[IAEP] What is a Lesson Plan?

[Edward Cherlin]

On Mon, Jul 7, 2008 at 3:56 AM, Bryan Berry <bryan at olenepal.org> wrote:
"Tony Forster" <forster at ozonline.com.au> wrote:
>>The power of the Sugar activities is in the opportunities they give for
>>self-directed problem-based learning. Achieving this is much more about how
>>teachers "set up" their classes and not about following a preset plan.

Although a great deal can be achieved in set-up, this turns out not to
be the case more generally. The teachers must know which problems are
appropriate to the subjects they are teaching and to their students'
states of development. This includes the Piagetan brain development
stage, and also the stage in the learning process, which is dependent
on culture and previous education. As Alan Kay pointed out in a
previous message, it takes about three years to do this process
correctly. We have to do it incorrectly to begin with, and refine our
understanding continuously.

Let us begin with Alan's favorite example, teaching children about
constant acceleration in software, and then getting them to recognize
it in the trajectory of a falling object. We can look at this from the
point of view of the teacher, the student, and the scientist. I am
going to start with the students.

First of all, you who are reading this and who learned something about
elementary calculations with gravity in school. I believe that I can
assume a common method of instruction in the schools you attended. In
high-school or introductory college physics you might have learned
about constant linear acceleration, about the parabolic path of
objects with a constant horizontal velocity and a uniformly
accelerated vertical velocity, and even a bit about the very nearly
elliptical orbits of the planets, or of moons around planets. You did
few or no experiments, and you were told the correct answers, but not
how to derive them. The names of Galileo, Kepler, and Newton were
probably mentioned, with incomplete and inaccurate accounts of their
insights and their work. The distinction between mass and weight was
probably brought up, and many of your classmates didn't get it. Very
few of you can now calculate how long it would take to fall a
kilometer at 1g, or how far an object will fall in two minutes,
ignoring air resistance. Almost none of you can calculate how much
fuel it would take to put a rocket into low Earth orbit, or when the
next eclipse will be. (I cannot do either under examination
conditions, but I know where to look up the methods and the data, and
I can both do and program the calculations.) Am I right so far?

I expect that none of you can do calculations on constant acceleration
in Special Relativity, or know how corrections from General Relativity
have to be applied to the atomic clocks in the orbiting GPS
satellites. (I would be delighted to be wrong in this conjecture.) I
have the books here, but I haven't learned it all myself.

Now contrast this with a discovery-based approach. Let us prepare the
teacher with the knowledge of what to investigate, and what
experiments to suggest. Alan has a demo that begins with the familiar
Etoys car. Children can tell the car how to move by snapping tiles
together. One of the tiles is Forward by some given amount. What if we
make that amount a variable, and add a constant to it at each step?
What if we tell the car to put a dot on the screen at each tick,
before moving the car? What do we get?

Suppose we say "Forward x" in one tile, and in other tiles set x to 5
(for reasons which I will not explain here) outside the loop, and
increment x: x=:x+10, say, inside the loop.

So we get

Position  Speed
0       5
5     15
20   25
45   35
80    etc.

Now making a pattern from these numbers poses some difficulties, but
look at what we get on the screen:

. .   .     .       .         .

Measure the distances in terms of the first distance, giving this pattern:

Position  Motion
0               1
1               3
4               5
9               7
16             etc.

This pattern is easy to recognize. It consists of square numbers and
successive odd numbers.

So far so good. Now have someone go up on the roof of the school and
drop a ball, while the children record the scene with their cameras in
video mode. Bring the video into Etoys, and select frames at constant
intervals (either somebody has to know what is a suitable interval, or
the children can try different values). Overlay the frames, and
examine the positions of the ball. It will be obvious to the eye that
the pattern of dots is the same one we just simulated.

So that is an outline of two lesson plans. What did the teacher have
to know? In an Instructionist setting, it would be sufficient to have
a list of instructions. In Constructionism, we want the teachers to
have done all of this themselves, and much more, so that they would
understand the physics they were teaching. For example, why I set x to
5 and incremented it by 10. To get from here to there, we must
compromise. But Alan has pointed out that students can learn from a
teacher thus equipped much more than the teacher understands. So we
can bootstrap.

At this point, I recommend reading Arthur Clarke's novel Childhood's
End, involving a considerably more radical bootstrapping process.

