Classroom tools

Tue Jan 15 17:11:40 EST 2008

On Jan 15, 2008 12:42 AM, Yoshiki Ohshima <yoshiki at vpri.org> wrote:
>   "One way or another" is what I wrote, and letting them cut papers
> and weigh is a great idea, I think.

Thank you. Of course, not every school can afford construction paper.
:-( But there are numerous alternatives, and I have no doubt that the
children will think of more. (One example: Make a shape from clay on a
flat surface, fill it with water to a measured depth, pour the water
into a cup and measure the volume of the water. Or weigh it.)

>   As you wrote, it is important to have teachers understand, or able
> to help, important ideas.

Discovery being the most important idea. We can't just tell teachers
that. We have to enable them to discover it. This is the most critical
and neglected part of the Laptop program. If we don't do it, and if
Nicholas keeps saying that teachers are irrelevant, we will get a
ferocious backlash, comparable to the New Math disaster.

I have started the outline of a book under the working title
Discovering Discovery, but I won't be able to write it alone.

Second on my list of important ideas is the difference between
know-how and understanding. This is well illustrated by the difference
between the ferocious rivals Thomas Edison, who simply tried
everything (most famously, over a thousand materials for light-bulb
filaments), and Nikola Tesla, who could visualize three-dimensional
magnetic fields, and believed in calculating likely possibilities
before starting experimentation.

At the schoolroom level, the difference is between knowing rules for
manipulating variables, and understanding what a variable is.
(Basically, a variable name is a pronoun that can refer to a different
number each time it is used.) Caleb Gattegno was particularly good at
inducing understanding of arithmetic and elementary algebra using
Cuisenaire rods. Everybody involved in XO software and content should
read his work. In fact, a Cuisenaire rod activity would be brilliant.

Another example that bit me in grade school: English does not have
vowel quantity, that is, longer and shorter vowels, in the manner of,
say, Latin, Hindi, or Japanese. But in schools we use the terminology
of long and short vowels taken from Latin. In fact, so-called long
vowels in English are not the same vowels spoken longer, but entirely
different vowels (actually diphthongs) that happen to be written with
the same letter (though not always), and marked by a following silent
e (but by no means always).

This is due to the great lack of vowel letters in alphabets descended
from Greek (Latin and Cyrillic mainly). The Greek alphabet was adapted
from a Semitic alphabet that had no vowel letters at all. Some other
alphabets such as Korean Hangeul and the Shavian alphabet for English
have many more vowel letters, and use unique combinations for writing
diphthongs. As though we wrote "Ai keim to yur haus," and didn't
pretend that 'ai' was a version of 'i', and 'ei' a version of 'a'.

a ei cap cape
e How would you write this clearly in Latin alphabet? We would have to
just make something up. met meet mete
i ai sit site
o ou for fore four, but not cop cope
u ?? tun (ton) tune, tun (ton) tune, cup coop, but not cut cute /kyut/
but note that book uses 'oo' for a different vowel than in coop.

It took me days to work out that the long and short distinction was
nonsense, and that I could and should ignore the plain meaning of the
words, and just memorize the list.

> And assembling a repository of what are
> important ideas and techiniques to teach them would be essential
> addition to the current OLPC effort.

Yes. Let's think about where and how to do that. There are too many
important ideas for just a Wiki page, but I'll start one and see where
it takes us. No, I won't. There is an Ideas page on the Wiki. See you
there.

> -- Yoshiki
>
> At Tue, 15 Jan 2008 00:13:58 -0800,
>
> Edward Cherlin wrote:
> >
> > On Jan 14, 2008 10:06 PM, Yoshiki Ohshima <yoshiki at vpri.org> wrote:
> > > > But let me say one more thing. Making use of "constructionism" theory
> > > > doesn't means the unnecessity of the teachers, but the role of the
> > > > teachers changes.
> > >
> > >   Yes, I think tools for supporting teacher who want to do the
> > > traditional style of teaching is eventually necessary.
> > >
> > >   And, even in "Learning learning", many subjects that are invented
> > > are not discoverable by kids' own.  (Alan Kay said "Children are not
> > > going to invent calculus".)  a kid should be helped by teacher(s) in
> > > one way or another to learn "powerful ideas".
> >
> > Alan Kay has examples of children discovering parts of calculus with
> > some assistance.
> >
> > It is important that teachers know about the really important ideas,
> > and about how to introduce children to them without thinking that they
> > can simply teach it in language. I started working on a Kindergarten
> > Calculus idea a while ago. Show the children that you can put a
> > straightedge against any shape to get the direction of that shape at
> > that point. Ask why the straightedge is level at the top or bottom.
> > Assist them to find the third case in which the tangent can be level.
> > That's the essence of differential calculus. The rest is deriving
> > formulas and doing calculations.
> >
> > Similarly for integral calculus. Draw a figure on paper, cut it out
> > and weigh it. Now, how can you help children to discover that these
> > two operations are inverses? That's the Fundamental Theorem of
> > Calculus. (I have a solution, but I am sure that there are others.)
> >
> > Given that we can teach understanding of the fundamental ideas in
> > Kindergarten, we have the opportunity to rethink at what ages the rest
> > can be brought in. Traditional thinking is that you can't start until
> > the students are capable of understanding all of the subject. This is
> > very close to complete nonsense. Weapons-grade bolonium, in fact.
> >
> > > -- Yoshiki
> > >
> > > _______________________________________________
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> > > Devel at lists.laptop.org
> > > http://lists.laptop.org/listinfo/devel
> > >
> >
> >
> >
> > --
> > Edward Cherlin
> > End Poverty at a Profit by teaching children business
> > http://www.EarthTreasury.org/
> > "The best way to predict the future is to invent it."--Alan Kay
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>

-- 
Edward Cherlin
End Poverty at a Profit by teaching children business
http://www.EarthTreasury.org/
"The best way to predict the future is to invent it."--Alan Kay