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Re: [Phys-L] proportional reasoning, scaling laws, et cetera



I have and have found it very exciting.

The equations generally taught are for specific contitions that the students never see. They constantly used to plug instantaneous speeds into equations requiring average speed etc.

I make students create a graph sketch of the problem and then derive the equation that represents that graph.

They complain a lot, but understand much more. They also start looking for salient points vs superficial elements.

In alg based physics we are more often than not, solving for a slope, axis, or area under the curve.



Robert Cohen <Robert.Cohen@po-box.esu.edu> wrote:

I have a simple question I now ask students who struggle with algebra:
which is larger, 3/5 or 8/9, and how do you know? It is amazing how
well this gets at the heart of their struggles and how they've managed
to "tread water", so to speak, through algebra, calculus, physics, etc.

In my own physics book, I no longer include any of the "magical"
kinematic equations (like x = x_0 + v_0 t + 1/2 a t^2) as I find they
just allow students to bypass understanding. Without them, students
must solve problems based on scientific laws (like Newton's laws) and
definitions (like average velocity). At least that is my intention.
Has anyone else tried this?

Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@esu.edu http://www.esu.edu/~bbq

-----Original Message-----
From: phys-l-bounces@mail.phys-l.org
[mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of John Denker
Sent: Tuesday, May 15, 2012 9:49 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] proportional reasoning, scaling laws, et cetera

On 05/15/2012 10:40 AM, Bill Nettles wrote:
I have found very few students who can do proportional reasoning when
they arrive, and they are very resistive to using it to solve
problems. For example studying Kepler's Laws, having them work
examples using ratio & proportion in class, I ask them on a test to
find the period of an asteroid orbiting the Sun at a distance of 3.5
AU. They ask me what the mass of the Sun is. I tell them they don't
need it. They stare at me like a calf looking at a new gate

I would love to see more discussion of this point.

There is a problem here that we should be able to solve. I don't
pretend to fully understand the problem, let alone know the solution(s),
but I know this is important.

Oddly enough, this topic is not covered in the typical physics text ...
even though it is more important than 99% of the stuff that is covered.

Some miscellaneous thoughts:

Remark: It is interesting -- and encouraging -- that even though they
ask for the mass of the sun, they don't ask for the mass of the
asteroid. That suggests that they have internalized the principle of
equivalence, or something like that. Not bad!

Question and/or possibly-constructive suggestion: Students probably
don't consider cosmology important to their daily lives. So perhaps
when broaching the subject of proportional reasoning and scaling laws,
would they do better if we start with something closer to home? For
example: Consider a skateboarder starting from rest at the top of a
half-pipe.
Neglecting friction, calculate the gee-force (in gees) he will
experience at the bottom. It turns out you do not need to know the
radius of the pipe.
Note that the skateboard problem has direct application to
cars, and has life-and-death application to airplanes.

Another remark: Perhaps I'm missing something here, but I don't think
proportional reasoning is a substitute for algebra, or in any way easier
than algebra. It is *part* of math, and not even the easiest part. For
example, I don't remember the exact form of the Kepler 1-2-3 law. I
don't even try to remember it, because I can rederive it when needed.
For me, the effort of rederiving it is negligible compared to the effort
that would be required to memorize it verbatim. However, rederiving it
requires algebra.
I decided long ago that if I'm going to go to the effort of
learning something, I will learn things that have the most
power and generality. If I know algebra, dimensional analysis,
the law of universal gravitation, and a couple other similarly
broad ideas, I get the details of the 1-2-3 law for free.

I am quite aware that it is possible to perform proportional reasoning
without algebra. Euclid did it and Galileo did it, to great effect.
Similarly, I am quite aware that it is possible start a fire by rubbing
two sticks together ... but I would rather not do so. There exist more
modern techniques, which are considerably more convenient.

I reckon trying to get by without algebra is a fool's errand.
High-school algebra is a prerequisite for high-school physics, not to
mention college physics, and it would be madness to pretend otherwise.
I am not interested in hearing pseudo- Piagetian claims that students
"can't" do algebra. That's a lame excuse. There's a big difference
between "never bothered to learn it" and "can't possibly ever learn it".

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

Maybe I'm off base here, but my first instinct would be to /not/ require
students to remember the exact form of Kepler's
1-2-3 law. That seems only fair, given that I don't remember it myself.
Similarly, I would not expect them to memorize the loop-de-loop scaling
laws. Instead, I would want them to learn that:
a) There are lots of scaling laws. They are very
convenient and very powerful. They have have been central
to physics for nigh on 400 years, and will remain so.
b) If you have never seen the scaling law that you need,
or if you have seen it but forgotten it, you can figure
it out on the spot. In simple cases you can use dimensional
analysis. In more challenging situations, you might need
non-dimensional scaling.
http://www.av8n.com/physics/dimensional-analysis.htm
http://www.av8n.com/physics/scaling.htm

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

Again I recommend picking some random adult non-scientists and asking
them what they remember from physics class. Most likely they will say
"Oh, let me think ... I remember there was something about
monkey-shooting, but I don't remember the details."

We can do better than this. We /need/ to do better than this. It is an
enormous waste of time and money to teach stuff that students will not
remember and/or not find useful.
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