Back so soon? Have you read it? Tsk-tsk, naughty, naughty. I mean it.
When you are trying to solve a jigsaw puzzle, you really need to have
_all_ of the pieces.

Well, let that pass. But let us look back at the lessons again. How
much did the children have to know in order to do them? Well, they
have to be comfortable with Etoys programming (Are you?), they have to
be able to work the video capture without any glitches (Can you?), and
they have to know how to import a video to Etoys and do a bit of image
processing (No, I don't know the details either. Alan?). That breaks
down into a fair number of previous lessons. Oh, and they have to be
able to recognize patterns in numbers. More previous lessons. It would
be worthwhile to get them to observe falling bodies without computer
assistance before launching these processes. It would also be helpful
to introduce them to conic sections through a flashlight or some other
source of a cone of light impinging on a sheet of paper or a wall, and
to get them to observe a water fountain or other liquid source. What
is the shape that the fountain makes? Why did the Greeks never notice,
and never work out what Galileo did? They had all the math they
needed. Galileo's book uses nothing outside Euclid.

Now let us look more closely at what the scientist sees in this.
Galileo did a number of critical experiments, establishing that the
rate at which objects fall does not depend on their weight (ignoring
air resistance); that horizontal motion has no effect on vertical
motion; that there is no way to detect uniform motion using gravity;
that the period of a pendulum is nearly independent of its amplitude
(the basis for the pendulum clock later in the century); that the
motion of a ball rolling down a straight groove is the same as a
falling body, except slower by a factor depending on the slope of the
groove; and much more. Each of these is a separate investigation.
Taken together, all of them except the pendulum are called Galilean
Relativity, in contrast to Einstein's later Special Relativity.

Galileo attempted to measure the speed of light, but was only able to
determine that it was too fast for him to measure. After the speed was
measured approximately, James Clerk Maxwell noticed that his theory of
electromagnetism predicted waves travelling at a high and constant
speed, which led to the elaboration of the electromagnetic spectrum,
and to two intractable problems of late 19th century physics, the
Ultraviolet Catastrophe in the theory of black-body radiation, and the
null result of the Michelson-Morley experiments, which established
conclusively that there was no material ether for light to travel in,
because the speed of light is the same for all observers in all
directions, no matter what their velocity in space. Problems solved by
Max Planck and Albert Einstein with the creation of quantum theory and
Special relativity.

Now we are way beyond what we currently teach in elementary school.
But here is the issue. If you have no idea about Special Relativity,
you cannot correctly teach Galilean Relativity. And there is another
issue, too. We do not know yet how much of this we could program in
Etoys so that it would make sense to elementary school students, or
more precisely what we could get them to program for themselves.
Certainly I have seen animations demonstrating the change in clock
speeds with changes in speed in space, or the fact that time does not
necessarily run at the same rate in different locations. I can provide
more information on that, but this message is already plenty long
enough.

>>Self-directed problem-based learning does not always follow a preset plan,
>>the teacher, the "guide on the side" gives things a nudge from time to time,
>>more recognising when learning is working well than following a preset plan.

That is not the best model. We want to have teachers who know where
education can go and how to get there in considerable detail. And why.
It is true that teachers need to provide only a moderate amount of
guidance at each stage, and let the children work out the consequences
of those suggestions. Teachers also need to understand how that
process can go wrong, and how to help children overcome obstacles
without doing the work for them.

Certainly, we want to have time for free exploration, but we also want
to achieve something quite definite: a basic understanding of the
world as it always is, and of society, technology and other such
matters as they have been, are, and can be, as the common basis for
the discussion of the society's plans for the future in politics,
economics, the arts, human development, and whatever else seems
relevant.

> Tony, we are comparing apples w/ oranges here. Your situation in
> Australia resembles in almost no aspect the situation of a typical
> Nepali school. Your advice may be great for a western school but it is
> not very applicable to Nepali schools for cultural, economic, and social
> reasons.

And fundamental educational reasons.

>> Edward wrote:
>>
>> Writing lesson plans needs to be a whole program in itself, integrated with
>> rethinking textbooks to make use of the available software and to implement
>> Constructionism, or possibly just creating textbooks within available
>> software.

Nobody has anything to say about this program?
-- 
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