[IAEP] What is a Lesson Plan?

[Albert Cahalan]

Edward Cherlin writes:

> 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.

Sure. My high school physics teacher taught about 30 days of the year
because he liked skipping class to sneak outside to smoke (!!!),
but introductory college physics fixed that.

> 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.

Of course not, and that was at two schools because a semester
oriented school wouldn't transfer credits from a quarterly one.

You can drop a weight that is trailing a strip of wax paper
through something like a spark plug. Measure the distance between
the burn marks. You can use an air track with light beams to
time the experiment. You can do a hybrid even, in 2D, with a
hovercraft that emits sparks into a piece of graph paper. Some
of these methods are good for collisions as well.

BTW, I recently had an 8-year-old figure out the formula by
using calculus. He was able to do this because he's been
instructed in a no-nonsense traditional way.

> 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?

Not really, but a proper answer (not likely to kill the astronauts)
would require a team of people with many years of study.

> 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.

This is getting to be incredibly obscure. One simply can't learn
everything. People who can do the above are neither commonly needed
nor likely to have a grasp of all the obscure things I can do.
People specialize; this is good.

> 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?

Using high-voltage to burn holes in a paper tape is more fun.

> 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

If you must, at least use a watermelon.

> 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.

Teachers have lives too. Extra hours (unpaid even?) won't go
over all that well.

>>> 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?

Lesson plans are needed; the existing ones are not free to copy.
It's no different from needing free codecs, a free encyclopedia,
or free wireless firmware.

There is however no reason to choose methods that have been
proven to fail. It's long past time to accept the results of
Project Follow Through. (a $3.3 billion study in 2008 dollars)

Cloning Saxon Math and Singapore Math would be a good start.

Info about Project Follow Through's results:

http://www.jefflindsay.com/EducData.shtml
http://www.illinoisloop.org/oswegomath.html
http://www.heartland.org/Article.cfm?artId=19790

That last article has a lovely graph.