to do in simulation,
especially in Etoys.  (The explosion part in my simulation is not real
simulation.)

> - More options to tweak would be good. Let the kids "pour" a substance

> in and examine the results. What if the "molecules" are made of milk 
> or oxygen or water or neon?  Have a small library of items and then 
> allow the kids to create new ones. Maybe they can try it in the 
> physical lab then try it on the computer. Can they adjust the 
> temperature? Dials, buttons and switches make it more fun to use.

  Well, this is an important point, I think.  It really just depends on
what you would like to simulate and teach.  Remember that computer
itself is rather like mathematics than physics.  For a simulation of
physics phenomenon, it is perfectly ok to do simplifications *as long as
it is honest*.  And, again, what we should avoid is to try to make
students believe something without proof from real world.

  If you provide the "library of substance" such as "milk" on computer,
how do students know that milk's behavior reflects the real world's
milk?  You can do whatever you like on computer, but imitating the
nature in false way on computer is more harmful than simple but honest
simulation.

  Yes, I think they should do it in the physics lab.

> I didn't look at the eToys implementation so maybe adjusting the 
> variables is more clear there.

  What?  (I was writing above under the assumption that you at least
looked at it.)  What do you mean by not looking at the Etoys
implementation?  All implementation is shown on that screen!  Clicking
on the shooting star icon to start Etoys, then click on the Gallery
cloud, and click on the thumbnail and all implementation is visible to
you.  It was three clicks but was I asking too much?  Or, you felt that
you need to look at how the entire particle system is implemented?

> However, I don't want to spend time looking for and tweaking the code.

> I just want to play with the options.

  You can certainly play with the options in Etoys version.

> If I wanted to learn
> how to program squeak that's different but here I want to learn 
> physics or chemistry and the programming is extra work.

  You don't have to learn how to program Squeak.  It is Etoys.

> - Just brainstorming suggestions. Let me know if any don't make sense.

> I suggest you get a science teacher to comment. Also, find a kid to 
> play with it.

  Do you think we have never done that?

> - The bubbling cauldron of experimentation paradigm looks like a real 
> winner to me! Let the kids throw stuff in and see what happens. E.g. 
> add water, then lower the temperature (may not fit as water expands 
> when temperature goes down!).
> 
> "Double, double toil and trouble;
> Fire burn and cauldron bubble. "
> >From Macbeth
> 
> HTHs. Nothing like a real application in development to get the 
> creative brain thinking :-)

-- Yoshiki
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