Re: [Phys-L] Freshman Physics / block by block approach

[John Denker <jsd@av8n.com>]

On 10/15/22 8:18 AM, Todd Pedlar via Phys-l wrote:

> Honestly I think the vast majority of students would be lost in the weeds
> and not be able to foresee the path through the algebra to make the
> necessary substitutions in an exam setting.

Yes, in an exam setting, it would get ugly.

As for getting lost in the algebra: It pays to write:
	g(x) = (x - root1)*(root2 - x)		[1]

where the general parabola is g(x) times some scale factor.

Technically g(x), as written, is not a polynomial (since a
polynomial is a sum not a product) but it *is* a parabola.

Then pin down the scale factor by writing the trajectory
of the ball as:
	        Yc * g(x)
	f(x) = ----------			[2]
	          g(Xc)

where Yc is the critical height and Xc is the horizontal
location thereof.

Students were "supposed" to learn this sort of thing in
HS algebra. Unfortunately HS physics is in large measure
remedial algebra.

It took me about 5 seconds to figure out that [2] was a
good representation. It will take some students two or
three orders of magnitude longer than that. Not a good
use of their time.

In a flipped classroom situation, you could let them
struggle with it for a few minutes, then bring up the
topic of /representation/ and see if anybody has a
representation they would recommend. Then give them
equation [1] and let them figure out how to make use
of it.

==================

You can editorialize as follows: Equation [2] uses the
g() function twice. So equation [1] does not solve the
problem directly; instead it creates a /building block/
that helps construct the overall solution.

The building-block approach is huuuugely important in real-
world problem solving. When faced with a problem you can't
solve, pick it apart into smaller problems that you can solve.

The first few times, I (the teacher) will help you by
picking the problem apart for you, and explaining things
step by step and block by block, but don't get spoiled.
Take a step back and look at the process. Internalize
the /process/. Learn to pick things apart on your own.

On the SAT, any question that can't be solved in a single
step is not worth solving ... but real-world problems are
a lot more complicated than that.